Finance - Canis Learning Systems

Transcription

Finance
Course:
Health Care Finance Readings
MBAHC−4
California College for Health Sciences
MBA Health Care Program
abc
McGraw-Hill/Irwin
McGraw−Hill Primis
ISBN: 0−390−55313−1
Text:
Advanced Financial Accounting, Sixth
Edition
Baker−Lembke−King
Harvard Business Review General
Management Articles
Harvard Business School Accounting Cases
Harvard Business School Finance Cases
Corporate Finance, Seventh Edition
Ross−Westerfield−Jaffe
This book was printed on recycled paper.
Finance
http://www.mhhe.com/primis/online/
Copyright ©2005 by The McGraw−Hill Companies, Inc. All rights
reserved. Printed in the United States of America. Except as
permitted under the United States Copyright Act of 1976, no part
of this publication may be reproduced or distributed in any form
or by any means, or stored in a database or retrieval system,
without prior written permission of the publisher.
This McGraw−Hill Primis text may include materials submitted to
McGraw−Hill for publication by the instructor of this course. The
instructor is solely responsible for the editorial content of such
materials.
111
FINAGEN
ISBN: 0−390−55313−1
Finance
Contents
Ross−Westerfield−Jaffe • Corporate Finance, Seventh Edition
I. Overview
1
1. Introduction to Corporate Finance
2. Accounting Statements and Cash Flow
1
20
II. Value and Capital Budgeting
34
4. Net Present Value
5. How to Value Bonds and Stocks
7. Net Present Value and Capital Budgeting
8. Risk Analysis, Real Options, and Capital Budgeting
34
69
97
129
III: Risk
151
10. Return and Risk: The Capital−Asset−Pricing Model (CAPM)
151
VII. Short−Term Finance
192
27. Cash Management
192
VIII. Special Topics
214
29. Mergers and Acquisitions
31. International Corporate Finance
214
248
Baker−Lembke−King • Advanced Financial Accounting, Sixth Edition
19. Not−for−Profit Entities
272
Text
272
Cambridge Hospital Community Health Network: The Primary Care Unit
350
Case
350
Health Stop (A): Strategy
369
Case
369
iii
Harvard Business Review General Management Articles
Fiscal Health and Quality Care: Montefiore Medical Center Scores with the BSC
382
Article
382
Montefiore Medical Center
387
Case
387
THG Management Services
403
Case
403
Harvard Business School Finance Cases
Investment Policy at New England Healthcare
415
Case
415
Ross−Westerfield−Jaffe • Corporate Finance, Seventh Edition
Back Matter
429
Appendix A: Mathematical Tables
429
iv
Ross−Westerfield−Jaffe:
Corporate Finance,
Seventh Edition
I. Overview
1. Introduction to Corporate
Finance
© The McGraw−Hill
Companies, 2004
Chapter 1
EXECUTIVE SUMMARY
Introduction to
Corporate Finance
The Video Product Company designs and
manufactures very popular software for video
game consoles. The company was started in
2002, and soon thereafter its game “Gadfly”
appeared on the cover of Billboard magazine.
Company sales in 2003 were over $20 million.
Video Product’s initial financing of $2 million
came from Seed Ltd., a venture-capital firm, in
exchange for a 15-percent equity stake in the
company. Now the financial management of
Video Product realizes that its initial financing
was too small. In the long run Video Product
would like to expand its design activity to the
education and business areas. It would also
like to significantly enhance its website for future Internet sales. However, at present the
company has a short-run cash flow problem
and cannot even buy $200,000 of materials to
fill its holiday orders.
Video Product’s experience illustrates the
basic concerns of corporate finance:
1. What long-term investment strategy
should a company take on?
2. How can cash be raised for the required
investments?
3. How much short-term cash flow does a
company need to pay its bills?
These are not the only questions of corporate finance. They are, however, among the
most important questions, and taken in order,
they provide a rough outline of our book.
One way that companies raise cash to
finance their investment activities is by selling
1
or “issuing” securities. The securities, sometimes called financial instruments or claims, may
be roughly classified as equity or debt, loosely
called stocks or bonds. The difference between
equity and debt is a basic distinction in the
modern theory of finance. All securities of a
firm are claims that depend on or are contingent on the value of the firm.1 In Section 1.2 we
show how debt and equity securities depend
on the firm’s value, and we describe them as
different contingent claims.
In Section 1.3 we discuss different organizational forms and the pros and cons of the
decision to become a corporation.
In Section 1.4 we take a close look at the
goals of the corporation and discuss why
maximizing shareholder wealth is likely to be
the primary goal of the corporation.Throughout the rest of the book, we assume that the
firm’s performance depends on the value it
creates for its shareholders. Shareholders are
better off when the value of their shares is
increased by the firm’s decisions.
A company raises cash by issuing securities
to the financial markets. The market value of
outstanding long-term corporate debt and
equity securities traded in the U.S. financial
markets is in excess of $25 trillion. In Section 1.5 we describe some of the basic
features of the financial markets. Roughly
speaking, there are two basic types of financial
markets: the money markets and the capital
markets. The last section of the chapter provides an outline of the rest of the book.
We tend to use the words firm, company, and business interchangeably. However, there is a difference between a firm and a
corporation. We discuss this difference in Section 1.3.
2
1
2
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
Finance
3
Chapter 1 Introduction to Corporate Finance
1.1 What Is Corporate Finance?
Suppose you decide to start a firm to make tennis balls. To do this, you hire managers to
buy raw materials, and you assemble a workforce that will produce and sell finished tennis
balls. In the language of finance, you make an investment in assets such as inventory,
machinery, land, and labor. The amount of cash you invest in assets must be matched by an
equal amount of cash raised by financing. When you begin to sell tennis balls, your firm
will generate cash. This is the basis of value creation. The purpose of the firm is to create
value for you, the owner. The firm must generate more cash flow than it uses. The value is
reflected in the framework of the simple balance-sheet model of the firm.
The Balance-Sheet Model of the Firm
Suppose we take a financial snapshot of the firm and its activities at a single point in time.
Figure 1.1 shows a graphic conceptualization of the balance sheet, and it will help introduce you to corporate finance.
The assets of the firm are on the left-hand side of the balance sheet. These assets can be
thought of as current and fixed. Fixed assets are those that will last a long time, such as
buildings. Some fixed assets are tangible, such as machinery and equipment. Other fixed assets are intangible, such as patents, trademarks, and the quality of management. The other
category of assets, current assets, comprises those that have short lives, such as inventory.
The tennis balls that your firm has made but has not yet sold are part of its inventory. Unless
you have overproduced, they will leave the firm shortly.
Before a company can invest in an asset, it must obtain financing, which means that it
must raise the money to pay for the investment. The forms of financing are represented on
the right-hand side of the balance sheet. A firm will issue (sell) pieces of paper called
debt (loan agreements) or equity shares (stock certificates). Just as assets are classified as
FIGURE 1.1
The Balance-Sheet
Model of the Firm
Current assets
Net
working
capital
Current liabilities
Long-term debt
Fixed assets
1. Tangible fixed
assets
2. Intangible fixed
assets
Total value of assets
Shareholders’ equity
Total value of the firm
to investors
Left side, total value of assets. Right side, total value of the firm to investors,
which determines how the value is distributed.
Corporate Finance,
Seventh Edition
4
I. Overview
Finance
Companies, 2004
Part I Overview
long-lived or short-lived, so too are liabilities. A short-term debt is called a current liability.
Short-term debt represents loans and other obligations that must be repaid within one year.
Long-term debt is debt that does not have to be repaid within one year. Shareholders’ equity
represents the difference between the value of the assets and the debt of the firm. In this
sense it is a residual claim on the firm’s assets.
From the balance-sheet model of the firm it is easy to see why finance can be thought of
as the study of the following three questions:
1. In what long-lived assets should the firm invest? This question concerns the left-hand
side of the balance sheet. Of course, the type and proportions of assets the firm needs tend
to be set by the nature of the business. We use the terms capital budgeting and capital
expenditures to describe the process of making and managing expenditures on long-lived
assets.
2. How can the firm raise cash for required capital expenditures? This question concerns the right-hand side of the balance sheet. The answer to this involves the firm’s capital
structure, which represents the proportions of the firm’s financing from current and longterm debt and equity.
3. How should short-term operating cash flows be managed? This question concerns
the upper portion of the balance sheet. There is often a mismatch between the timing of
cash inflows and cash outflows during operating activities. Furthermore, the amount and
timing of operating cash flows are not known with certainty. The financial managers must
attempt to manage the gaps in cash flow. From a balance-sheet perspective, short-term
management of cash flow is associated with a firm’s net working capital. Net working
capital is defined as current assets minus current liabilities. From a financial perspective,
the short-term cash flow problem comes from the mismatching of cash inflows and outflows. It is the subject of short-term finance.
Capital Structure
Financing arrangements determine how the value of the firm is sliced up. The persons or
institutions that buy debt from the firm are called creditors.2 The holders of equity shares
are called shareholders.
Sometimes it is useful to think of the firm as a pie. Initially, the size of the pie will depend
on how well the firm has made its investment decisions. After a firm has made its investment
decisions, it determines the value of its assets (e.g., its buildings, land, and inventories).
The firm can then determine its capital structure. The firm might initially have raised the
cash to invest in its assets by issuing more debt than equity; now it can consider changing
that mix by issuing more equity and using the proceeds to buy back some of its debt.
Financing decisions like this can be made independently of the original investment decisions. The decisions to issue debt and equity affect how the pie is sliced.
The pie we are thinking of is depicted in Figure 1.2. The size of the pie is the value of
the firm in the financial markets. We can write the value of the firm, V, as
VBS
where B is the value of the debt and S is the value of the equity. The pie diagrams consider two ways of slicing the pie: 50 percent debt and 50 percent equity, and 25 percent
debt and 75 percent equity. The way the pie is sliced could affect its value. If so, the goal
of the financial manager will be to choose the ratio of debt to equity that makes the value
of the pie—that is, the value of the firm, V—as large as it can be.
2
We tend to use the words creditors, debtholders, and bondholders interchangeably. In later chapters we examine the differences
among the kinds of creditors. In algebraic notation, we will usually refer to the firm’s debt with the letter B (for bondholders).
3
4
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
Finance
5
FIGURE 1.2
25% debt
Two Pie Models of
the Firm
50% debt
50% equity
75% equity
Capital structure 1
Capital structure 2
FIGURE 1.3
Hypothetical
Organization Chart
Board of Directors
Chairman of the Board and
Chief Executive Officer (CEO)
President and Chief
Operations Officer (COO)
Vice President and Chief
Financial Officer (CFO)
Treasurer
Controller
Cash Manager
Credit Manager
Tax Manager
Cost Accounting
Manager
Capital
Expenditures
Financial
Planning
Financial
Accounting
Manager
Data Processing
Manager
The Financial Manager
In large firms the finance activity is usually associated with a top officer of the firm, such as
the vice president and chief financial officer, and some lesser officers. Figure 1.3 depicts a
general organizational structure emphasizing the finance activity within the firm. Reporting
to the chief financial officer are the treasurer and the controller. The treasurer is responsible
Corporate Finance,
Seventh Edition
6
I. Overview
Finance
Companies, 2004
Part I Overview
for handling cash flows, managing capital-expenditures decisions, and making financial
plans. The controller handles the accounting function, which includes taxes, cost and financial accounting, and information systems.
We think that the most important job of a financial manager is to create value from the
firm’s capital budgeting, financing, and net working-capital activities. How do financial
managers create value?
1. The firm should try to buy assets that generate more cash than they cost.
2. The firm should sell bonds and stocks and other financial instruments that raise more
cash than they cost.
Thus the firm must create more cash flow than it uses. The cash flows paid to bondholders and stockholders of the firm should be higher than the cash flows put into the firm
by the bondholders and stockholders. To see how this is done, we can trace the cash flows
from the firm to the financial markets and back again.
The interplay of the firm’s finance with the financial markets is illustrated in Figure 1.4.
The arrows in Figure 1.4 trace cash flow from the firm to the financial markets and back
again. Suppose we begin with the firm’s financing activities. To raise money the firm sells
debt and equity shares to investors in the financial markets. This results in cash flows from
the financial markets to the firm (A). This cash is invested in the investment activities of the
firm (B) by the firm’s management. The cash generated by the firm (C) is paid to shareholders and bondholders (F). The shareholders receive cash in the form of dividends; the
bondholders who lent funds to the firm receive interest and, when the initial loan is repaid,
principal. Not all of the firm’s cash is paid out. Some is retained (E), and some is paid to
the government as taxes (D).
FIGURE 1.4
Cash Flows between
the Firm and the
Financial Markets
Firm issues securities (A)
Firm invests
in assets
(B)
Retained cash flows (E)
Cash flow
from firm (C)
Dividends and
debt payments (F )
Short-term debt
Long-term debt
Equity shares
Taxes
Current assets
Fixed assets
Financial
markets
Total value of assets
(A)
(B)
(C)
(D)
(E)
(F)
Government
(D)
Firm issues securities to raise cash (the financing decision).
Firm invests in assets (capital budgeting).
Firm’s operations generate cash flow.
Cash is paid to government as taxes.
Retained cash flows are reinvested in firm.
Cash is paid out to investors in the form of interest and dividends.
Total value of the firm
to investors in
the financial markets
5
6
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
Finance
In Their Own Words
Skills Needed for the Chief Financial Officers of
eFinance.com
Chief strategist: CFOs will need to use real-time financial information to make crucial decisions fast.
Chief dealmaker: CFOs must be adept at venture capital,
mergers and acquisitions, and strategic partnerships.
Chief risk officer: Limiting risk will be even more important as markets become more global and hedging instruments become more complex.
Chief communicator: Gaining the confidence of Wall
Street and the media will be essential.
SOURCE: Business Week, August 28, 2000, p. 120.
Over time, if the cash paid to shareholders and bondholders (F) is greater than the cash
raised in the financial markets (A), value will be created.
Identification of Cash Flows Unfortunately, it is not all that easy to observe cash
flows directly. Much of the information we obtain is in the form of accounting statements,
and much of the work of financial analysis is to extract cash flow information from accounting statements. The following example illustrates how this is done.
EXAMPLE
The Midland Company refines and trades gold. At the end of the year it sold 2,500 ounces of gold
for $1 million. The company had acquired the gold for $900,000 at the beginning of the year. The
company paid cash for the gold when it was purchased. Unfortunately, it has yet to collect from the
customer to whom the gold was sold. The following is a standard accounting of Midland’s financial
circumstances at year-end:
THE MIDLAND COMPANY
Accounting View
Income Statement
Year Ended December 31
Sales
Costs
______
Profit
$1,000,000
900,000
_________
$ 100,000
By generally accepted accounting principles (GAAP), the sale is recorded even though the customer
has yet to pay. It is assumed that the customer will pay soon. From the accounting perspective,
Midland seems to be profitable. However, the perspective of corporate finance is different. It focuses
on cash flows:
THE MIDLAND COMPANY
Corporate Finance View
Income Statement
Year Ended December 31
Cash inflow
Cash outflow
$
0
900,000
_________
$900,000
The perspective of corporate finance is interested in whether cash flows are being created by the
gold-trading operations of Midland. Value creation depends on cash flows. For Midland, value
creation depends on whether and when it actually receives $1 million.
7
Corporate Finance,
Seventh Edition
8
I. Overview
Companies, 2004
Finance
Part I Overview
Timing of Cash Flows
The value of an investment made by the firm depends on the
timing of cash flows. One of the most important assumptions of finance is that individuals
prefer to receive cash flows earlier rather than later. One dollar received today is worth more
than one dollar received next year. This time preference plays a role in stock and bond prices.
EXAMPLE
The Midland Company is attempting to choose between two proposals for new products. Both
proposals will provide additional cash flows over a four-year period and will initially cost $10,000.
The cash flows from the proposals are as follows:
Year
New Product A
New Product B
1
2
3
4
$
0
0
0
20,000
_______
$ 4,000
4,000
4,000
4,000
_______
Total
$20,000
$16,000
At first it appears that new product A would be best. However, the cash flows from proposal B come
earlier than those of A. Without more information we cannot decide which set of cash flows would
create the most value to the bondholders and shareholders. It depends on whether the value of getting cash from B up front outweighs the extra total cash from A. Bond and stock prices reflect this
preference for earlier cash, and we will see how to use them to decide between A and B.
Risk of Cash Flows
The firm must consider risk. The amount and timing of cash flows
are not usually known with certainty. Most investors have an aversion to risk.
EXAMPLE
The Midland Company is considering expanding operations overseas. It is evaluating Europe and
Japan as possible sites. Europe is considered to be relatively safe, whereas operating in Japan is seen
as very risky. In both cases the company would close down operations after one year.
After doing a complete financial analysis, Midland has come up with the following cash flows of
the alternative plans for expansion under three equally likely scenarios—pessimistic, most likely, and
optimistic:
Europe
Japan
Pessimistic
Most Likely
Optimistic
$75,000
0
$100,000
150,000
$125,000
200,000
If we ignore the pessimistic scenario, perhaps Japan is the best alternative. When we take the pessimistic scenario into account, the choice is unclear. Japan appears to be riskier, but it also offers a
higher expected level of cash flow. What is risk and how can it be defined? We must try to answer
this important question. Corporate finance cannot avoid coping with risky alternatives, and much of
our book is devoted to developing methods for evaluating risky opportunities.
Concept
Questions
1.
2.
3.
4.
What are three basic questions of corporate finance?
Describe capital structure.
How is value created?
List the three reasons why value creation is difficult.
7
8
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
Finance
9
1.2 Corporate Securities as Contingent Claims
on Total Firm Value
What is the essential difference between debt and equity? The answer can be found by thinking about what happens to the payoffs to debt and equity when the value of the firm changes.
The basic feature of a debt is that it is a promise by the borrowing firm to repay a fixed
dollar amount by a certain date.
EXAMPLE
FIGURE 1.5
Debt and Equity as
Contingent Claims
The Officer Corporation promises to pay $100 to the Brigham Insurance Company at the end of
one year. This is a debt of the Officer Corporation. Holders of the debt will receive $100 if the value
of the Officer Corporation’s assets is equal to or more than $100 at the end of the year.
Formally, the debtholders have been promised an amount F at the end of the year. If the value of
the firm, X, is equal to or greater than F at year-end, debtholders will get F. Of course, if the firm does
not have enough to pay off the promised amount, the firm will be “broke.” It may be forced to liquidate its assets for whatever they are worth, and the bondholders will receive X. Mathematically this
means that the debtholders have a claim to X or F, whichever is smaller. Figure 1.5 illustrates the general nature of the payoff structure to debtholders.
Suppose at year-end the Officer Corporation’s value is equal to $100. The firm has promised to
pay the Brigham Insurance Company $100, so the debtholders will get $100.
Now suppose the Officer Corporation’s value is $200 at year-end and the debtholders are
promised $100. How much will the debtholders receive? It should be clear that they will receive the
same amount as when the Officer Corporation was worth $100.
Suppose the firm’s value is $75 at year-end and debtholders are promised $100. How much will
the debtholders receive? In this case the debtholders will get $75.
Payoff to
equity shareholders
Payoff to
debtholders
Payoffs to debtholders
and equity shareholders
Payoff to
equity
shareholders
F
F
F
Value
of the
firm
(X )
F
Value
of the
firm
(X )
Payoff to
debtholders
F
Value
of the
firm
(X)
F is the promised payoff to debtholders. X F is the payoff to equity shareholders if X F 0. Otherwise the
payoff is 0.
The stockholders’ claim on firm value at the end of the period is the amount that remains
after the debtholders are paid. Of course, stockholders get nothing if the firm’s value is
equal to or less than the amount promised to the debtholders.
EXAMPLE
The Officer Corporation will sell its assets for $200 at year-end. The firm has promised to pay the
Brigham Insurance Company $100 at that time. The stockholders will get the residual value of $100.
Corporate Finance,
Seventh Edition
10
I. Overview
Finance
Companies, 2004
Part I Overview
Algebraically, the stockholders’ claim is X F if X F and zero if X F. This is
depicted in Figure 1.5. The sum of the debtholders’ claim and the stockholders’ claim is
always the value of the firm at the end of the period.
The debt and equity securities issued by a firm derive their value from the total value of
the firm. In the words of finance theory, debt and equity securities are contingent claims
on the total firm value.
When the value of the firm exceeds the amount promised to the debtholders, the shareholders obtain the residual of the firm’s value over the amount promised the debtholders,
and the debtholders obtain the amount promised. When the value of the firm is less than the
amount promised the debtholders, the shareholders receive nothing and the debtholders get
the value of the firm.
Concept
Questions
1. What is a contingent claim?
2. Describe equity and debt as contingent claims.
1.3 The Corporate Firm
The firm is a way of organizing the economic activity of many individuals, and there are
many reasons why so much economic activity is carried out by firms and not by individuals.
The theory of firms, however, does not tell us much about why most large firms are corporations rather than any of the other legal forms that firms can assume.
A basic problem of the firm is how to raise cash. The corporate form of business, that is,
organizing the firm as a corporation, is the standard method for solving problems encountered in raising large amounts of cash. However, businesses can take other forms. In this
section we consider the three basic legal forms of organizing firms, and we see how firms
go about the task of raising large amounts of money under each form.
The Sole Proprietorship
A sole proprietorship is a business owned by one person. Suppose you decide to start a
business to produce mousetraps. Going into business is simple: You announce to all who
will listen, “Today I am going to build a better mousetrap.”
Most large cities require that you obtain a business license. Afterward you can begin to
hire as many people as you need and borrow whatever money you need. At year-end all the
profits and the losses will be yours.
Here are some factors that are important in considering a sole proprietorship:
1. The sole proprietorship is the cheapest business to form. No formal charter is required,
and few government regulations must be satisfied for most industries.
2. A sole proprietorship pays no corporate income taxes. All profits of the business are
taxed as individual income.
3. The sole proprietorship has unlimited liability for business debts and obligations. No
distinction is made between personal and business assets.
4. The life of the sole proprietorship is limited by the life of the sole proprietor.
5. Because the only money invested in the firm is the proprietor’s, the equity money that
can be raised by the sole proprietor is limited to the proprietor’s personal wealth.
The Partnership
Any two or more persons can get together and form a partnership. Partnerships fall into
two categories: (1) general partnerships and (2) limited partnerships.
9
10
Corporate Finance,
Seventh Edition
I. Overview
Finance
Companies, 2004
11
In a general partnership all partners agree to provide some fraction of the work and cash
and to share the profits and losses. Each partner is liable for the debts of the partnership. A
partnership agreement specifies the nature of the arrangement. The partnership agreement
may be an oral agreement or a formal document setting forth the understanding.
Limited partnerships permit the liability of some of the partners to be limited to the
amount of cash each has contributed to the partnership. Limited partnerships usually require that (1) at least one partner be a general partner and (2) the limited partners do not
participate in managing the business. Here are some things that are important when considering a partnership:
1. Partnerships are usually inexpensive and easy to form. Written documents are required
in complicated arrangements, including general and limited partnerships. Business
licenses and filing fees may be necessary.
2. General partners have unlimited liability for all debts. The liability of limited partners is
usually limited to the contribution each has made to the partnership. If one general partner is unable to meet his or her commitment, the shortfall must be made up by the other
general partners.
3. The general partnership is terminated when a general partner dies or withdraws (but this
is not so for a limited partner). It is difficult for a partnership to transfer ownership without dissolving. Usually, all general partners must agree. However, limited partners may
sell their interest in a business.
4. It is difficult for a partnership to raise large amounts of cash. Equity contributions are
usually limited to a partner’s ability and desire to contribute to the partnership. Many
companies, such as Apple Computer, start life as a proprietorship or partnership, but at
some point they choose to convert to corporate form.
5. Income from a partnership is taxed as personal income to the partners.
6. Management control resides with the general partners. Usually a majority vote is required on important matters, such as the amount of profit to be retained in the business.
It is very difficult for large business organizations to exist as sole proprietorships or partnerships. The main advantage to a sole proprietorship or partnership is the cost of getting
started. Afterward, the disadvantages, which may become severe, are (1) unlimited liability, (2) limited life of the enterprise, and (3) difficulty of transferring ownership. These
three disadvantages lead to (4) the difficulty of raising cash.
The Corporation
Of the many forms of business enterprises, the corporation is by far the most important. It
is a distinct legal entity. As such, a corporation can have a name and enjoy many of the
legal powers of natural persons. For example, corporations can acquire and exchange property. Corporations can enter into contracts and may sue and be sued. For jurisdictional purposes, the corporation is a citizen of its state of incorporation. (It cannot vote, however.)
Starting a corporation is more complicated than starting a proprietorship or partnership.
The incorporators must prepare articles of incorporation and a set of bylaws. The articles
of incorporation must include the following:
1.
2.
3.
4.
Name of the corporation.
Intended life of the corporation (it may be forever).
Business purpose.
Number of shares of stock that the corporation is authorized to issue, with a statement
of limitations and rights of different classes of shares.
Corporate Finance,
Seventh Edition
12
I. Overview
Finance
Companies, 2004
Part I Overview
5. Nature of the rights granted to shareholders.
6. Number of members of the initial board of directors.
The bylaws are the rules to be used by the corporation to regulate its own existence, and
they concern its shareholders, directors, and officers. Bylaws range from the briefest possible statement of rules for the corporation’s management to hundreds of pages of text.
In its simplest form, the corporation comprises three sets of distinct interests: the shareholders (the owners), the directors, and the corporation officers (the top management). Traditionally, the shareholders control the corporation’s direction, policies, and activities. The
shareholders elect a board of directors, who in turn selects top management. Members of
top management serve as corporate officers and manage the operation of the corporation
in the best interest of the shareholders. In closely held corporations with few shareholders,
there may be a large overlap among the shareholders, the directors, and the top management. However, in larger corporations the shareholders, directors, and the top management
are likely to be distinct groups.
The potential separation of ownership from management gives the corporation several
advantages over proprietorships and partnerships:
1. Because ownership in a corporation is represented by shares of stock, ownership can be
readily transferred to new owners. Because the corporation exists independently of
those who own its shares, there is no limit to the transferability of shares as there is in
partnerships.
2. The corporation has unlimited life. Because the corporation is separate from its owners,
the death or withdrawal of an owner does not affect its legal existence. The corporation
can continue on after the original owners have withdrawn.
3. The shareholders’ liability is limited to the amount invested in the ownership shares. For
example, if a shareholder purchased $1,000 in shares of a corporation, the potential loss
would be $1,000. In a partnership, a general partner with a $1,000 contribution could
lose the $1,000 plus any other indebtedness of the partnership.
CASE STUDY
Limited liability, ease of ownership transfer, and perpetual succession are the major
advantages of the corporation form of business organization. These give the corporation
an enhanced ability to raise cash.
There is, however, one great disadvantage to incorporation. The federal government
taxes corporate income. This tax is in addition to the personal income tax that shareholders
pay on dividend income they receive. This is double taxation for shareholders when compared to taxation on proprietorships and partnerships.
Making the Decision to Become a Corporation:
The Case of PLM International, Inc.*
In 1972, several entrepreneurs agreed to start a company they called PLM (Professional Lease
Management, Inc.). Their idea was to sponsor, syndicate, and manage public and private limited
partnerships with the purpose of acquiring and leasing transportation equipment. They created an
operating subsidiary called FSI (Financial Services, Inc.) to be the general partner of each of the partnerships. PLM had limited success in its early years, but during the period 1981 to 1986 more than
*The S–4 Registration Statement, PLM International, Inc., filed with the Securities and Exchange Commission,Washington, D.C.,
August 1987, gives further details.
11
12
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
Finance
13
27 public partnerships were formed. Each partnership was set up to acquire and lease transportation equipment, such as aircraft, tractors and trailers, cargo containers, and railcars, to transportation
companies.
Until the Tax Reform Act of 1986, PLM enjoyed considerable success with its partnerships. It became one of the largest equipment-leasing firms in the United States.The partnerships appealed to
high-tax-bracket individuals because unlike corporations, partnerships are not taxed. The partnerships were set up to be self-liquidating (i.e., all excess cash flow was to be distributed to the partners), and no reinvestment could take place. No ready market for the partnership units existed, and
each partnership invested in a narrow class of transportation equipment. PLM’s success depended
on creating tax-sheltered cash flow from accelerated depreciation and investment tax credits. However, the 1986 Tax Reform Act had a devastating impact on tax-sheltered limited partnerships.The
act substantially flattened personal tax rates, eliminated the investment tax credit, shortened depreciation schedules, and established an alternative minimum tax rate. The act caused PLM to think
about different types of equipment-leasing organizational forms. What was needed was an organization form that could take advantage of potential growth and diversification opportunities and that
wasn’t based entirely upon tax sheltering.
In 1987 PLM, with the advice and assistance of the now-bankrupt Drexel Burnham Lambert
investment banking firm, terminated its partnerships and converted consenting partnerships to a
new umbrella corporation called PLM International. After much legal maneuvering, PLM International publicly announced that a majority of the partnerships had consented to the consolidation and
incorporation. (A majority vote was needed for voluntary termination and some partnerships decided not to incorporate.) On February 2, 1988, PLM International’s common stock began trading
A Comparison of Partnership and Corporations
Corporation
Partnership
Liquidity and marketability
Shares can be exchanged without
termination of the corporation.
Common stock can be listed on
stock exchange.
Units are subject to substantial
restrictions on transferability. There
is usually no established trading
market for partnership units.
Voting rights
Usually each share of common stock
entitles the holder to one vote per
share on matters requiring a vote
and on the election of the directors.
Directors determine top management.
Some voting rights by limited
partners. However, general partner
has exclusive control and
management of operations.
Taxation
Corporations have double taxation:
Corporate income is taxable, and
dividends to shareholders are also
taxable.
Partnerships are not taxable. Partners
pay taxes on distributed shares of
partnership.
Reinvestment and dividend
payout
Corporations have broad latitude on
dividend payout decisions.
Partnerships are generally prohibited
from reinvesting partnership cash
flow. All net cash flow is distributed
to partners.
Liability
Shareholders are not personally liable
for obligations of the corporation.
Limited partners are not liable for
obligations of partnerships. General
partners may have unlimited liability.
Continuity of existence
Corporations have perpetual life.
Partnerships have limited life.
Corporate Finance,
Seventh Edition
14
I. Overview
Finance
Companies, 2004
Part I Overview
on the American Stock Exchange (AMEX) at about $8 per share. On February 6, 2002, MILPI
Acquisition Corp. acquired PLM International for a price of 3.46 per share of stock. PLM International ceased to be a publicly traded corporation.
The decision to become a corporation is complicated, and there are several pros and cons. PLM
International cited several basic reasons to support the consolidation and incorporation of its
transportation-equipment–leasing activities.
• Enhanced access to equity and debt capital for future growth.
• The possibility of reinvestment for future profit opportunities.
• Better liquidity for investors through common stock listing on AMEX.
These are all good reasons for incorporating, and they provided potential benefits to the new
shareholders of PLM International that may have outweighed the disadvantages of double taxation
that came from incorporating. However, not all the PLM partnerships wanted to convert to the
corporation. Sometimes it is not easy to determine whether a partnership or a corporation is the
best organizational form. Corporate income is taxable at the personal and corporation levels.
Because of this double taxation, firms having the most to gain from incorporation share the following characteristics:
• Low taxable income.
• Low marginal corporate tax rates.
• Low marginal personal tax rates among potential shareholders.
In addition, firms with high rates of reinvestment relative to current income are good candidates
for the corporate form because corporations can more easily retain profits for reinvestment than
partnerships. Also, it is easier for corporations to sell shares of stock on public stock markets to
finance possible investment opportunities.
Concept
Questions
1. Define a proprietorship, a partnership, and a corporation.
2. What are the advantages of the corporate form of business organization?
1.4 Goals of the Corporate Firm
What is the primary goal of the corporation? The traditional answer is that managers in a
corporation make decisions for the stockholders because the stockholders own and control
the corporation. If so, the goal of the corporation is to add value for the stockholders. This
goal is a little vague and so we will try to come up with a precise formulation. It is also impossible to give a definitive answer to this important question because the corporation is an
artificial being, not a natural person. It exists in the “contemplation of the law.”3
It is necessary to precisely identify who controls the corporation. We shall consider the
set-of-contracts viewpoint. This viewpoint suggests the corporate firm will attempt to
maximize the shareholders’ wealth by taking actions that increase the current value per
share of existing stock of the firm.
Agency Costs and the Set-of-Contracts Perspective
The set-of-contracts theory of the firm states that the firm can be viewed as a set of contracts.4 One of the contract claims is a residual claim (equity) on the firm’s assets and cash
3
4
These are the words of Chief Justice John Marshall from The Trustees of Dartmouth College v. Woodward, 4, Wheaton 636 (1819).
M. C. Jensen and W. Meckling, “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure,” Journal of
Financial Economics 3 (1976).
13
14
Corporate Finance,
Seventh Edition
I. Overview
Finance
Companies, 2004
15
flows. The equity contract can be defined as a principal-agent relationship. The members of
the management team are the agents, and the equity investors (shareholders) are the principals. It is assumed that the managers and the shareholders, if left alone, will each attempt
to act in his or her own self-interest.
The shareholders, however, can discourage the managers from diverging from the
shareholders’ interests by devising appropriate incentives for managers and then monitoring their behavior. Doing so, unfortunately, is complicated and costly. The cost of resolving the conflicts of interest between managers and shareholders are special types of costs
called agency costs. These costs are defined as the sum of (1) the monitoring costs of the
shareholders and (2) the costs of implementing control devices. It can be expected that contracts will be devised that will provide the managers with appropriate incentives to maximize the shareholders’ wealth. Thus, the set-of-contracts theory suggests that managers in
the corporate firm will usually act in the best interest of shareholders. However, agency
problems can never be perfectly solved and, as a consequence, shareholders may experience residual losses. Residual losses are the lost wealth of the shareholders due to divergent
behavior of the managers.
Managerial Goals
Managerial goals may be different from those of shareholders. What goals will managers
maximize if they are left to pursue their own rather than shareholders’ goals?
Williamson proposes the notion of expense preference.5 He argues that managers obtain
value from certain kinds of expenses. In particular, company cars, office furniture, office
location, and funds for discretionary investment have value to managers beyond that which
comes from their productivity.
Donaldson conducted a series of interviews with the chief executives of several large
companies.6 He concluded that managers are influenced by two basic motivations:
1. Survival. Organizational survival means that management will always try to command
sufficient resources to avoid the firm’s going out of business.
2. Independence and self-sufficiency. This is the freedom to make decisions without encountering external parties or depending on outside financial markets. The Donaldson
interviews suggested that managers do not like to issue new shares of stock. Instead,
they like to be able to rely on internally generated cash flow.
These motivations lead to what Donaldson concludes is the basic financial objective of
managers: the maximization of corporate wealth. Corporate wealth is that wealth over
which management has effective control; it is closely associated with corporate growth and
corporate size. Corporate wealth is not necessarily shareholder wealth. Corporate wealth
tends to lead to increased growth by providing funds for growth and limiting the extent to
which new equity is raised. Increased growth and size are not necessarily the same thing as
increased shareholder wealth.
Separation of Ownership and Control
Some people argue that shareholders do not completely control the corporation. They argue
that shareholder ownership is too diffuse and fragmented for effective control of management.7 A striking feature of the modern large corporation is the diffusion of ownership
5
O. Williamson, “Managerial Discretion and Business Behavior,” American Economic Review 53 (1963).
6
G. Donaldson, Managing Corporate Wealth: The Operations of a Comprehensive Financial Goals System (New York: Praeger
Publishers, 1984).
7
Work by Gerald T. Garvey and Peter L. Swan, “The Economics of Corporate Governance: Beyond the Marshallian Firm,”
Journal of Corporate Finance 1 (1994), surveys literature on the stated assumption of shareholder maximization.
Corporate Finance,
Seventh Edition
16
I. Overview
Part I Overview
TABLE 1.1
Some of the World’s
Largest Industrial
Corporations, 2003
Companies, 2004
Finance
Company
Microsoft
General Electric
Pfizer
IBM
Merck
Intel
Coca-Cola
Toyota
Market Value*
(in $ billions)
Shares Outstanding
(in millions)
$266.0
255.6
179.4
136.4
114.1
112.4
98.9
80.4
10715
3714
4138
1875
2968
3555
3464
1802
Number of
Shareholders
92,130
534,000
105,000
616,000
269,600
203,000
366,000
100,000
*Market price multiplied by shares outstanding.
SOURCES: Value Line, Business Week, and Standard & Poor’s Security Owners Stock Guide.
among thousands of investors. For example, Table 1.1 shows that approximately 616,000
persons and institutions own shares of IBM stock.
One of the most important advantages of the corporate form of business organization is
that it allows ownership of shares to be transferred. The resulting diffuse ownership, however,
brings with it the separation of ownership and control of the large corporation. The possible
separation of ownership and control raises an important question: Who controls the firm?
Do Shareholders Control Managerial Behavior?
The claim that managers can ignore the interests of shareholders is deduced from the fact
that ownership in large corporations is widely dispersed. As a consequence, it is often
claimed that individual shareholders cannot control management. There is some merit in
this argument, but it is too simplistic.
When a conflict of interest exists between management and shareholders, who wins?
Does management or the shareholders control the firm? There is no doubt that ownership
in large corporations is diffuse when compared to the closely held corporation. However,
several control devices used by shareholders bond management to the self-interest of
shareholders:
1. Shareholders determine the membership of the board of directors by voting. Thus,
shareholders control the directors, who in turn select the management team.
2. Contracts with management and arrangements for compensation, such as stock option
plans, can be made so that management has an incentive to pursue the goal of the shareholders. Another device is called performance shares. These are shares of stock given to
managers on the basis of performance as measured by earnings per share and similar
criteria.
3. If the price of a firm’s stock drops too low because of poor management, the firm may
be acquired by another group of shareholders, by another firm, or by an individual. This
is called a takeover. In a takeover, the top management of the acquired firm may find
themselves out of a job. This puts pressure on the management to make decisions in the
stockholders’ interests. Fear of a takeover gives managers an incentive to take actions
that will maximize stock prices.
4. Competition in the managerial labor market may force managers to perform in the best
interest of stockholders. Otherwise they will be replaced. Firms willing to pay the most
will lure good managers. These are likely to be firms that compensate managers based
on the value they create.
15
16
Corporate Finance,
Seventh Edition
I. Overview
Finance
Companies, 2004
17
The available evidence and theory are consistent with the ideas of shareholder control
and shareholder value maximization. Indeed, our emphasis will be on how the corporate
firm can maximize shareholder value. However, there can be no doubt that at times corporations pursue managerial goals at the expense of shareholders. There is also evidence that
the diverse claims of customers, vendors, and employees must frequently be considered in
the goals of the corporation.
Concept
Questions
1.
2.
3.
4.
What are the two types of agency costs?
How are managers bonded to shareholders?
Can you recall some managerial goals?
What is the set-of-contracts perspective?
1.5 Financial Markets
As indicated in Section 1.1, firms offer two basic types of securities to investors. Debt securities are contractual obligations to repay corporate borrowing. Equity securities are
shares of common stock and preferred stock that represent noncontractual claims to the
residual cash flow of the firm. Issues of debt and stock that are publicly sold by the firm are
then traded on the financial markets.
The financial markets are composed of the money markets and the capital markets.
Money markets are the markets for debt securities that will pay off in the short term (usually less than one year). Capital markets are the markets for long-term debt (with a maturity at over one year) and for equity shares.
The term money market applies to a group of loosely connected markets. They are
dealer markets. Dealers are firms that make continuous quotations of prices for which they
stand ready to buy and sell money-market instruments for their own inventory and at their
own risk. Thus, the dealer is a principal in most transactions. This is different from a stockbroker acting as an agent for a customer in buying or selling common stock on most stock
exchanges; an agent does not actually acquire the securities.
At the core of the money markets are the money-market banks (these are large banks
mostly in New York), more than 30 government securities dealers (some of which are the
large banks), a dozen or so commercial-paper dealers, and a large number of money brokers. Money brokers specialize in finding short-term money for borrowers and placing
money for lenders. The financial markets can be classified further as the primary market
and the secondary markets.
The Primary Market: New Issues
The primary market is used when governments and corporations initially sell securities.
Corporations engage in two types of primary-market sales of debt and equity: public offerings and private placements.
Most publicly offered corporate debt and equity come to the market underwritten by a syndicate of investment banking firms. The underwriting syndicate buys the new securities from
the firm for the syndicate’s own account and resells them at a higher price. Publicly issued debt
and equity must be registered with the Securities and Exchange Commission. Registration
requires the corporation to disclose all of the material information in a registration statement.
The legal, accounting, and other costs of preparing the registration statement are not negligible. In part to avoid these costs, privately placed debt and equity are sold on the basis of
private negotiations to large financial institutions, such as insurance companies and mutual
funds. Private placements are not registered with the Securities and Exchange Commission.
Corporate Finance,
Seventh Edition
18
I. Overview
Finance
Companies, 2004
Part I Overview
Secondary Markets
After debt and equity securities are originally sold, they are traded in the secondary markets. There are two kinds of secondary markets: the auction markets and the dealer markets.
The equity securities of most large U.S. firms trade in organized auction markets, such
as the New York Stock Exchange, the American Stock Exchange, and regional exchanges,
such as the Midwest Stock Exchange. The New York Stock Exchange (NYSE) is the most
important auction exchange. It usually accounts for more than 85 percent of all shares
traded in U.S. auction exchanges. Bond trading on auction exchanges is inconsequential.
Most debt securities are traded in dealer markets. The many bond dealers communicate
with one another by telecommunications equipment—wires, computers, and telephones.
Investors get in touch with dealers when they want to buy or sell, and can negotiate a deal.
Some stocks are traded in the dealer markets. When they are, it is referred to as the overthe-counter (OTC) market.
In February 1971, the National Association of Securities Dealers made available to
dealers and brokers in the OTC market an automated quotation system called the National
Association of Securities Dealers Automated Quotation (NASDAQ) system. The market
value of shares of OTC stocks in the NASDAQ system at the end of 1998 was about 25 percent of the market value of the shares on the NYSE.
Exchange Trading of Listed Stocks
Auction markets are different from dealer markets in two ways. First, trading in a given
auction exchange takes place at a single site on the floor of the exchange. Second, transaction prices of shares traded on auction exchanges are communicated almost immediately to
the public by computer and other devices.
The NYSE is one of the preeminent securities exchanges in the world. All transactions
in stocks listed on the NYSE occur at a particular place on the floor of the exchange called
a post. At the heart of the market is the specialist. Specialists are members of the NYSE
who make a market in designated stocks. Specialists have an obligation to offer to buy and
sell shares of their assigned NYSE stocks. It is believed that this makes the market liquid
because the specialist assumes the role of a buyer for investors if they wish to sell and a
seller if they wish to buy.
Listing
Firms that want their equity shares to be traded on the NYSE must apply for listing. To be
listed initially on the NYSE a company is expected to satisfy certain minimum requirements. Some of these for U.S. companies are as follows:
1. Demonstrated earning power of either $2.5 million before taxes for the most recent year
and $2 million before taxes for each of the preceding two years, or an aggregate for
the last three years of $6.5 million together with a minimum in the most recent year of
$4.5 million (all years must be profitable).
2. Net tangible assets equal to at least $40 million.
3. A market value for publicly held shares of $40 million.
4. A total of at least 1.1 million publicly held shares.
5. A total of at least 2,000 holders of 100 shares of stock or more.
The listing requirements for non–U.S. companies are somewhat more stringent. Table 1.2
gives the market value of NYSE-listed stocks and bonds.
17
18
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
Finance
19
TABLE 1.2
Market Value of
NYSE-Listed
Securities
End-of-Year
NYSE-listed stocks*
2001
2000
1999
1998
NYSE-listed bonds†
2001
2000
1999
1998
Number of
Companies
Market Value
($ millions)
2798
2862
3025
3114
11,713,707
12,372,304
12,296,057
10,864,472
369
392
416
474
1,653,549
2,124,789
2,401,605
2,554,122
*Includes preferred stock and common stock.
†
Includes government issues.
SOURCE: Data from the New York Stock Exchange Fact Book 2001, published by the New York Stock Exchange. In the case of
bonds, in some instances we report the face value.
Concept
Questions
1. Distinguish between money markets and capital markets.
2. What is listing?
3. What is the difference between a primary market and a secondary market?
1.6 OUTLINE OF THE TEXT
Now that we’ve taken the quick tour through all of corporate finance, we can take a closer
look at this book. The book is divided into eight parts. The long-term investment decision
is covered first. Financing decisions and working capital are covered next. Finally a series
of special topics are covered. Here are the eight parts:
Part I
Part II
Part III
Part IV
Part V
Part VI
Part VII
Part VIII
Overview
Value and Capital Budgeting
Risk
Capital Structure and Dividend Policy
Long-Term Financing
Options, Futures, and Corporate Finance
Short-Term Finance
Special Topics
Part II describes how investment opportunities are valued in financial markets. This part
contains basic theory. Because finance is a subject that builds understanding from the
ground up, the material is very important. The most important concept in Part II is net
present value. We develop the net present value rule into a tool for valuing investment
alternatives. We discuss general formulas and apply them to a variety of different financial
instruments.
Part III introduces basic measures of risk. The capital-asset pricing model (CAPM) and
the arbitrage pricing theory (APT) are used to devise methods for incorporating risk in
valuation. As part of this discussion, we describe the famous beta coefficient. Finally, we
use the above pricing models to handle capital budgeting under risk.
Corporate Finance,
Seventh Edition
20
I. Overview
Finance
Companies, 2004
Part I Overview
Visit us at www.mhhe.com/rwj
Part IV examines two interrelated topics: capital structure and dividend policy. Capital
structure is the extent to which the firm relies on debt. It cannot be separated from the
amount of cash dividends the firm decides to pay out to its equity shareholders.
Part V concerns long-term financing. We describe the securities that corporations issue
to raise cash, as well as the mechanics of offering securities for a public sale. Here we discuss call provisions, warrants, convertibles, and leasing.
Part VI discusses special contractual arrangements called Options.
Part VII is devoted to financial planning and short-term finance. The first chapter describes financial planning. Next we focus on managing the firm’s current assets and current
liabilities. We describe aspects of the firm’s short-term financial management. Separate
chapters on cash management and on credit management are included.
Part VIII covers two important special topics: mergers and international corporate
finance.
KEY TERMS
capital budgeting, 4
capital markets, 17
capital structure, 4
contingent claims, 10
corporation, 11
SUGGESTED
READINGS
Evidence is provided on the tax factor in choosing to incorporate in:
Mackie-Mason, J. K., and R. H. Gordon.“How Much Do Taxes Discourage Incorporation?” Journal of
Finance ( June 1997).
Do American managers pay too little attention to shareholders? This is the question posed in:
Miller, M. “Is American Corporate Governance Fatally Flawed?” Journal of Applied Corporate Finance
(Winter 1994).
What are the patterns of corporate ownership around the world? This is the question posed by:
La Porta, R., F. Lopez-De-Silanes, and A. Shleifer. “Corporate Ownership Around the World.” Journal
of Finance 54 (1999).
A recent survey of international corporate governance can be found in:
Denis, D. K., and J. S. McConnel.“International Corporate Governance.” Journal of Financial Quantitative Analysis 38 (March 2003).
Barca, F., and M. Becht. The Corporate Control of Europe. Oxford University Press, 2002.
S&P
PROBLEM
1.1
money markets, 17
net working capital, 4
partnership, 10
set-of-contracts viewpoint, 14
sole proprietorship, 10
On the Market Insight Home Page, follow the “Industry” link. From the pull down menu you
can select various industries.Answer the following questions for these industries: Aerospace
& Defense, Application Software, Diversified Capital Markets, Homebuilding, Personal Products, Restaurants, and Precious Metals & Minerals.
a. How many companies are in each industry?
b. What are the total sales of each industry?
c. Does the industry with the largest total sales have the largest number of competitors?
What does this tell you about the competition in each industry?
19
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
2. Accounting Statements
and Cash Flow
Chapter 2
Accounting Statements
and Cash Flow
EXECUTIVE
SUMMARY
20
Chapter 2 describes the basic accounting
statements used for reporting corporate activity. The focus of the chapter is the practical
details of cash flow. It will become obvious to
you in the next several chapters that knowing
how to determine cash flow helps the financial
manager make better decisions. Students who
have had accounting courses will not find the
material new and can think of it as a review
with an emphasis on finance. We will discuss
cash flow further in later chapters.
2.1 The Balance Sheet
The balance sheet is an accountant’s snapshot of the firm’s accounting value on a particular date, as though the firm stood momentarily still. The balance sheet has two sides: On the
left are the assets and on the right are the liabilities and stockholders’ equity. The balance
sheet states what the firm owns and how it is financed. The accounting definition that underlies the balance sheet and describes the balance is
Assets ⬅ Liabilities Stockholders’ equity
We have put a three-line equality in the balance equation to indicate that it must always
hold, by definition. In fact, the stockholders’ equity is defined to be the difference between
the assets and the liabilities of the firm. In principle, equity is what the stockholders would
have remaining after the firm discharged its obligations.
Table 2.1 gives the 20X2 and 20X1 balance sheet for the fictitious U.S. Composite
Corporation. The assets in the balance sheet are listed in order by the length of time it normally would take an ongoing firm to convert them to cash. The asset side depends on the
nature of the business and how management chooses to conduct it. Management must make
decisions about cash versus marketable securities, credit versus cash sales, whether to make
or buy commodities, whether to lease or purchase items, the types of business in which to
engage, and so on. The liabilities and the stockholders’ equity are listed in the order in
which they must be paid.
The liabilities and stockholders’ equity side reflects the types and proportions of financing, which depend on management’s choice of capital structure, as between debt and equity
and between current debt and long-term debt.
21
Corporate Finance,
Seventh Edition
22
TABLE 2.1
I. Overview
and Cash Flow
Companies, 2004
Part I Overview
The Balance Sheet of the U.S. Composite Corporation
U.S. COMPOSITE CORPORATION
Balance Sheet
20X2 and 20X1
(in $ millions)
Assets
20X2
20X1
Current assets:
Cash and equivalents
Accounts receivable
Inventories
Other
Total current assets
$ 140
294
269
58
$ 761
$ 107
270
280
50
$ 707
Fixed assets:
Property, plant, and equipment
Less accumulated depreciation
Net property, plant, and equipment
Intangible assets and others
Total fixed assets
$1,423
(550)
873
245
$1,118
$1,274
(460)
814
221
$1,035
Total assets
$1,879
$1,742
Liabilities (Debt)
and Stockholders’
Equity
20X2
20X1
Current liabilities:
Accounts payable
Notes payable
Accrued expenses
Total current liabilities
$ 213
50
223
$ 486
$ 197
53
205
$ 455
$ 117
471
$ 588
$ 104
458
$ 562
$
39
55
347
390
(26)
$ 805
$
$1,879
$1,742
Long-term liabilities:
Deferred taxes
Long-term debt1
Total long-term liabilities
Stockholders’ equity:
Preferred stock
Common stock ($1 par value)
Capital surplus
Accumulated retained earnings
Less treasury stock2
Total equity
Total liabilities and
stockholders’ equity3
39
32
327
347
(20)
$ 725
1
Long-term debt rose by $471 million – $458 million $13 million.This is the difference between $86 million new debt and $73 million in retirement of
old debt.
2
Treasury stock rose by $6 million.This reflects the repurchase of $6 million of U.S. Composite’s company stock.
3
U.S. Composite reports $43 million in new equity.The company issued 23 million shares at a price of $1.87.The par value of common stock increased
by $23 million, and capital surplus increased by $20 million.
When analyzing a balance sheet, the financial manager should be aware of three concerns: accounting liquidity, debt versus equity, and value versus cost.
Accounting Liquidity
Accounting liquidity refers to the ease and quickness with which assets can be converted
to cash. Current assets are the most liquid and include cash and those assets that will be
turned into cash within a year from the date of the balance sheet. Accounts receivable are
amounts not yet collected from customers for goods or services sold to them (after adjustment for potential bad debts). Inventory is composed of raw materials to be used in production, work in process, and finished goods. Fixed assets are the least liquid kind of assets.
Tangible fixed assets include property, plant, and equipment. These assets do not convert to
cash from normal business activity, and they are not usually used to pay expenses, such as
payroll.
Some fixed assets are not tangible. Intangible assets have no physical existence but can
be very valuable. Examples of intangible assets are the value of a trademark or the value of
a patent. The more liquid a firm’s assets, the less likely the firm is to experience problems
21
22
Corporate Finance,
Seventh Edition
I. Overview
and Cash Flow
Companies, 2004
Chapter 2 Accounting Statements and Cash Flow
23
meeting short-term obligations. Thus, the probability that a firm will avoid financial
distress can be linked to the firm’s liquidity. Unfortunately, liquid assets frequently have
lower rates of return than fixed assets; for example, cash generates no investment income.
To the extent a firm invests in liquid assets, it sacrifices an opportunity to invest in more
profitable investment vehicles.
Debt versus Equity
Liabilities are obligations of the firm that require a payout of cash within a stipulated time
period. Many liabilities involve contractual obligations to repay a stated amount and interest over a period. Thus, liabilities are debts and are frequently associated with nominally
fixed cash burdens, called debt service, that put the firm in default of a contract if they are
not paid. Stockholders’ equity is a claim against the firm’s assets that is residual and not
fixed. In general terms, when the firm borrows, it gives the bondholders first claim on the
firm’s cash flow.1 Bondholders can sue the firm if the firm defaults on its bond contracts.
This may lead the firm to declare itself bankrupt. Stockholders’ equity is the residual difference between assets and liabilities:
Assets Liabilities ⬅ Stockholders’ equity
This is the stockholders’ share in the firm stated in accounting terms. The accounting value
of stockholders’ equity increases when retained earnings are added. This occurs when the
firm retains part of its earnings instead of paying them out as dividends.
Value versus Cost
The accounting value of a firm’s assets is frequently referred to as the carrying value or the
book value of the assets.2 Under generally accepted accounting principles (GAAP),
audited financial statements of firms in the United States carry the assets at cost.3 Thus the
terms carrying value and book value are unfortunate. They specifically say “value,” when
in fact the accounting numbers are based on cost. This misleads many readers of financial
statements to think that the firm’s assets are recorded at true market values. Market value
is the price at which willing buyers and sellers trade the assets. It would be only a coincidence if accounting value and market value were the same. In fact, management’s job is to
create a value for the firm that is higher than its cost.
Many people use the balance sheet although the information each may wish to extract
is not the same. A banker may look at a balance sheet for evidence of accounting liquidity and working capital. A supplier may also note the size of accounts payable and therefore the general promptness of payments. Many users of financial statements, including
managers and investors, want to know the value of the firm, not its cost. This is not found
on the balance sheet. In fact, many of the true resources of the firm do not appear on the
balance sheet: good management, proprietary assets, favorable economic conditions,
and so on.
1
Bondholders are investors in the firm’s debt. They are creditors of the firm. In this discussion, the term bondholder means the
same thing as creditor.
2
Confusion often arises because many financial accounting terms have the same meaning. This presents a problem with jargon
for the reader of financial statements. For example, the following terms usually refer to the same thing: assets minus liabilities,
net worth, stockholders’ equity, owner’s equity, and equity capitalization.
3
Generally, GAAP requires assets to be carried at the lower of cost or market value. In most instances cost is lower than market
value. However, in some cases when a fair market value can be readily determined, the assets have their value adjusted to the
fair market value.
Corporate Finance,
Seventh Edition
24
Concept
Questions
I. Overview
and Cash Flow
Companies, 2004
Part I Overview
1. What is the balance-sheet equation?
2. What three things should be kept in mind when looking at a balance sheet?
2.2 The Income Statement
The income statement measures performance over a specific period of time, say, a year.
The accounting definition of income is
Revenue Expenses ⬅ Income
If the balance sheet is like a snapshot, the income statement is like a video recording of
what the people did between two snapshots. Table 2.2 gives the income statement for the
U.S. Composite Corporation for 20X2.
The income statement usually includes several sections. The operations section reports
the firm’s revenues and expenses from principal operations. One number of particular importance is earnings before interest and taxes (EBIT), which summarizes earnings before
taxes and financing costs. Among other things, the nonoperating section of the income
TABLE 2.2
The Income
Statement of the
U.S. Composite
Corporation
Income Statement
20X2
(in $ millions)
Total operating revenues
Cost of goods sold
Selling, general, and administrative expenses
Depreciation
$2,262
(1,655)
(327)
(90)
______
Operating income
Other income
$ 190
29
______
Earnings before interest and taxes (EBIT)
Interest expense
$ 219
(49)
______
Pretax income
Taxes
Current: $
Deferred: $
$ 170
(84)
71
13
______
$ 86
______
______
$ 43
$ 43
Net income
Retained earnings:
Dividends:
NOTE:
There are 29 million shares outstanding. Earnings per share and dividends per share can be calculated as follows:
Earnings per share Net income
Total shares outstanding
$86
29
$2.97 per share
Dividends
Total shares outstanding
$43
29
Dividends per share $1.48 per share
23
24
Corporate Finance,
Seventh Edition
I. Overview
and Cash Flow
Companies, 2004
25
statement includes all financing costs, such as interest expense. Usually a second section
reports as a separate item the amount of taxes levied on income. The last item on the
income statement is the bottom line, or net income. Net income is frequently expressed per
share of common stock, that is, earnings per share.
When analyzing an income statement, the financial manager should keep in mind GAAP,
noncash items, time, and costs.
Generally Accepted Accounting Principles
Revenue is recognized on an income statement when the earnings process is virtually completed and an exchange of goods or services has occurred. Therefore, the unrealized appreciation in owning property will not be recognized as income. This provides a device for
smoothing income by selling appreciated property at convenient times. For example, if the
firm owns a tree farm that has doubled in value, then, in a year when its earnings from
other businesses are down, it can raise overall earnings by selling some trees. The matching principle of GAAP dictates that revenues be matched with expenses. Thus, income is
reported when it is earned, or accrued, even though no cash flow has necessarily occurred
(for example, when goods are sold for credit, sales and profits are reported).
Noncash Items
The economic value of assets is intimately connected to their future incremental cash
flows. However, cash flow does not appear on an income statement. There are several
noncash items that are expenses against revenues, but that do not affect cash flow. The
most important of these is depreciation. Depreciation reflects the accountant’s estimate of
the cost of equipment used up in the production process. For example, suppose an asset
with a five-year life and no resale value is purchased for $1,000. According to accountants,
the $1,000 cost must be expensed over the useful life of the asset. If straight-line depreciation is used, there will be five equal installments and $200 of depreciation expense will be
incurred each year. From a finance perspective, the cost of the asset is the actual negative
cash flow incurred when the asset is acquired (that is, $1,000, not the accountant’s smoothed
$200-per-year depreciation expense).
Another noncash expense is deferred taxes. Deferred taxes result from differences
between accounting income and true taxable income.4 Notice that the accounting tax shown
on the income statement for the U.S. Composite Corporation is $84 million. It can be broken down as current taxes and deferred taxes. The current tax portion is actually sent to the
tax authorities (for example, the Internal Revenue Service). The deferred tax portion is not.
However, the theory is that if taxable income is less than accounting income in the current
year, it will be more than accounting income later on. Consequently, the taxes that are not
paid today will have to be paid in the future, and they represent a liability of the firm. This
shows up on the balance sheet as deferred tax liability. From the cash flow perspective,
though, deferred tax is not a cash outflow.
Time and Costs
It is often useful to think of all of future time as having two distinct parts, the short run and
the long run. The short run is that period of time in which certain equipment, resources,
and commitments of the firm are fixed; but the time is long enough for the firm to vary its
4
One situation in which taxable income may be lower than accounting income is when the firm uses accelerated depreciation
expense procedures for the IRS but uses straight-line procedures allowed by GAAP for reporting purposes.
Corporate Finance,
Seventh Edition
26
I. Overview
Companies, 2004
and Cash Flow
Part I Overview
output by using more labor and raw materials. The short run is not a precise period of time
that will be the same for all industries. However, all firms making decisions in the short run
have some fixed costs, that is, costs that will not change because of fixed commitments. In
real business activity, examples of fixed costs are bond interest, overhead, and property
taxes. Costs that are not fixed are variable. Variable costs change as the output of the firm
changes; some examples are raw materials and wages for laborers on the production line.
In the long run, all costs are variable.5 Financial accountants do not distinguish between
variable costs and fixed costs. Instead, accounting costs usually fit into a classification that
distinguishes product costs from period costs. Product costs are the total production costs
incurred during a period—raw materials, direct labor, and manufacturing overhead—and
are reported on the income statement as cost of goods sold. Both variable and fixed costs are
included in product costs. Period costs are costs that are allocated to a time period; they are
called selling, general, and administrative expenses. One period cost would be the company
president’s salary.
Concept
Questions
1. What is the income statement equation?
2. What are three things to keep in mind when looking at an income statement?
3. What are noncash expenses?
2.3 Net Working Capital
Net working capital is current assets minus current liabilities. Net working capital is positive when current assets are greater than current liabilities. This means the cash that will become available over the next 12 months will be greater than the cash that must be paid out.
The net working capital of the U.S. Composite Corporation is $275 million in 20X2 and
$252 million in 20X1:
20X2
20X1
Current assets
($ millions)
$761
707
Current liabilities
($ millions)
$486
455
Net working capital
($ millions)
$275
252
In addition to investing in fixed assets (i.e., capital spending), a firm can invest in net working capital. This is called the change in net working capital. The change in net working
capital in 20X2 is the difference between the net working capital in 20X2 and 20X1; that is,
$275 million $252 million $23 million. The change in net working capital is usually
positive in a growing firm.
Concept
Questions
1. What is net working capital?
2. What is the change in net working capital?
2.4 Financial Cash Flow
Perhaps the most important item that can be extracted from financial statements is the actual cash flow of the firm. There is an official accounting statement called the statement of
cash flows. This statement helps to explain the change in accounting cash and equivalents,
5
When one famous economist was asked about the difference between the long run and the short run, he said, “In the long run
we are all dead.”
25
26
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
and Cash Flow
27
TABLE 2.3
Financial Cash
Flow of the
U.S. Composite
Corporation
Financial Cash Flow
20X2
(in $ millions)
Cash Flow of the Firm
Operating cash flow
(Earnings before interest and taxes
plus depreciation minus taxes)
Capital spending
(Acquisitions of fixed assets
minus sales of fixed assets)
Additions to net working capital
$238
(173)
(23)
____
$
42
____
____
Total
Cash Flow to Investors in the Firm
Debt
(Interest plus retirement of debt
minus long-term debt financing)
Equity
(Dividends plus repurchase of
equity minus new equity financing)
Total
$ 36
6
____
$
42
____
____
which for U.S. Composite is $33 million in 20X2. (See Section 2.5.) Notice in Table 2.1
that cash and equivalents increase from $107 million in 20X1 to $140 million in 20X2.
However, we will look at cash flow from a different perspective, the perspective of finance.
In finance the value of the firm is its ability to generate financial cash flow. (We will talk
more about financial cash flow in Chapter 7.)
The first point we should mention is that cash flow is not the same as net working capital. For example, increasing inventory requires using cash. Because both inventories and
cash are current assets, this does not affect net working capital. In this case, an increase in
a particular net working capital account, such as inventory, is associated with decreasing
cash flow.
Just as we established that the value of a firm’s assets is always equal to the value of the
liabilities and the value of the equity, the cash flows received from the firm’s assets (that is,
its operating activities), CF(A), must equal the cash flows to the firm’s creditors, CF(B),
and equity investors, CF(S):
CF(A) ⬅ CF(B) CF(S)
The first step in determining cash flows of the firm is to figure out the cash flow from operations. As can be seen in Table 2.3, operating cash flow is the cash flow generated by business activities, including sales of goods and services. Operating cash flow reflects tax payments, but not financing, capital spending, or changes in net working capital.
In $ Millions
Earnings before interest and taxes
Depreciation
Current taxes
$219
90
____
(71)
$238
Corporate Finance,
Seventh Edition
28
I. Overview
Companies, 2004
and Cash Flow
Part I Overview
Another important component of cash flow involves changes in fixed assets. For example, when U.S. Composite sold its power systems subsidiary in 20X2 it generated $25 in
cash flow. The net change in fixed assets equals sales of fixed assets minus the acquisition
of fixed assets. The result is the cash flow used for capital spending:
Acquisition of fixed assets
Sales of fixed assets
Capital spending
$198
(25)
____
$173
____
____
($149 $24 Increase in property,
plant, and equipment Increase in
intangible assets)
Cash flows are also used for making investments in net working capital. In U.S. Composite
Corporation in 20X2, additions to net working capital are:
$23
Total cash flows generated by the firm’s assets are the sum of:
Capital spending
Total cash flow of the firm
$238
(173)
(23)
____
$
42
____
____
The total outgoing cash flow of the firm can be separated into cash flow paid to creditors
and cash flow paid to stockholders. The cash flow paid to creditors represents a regrouping
of the data in Table 2.3 and an explicit recording of interest expense. Creditors are paid an
amount generally referred to as debt service. Debt service is interest payments plus repayments of principal (that is, retirement of debt).
An important source of cash flow is from selling new debt. U.S. Composite’s long-term
debt increased by $13 million (the difference between $86 million in new debt and $73 million in retirement of old debt).6 Thus, an increase in long-term debt is the net effect of new
borrowing and repayment of maturing obligations plus interest expense.
Cash Flow Paid to Creditors
(in $ millions)
Interest
Retirement of debt
Debt service
Proceeds from long-term debt sales
Total
$49
73
____
122
(86)
____
$36
____
____
Cash flow of the firm also is paid to the stockholders. It is the net effect of paying dividends plus repurchasing outstanding shares of stock and issuing new shares of stock.
6
New debt and the retirement of old debt are usually found in the “notes” to the balance sheet.
27
28
Corporate Finance,
Seventh Edition
I. Overview
and Cash Flow
Companies, 2004
29
Cash Flow to Stockholders
(in $ millions)
Dividends
Repurchase of stock
Cash to stockholders
Proceeds from new stock issue
Total
$43
____6
49
(43)
____
$ 6
____
____
Some important observations can be drawn from our discussion of cash flow:
1. Several types of cash flow are relevant to understanding the financial situation of the
firm. Operating cash flow, defined as earnings before interest and depreciation minus taxes,
measures the cash generated from operations not counting capital spending or working
capital requirements. It should usually be positive; a firm is in trouble if operating cash flow
is negative for a long time because the firm is not generating enough cash to pay operating
costs. Total cash flow of the firm includes adjustments for capital spending and additions
to net working capital. It will frequently be negative. When a firm is growing at a rapid rate,
the spending on inventory and fixed assets can be higher than cash flow from sales.7
2. Net income is not cash flow. The net income of the U.S. Composite Corporation in
20X2 was $86 million, whereas cash flow was $42 million. The two numbers are not
usually the same. In determining the economic and financial condition of a firm, cash flow
is more revealing.
Concept
Questions
1. How is cash flow different from changes in net working capital?
2. What is the difference between operating cash flow and total cash flow of the firm?
2.5 The Accounting Statement of Cash Flows
As previously mentioned, there is an official accounting statement called the statement of
cash flows. This statement helps explain the change in accounting cash, which for U.S.
Composite is $33 million in 20X2. It is very useful in understanding financial cash flow.
The first step in determining the change in cash is to figure out cash flow from operating
activities. This is the cash flow that results from the firm’s normal activities producing and
selling goods and services. The second step is to make an adjustment for cash flow from
investing activities. The final step is to make an adjustment for cash flow from financing
activities. Financing activities are the net payments to creditors and owners (excluding
interest expense) made during the year.
The three components of the statement of cash flows are determined below.
Cash Flow from Operating Activities
To calculate cash flow from operating activities we start with net income. Net income can
be found on the income statement and is equal to $86 million. We now need to add back
noncash expenses and adjust for changes in current assets and liabilities (other than cash).
The result is cash flow from operating activities.
7
Sometimes financial analysts refer to a firm’s free cash flow. Free cash flow is the cash flow in excess of that required to fund
profitable capital projects. We call free cash flow the total cash flow of the firm.
Corporate Finance,
Seventh Edition
30
I. Overview
Companies, 2004
and Cash Flow
Part I Overview
Cash Flow from Operating Activities
20X2
(in $ millions)
Net income
Depreciation
Deferred taxes
Change in assets and liabilities
Accounts receivable
Inventories
Accounts payable
Accrued expense
Notes payable
Other
Cash flow from operating activities
$ 86
90
13
(24)
11
16
18
(3)
(8)
____
$199
____
____
Cash Flow from Investing Activities
Cash flow from investing activities involves changes in capital assets: acquisition of fixed
assets and sales of fixed assets (i.e., net capital expenditures). The result for U.S. Composite
is below.
Cash Flow from Investing Activities
20X2
(in $ millions)
Cash flow from investing activities
$(198)
25
_____
$(173)
_____
_____
Cash Flow from Financing Activities
Cash flows to and from creditors and owners include changes in equity and debt.
Cash Flow from Financing Activities
20X2
(in $ millions)
Retirement of debt (includes notes)
Proceeds from long-term debt sales
Dividends
Repurchase of stock
Proceeds from new stock issue
Cash flow from financing activities
$(73)
86
(43)
(6)
43
_____
$ 7
_____
_____
The statement of cash flows is the addition of cash flows from operations, cash flows from
investing activities, and cash flows from financing activities, and is produced in Table 2.4.
When we add all the cash flows together, we get the change in cash on the balance sheet of
$33 million.
There is a close relationship between the official accounting statement called the statement of cash flows and the total cash flow of the firm used in finance. Going back to the
previous section, you should note a slight conceptual problem here. Interest paid should
29
Corporate Finance,
Seventh Edition
I. Overview
and Cash Flow
TABLE 2.4
Statement of
Consolidated Cash
Flows of the
U.S. Composite
Corporation
Companies, 2004
31
Statement of Cash Flows
20X2
(in $ millions)
Operations
Net income
Depreciation
Deferred taxes
Changes in assets and liabilities
Accounts receivable
Inventories
Accounts payable
Accrued expenses
Notes payable
Other
Total cash flow from operations
(24)
11
16
18
(3)
(8)
_____
$ 199
_____
_____
Investing activities
Total cash flow from investing activities
$(198)
25
_____
$(173)
_____
_____
Financing activities
Retirement of debt (including notes)
Proceeds of long-term debt
Dividends
Repurchase of stock
Proceeds from new stock issues
Total cash flow from financing activities
Change in cash (on the balance sheet)
$ 86
90
13
$ (73)
86
(43)
(6)
43
_____
$ 7
_____
_____
$ 33
_____
_____
really go under financing activities, but unfortunately that is not how the accounting is handled. The reason is that interest is deducted as an expense when net income is computed.
As a consequence the primary difference between the accounting cash flow and the financial cash flow of the firm (see Table 2.3) is interest expense.
Concept
Question
1. How is the statement of cash flows in Table 2.4 different from cash flow of the
firm in Table 2.3?
2.6 SUMMARY AND CONCLUSIONS
Besides introducing you to corporate accounting, the purpose of this chapter has been to teach you
how to determine cash flow from the accounting statements of a typical company.
1. Cash flow is generated by the firm and paid to creditors and shareholders. It can be classified as:
a. Cash flow from operations.
b. Cash flow from changes in fixed assets.
c. Cash flow from changes in working capital.
2. Calculations of cash flow are not difficult, but they require care and particular attention to detail in
properly accounting for noncash expenses such as depreciation and deferred taxes. It is especially
important that you do not confuse cash flow with changes in net working capital and net income.
30
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
and Cash Flow
32
Part I Overview
KEY TERMS
balance sheet, 21
cash flow, 26
change in net working capital, 26
free cash flow, 29
generally accepted accounting
principles (GAAP), 23
SUGGESTED
READING
There are many excellent textbooks on accounting. The one that we have found helpful is:
Kieso, D. E., J. J.Weygandt, and T. O.Warfield. Intermediate Accounting, 10th ed. New York: John Wiley.
2001.
QUESTIONS
& PROBLEMS
2.1
Prepare a December 31 balance sheet using the following data:
Cash
Patents
Accounts payable
Accounts receivable
Taxes payable
Machinery
Bonds payable
Accumulated retained earnings
Capital surplus
THE BALANCE
SHEET
income statement, 24
noncash items, 25
operating cash flow, 29
total cash flow of the firm, 29
$ 4,000
82,000
6,000
8,000
2,000
34,000
7,000
6,000
19,000
The par value of the firm’s common stock is $100.
2.2
The following table presents the long-term liabilities and stockholders’ equity of Information
Control Corp. of one year ago.
Long-term debt
Preferred stock
Common stock
Retained earnings
$50,000,000
30,000,000
100,000,000
20,000,000
During the past year, Information Control issued $10 million of new common stock.The firm
generated $5 million of net income and paid $3 million of dividends. Construct today’s balance
sheet reflecting the changes that occurred at Information Control Corp. during the year.
THE INCOME
STATEMENT
2.3
Prepare an income statement using the following data.
Sales
Cost of goods sold
Administrative expenses
Interest expense
$500,000
200,000
100,000
50,000
The firm’s tax rate is 34 percent.
2.4
The Flying Lion Corporation reported the following data on the income statement of one of
its divisions. Flying Lion Corporation has other profitable divisions.
Net sales
Cost of goods sold
Operating expenses
Depreciation
Tax rate (%)
20X2
20X1
$800,000
560,000
75,000
300,000
30
$500,000
320,000
56,000
200,000
30
31
Corporate Finance,
Seventh Edition
I. Overview
Companies, 2004
and Cash Flow
33
a. Prepare an income statement for each year.
b. Determine the operating cash flow during each year.
FINANCIAL CASH
FLOW
2.5
What are the differences between accounting profit and cash flow?
2.6
During 1998, the Senbet Discount Tire Company had gross sales of $1 million.The firm’s cost of
goods sold and selling expenses were $300,000 and $200,000, respectively.These figures do not
include depreciation. Senbet also had notes payable of $1 million.These notes carried an interest rate of 10 percent. Depreciation was $100,000. Senbet’s tax rate in 1998 was 35 percent.
a. What was Senbet’s net operating income?
b. What were the firm’s earnings before taxes?
c. What was Senbet’s net income?
d. What was Senbet’s operating cash flow?
2.7
The Stancil Corporation provided the following current information:
Proceeds from short-term borrowing
Proceeds from long-term borrowing
Proceeds from the sale of common stock
Purchases of fixed assets
Purchases of inventories
Payment of dividends
$ 6,000
20,000
1,000
1,000
4,000
22,000
Determine the cash flow of the Stancil Corporation.
2.8
Ritter Corporation’s accountants prepared the following financial statements for year-end
20X2.
RITTER CORPORATION
Income Statement
20X2
Revenue
Expenses
Depreciation
$400
250
50
____
Net income
Dividends
$100
$ 50
RITTER CORPORATION
Balance Sheets
December 31
20X2
Assets
Cash
Other current assets
Net fixed assets
Total assets
Liabilities and Equity
Current liabilities
Long-term debt
Stockholders’ equity
Total liabilities and equity
20X1
$ 25
125
200
____
$
$350
$200
$ 75
75
200
____
$ 50
0
150
____
$350
$200
a. Explain the change in cash during the year 20X2.
b. Determine the change in net working capital in 20X2.
c. Determine the cash flow of the firm during the year 20X2.
5
95
100
____
32
Corporate Finance,
Seventh Edition
I. Overview
34
Part I Overview
S&P
PROBLEMS
2.9
and Cash Flow
Companies, 2004
Enter the ticker symbol “MMM” for 3M (Minnesota Mining and Manufacturing) and follow
the “Excel Analytics” link.You will find the annual balance sheets for MMM for each of the past
five years. Calculate the change in net working capital for each year. How has net working
capital for MMM changed over this entire period?
2.10 Under the “Excel Analytics” link for Amgen, download the annual income statements and
balance sheets for Amgen (AMGN). Calculate the operating cash flow, cash flow to creditors,
and cash flow to stockholders for the most recent year. After you have completed your
calculations, download the annual cash flow report and compare the numbers given to your
calculations.
Appendix 2A
Financial Statement Analysis
The objective of this appendix is to show how to rearrange information from financial
statements into financial ratios that provide information about five areas of financial
performance:
1.
2.
3.
4.
5.
Short-term solvency—the ability of the firm to meet its short-run obligations.
Activity—the ability of the firm to control its investment in assets.
Financial leverage—the extent to which a firm relies on debt financing.
Profitability—the extent to which a firm is profitable.
Value—the value of the firm.
Financial statements cannot provide the answers to the preceding five measures of
performance. However, management must constantly evaluate how well the firm is doing,
and financial statements provide useful information. The financial statements of the U.S.
Composite Corporation, which appear in Tables 2.1, 2.2, and 2.3, provide the information
for the examples that follow. (Monetary values are given in $ millions.)
Short-Term Solvency
Ratios of short-term solvency measure the ability of the firm to meet recurring financial
obligations (that is, to pay its bills). To the extent a firm has sufficient cash flow, it will be
able to avoid defaulting on its financial obligations and, thus, avoid experiencing financial
distress. Accounting liquidity measures short-term solvency and is often associated with
net working capital, the difference between current assets and current liabilities. Recall that
current liabilities are debts that are due within one year from the date of the balance sheet.
The basic source from which to pay these debts is current assets.
The most widely used measures of accounting liquidity are the current ratio and the
quick ratio.
Current Ratio To find the current ratio, divide current assets by current liabilities. For
the U.S. Composite Corporation, the figure for 20X2 is
Current ratio Total current assets
761
1.57
Total current liabilities
486
If a firm is having financial difficulty, it may not be able to pay its bills (accounts payable)
on time or it may need to extend its bank credit (notes payable). As a consequence, current
liabilities may rise faster than current assets and the current ratio may fall. This may be the
first sign of financial trouble. Of course, a firm’s current ratio should be calculated over
33
34
Corporate Finance,
Seventh Edition
II. Value and Capital
Budgeting
Companies, 2004
Chapter 4
EXECUTIVE
SUMMARY
Net Present Value
We now examine one of the most important
concepts in all of corporate finance, the relationship between $1 today and $1 in the future.
Consider the following example: A firm is
contemplating investing $1 million in a project
that is expected to pay out $200,000 per year
for nine years. Should the firm accept the project? One might say yes at first glance, since
total inflows of $1.8 million ( $200,000 9)
are greater than $1 million outflow. However,
the $1 million is paid out immediately, whereas
the $200,000 per year will be received in the
future. Also, the immediate payment is known
with certainty, whereas the later inflows can
only be estimated.Thus, we need to know the
relationship between a dollar today and a
(possibly uncertain) dollar in the future before
deciding on the project.
This relationship is called the time-value-ofmoney concept. It is important in such areas as
capital budgeting, lease versus buy decisions,
accounts receivable analysis, financing arrangements, mergers, and pension funding.
The basics are presented in this chapter.
We begin by discussing two fundamental concepts, future value and present value. Next,
we treat simplifying formulas such as perpetuities and annuities.
4.1 The One-Period Case
EXAMPLE
Keith Vaughn is trying to sell a piece of raw land in Alaska.Yesterday, he was offered $10,000 for the
property. He was about ready to accept the offer when another individual offered him $11,424.
However, the second offer was to be paid a year from now. Keith has satisfied himself that both buyers are honest and financially solvent, so he has no fear that the offer he selects will fall through.
These two offers are pictured as cash flows in Figure 4.1. Which offer should Mr.Vaughn choose?
Mike Tuttle, Keith’s financial advisor, points out that if Keith takes the first offer, he could invest
the $10,000 in the bank at an insured rate of 12 percent. At the end of one year, he would have
$10,000 (0.12 $10,000) $10,000 1.12 $11,200
Return of
principal
Interest
Because this is less than the $11,424 Keith could receive from the second offer, Mr. Tuttle recommends that he take the latter. This analysis uses the concept of future value or compound value,
which is the value of a sum after investing over one or more periods. The compound or future value
of $10,000 is $11,200.
60
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
61
Chapter 4 Net Present Value
FIGURE 4.1
Alternative
sale prices
Cash Flow for
Mr. Vaughn’s Sale
35
Year:
$10,000
$11,424
0
1
An alternative method employs the concept of present value. One can determine present value by asking the following question: How much money must Keith put in the bank
today so that he will have $11,424 next year? We can write this algebraically as
PV 1.12 $11,424
(4.1)
We want to solve for present value (PV), the amount of money that yields $11,424 if invested at 12 percent today. Solving for PV, we have
PV $11,424
$10,200
1.12
The formula for PV can be written as
Present Value of Investment:
C
PV 1
1r
where C1 is cash flow at date 1 and r is the appropriate interest rate. r is the rate of return that
Keith Vaughn requires on his land sale. It is sometimes referred to as the discount rate.
Present value analysis tells us that a payment of $11,424 to be received next year has a
present value of $10,200 today. In other words, at a 12-percent interest rate, Mr. Vaughn
could not care less whether you gave him $10,200 today or $11,424 next year. If you gave
him $10,200 today, he could put it in the bank and receive $11,424 next year.
Because the second offer has a present value of $10,200, whereas the first offer is for
only $10,000, present value analysis also indicates that Mr. Vaughn should take the second
offer. In other words, both future value analysis and present value analysis lead to the same
decision. As it turns out, present value analysis and future value analysis must always lead
to the same decision.
As simple as this example is, it contains the basic principles that we will be working
with over the next few chapters. We now use another example to develop the concept of net
present value.
EXAMPLE
Lida Jennings, a financial analyst at Kaufman & Broad, a leading real estate firm, is thinking about recommending that Kaufman & Broad invest in a piece of land that costs $85,000. She is certain that
next year the land will be worth $91,000, a sure $6,000 gain. Given that the guaranteed interest rate
in the bank is 10 percent, should Kaufman & Broad undertake the investment in land? Ms. Jennings’
choice is described in Figure 4.2 with the cash flow time chart.
A moment’s thought should be all it takes to convince her that this is not an attractive business
deal. By investing $85,000 in the land, she will have $91,000 available next year. Suppose, instead, that
Kaufman & Broad puts the same $85,000 into the bank. At the interest rate of 10 percent, this
$85,000 would grow to
(1 0.10) $85,000 $93,500
next year.
36
Corporate Finance,
Seventh Edition
62
FIGURE 4.2
Budgeting
Companies, 2004
Part II Value and Capital Budgeting
Cash inflow
$91,000
Cash Flows for Land
Investment
Time
0
1
– $85,000
Cash outflow
It would be foolish to buy the land when investing the same $85,000 in the financial market would
produce an extra $2,500 (that is, $93,500 from the bank minus $91,000 from the land investment).
This is a future-value calculation.
Alternatively, she could calculate the present value of the sale price next year as
Present value $91,000
$82,727.27
1.10
Because the present value of next year’s sales price is less than this year’s purchase price of $85,000,
present-value analysis also indicates that she should not recommend purchasing the property.
Frequently, businesspeople want to determine the exact cost or benefit of a decision. The
decision to buy this year and sell next year can be evaluated as
Net Present Value of Investment:
$91,000
$2,273 $85,000 1.10
Cost of land
Present value of
today
next year’s sales price
(4.2)
The formula for NPV can be written as
NPV Cost
PV
Equation (4.2) says that the value of the investment is $2,273, after stating all the benefits and all the costs as of date 0. We say that $2,273 is the net present value (NPV) of
the investment. That is, NPV is the present value of future cash flows minus the present
value of the cost of the investment. Because the net present value is negative, Lida Jennings
should not recommend purchasing the land.
Both the Vaughn and the Jennings examples deal with perfect certainty. That is, Keith
Vaughn knows with perfect certainty that he could sell his land for $11,424 next year. Similarly, Lida Jennings knows with perfect certainty that Kaufman & Broad could receive
$91,000 for selling its land. Unfortunately, businesspeople frequently do not know future
cash flows. This uncertainty is treated in the next example.
EXAMPLE
Professional Artworks, Inc., is a firm that speculates in modern paintings. The manager is thinking
of buying an original Picasso for $400,000 with the intention of selling it at the end of one year.
The manager expects that the painting will be worth $480,000 in one year.The relevant cash flows
are depicted in Figure 4.3.
Of course, this is only an expectation—the painting could be worth more or less than $480,000.
Suppose the guaranteed interest rate granted by banks is 10 percent. Should the firm purchase the
piece of art?
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
63
FIGURE 4.3
Expected cash inflow
Cash Flows for
Investment in
Painting
$480,000
Time
Cash outflow
37
0
1
– $400,000
Our first thought might be to discount at the interest rate, yielding
$480,000
$436,364
1.10
Because $436,364 is greater than $400,000, it looks at first glance as if the painting should be purchased. However, 10 percent is the return one can earn on a riskless investment. Because the painting
is quite risky, a higher discount rate is called for. The manager chooses a rate of 25 percent to reflect
this risk. In other words, he argues that a 25-percent expected return is fair compensation for an investment as risky as this painting.
The present value of the painting becomes
$480,000
$384,000
1.25
Thus, the manager believes that the painting is currently overpriced at $400,000 and does not make
the purchase.
The preceding analysis is typical of decision making in today’s corporations, though
real-world examples are, of course, much more complex. Unfortunately, any example with
risk poses a problem not faced by a riskless example. In an example with riskless cash
flows, the appropriate interest rate can be determined by simply checking with a few banks.1
The selection of the discount rate for a risky investment is quite a difficult task. We simply
don’t know at this point whether the discount rate on the painting should be 11 percent,
25 percent, 52 percent, or some other percentage.
Because the choice of a discount rate is so difficult, we merely wanted to broach the subject here. The rest of the chapter will revert to examples under perfect certainty. We must
wait until the specific material on risk and return is covered in later chapters before a riskadjusted analysis can be presented.
Concept
Questions
1. Define future value and present value.
2. How does one use net present value when making an investment decision?
4.2 The Multiperiod Case
The previous section presented the calculation of future value and present value for one period only. We will now perform the calculations for the multiperiod case.
Future Value and Compounding
Suppose an individual were to make a loan of $1. At the end of the first year, the borrower
would owe the lender the principal amount of $1 plus the interest on the loan at the interest
1
In Chapter 9, we discuss estimation of the riskless rate in more detail.
38
Corporate Finance,
Seventh Edition
64
Budgeting
Companies, 2004
rate of r. For the specific case where the interest rate is, say, 9 percent, the borrower owes
the lender
$1 (1 r) $1 1.09 $1.09
At the end of the year, though, the lender has two choices. She can either take the $1.09—
or, more generally, (1 r)—out of the capital market, or she can leave it in and lend it
again for a second year. The process of leaving the money in the capital market and lending it for another year is called compounding.
Suppose that the lender decides to compound her loan for another year. She does this by
taking the proceeds from her first one-year loan, $1.09, and lending this amount for the
next year. At the end of next year, then, the borrower will owe her
$1 (1 r) (1 r) $1 (1 r)2 1 2r r2
$1 (1.09) (1.09) $1 (1.09)2 $1 $0.18 $0.0081 $1.1881
This is the total she will receive two years from now by compounding the loan.
In other words, the capital market enables the investor, by providing a ready opportunity
for lending, to transform $1 today into $1.1881 at the end of two years. At the end of three
years, the cash will be $1 (1.09)3 $1.2950.
The most important point to notice is that the total amount that the lender receives is not
just the $1 that she lent out plus two years’ worth of interest on $1:
2 r 2 $0.09 $0.18
The lender also gets back an amount r2, which is the interest in the second year on the interest that was earned in the first year. The term, 2 r, represents simple interest over the
two years, and the term, r2, is referred to as the interest on interest. In our example this latter
amount is exactly
r2 ($0.09)2 $0.0081
When cash is invested at compound interest, each interest payment is reinvested. With
simple interest, the interest is not reinvested. Benjamin Franklin’s statement, “Money makes
money and the money that money makes makes more money,” is a colorful way of explaining compound interest. The difference between compound interest and simple interest is
illustrated in Figure 4.4. In this example the difference does not amount to much because the
FIGURE 4.4
Simple and
Compound Interest
$1.295
$1.270
$1.188
$1.180
$1.09
$1
1 year
2 years
3 years
The dark-shaded area indicates the difference between
compound and simple interest. The difference is substantial over a period of many years or decades.
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
39
65
loan is for $1. If the loan were for $1 million, the lender would receive $1,188,100 in two
years’ time. Of this amount, $8,100 is interest on interest. The lesson is that those small
numbers beyond the decimal point can add up to big dollar amounts when the transactions
are for big amounts. In addition, the longer-lasting the loan, the more important interest on
interest becomes.
The general formula for an investment over many periods can be written as
Future Value of an Investment:
FV C0 (1 r)T
where C0 is the cash to be invested at date 0, r is the interest rate, and T is the number of
periods over which the cash is invested.
EXAMPLE
Suh-Pyng Ku has put $500 in a savings account at the First National Bank of Kent. The account earns
7 percent, compounded annually. How much will Ms. Ku have at the end of three years?
$500 1.07 1.07 1.07 $500 (1.07)3 $612.52
Figure 4.5 illustrates the growth of Ms. Ku’s account.
FIGURE 4.5
Suh-Pyng Ku’s
Savings Account
Dollars
$612.52
$500
$612.52
Time
0
1
2
0
3
1
2
Time
3
–$500
EXAMPLE
Jay Ritter invested $1,000 in the stock of the SDH Company. The company pays a current dividend
of $2, which is expected to grow by 20 percent per year for the next two years. What will the dividend of the SDH Company be after two years?
$2 (1.20)2 $2.88
Figure 4.6 illustrates the increasing value of SDH’s dividends.
FIGURE 4.6
The Growth of the
SDH Dividends
Dollars
$2.88
$2.88
Cash inflows $2.40
$2.40
$2.00
$2.00
Time
Time
0
1
2
0
1
2
The two previous examples can be calculated in any one of three ways. The computations could be done by hand, by calculator, or with the help of a table. The appropriate table
40
Corporate Finance,
Seventh Edition
66
Budgeting
Companies, 2004
is Table A.3, which appears in the back of the text. This table presents Future values of $1
at the end of t periods. The table is used by locating the appropriate interest rate on the horizontal and the appropriate number of periods on the vertical.
For example, Suh-Pyng Ku would look at the following portion of Table A.3:
Interest Rate
Period
6%
7%
8%
1
2
3
4
1.0600
1.1236
1.1910
1.2625
1.0700
1.1449
1.2250
1.3108
1.0800
1.1664
1.2597
1.3605
She could calculate the future value of her $500 as
$500
1.2250
$612.50
Initial
Future value
investment
of $1
In the example concerning Suh-Pyng Ku, we gave you both the initial investment and the
interest rate and then asked you to calculate the future value. Alternatively, the interest rate
could have been unknown, as shown in the following example.
EXAMPLE
Carl Voigt, who recently won $10,000 in the lottery, wants to buy a car in five years. Carl estimates
that the car will cost $16,105 at that time. His cash flows are displayed in Figure 4.7.
What interest rate must he earn to be able to afford the car?
FIGURE 4.7
Cash inflow
$10,000
Cash Flows for
Purchase of Carl
Voigt’s Car
5
0
Cash outflow
Time
– $16,105
The ratio of purchase price to initial cash is
$16,105
1.6105
$10,000
Thus, he must earn an interest rate that allows $1 to become $1.6105 in five years. Table A.3 tells us
that an interest rate of 10 percent will allow him to purchase the car.
One can express the problem algebraically as
$10,000 (1 r)5 $16,105
where r is the interest rate needed to purchase the car. Because $16,105兾$10,000 1.6105, we have
(1 r)5 1.6105
Either the table or any sophisticated hand calculator solves2 for r.
2
Conceptually, we are taking the fifth roots of both sides of the equation. That is,
r 兹1.6105 1
5
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
41
67
The Power of Compounding: A Digression
Most people who have had any experience with compounding are impressed with its power
over long periods of time. Take the stock market, for example. Ibbotson and Sinquefield
have calculated what the stock market returned as a whole from 1926 through 2001.3 They
find that one dollar placed in these stocks at the beginning of 1926 would have been worth
$2,279.13 at the end of 2001. This is 10.71 percent compounded annually for 76 years, i.e.,
(1.1071)76 $2,279.13. (Note: We are rounding 10.7086% to 10.71%.)
The example illustrates the great difference between compound and simple interest. At
10.71 percent, simple interest on $1 is 10.71 cents a year. Simple interest over 76 years is
$8.14 (76 $0.1071). That is, an individual withdrawing 10.71 cents every year would
have withdrawn $8.14 (76 $0.1071) over 76 years. This is quite a bit below the $2,279.13
that was obtained by reinvestment of all principal and interest.
The results are more impressive over even longer periods of time. A person with no
experience in compounding might think that the value of $1 at the end of 152 years would
be twice the value of $1 at the end of 76 years, if the yearly rate of return stayed the same.
Actually the value of $1 at the end of 152 years would be the square of the value of $1 at
the end of 76 years. That is, if the annual rate of return remained the same, a $1 investment
in common stocks should be worth $5,194,443.36 [$1 (2,279.13 2,279.13)].
A few years ago an archaeologist unearthed a relic stating that Julius Caesar lent the
Roman equivalent of one penny to someone. Since there was no record of the penny ever
being repaid, the archaeologist wondered what the interest and principal would be if a
descendant of Caesar tried to collect from a descendant of the borrower in the 20th century.
The archaeologist felt that a rate of 6 percent might be appropriate. To his surprise, the
principal and interest due after more than 2,000 years was far greater than the entire wealth
on earth.
The power of compounding can explain why the parents of well-to-do families frequently bequeath wealth to their grandchildren rather than to their children. That is, they
skip a generation. The parents would rather make the grandchildren very rich than make
the children moderately rich. We have found that in these families the grandchildren have
a more positive view of the power of compounding than do the children.
EXAMPLE
Some people have said that it was the best real estate deal in history. Peter Minuit, director–general
of New Netherlands, the Dutch West India Company’s Colony in North America, in 1626 allegedly
bought Manhattan Island for 60 guilders’ worth of trinkets from native Americans. By 1667 the
Dutch were forced to exchange it for Suriname with the British (perhaps the worst real estate deal
ever).This sounds cheap but did the Dutch really get the better end of the deal? It is reported that
60 guilders was worth about $24 at the prevailing exchange rate. If the native Americans had sold
the trinkets at a fair market value and invested the $24 at 5 percent (tax free), it would now,
377 years later, be worth more than $2.0 billion.Today, Manhattan is undoubtedly worth more than
$2 billion, and so at a 5 percent rate of return, the native Americans got the worst of the deal. However, if invested at 10 percent, the amount of money they received would be worth about
$24(1 r)T 1.1377 艑 $97 quadrillion
This is a lot of money. In fact, $97 quadrillion is more than all the real estate in the world is worth
today. No one in the history of the world has ever been able to find an investment yielding 10 percent every year for 377 years.
3
Stocks, Bonds, Bills and Inflation [SBBI]. 2002 Yearbook. Ibbotson Associates, Chicago, 2003.
42
Corporate Finance,
Seventh Edition
68
Budgeting
Companies, 2004
Present Value and Discounting
We now know that an annual interest rate of 9 percent enables the investor to transform $1
today into $1.1881 two years from now. In addition, we would like to know:
How much would an investor need to lend today so that she could receive $1 two years from
today?
Algebraically, we can write this as
PV (1.09)2 $1
In the preceding equation, PV stands for present value, the amount of money we must lend
today in order to receive $1 in two years’ time.
Solving for PV in this equation, we have
PV $1
$0.84
1.1881
This process of calculating the present value of a future cash flow is called discounting. It
is the opposite of compounding. The difference between compounding and discounting is
illustrated in Figure 4.8.
To be certain that $0.84 is in fact the present value of $1 to be received in two years, we must
check whether or not, if we loaned out $0.84 and rolled over the loan for two years, we would
get exactly $1 back. If this were the case, the capital markets would be saying that $1 received
in two years’ time is equivalent to having $0.84 today. Checking the exact numbers, we get
$0.84168 1.09 1.09 $1
In other words, when we have capital markets with a sure interest rate of 9 percent, we
are indifferent between receiving $0.84 today or $1 in two years. We have no reason to treat
these two choices differently from each other, because if we had $0.84 today and loaned it
out for two years, it would return $1 to us at the end of that time. The value 0.84 [1兾(1.09)2]
is called the present value factor. It is the factor used to calculate the present value of a
future cash flow.
FIGURE 4.8
Compounding and
Discounting
Dollars
$2,367.36
Compound interest
Compounding
at 9%
$1,900
Simple interest
$1,000
$1,000
$422.41
Discounting at
9%
Future years
1
2
3
4
5
6
7
8
9
10
The top line shows the growth of $1,000 at compound interest with the funds
invested at 9 percent: $1,000 (1.09)10 $2,367.36. Simple interest is shown
on the next line. It is $1,000 [10 ($1,000 0.09)] $1,900. The bottom
line shows the discounted value of $1,000 if the interest rate is 9 percent.
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
43
69
In the multiperiod case, the formula for PV can be written as
Present Value of Investment
CT
PV (1 r) T
(4.3)
where CT is cash flow at date T and r is the appropriate interest rate.
EXAMPLE
Bernard Dumas will receive $10,000 three years from now. Bernard can earn 8 percent on his
investments, and so the appropriate discount rate is 8 percent. What is the present value of his
future cash flow?
PV $10,000 冢1.08冣
1
3
$10,000 0.7938
$7,938
Figure 4.9 illustrates the application of the present value factor to Bernard’s investment.
FIGURE 4.9
Discounting Bernard
Dumas’ Opportunity
Dollars
$10,000
$10,000
Cash inflows
$7,938
Time
0
1
2
Time
0
1
2
3
3
When his investments grow at an 8 percent rate of interest, Bernard Dumas is equally inclined
toward receiving $7,938 now and receiving $10,000 in three years’ time.After all, he could convert
the $7,938 he receives today into $10,000 in three years by lending it at an interest rate of 8 percent.
Bernard Dumas could have reached his present value calculation in one of three ways. The
computation could have been done by hand, by calculator, or with the help of Table A.1, which
appears in the back of the text.This table presents present value of $1 to be received after t periods.
The table is used by locating the appropriate interest rate on the horizontal and the appropriate
number of periods on the vertical. For example, Bernard Dumas would look at the following portion of Table A.1:
Interest Rate
Period
7%
8%
9%
1
2
3
4
0.9346
0.8734
0.8163
0.7629
0.9259
0.8573
0.7938
0.7350
0.9174
0.8417
0.7722
0.7084
The appropriate present value factor is 0.7938.
In the preceding example, we gave both the interest rate and the future cash flow.
Alternatively, the interest rate could have been unknown.
44
Corporate Finance,
Seventh Edition
70
EXAMPLE
Budgeting
Companies, 2004
A customer of the Chaffkin Corp. wants to buy a tugboat today. Rather than paying immediately, he
will pay $50,000 in three years. It will cost the Chaffkin Corp. $38,610 to build the tugboat immediately. The relevant cash flows to Chaffkin Corp. are displayed in Figure 4.10. By charging what interest rate would the Chaffkin Corp. neither gain nor lose on the sale?
FIGURE 4.10
Cash inflows
$50,000
Cash Flows for
Tugboat
Time
3
0
– $38,610
Cash outflows
The ratio of construction cost to sale price is
$38,610
0.7722
$50,000
We must determine the interest rate that allows $1 to be received in three years to have a present
value of $0.7722.Table A.1 tells us that 9 percent is that interest rate.4
Frequently, an investor or a business will receive more than one cash flow. The present
value of the set of cash flows is simply the sum of the present values of the individual cash
flows. This is illustrated in the following example.
EXAMPLE
Dennis Draper has won the Kentucky state lottery and will receive the following set of cash flows
over the next two years:
Year
Cash Flow
1
2
$2,000
$5,000
Mr. Draper can currently earn 6 percent in his passbook savings account, and so, the appropriate discount rate is 6 percent.The present value of the cash flows is
Year
1
2
Cash Flow ⴛ Present Value Factor ⴝ Present Value
1
1.06
1
$5,000 1.06
$2,000 冢冣
2
0.943
$1,887
0.890
$4,450
______
Total
$6,337
In other words, Mr. Draper is equally inclined toward receiving $6,337 today and receiving $2,000
and $5,000 over the next two years.
4
Algebraically, we are solving for r in the equation
$50,000
$38,610
(1 r) 3
or, equivalently,
$1
$0.7722
(1 r) 3
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
71
EXAMPLE
45
Finance.com has an opportunity to invest in a new high-speed computer that costs $50,000. The
computer will generate cash flows (from cost savings) of $25,000 one year from now, $20,000
two years from now, and $15,000 three years from now. The computer will be worthless after three
years, and no additional cash flows will occur. Finance.com has determined that the appropriate
discount rate is 7 percent for this investment. Should Finance.com make this investment in a new
high-speed computer? What is the present value of the investment?
The cash flows and present value factors of the proposed computer are as follows.
Cash Flows
Year 0
$50,000
1
$25,000
2
$20,000
3
$15,000
Present Value Factor
1
1
1.07
1
1.07
1
1.07
1
0.9346
冢冣
冢冣
2
3
0.8734
0.8163
The present values of the cash flows are:
Cash flows Present value factor Present value
Year 0
1
2
3
$50,000 1
–$50,000
$25,000 0.9346 $23,365
$20,000 0.8734 $17,468
$15,000 0.8163 ________
$12,244.5
Total: $3,077.5
Finance.com should invest in a new high-speed computer because the present value of its future
cash flows is greater than its cost. The NPV is $3,077.5.
The Algebraic Formula
To derive an algebraic formula for net present value of a cash flow, recall that the PV of receiving a cash flow one year from now is
PV C1兾(1 r)
and the PV of receiving a cash flow two years from now is
PV C2兾(1 r)2
We can write the NPV of a T-period project as
NPV C0
T
C1
C2
CT
Ci
... 2 T C0 (1 r)
(1 r)
(1
1r
r) i
i1
兺
The initial flow, C0, is assumed to be negative because it represents an investment. The
is shorthand for the sum of the series.
Concept
Questions
1. What is the difference between simple interest and compound interest?
2. What is the formula for the net present value of a project?
46
Corporate Finance,
Seventh Edition
72
Budgeting
Companies, 2004
4.3 Compounding Periods
So far we have assumed that compounding and discounting occur yearly. Sometimes compounding may occur more frequently than just once a year. For example, imagine that a bank
pays a 10-percent interest rate “compounded semiannually.” This means that a $1,000 deposit
in the bank would be worth $1,000 1.05 $1,050 after six months, and $1,050 1.05 $1,102.50 at the end of the year.
The end-of-the-year wealth can be written as5
冢
$1,000 1 0.10
2
冣
2
$1,000 (1.05)2 $1,102.50
Of course, a $1,000 deposit would be worth $1,100 ($1,000 1.10) with yearly compounding. Note that the future value at the end of one year is greater with semiannual compounding than with yearly compounding. With yearly compounding, the original $1,000
remains the investment base for the full year. The original $1,000 is the investment base
only for the first six months with semiannual compounding. The base over the second six
months is $1,050. Hence, one gets interest on interest with semiannual compounding.
Because $1,000 1.1025 $1,102.50, 10 percent compounded semiannually is the
same as 10.25 percent compounded annually. In other words, a rational investor could not
care less whether she is quoted a rate of 10 percent compounded semiannually, or a rate of
10.25 percent compounded annually.
Quarterly compounding at 10 percent yields wealth at the end of one year of
冢
$1,000 1 0.10
4
冣
4
$1,103.81
More generally, compounding an investment m times a year provides end-of-year wealth of
r m
C0 1 (4.4)
m
冢
冣
where C0 is one’s initial investment and r is the stated annual interest rate. The stated
annual interest rate is the annual interest rate without consideration of compounding. Banks
and other financial institutions may use other names for the stated annual interest rate.
Annual percentage rate is perhaps the most common synonym.
EXAMPLE
What is the end-of-year wealth if Jane Christine receives a stated annual interest rate of 24 percent
compounded monthly on a $1 investment?
Using (4.4), her wealth is
冢
$1 1 0.24
12
冣
12
$1 (1.02)12
$1.2682
The annual rate of return is 26.82 percent.This annual rate of return is either called the effective
annual interest rate or the effective annual yield. Due to compounding, the effective annual
interest rate is greater than the stated annual interest rate of 24 percent. Algebraically, we can
rewrite the effective annual interest rate as
Effective Annual Interest Rate:
冢1 m冣
r
m
1
(4.5)
5
In addition to using a calculator, one can still use Table A.3 when the compounding period is less than a year. Here, one sets the
interest rate at 5 percent and the number of periods at two.
Corporate Finance,
Seventh Edition
Budgeting
47
Companies, 2004
73
Students are often bothered by the subtraction of 1 in (4.5). Note that end-of-year wealth is composed of both the interest earned over the year and the original principal.We remove the original
principal by subtracting one in (4.5).
EXAMPLE
If the stated annual rate of interest, 8 percent, is compounded quarterly, what is the effective annual
rate of interest?
Using (4.5), we have
r m
0.08 4
1 0.0824 8.24%
1
1 1
m
4
冢
冣
冢
冣
Referring back to our original example where C0 $1,000 and r 10%, we can generate the
following table:
C0
$1,000
1,000
1,000
1,000
Compounding Frequency (m)
C1
Yearly (m 1)
Semiannually (m 2)
Quarterly (m 4)
Daily (m 365)
$1,100.00
1,102.50
1,103.81
1,105.16
Effective Annual
Interest Rate ⴝ
r m
1ⴙ
ⴚ1
m
冢
冣
0.10
0.1025
0.10381
0.10516
Distinction between Stated Annual Interest Rate
and Effective Annual Interest Rate
The distinction between the stated annual interest rate (SAIR) and the effective annual interest rate (EAIR) is frequently quite troubling to students. One can reduce the confusion
by noting that the SAIR becomes meaningful only if the compounding interval is given. For
example, for an SAIR of 10 percent, the future value at the end of one year with semiannual
compounding is [1 (.10兾2)]2 1.1025. The future value with quarterly compounding is
[1 (.10兾4)]4 1.1038. If the SAIR is 10 percent but no compounding interval is given,
one cannot calculate future value. In other words, one does not know whether to compound
semiannually, quarterly, or over some other interval.
By contrast, the EAIR is meaningful without a compounding interval. For example, an
EAIR of 10.25 percent means that a $1 investment will be worth $1.1025 in one year. One
can think of this as an SAIR of 10 percent with semiannual compounding or an SAIR of
10.25 percent with annual compounding, or some other possibility.
Compounding over Many Years
Formula (4.4) applies for an investment over one year. For an investment over one or more
(T) years, the formula becomes
Future Value with Compounding:
r mT
FV C0 1 m
冢
EXAMPLE
冣
(4.6)
Harry DeAngelo is investing $5,000 at a stated annual interest rate of 12 percent per year, compounded quarterly, for five years.What is his wealth at the end of five years?
Using formula (4.6), his wealth is
冢
$5,000 1 0.12
4
冣
45
$5,000 (1.03)20 $5,000 1.8061 $9,030.50
48
Corporate Finance,
Seventh Edition
74
Budgeting
Companies, 2004
Continuous Compounding (Advanced)
The previous discussion shows that one can compound much more frequently than once a
year. One could compound semiannually, quarterly, monthly, daily, hourly, each minute, or
even more often. The limiting case would be to compound every infinitesimal instant, which
is commonly called continuous compounding. Surprisingly, banks and other financial institutions frequently quote continuously compounded rates, which is why we study them.
Though the idea of compounding this rapidly may boggle the mind, a simple formula is
involved. With continuous compounding, the value at the end of T years is expressed as
C0 erT
(4.7)
where C0 is the initial investment, r is the stated annual interest rate, and T is the number of
years over which the investment runs. The number e is a constant and is approximately
equal to 2.718. It is not an unknown like C0, r, and T.
EXAMPLE
Linda DeFond invested $1,000 at a continuously compounded rate of 10 percent for one year.
What is the value of her wealth at the end of one year?
From formula (4.7) we have
$1,000 e0.10 $1,000 1.1052 $1,105.20
This number can easily be read from our Table A.5. One merely sets r, the value on the horizontal
dimension, to 10% and T, the value on the vertical dimension, to 1. For this problem, the relevant
portion of the table is
Period
(T )
1
2
3
Continuously Compounded Rate (r)
9%
10%
11%
1.0942
1.1972
1.3100
1.1052
1.2214
1.3499
1.1163
1.2461
1.3910
Note that a continuously compounded rate of 10 percent is equivalent to an annually compounded
rate of 10.52 percent. In other words, Linda DeFond could not care less whether her bank quoted a
continuously compounded rate of 10 percent or a 10.52-percent rate, compounded annually.
EXAMPLE
Linda DeFond’s brother, Mark, invested $1,000 at a continuously compounded rate of 10 percent for
two years.
The appropriate formula here is
$1,000 e0.102 $1,000 e0.20 $1,221.40
Using the portion of the table of continuously compounded rates reproduced above, we find the
value to be 1.2214.
Figure 4.11 illustrates the relationship among annual, semiannual, and continuous compounding. Semiannual compounding gives rise to both a smoother curve and a higher ending
value than does annual compounding. Continuous compounding has both the smoothest
curve and the highest ending value of all.
Corporate Finance,
Seventh Edition
Budgeting
49
Companies, 2004
75
FIGURE 4.11
Dollars
Annual, Semiannual,
and Continuous
Compounding
Dollars
4
4
Interest
earned
3
3
3
2
2
1
1
1
1
2
3
Years
4
5
Annual compounding
0
1
2
3
Years
4
5
Semiannual compounding
Interest
earned
0
1
2
3
Years
4
5
Continuous compounding
The Michigan state lottery is going to pay you $1,000 at the end of four years. If the annual continuously compounded rate of interest is 8 percent, what is the present value of this payment?
$1,000 Concept
Questions
4
Interest
earned
2
0
EXAMPLE
Dollars
1
1
$1,000 $726.16
e0.084
1.3771
1. What is a stated annual interest rate?
2. What is an effective annual interest rate?
3. What is the relationship between the stated annual interest rate and the effective annual interest rate?
4. Define continuous compounding.
4.4 Simplifications
The first part of this chapter has examined the concepts of future value and present value.
Although these concepts allow one to answer a host of problems concerning the time value
of money, the human effort involved can frequently be excessive. For example, consider a
bank calculating the present value on a 20-year monthly mortgage. Because this mortgage
has 240 (20 12) payments, a lot of time is needed to perform a conceptually simple task.
Because many basic finance problems are potentially so time-consuming, we search out
simplifications in this section. We provide simplifying formulas for four classes of cash flow
streams:
•
•
•
•
Perpetuity
Growing perpetuity
Annuity
Growing annuity
Perpetuity
A perpetuity is a constant stream of cash flows without end. If you are thinking that perpetuities have no relevance to reality, it will surprise you that there is a well-known case of
50
76
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
an unending cash flow stream: the British bonds called consols. An investor purchasing a
consol is entitled to receive yearly interest from the British government forever.
How can the price of a consol be determined? Consider a consol that pays a coupon of
C dollars each year and will do so forever. Simply applying the PV formula gives us
PV C
C
C
(1 r) 2
(1 r) 3
1r
where the dots at the end of the formula stand for the infinite string of terms that continues
the formula. Series like the preceding one are called geometric series. It is well known that
even though they have an infinite number of terms, the whole series has a finite sum because each term is only a fraction of the preceding term. Before turning to our calculus
books, though, it is worth going back to our original principles to see if a bit of financial
intuition can help us find the PV.
The present value of the consol is the present value of all of its future coupons. In other
words, it is an amount of money that, if an investor had it today, would enable him to
achieve the same pattern of expenditures that the consol and its coupons would. Suppose
that an investor wanted to spend exactly C dollars each year. If he had the consol, he could
do this. How much money must he have today to spend the same amount? Clearly he would
need exactly enough so that the interest on the money would be C dollars per year. If he had
any more, he could spend more than C dollars each year. If he had any less, he would eventually run out of money spending C dollars per year.
The amount that will give the investor C dollars each year, and therefore the present
value of the consol, is simply
C
PV (4.8)
r
To confirm that this is the right answer, notice that if we lend the amount C兾r, the interest
it earns each year will be
C
Interest r C
r
which is exactly the consol payment.6 To sum up, we have shown that for a consol
Formula for Present Value of Perpetuity:
C
C
C
PV 2 (1 r)
(1 r) 3
1r
C
r
It is comforting to know how easily we can use a bit of financial intuition to solve this
mathematical problem.
6
We can prove this by looking at the PV equation:
PV C兾(1 r) C兾(1 r)2 Let C兾(1 r) a and 1兾(1 r) x. We now have
PV a(1 x x2 )
(1)
xPV ax ax2 (2)
Next we can multiply by x:
Subtracting (2) from (1) gives
PV(1 x) a
Now we substitute for a and x and rearrange:
PV C兾r
Corporate Finance,
Seventh Edition
Budgeting
51
Companies, 2004
77
EXAMPLE
Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value
of the consol?
Using formula (4.8), we have
PV $100
$1,250
0.08
Now suppose that interest rates fall to 6 percent. Using (4.8), the value of the perpetuity is
PV $100
$1,666.67
0.06
Note that the value of the perpetuity rises with a drop in the interest rate. Conversely, the value of
the perpetuity falls with a rise in the interest rate.
Growing Perpetuity
Imagine an apartment building where cash flows to the landlord after expenses will be
$100,000 next year. These cash flows are expected to rise at 5 percent per year. If one assumes that this rise will continue indefinitely, the cash flow stream is termed a growing
perpetuity. The relevant interest rate is 11 percent. Therefore, the appropriate discount rate
is 11 percent and the present value of the cash flows can be represented as
PV $100,000 $100,000(1.05) $100,000(1.05) 2 . . . $100,000(1.05) N1 . . .
(1.11) 2
(1.11) 3
(1.11) N
1.11
Algebraically, we can write the formula as
PV C
C (1 g) C (1 g) 2 . . . C (1 g) N1 . . .
(1 r) 2
(1 r) 3
(1 r) N
1r
(4.9)
where C is the cash flow to be received one period hence, g is the rate of growth per period,
expressed as a percentage, and r is the appropriate discount rate.
Fortunately, formula (4.9) reduces to the following simplification:7
Formula for Present Value of Growing Perpetuity:
C
PV rg
(4.10)
From formula (4.10), the present value of the cash flows from the apartment building is
$100,000
$1,666,667
0.11 0.05
7
PV is the sum of an infinite geometric series:
PV a(1 x x2 . . .)
where a C兾(1 r) and x (1 g)兾(1 r). Previously we showed that the sum of an infinite geometric series is a兾(1 x).
Using this result and substituting for a and x, we find
PV C兾(r g)
Note that this geometric series converges to a finite sum only when x is less than 1. This implies that the growth rate, g, must be
less than the interest rate, r.
52
Corporate Finance,
Seventh Edition
78
Budgeting
Companies, 2004
There are three important points concerning the growing perpetuity formula:
1. The Numerator. The numerator in (4.10) is the cash flow one period hence, not at
date 0. Consider the following example:
EXAMPLE
Rothstein Corporation is just about to pay a dividend of $3.00 per share. Investors anticipate that the
annual dividend will rise by 6 percent a year forever.The applicable interest rate is 11 percent.What
is the price of the stock today?
The numerator in formula (4.10) is the cash flow to be received next period. Since the growth
rate is 6 percent, the dividend next year is $3.18 ($3.00 1.06).The price of the stock today is
$66.60 $3.00
Imminent
dividend
$3.18
0.11 0.06
Present value of all
dividends beginning
a year from now
The price of $66.60 includes both the dividend to be received immediately and the present value of
all dividends beginning a year from now. Formula (4.10) only makes it possible to calculate the present value of all dividends beginning a year from now. Be sure you understand this example; test
questions on this subject always seem to trip up a few of our students.
2. The Interest Rate and the Growth Rate. The interest rate r must be greater than the
growth rate g for the growing perpetuity formula to work. Consider the case in which the
growth rate approaches the interest rate in magnitude. Then the denominator in the growing
perpetuity formula gets infinitesimally small and the present value grows infinitely large.
The present value is in fact undefined when r is less than g.
3. The Timing Assumption. Cash generally flows into and out of real-world firms both
randomly and nearly continuously. However, formula (4.10) assumes that cash flows are received and disbursed at regular and discrete points in time. In the example of the apartment,
we assumed that the net cash flows of $100,000 only occurred once a year. In reality, rent
checks are commonly received every month. Payments for maintenance and other expenses
may occur anytime within the year.
The growing perpetuity formula of (4.10) can be applied only by assuming a regular and
discrete pattern of cash flow. Although this assumption is sensible because the formula
saves so much time, the user should never forget that it is an assumption. This point will be
mentioned again in the chapters ahead.
A few words should be said about terminology. Authors of financial textbooks generally
use one of two conventions to refer to time. A minority of financial writers treat cash flows
as being received on exact dates, for example date 0, date 1, and so forth. Under this convention, date 0 represents the present time. However, because a year is an interval, not a
specific moment in time, the great majority of authors refer to cash flows that occur at the
end of a year (or alternatively, the end of a period). Under this end-of-the-year convention,
the end of year 0 is the present, the end of year 1 occurs one period hence, and so on. (The
beginning of year 0 has already passed and is not generally referred to.)8
8
Sometimes financial writers merely speak of a cash flow in year x. Although this terminology is ambiguous, such writers
generally mean the end of year x.
Corporate Finance,
Seventh Edition
Budgeting
53
Companies, 2004
79
The interchangeability of the two conventions can be seen from the following chart:
Date 0
Now
End of year 0
Now
Date 1
Date 2
Date 3
...
End of year 1
End of year 2
End of year 3
...
We strongly believe that the dates convention reduces ambiguity. However, we use both
conventions because you are likely to see the end-of-year convention in later courses. In
fact, both conventions may appear in the same example for the sake of practice.
Annuity
An annuity is a level stream of regular payments that lasts for a fixed number of periods.
Not surprisingly, annuities are among the most common kinds of financial instruments. The
pensions that people receive when they retire are often in the form of an annuity. Leases
and mortgages are also often annuities.
To figure out the present value of an annuity we need to evaluate the following equation:
C
C
C
C
(1 r) 2
(1 r) 3
(1 r) T
1r
The present value of only receiving the coupons for T periods must be less than the present
value of a consol, but how much less? To answer this we have to look at consols a bit more
closely.
Consider the following time chart:
Now
Date (or end of year)
Consol 1
Consol 2
Annuity
0
1
C
2
C
3
C...
T
C
C
C
C...
C
(T 1) (T 2)
C
C...
C
C...
Consol 1 is a normal consol with its first payment at date 1. The first payment of consol 2
occurs at date T 1.
The present value of having a cash flow of C at each of T dates is equal to the present value
of consol 1 minus the present value of consol 2. The present value of consol 1 is given by
PV C
r
(4.11)
Consol 2 is just a consol with its first payment at date T 1. From the perpetuity formula,
this consol will be worth C兾r at date T.9 However, we do not want the value at date T. We
want the value now; in other words, the present value at date 0. We must discount C兾r back
by T periods. Therefore, the present value of consol 2 is
PV 冤
C
1
(1
r
r) T
冥
(4.12)
Students frequently think that C兾r is the present value at date T 1 because the consol’s first payment is at date T 1.
However, the formula values the annuity as of one period prior to the first payment.
9
54
Corporate Finance,
Seventh Edition
80
Budgeting
Companies, 2004
The present value of having cash flows for T years is the present value of a consol with its
first payment at date 1 minus the present value of a consol with its first payment at date
T 1. Thus, the present value of an annuity is formula (4.11) minus formula (4.12). This
can be written as
C C
1
r
r (1 r) T
This simplifies to
冤
冥
Formula for Present Value of Annuity:10, 11
1
1
PV C r r(1 r) T
冤
EXAMPLE
冥
(4.13)
Mark Young has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his
first payment a year from now. The state advertises this as the Million Dollar Lottery because
$1,000,000 $50,000 20. If the interest rate is 8 percent, what is the true value of the lottery?
Formula (4.13) yields
Present value of
Million Dollar Lottery $50,000 冤0.08 0.08(1.08) 冥
1
1
20
Periodic payment
Annuity factor
$50,000
9.8181
$490,905
Rather than being overjoyed at winning, Mr. Young sues the state for misrepresentation and fraud.
His legal brief states that he was promised $1 million but received only $490,905.12
The term we use to compute the value of the stream of level payments, C, for T years is
called an annuity factor. The annuity factor in the current example is 9.8181. Because the
annuity factor is used so often in PV calculations, we have included it in Table A.2 in the
back of this book. The table gives the values of these factors for a range of interest rates, r,
and maturity dates, T.
The annuity factor as expressed in the brackets of (4.13) is a complex formula. For simplification, we may from time to time refer to the annuity factor as
ATr
(4.14)
That is, expression (4.14) stands for the present value of $1 a year for T years at an interest
rate of r.
10
This can also be written as
C[1 1兾(1 r) T ]兾r
11
We can also provide a formula for the future value of an annuity.
FV C
12
冤
(1 r) T 1
r
r
冥
To solve this problem on a common type HP19B II financial calculator, you should do the following:
a. Press “FIN” and “TVM.”
b. Enter the payment 50,000 and press “PMT.”
c. Enter the interest rate 8 and press “I % YR.”
d. Enter the number of periods 20 and press “N.”
e. Finally, press “PV” to solve.
Notice your answer is $490,907.370372. The calculator uses 11 digits for the annuity factor and the answer, whereas the example
uses only 4 digits in the annuity factor and rounds the final answer to the nearest dollar. That is why the answer in the text example
differs from the one using the calculator. In practice, the answer using the calculator is the best because it is more precise.
Corporate Finance,
Seventh Edition
Budgeting
55
Companies, 2004
81
Our experience is that annuity formulas are not hard, but tricky, for the beginning student.
We present four tricks below.
Trick 1: A Delayed Annuity One of the tricks in working with annuities or perpetuities
is getting the timing exactly right. This is particularly true when an annuity or perpetuity
begins at a date many periods in the future. We have found that even the brightest beginning student can make errors here. Consider the following example.
EXAMPLE
Danielle Caravello will receive a four-year annuity of $500 per year, beginning at date 6. If the interest rate is 10 percent, what is the present value of her annuity? This situation can be graphed as:
0
1
2
3
4
5
6
$500
7
$500
8
$500
9
$500
10
The analysis involves two steps:
1. Calculate the present value of the annuity using (4.13).This is
Present Value of Annuity at Date 5:
$500
冤0.10 0.10(1.10) 冥 $500 A
1
1
4
0.10
4
$500 3.1699
$1,584.95
Note that $1,584.95 represents the present value at date 5.
Students frequently think that $1,584.95 is the present value at date 6, because the annuity begins at date 6. However, our formula values the annuity as of one period prior to the first payment.
This can be seen in the most typical case where the first payment occurs at date 1.The formula values the annuity as of date 0 here.
2. Discount the present value of the annuity back to date 0.That is
Present Value at Date 0:
$1,584.95
$984.13
(1.10) 5
Again, it is worthwhile mentioning that, because the annuity formula brings Danielle’s annuity back
to date 5, the second calculation must discount over the remaining 5 periods.The two-step procedure is graphed in Figure 4.12.
FIGURE 4.12
Discounting Danielle
Caravello’s Annuity
Date
0
Cash flow
$984.13
1
2
3
4
5
6
$500
7
$500
8
$500
$1,584.95
Step one: Discount the four payments back to date 5 by using the annuity formula.
Step two: Discount the present value at date 5 ($1,584.95) back to present value at date 0.
9
$500
10
56
Corporate Finance,
Seventh Edition
82
Budgeting
Companies, 2004
Trick 2: Annuity in Advance
The annuity formula of (4.13) assumes that the first annuity
payment begins a full period hence. This type of annuity is frequently called an annuity in
arrears. What happens if the annuity begins today, in other words, at date 0?
EXAMPLE
In a previous example, Mark Young received $50,000 a year for 20 years from the state lottery. In
that example, he was to receive the first payment a year from the winning date. Let us now assume
that the first payment occurs immediately.The total number of payments remains 20.
Under this new assumption,we have a 19-date annuity with the first payment occurring at date 1—
plus an extra payment at date 0. The present value is
$50,000 A19
0.08
19-year annuity
$50,000 ($50,000 9.6036)
$50,000
Payment at date 0
$530,180
$530,180, the present value in this example, is greater than $490,905, the present value in the earlier lottery example. This is to be expected because the annuity of the current example begins earlier. An annuity with an immediate initial payment is called an annuity in advance. Always remember
that formula (4.13), as well as Table A.2, in this book refers to an annuity in arrears.
Trick 3: The Infrequent Annuity The following example treats an annuity with payments occurring less frequently than once a year.
EXAMPLE
Ms. Ann Chen receives an annuity of $450, payable once every two years.The annuity stretches out
over 20 years.The first payment occurs at date 2, that is, two years from today. The annual interest
rate is 6 percent.
The trick is to determine the interest rate over a two-year period. The interest rate over two
years is
(1.06 1.06) 1 12.36%
That is, $100 invested over two years will yield $112.36.
What we want is the present value of a $450 annuity over 10 periods, with an interest rate of
12.36 percent per period.This is
$450
冤0.1236 0.1236 (1.1236) 冥 $450 A
1
1
10
10
0.1236
$2,505.57
Trick 4: Equating Present Value of Two Annuities
The following example equates
the present value of inflows with the present value of outflows.
EXAMPLE
Harold and Helen Nash are saving for the college education of their newborn daughter, Susan.The
Nashes estimate that college expenses will run $30,000 per year when their daughter reaches college in 18 years. The annual interest rate over the next few decades will be 14 percent. How much
money must they deposit in the bank each year so that their daughter will be completely supported
through four years of college?
To simplify the calculations, we assume that Susan is born today. Her parents will make the first
of her four annual tuition payments on her 18th birthday. They will make equal bank deposits on
Corporate Finance,
Seventh Edition
Budgeting
57
Companies, 2004
83
each of her first 17 birthdays, but no deposit at date 0.This is illustrated as
Date 0
Susan’s
birth
1
2
Parents’
1st
deposit
Parents’
2nd
deposit
...
17
18
19
20
21
Parents’
17th and
last
deposit
Tuition
payment
1
Tuition
payment
2
Tuition
payment
3
Tuition
payment
4
Mr. and Ms. Nash will be making deposits to the bank over the next 17 years.They will be withdrawing $30,000 per year over the following four years. We can be sure they will be able to withdraw fully $30,000 per year if the present value of the deposits is equal to the present value of the
four $30,000 withdrawals.
This calculation requires three steps. The first two determine the present value of the withdrawals.The final step determines yearly deposits that will have a present value equal to that of the
withdrawals.
1. We calculate the present value of the four years at college using the annuity formula.
$30,000 冤0.14 0.14 (1.14) 冥 $30,000 A
1
1
4
4
0.14
$30,000 2.9137 $87,411
We assume that Susan enters college on her 18th birthday. Given our discussion in Trick 1
$87,411 represents the present value at date 17.
2. We calculate the present value of the college education at date 0 as
$87,411
$9,422.91
(1.14) 17
3. Assuming that Helen and Harold Nash make deposits to the bank at the end of each of the
17 years, we calculate the annual deposit that will yield a present value of all deposits of
$9,422.91.This is calculated as
C A17
0.14 $9,422.91
Because A17
0.14 6.3729,
C
$9,422.91
$1,478.59
6.3729
Thus, deposits of $1,478.59 made at the end of each of the first 17 years and invested at 14 percent
will provide enough money to make tuition payments of $30,000 over the following four years.
An alternative method would be to (1) calculate the present value of the tuition payments at Susan’s 18th birthday and (2) calculate annual deposits such that the future value
of the deposits at her 18th birthday equals the present value of the tuition payments at that
date. Although this technique can also provide the right answer, we have found that it is more
likely to lead to errors. Therefore, we only equate present values in our presentation.
Growing Annuity
Cash flows in business are very likely to grow over time, due either to real growth or to inflation. The growing perpetuity, which assumes an infinite number of cash flows, provides
58
Corporate Finance,
Seventh Edition
84
Budgeting
Companies, 2004
one formula to handle this growth. We now consider a growing annuity, which is a finite
number of growing cash flows. Because perpetuities of any kind are rare, a formula for a
growing annuity would be useful indeed. The formula is13
Formula for Present Value of Growing Annuity:
1
1
1g T
PV C
rg rg
1r
冤
冢
冣冥
(4.15)
where, as before, C is the payment to occur at the end of the first period, r is the interest
rate, g is the rate of growth per period, expressed as a percentage, and T is the number of
periods for the annuity.
EXAMPLE
Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He anticipates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate
of 20 percent, what is the present value of his lifetime salary?
We simplify by assuming he will be paid his $80,000 salary exactly one year from now, and that
his salary will continue to be paid in annual installments.The appropriate discount rate is 20 percent.
From (4.15), the calculation is
Present value
1
1
1.09
of Stuart’s $80,000 0.20 0.09 0.20 0.09 1.20
lifetime salary
冤
冢冣冥 $711,731
40
Though the growing annuity is quite useful, it is more tedious than the other simplifying formulas.
Whereas most sophisticated calculators have special programs for perpetuity, growing perpetuity,
and annuity, there is no special program for growing annuity. Hence, one must calculate all the terms
in formula (4.15) directly.
EXAMPLE
In a previous example, Harold and Helen Nash planned to make 17 identical payments in order to
fund the college education of their daughter, Susan. Alternatively, imagine that they planned to increase their payments at 4 percent per year. What would their first payment be?
The first two steps of the previous Nash family example showed that the present value of the
college costs was $9,422.91. These two steps would be the same here. However, the third step must
be altered. Now we must ask, How much should their first payment be so that, if payments increase
by 4 percent per year, the present value of all payments will be $9,422.91?
13
This can be proved as follows. A growing annuity can be viewed as the difference between two growing perpetuities. Consider
a growing perpetuity A, where the first payment of C occurs at date 1. Next, consider growing perpetuity B, where the first
payment of C(1 g)T is made at date T 1. Both perpetuities grow at rate g. The growing annuity over T periods is the
difference between annuity A and annuity B. This can be represented as:
Date
0
1
2
Perpetuity A
C
C (1 g)
3
...
T
C (1 g)2 . . . C (1 g)T1
C
C (1 g)
C (1 g)2 . . . C (1 g)T1
Perpetuity B
Annuity
T1
T2
T3
C (1 g)T
C (1 g)T1
C (1 g)T2 C (1 g)T
C (1 g)T1
C (1 g)T2 The value of perpetuity A is
The value of perpetuity B is
C
rg
1
C (1 g) T
(1 r) T
rg
The difference between the two perpetuities is given by (4.15).
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
59
85
We set the growing-annuity formula equal to $9,422.91 and solve for C .
C
1g
冤r g r g 冢 1 r 冣冥 C冤0.14 0.04 0.14 0.04 冢1.14冣冥
1
1
T
1
1
1.04
17
$9,422.91
Here, C $1,192.78. Thus, the deposit on their daughter’s first birthday is $1,192.78, the deposit on
the second birthday is $1,240.49 (1.04 $1,192.78), and so on.
1. What are the formulas for perpetuity, growing perpetuity, annuity, and growing
annuity?
2. What are three important points concerning the growing-perpetuity formula?
3. What are four tricks concerning annuities?
Making the Decision to Convert Lottery Prize Winnings:
The Case of the Singer Asset Finance Company
In 1987, Rosalind Setchfield won more than $1.3 million in the Arizona state lottery.The winnings
were to be paid in 20 yearly installments of $65,276.79. Six years later, in 1995, Mrs. Setchfield received a phone call from a salesman for the Singer Asset Finance Company of West Palm Beach,
Florida.The Singer company offered to give her $140,000 immediately for one-half of the next nine
lottery checks (i.e., $140,000 now for $32,638.39 9 $293,745.51 over nine years). Singer is a
prize broker with many employees whose main job is to track down million-dollar-lottery prizewinners like Mrs. Setchfield. Singer knows that many people are eager to trade all or part of their
promised winnings for a discounted lump sum immediately. Singer is part of a growing $700 million prize-broker business. Singer and Woodbridge Sterling Capital currently account for about
80 percent of the market for lottery prize conversions. Prize brokers like Singer resell their rights
to receive future payouts (called structured payouts) to institutional investors such as SunAmerica,
Inc., or the John Hancock Mutual Life Insurance Co. In the case of Mrs. Setchfield, the investor was
the Enhance Financial Service Group, a New York municipal bond reinsurer. Singer had arranged to
sell its stake in Mrs. Setchfield’s lottery prize to Enhance for $196,000 and would make a quick
$56,000 profit if she accepted the offer. Mrs. Setchfield accepted Singer’s offer and the deal was
made.
How was Singer able to structure a deal that resulted in a $56,000 profit? The answer is that
individuals and institutions have different intertemporal consumption preferences. Mrs. Setchfield’s
family had experienced some financial difficulties and was in need of some immediate cash. She didn’t
want to wait nine years for her prize winnings. On the other hand, the Enhance Group had some
excess cash and was very willing to make a $196,000 investment in order to receive the rights to
obtain half of Mrs. Setchfield’s prize winnings, or $32,638.39 a year for nine years.The discount rate
the Enhance Group applied to the future payouts was about 8.96 percent (i.e., the discount rate
that equates the present value of $196,000 with Singer’s right to receive their equal payments of
$32,638.39).
The discount rate that Mrs. Setchfield used was 18.1 percent, reflecting her aversion to deferred
cash flows.
SOURCE: Vanessa Williams,“How Major Players Turn Lottery Jackpots into Guaranteed Bet,” The Wall Street Journal,
September 23, 1997.
CASE STUDY
Concept
Questions
60
Corporate Finance,
Seventh Edition
86
Budgeting
Companies, 2004
4.5 What Is a Firm Worth?
Suppose you are in the business of trying to determine the value of small companies. (You
are a business appraiser.) How can you determine what a firm is worth? One way to think
about the question of how much a firm is worth is to calculate the present value of its future
cash flows.
Let us consider the example of a firm that is expected to generate net cash flows (cash
inflows minus cash outflows) of $5,000 in the first year and $2,000 for each of the next five
years. The firm can be sold for $10,000 seven years from now. The owners of the firm
would like to be able to make 10 percent on their investment in the firm.
The value of the firm is found by multiplying the net cash flows by the appropriate
present-value factor. The value of the firm is simply the sum of the present values of the
individual net cash flows.
The present value of the net cash flows is given next.
The Present Value of the Firm
End of
Year
Net Cash Flow
of the Firm
Present Value
Factor (10%)
Present Value of
Net Cash Flows
1
2
3
4
5
6
7
$ 5,000
2,000
2,000
2,000
2,000
2,000
10,000
.90909
.82645
.75131
.68301
.62092
.56447
.51315
Present value of firm
$ 4,545.45
1,652.90
1,502.62
1,366.02
1,241.84
1,128.94
5,131.58
_________
$16,569.35
We can also use the simplifying formula for an annuity to give us
$5,000 (2,000 A50.10 ) 10,000
$16,569.35
(1.1) 7
1.1
1.1
Suppose you have the opportunity to acquire the firm for $12,000. Should you acquire the
firm? The answer is yes because the NPV is positive.
NPV PV Cost
$4,569.35 $16,569.35 $12,000
The incremental value (NPV) of acquiring the firm is $4,569.35.
EXAMPLE
The Trojan Pizza Company is contemplating investing $1 million in four new outlets in Los Angeles.
Andrew Lo, the firm’s Chief Financial Officer (CFO), has estimated that the investments will pay out
cash flows of $200,000 per year for nine years and nothing thereafter. (The cash flows will occur at
the end of each year and there will be no cash flow after year 9.) Mr. Lo has determined that the
relevant discount rate for this investment is 15 percent.This is the rate of return that the firm can
earn at comparable projects. Should the Trojan Pizza Company make the investments in the new
outlets?
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
61
87
The decision can be evaluated as:
NPV $1,000,000 $200,000 $200,000
$200,000
(1.15) 2
(1.15) 9
1.15
$1,000,000 $200,000 A90.15
$1,000,000 $954,316.78
$45,683.22
The present value of the four new outlets is only $954,316.78.The outlets are worth less than
they cost. The Trojan Pizza Company should not make the investment because the NPV is
$45,683.22. If the Trojan Pizza Company requires a 15 percent rate of return, the new outlets are
not a good investment.
1. Two basic concepts, future value and present value, were introduced in the beginning of this chapter.
With a 10-percent interest rate, an investor with $1 today can generate a future value of $1.10 in
a year, $1.21 [$1 (1.10)2] in two years, and so on. Conversely, present-value analysis places a
current value on a later cash flow. With the same 10-percent interest rate, a dollar to be received
in one year has a present value of $0.909 ($1兾1.10) in year 0. A dollar to be received in two years
has a present value of $0.826 [$1兾(1.10)2].
2. One commonly expresses the interest rate as, say, 12 percent per year. However, one can speak
of the interest rate as 3 percent per quarter. Although the stated annual interest rate remains
12 percent (3 percent 4), the effective annual interest rate is 12.55 percent [(1.03)4 1]. In
other words, the compounding process increases the future value of an investment.The limiting
case is continuous compounding, where funds are assumed to be reinvested every infinitesimal
instant.
3. A basic quantitative technique for financial decision making is net present value analysis.The net
present value formula for an investment that generates cash flows (Ci ) in future periods is
NPV C0 N
CN
C1
Ci
C2
2 N C0 (1 r)
(1 r)
(1 r)
(1
r) i
i1
兺
The formula assumes that the cash flow at date 0 is the initial investment (a cash outflow).
4. Frequently, the actual calculation of present value is long and tedious. The computation of the
present value of a long-term mortgage with monthly payments is a good example of this. We
presented four simplifying formulas:
Perpetuity: PV Growing perpetuity: PV C
r
C
rg
Annuity: PV C
Growing annuity: PV C
冤 r r (1 r) 冥
1
1
T
1g
冤r g r g 冢 1 r 冣冥
1
1
T
5. We stressed a few practical considerations in the application of these formulas:
a. The numerator in each of the formulas, C, is the cash flow to be received one full period
hence.
62
Corporate Finance,
Seventh Edition
88
Budgeting
Companies, 2004
b. Cash flows are generally irregular in practice. To avoid unwieldy problems, assumptions to
create more regular cash flows are made both in this textbook and in the real world.
c. A number of present value problems involve annuities (or perpetuities) beginning a few
periods hence. Students should practice combining the annuity (or perpetuity) formula with
the discounting formula to solve these problems.
d. Annuities and perpetuities may have periods of every two or every n years, rather than once
a year. The annuity and perpetuity formulas can easily handle such circumstances.
e. One frequently encounters problems where the present value of one annuity must be equated
with the present value of another annuity.
effective annual yield, 72
future value, 60
growing annuity, 84
growing perpetuity, 77
net present value, 62
perpetuity, 75
present value, 61
present value factor, 68
simple interest, 64
stated annual interest rate, 72
KEY TERMS
annual percentage rate, 72
annuity, 79
annuity factor, 80
appropriate discount rate, 69
compounding, 64
compound interest, 64
compound value, 60
continuous compounding, 74
discounting, 68
effective annual interest rate, 72
SUGGESTED
READINGS
To learn how to perform the mathematics of present value, we encourage you to see the handbooks that
come with the Hewlett-Packard HP 19BII calculator.
We also recommend:
White, M. Financial Analysis with a Calculator. 5th ed. Burr Ridge, Ill.: McGraw-Hill/Irwin, 2004.
QUESTIONS &
PROBLEMS14
4.1
Compute the future value of $1,000 compounded annually for
a. 10 years at 5 percent
b. 10 years at 7 percent
c. 20 years at 5 percent
d. Why is the interest earned in part (c) not twice the amount earned in part (a)?
4.2
Calculate the present value of the following cash flows discounted at 10 percent.
a. $1,000 received seven years from today.
b. $2,000 received one year from today.
c. $500 received eight years from today.
4.3
Would you rather receive $1,000 today or $2,000 in 10 years? Assume a discount rate of
8 percent.
4.4
The government has issued a bond that will pay $1,000 in 25 years.The bond will pay no interim
coupon payments.What is the present value of the bond if the discount rate is 10 percent?
4.5
A firm has an estimated pension liability of $1.5 million due 27 years from today. If the firm
can invest in a risk-free security with an interest rate of 8 percent, how much must the firm
invest today to be able to make the $1.5 million payment?
ANNUAL
COMPOUNDING
14
The following conventions are used in the questions and problems for this chapter.
If more frequent compounding than once a year is indicated, the problem will either state: (1) both a stated annual interest
rate and a compounding period, or (2) an effective annual interest rate.
If annual compounding is indicated, the problem will provide an annual interest rate. Since the stated annual interest rate
and the effective annual interest rate are the same here, we use the simpler annual interest rate.
Budgeting
Companies, 2004
63
89
4.6
You have won the Florida state lottery. Lottery officials offer you the choice of the following
alternative payouts:
Alternative 1: $10,000,000 one year from now.
Alternative 2: $20,000,000 five years from now.
Which alternative should you choose if the discount rate is:
a. 0 percent?
b. 10 percent?
c. 20 percent?
d. What discount rate makes the two alternatives equally attractive to you?
4.7
You are selling your house. The Smiths have offered you $115,000.They will pay you immediately.The Joneses have offered you $150,000, but they cannot pay you until three years from
today.The interest rate is 10 percent.Which offer should you choose?
4.8
Suppose you bought a bond that will pay $1,000 in 20 years. No intermediate coupon payments will be made. If the appropriate interest rate is 8 percent,
a. what is the current price of the bond?
b. what will the price be 10 years from today?
c. what will the price be 15 years from today?
Assume the interest rate does not change over the life of the bond.
4.9
Ann Woodhouse wants to invest in raw land. She expects to own the property for 10 years
and to sell it at the end of the 10th year for $5 million.There are no other cash flows.What is
the most she would be willing to pay for the property if the appropriate discount rate is
12 percent?
4.10 You have the opportunity to make an investment of $900,000. If you make this investment
now, you will receive $120,000, $250,000 and $800,000 one, two, and three years from today,
respectively.The appropriate discount rate for this investment is 12 percent.
a. Should you make the investment?
b. What is the net present value (NPV) of this opportunity?
c. If the discount rate is 11 percent, should you invest? Compute the NPV to support your
answer.
4.11 You have the opportunity to invest in a machine that costs $340,000. The machine generates revenues of $100,000 at the end of each year and requires maintenance costs of
$10,000 at the beginning of each year. The machine incurs a maintenance cost today because of start-up expenses. If the economic life of the machine is five years and the relevant
discount rate is 10 percent, should you buy the machine? What if the relevant discount rate
is 9 percent?
4.12 Today a firm signed a contract to sell a capital asset for $90,000. The firm will receive the
payment five years from today. The asset costs $60,000 to produce, payable immediately.
a. If the appropriate discount rate is 10 percent, what is the NPV of the contract?
b. At what discount rate will the firm break even on the sale of the asset?
4.13 Your aunt owns an auto dealership. She promised to pay you $3,000 for your car when you
graduate one year from now. However, your roommate offered you $3,500 for the car now.
The prevailing interest rate is 12 percent. If the future value of the benefit from owning the
car for one additional year is $1,000, should you accept your aunt’s offer? You are not planning to buy another car and will not need the car after you graduate.
4.14 You wish to purchase a new convertible 12 years from today. At that time, the car will cost
$80,000. You currently have $10,000 to invest. What rate of interest must your investment
earn so that you can pay for the car?
4.15 Suppose you deposit $1,000 in an account at the end of each of the next four years. If the
account earns 12 percent annually, how much will be in the account at the end of seven
years?
Corporate Finance,
Seventh Edition
64
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
90
COMPOUNDING
PERIODS
4.16 What is the future value three years hence of $1,000 invested in an account with a stated annual interest rate of 8 percent,
a. compounded annually?
b. compounded semiannually?
c. compounded monthly?
d. compounded continuously?
e. Why does the future value increase as the compounding period shortens?
4.17 Compute the future value of $1,000 continuously compounded for
a. five years at a stated annual interest rate of 12 percent.
b. three years at a stated annual interest rate of 10 percent.
c. 10 years at a stated annual interest rate of 5 percent.
d. eight years at a stated annual interest rate of 7 percent.
4.18 Calculate the present value of $5,000 received 12 years from today. Assume a stated annual
interest rate of 10 percent, compounded quarterly.
4.19 Bank America offers a stated annual interest rate of 4.1 percent, compounded quarterly, while
Bank USA offers a stated annual interest rate of 4.05 percent, compounded monthly. In
which bank should you deposit your money?
PERPETUITIES AND
GROWING
PERPETUITIES
4.20 An investor purchasing a British consol is entitled to receive annual payments from the British
government forever. What is the price of a consol that pays $120 annually if the next payment
occurs one year from today? The market interest rate is 15 percent.
ANNUAL
COMPOUNDING
4.21 Assuming an interest rate of 10 percent, calculate the present value of the following streams
of yearly payments:
a. $1,000 per year, forever, with the first payment one year from today.
b. $500 per year, forever, with the first payment two years from today.
c. $2,420 per year, forever, with the first payment three years from today.
4.22 Given an interest rate of 10 percent per year, what is the value at the end of year 5 of a perpetual stream of $120 annual payments starting at the end of year 9?
4.23 Harris, Inc., paid a $3 dividend yesterday. If the firm raises its dividend 5 percent every year
and the appropriate discount rate is 12 percent, what is the price of Harris stock?
4.24 In its most recent corporate report, Williams, Inc., apologized to its stockholders for not
paying a dividend. The report states that management will pay a $1 dividend next year. That
dividend will grow at four percent every year thereafter. If the discount rate is 10 percent,
how much are you willing to pay for a share of Williams, Inc.?
4.25 Mark Weinstein has been working on an advanced technology in laser eye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the
technology to be $200,000, received two years from today. Subsequent annual cash flows will
grow at 5 percent, in perpetuity.What is the present value of the technology if the discount
rate is 10 percent?
4.26 Barrett Pharmaceuticals is considering a drug project that costs $100,000 today and is expected to generate end-of-year annual cash flow of $50,000, forever. At what discount rate
would Barrett be indifferent between accepting or rejecting the project?
COMPOUNDING
PERIODS
4.27 A prestigious investment bank designed a new security that pays a quarterly dividend of $10
in perpetuity. The first dividend occurs one quarter from today. What is the price of the
security if the stated annual interest rate is 12 percent, compounded quarterly?
4.28 World Transportation, Inc., is expected to initiate its quarterly dividend of $1 five years
from today and the dividend is expected to remain constant, forever. What is the price of
World Transportation stock if the stated annual interest rate is 15 percent, compounded
quarterly?
Budgeting
Companies, 2004
65
91
ANNUITIES AND
GROWING
ANNUITIES
4.29 Should you buy an asset that will generate income of $1,200 at the end of each year for eight
years? The price of the asset is $6,200 and the annual interest rate is 10 percent.
ANNUAL
COMPOUNDING
4.30 What is the present value of an annuity of $2,000 per year, with the first cash flow received
three years from today and the last one received 22 years from today? Use a discount rate of
8 percent.
4.31 What is the value today of a 15-year annuity that pays $500 a year? The annuity’s first payment
occurs at the end of year 6.The annual interest rate is 12 percent for years 1 through 5, and
15 percent thereafter.
4.32 You are offered the opportunity to buy a note for $12,800.The note will pay $2,000 at the
end of each of the next 10 years. If you buy the note, what rate of interest will you receive?
4.33 You need $25,000 to buy a car five years from now.
a. In order to buy the car, you plan to make equal payments at the end of every year into an
account yielding 7 percent per year.What are these annual payments?
b. Your rich uncle died and left you $20,000. How much of it must you put into the same
account as a lump sum today to meet your goal if you do not want to make any of the
annual payments calculated in part (a)?
4.34 Nancy Ferris bought a building for $120,000. She paid 15 percent down and agreed to pay the
balance in 20 equal, end-of-year, installments. What are the equal installments if the annual
interest rate is 10 percent?
4.35 You have recently won the super jackpot in the Washington state lottery. On reading the fine
print, you discover that you have the following two options:
a. You receive 31 annual payments of $160,000, with the first payment being delivered today.
The income will be taxed at a rate of 28 percent.Taxes are withheld when the checks are
issued.
b. You receive $446,000 now, and you will not have to pay taxes on this amount. In addition,
beginning one year from today, you will receive $101,055 each year for 30 years.The cash
flows from this annuity will be taxed at 28 percent.
Using a discount rate of 10 percent, which option should you select?
4.36 You are saving for the college education of your two children.They are two years apart in age;
one will begin college 15 years from today and the other will begin 17 years from today.You
estimate your children’s college expenses to be $21,000 per year per child, payable at the end
of each school year.The annual interest rate is 15 percent. How much money must you deposit in an account each year to fund your children’s education? Your deposits begin one year
from today.You will make your last deposit when your oldest child enters college.
4.37 A well-known insurance company offers a policy known as the “Estate Creator Six Pay.” Typically, a parent or grandparent buys a policy for a child at the child’s birth.The details of the
policy are as follows.The purchaser (say, the parent) makes the following six payments to the
insurance company.
First birthday
Second birthday
Third birthday
$750
$750
$750
Fourth birthday
Fifth birthday
Sixth birthday
$800
$800
$800
No more payments are made after the child’s sixth birthday.When the child reaches the age
of 65, he or she receives $250,000. If the relevant interest rate is 6 percent for the first six
years and 7 percent for all subsequent years, is the policy worth buying?
4.38 Your company is considering either buying or leasing a $120,000 piece of equipment for the
next 10 years.The company plans to use the equipment indefinitely.The annual lease payments
of $15,000 begin today.The lease includes an option for your company to buy the equipment
Corporate Finance,
Seventh Edition
66
92
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
for $25,000 at the end of the leasing period (i.e., 10 years). Assume that, if the company decides to lease, the company will exercise the option to buy the equipment at the end of the
10-year lease. Should your company accept the lease offer if the appropriate discount rate is
8 percent per year?
4.39 Your job pays you only once a year, for all the work you did over the previous 12 months.
Today, December 31, you just received your salary of $50,000 and you plan to spend all of it.
However, you want to start saving for retirement beginning next year.You have decided that
one year from today you will begin depositing 2 percent of your annual salary in an account that
will earn 8 percent per year.Your salary will increase at 4 percent per year throughout your
career. How much money will you have on the date of your retirement 40 years from today?
4.40 You must decide whether or not to purchase new capital equipment.The cost of the machine
is $5,000. It will produce the following cash flows.
Year
Cash Flow
1
2
3
4
5
6
7
8
$ 700
900
1,000
1,000
1,000
1,000
1,250
1,375
The appropriate discount rate is 10 percent. Should you purchase the equipment?
4.41 Your younger brother has come to you for advice. He is about to enter college and has two
options open to him. His first option is to study engineering. If he does this, his undergraduate
degree would cost him $12,000 a year for four years. Having obtained his undergraduate degree, he would need to gain two years of practical experience. He would earn $20,000 in the
first year and he would earn $25,000 in the second year. He would then need to obtain his
master’s degree, which will cost $15,000 a year for two years.After completion of his master’s
degree, he will be fully qualified as an engineer and can earn $40,000 per year for 25 years.
His other alternative is to study accounting. If he does this, he would pay $13,000 a year
for four years and then he would earn $31,000 per year for 30 years.
The effort involved in the two careers is the same, so he is only interested in the earnings
that the jobs provide.All earnings and costs are paid at the end of the year.
a. What advice would you give him if the market interest rate is 5 percent?
b. A day later he comes back and says that he took your advice, but in fact, the market interest rate was 6 percent. Has your brother made the right choice?
4.42 Tom Adams has received a job offer from a large investment bank as a clerk to an associate
banker. His base salary will be $35,000. He will receive his first annual salary payment one year
from the day he begins to work. In addition, he will get an immediate $10,000 bonus for joining the company. His salary will grow at 4 percent each year. Each year he will receive a bonus
equal to 10 percent of his salary. Mr. Adams is expected to work for 25 years. What is the
present value of the offer if the discount rate is 12 percent?
4.43 Southern California Publishing Company is trying to decide whether or not to revise its popular textbook, Financial Psychoanalysis Made Simple. They have estimated that the revision will
cost $40,000. Cash flows from increased sales will be $10,000 the first year.These cash flows
will increase by 7 percent per year.The book will go out of print five years from now.Assume
that the initial cost is paid now and revenues are received at the end of each year. If the company requires a 10 percent return for such an investment, should it undertake the revision?
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
67
93
4.44 Ian Krassner wants to save money to meet two objectives. First, he wants to retire 31 years
from today with a retirement income of $300,000 per year for 20 years.The first retirement
payment will occur 31 years from today. Second, he would like to purchase a cabin in the
mountains 10 years from today at an estimated cost of $350,000. He can afford to save only
$40,000 at the end of each year for the first 10 years. He expects to earn 7 percent per year
on his savings.Assuming he saves the same amount each year, what must Ian save annually at
the end of year 11 through year 30 to meet his objectives?
4.45 On January 1, Jack Ferguson signed a three-year contract to work for a computer software
company. He will be paid $5,000 at the end of each month and will receive a bonus of $10,000
at each year-end.What is the present value of the contract if the stated annual interest rate,
compounded monthly, is 12 percent?
4.46 Sarah Buchwalter bought a $15,000 Honda Civic with 20 percent down and financed the rest
with a four-year loan at an 8 percent stated annual interest rate, compounded monthly.What
is her monthly payment if she makes the first payment one month after the purchase?
4.47 On September 1, 2000, Susan Chao bought a motorcycle for $10,000. She paid $1,000 down
and financed the balance with a five-year loan at a stated annual interest rate of 9.6 percent,
compounded monthly. She started the monthly payments exactly one month after the purchase, i.e., October 1, 2000.Two years later, at the end of October, 2002, Susan got a new job
and decided to pay off the loan. If the bank charges her a 1 percent prepayment penalty based
on the loan balance, how much must she pay the bank on November 1, 2002?
4.48 When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her
grave every Sunday as long as he lived.The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $5. Based on
actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died. Assume
that the stated annual interest rate, compounded weekly, is 10.4 percent.Also, assume that the
price of the flowers will increase at 3.9 percent per year, when expressed as a stated annual
growth rate, compounded weekly.Assuming that each year has exactly 52 weeks, what is the
present value of this commitment? Joe began purchasing flowers the week after Marilyn died.
4.49 In January 1984, Richard “Goose” Gossage signed a contract to play for the San Diego Padres
that guaranteed him a minimum of $9,955,000 (undiscounted). The guaranteed payments
were $875,000 in 1984, $650,000 in 1985, $800,000 in 1986, $1 million in 1987, $1 million in
1988, and $300,000 in 1989. In addition, the contract called for $5,330,000 (undiscounted) in
deferred money payable at the rate of $240,000 per year from 1990 through 2006 and then
$125,000 a year from 2007 through 2016. If the annual interest rate is 9 percent and all payments are made on July 1 of each year, what would the present value of these guaranteed
payments be on January 1, 1984? Assume an interest rate of 4.4 percent per six months. If he
were to receive an equal annual salary at the end of each of the five years from 1984 through
1988, what would his equivalent annual salary be? Ignore taxes throughout this problem.
4.50 Mike Bayles has just arranged to purchase a $400,000 vacation home in the Bahamas with a
20 percent down payment.The mortgage has an 8 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. His first payment will be due one month from now. However, the mortgage has an eight-year balloon
payment, meaning that the balance of the loan must be paid off at the end of year 8. There
were no other transaction costs or finance charges. How much will Mike’s balloon payment
be in eight years?
4.51 You want to lease a set of golf clubs from Pings Ltd.The lease contract is in the form of 24 equal
monthly payments at a 12 percent stated annual interest rate, compounded monthly. Since the
clubs cost $4,000 retail, Pings wants the PV of the lease payments to equal $4,000. Suppose
that your first payment is due immediately.What will your monthly lease payments be?
4.52 A 10-year annuity pays $900 per year.The first $900 will be paid five years from now. If the
stated interest rate is 8 percent, compounded quarterly, what is the present value of this
annuity?
COMPOUNDING
PERIODS
68
Corporate Finance,
Seventh Edition
94
Budgeting
Companies, 2004
4.53 Larry Harris,CFO of MakeMyDecision,is evaluating the financial viability of a new production line
for graphite electrodes. His research team has provided him with the following information:
Investment required to set up the production line: $1.8 million
Cash flow projections:
First year of production (production begins 3 years after initial investment): $60,000
Cash flow grows at 4% annually for first 5 years and then at a constant rate forever
Required rate of return: 10%
For Larry to accept the project, what should the growth rate be after first 5 years of operation?
4.54 Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual
fee of $400 and has an existing customer base of 500. Paul plans to raise the annual fee by
10 percent every year and expects the club membership to grow at a constant rate of 3 percent for the next five years.The overall expenses of running the health club are $80,000 a year
and are expected to grow at the inflation rate of 2 percent annually.After five years, Paul plans
to buy a luxury boat for $500,000, close the health club, and travel the world in his boat for
the rest of his life.What is the annual amount that Paul can spend while on his world tour if
he will have no money left in the bank when he dies? Assume Paul has a remaining life of
15 years and earns 8 percent on his savings.
S&P
PROBLEM
Appendix 4A
4.55 Under the “Excel Analytics” link find the “Mthly. Adj. Price” for Elizabeth Arden (RDEN) stock.
What was your annual return over the last four years assuming you purchased the stock at
the close price four years ago? (Assume no dividends were paid.) Using this same return, what
price will Elizabeth Arden stock sell for five years from now? Ten years from now? What if the
stock prices increases at 11 percent per year?
Net Present Value: First Principles of Finance
In this appendix, we show the theoretical underpinnings of the net present value rule. We
first show how individuals make intertemporal consumption choices, and then we explain
the net present value (NPV) rule. The appendix should appeal to students who like a theoretical model. Those of you who can accept the NPV analysis contained in Chapter 4 can
skip to Chapter 5.
4A.1 Making Consumption Choices over Time
Figure 4A.1 illustrates the situation faced by a representative individual in the financial
market. This person is assumed to have an income of $50,000 this year and an income of
$60,000 next year. The market allows him not only to consume $50,000 worth of goods
this year and $60,000 next year, but also to borrow and lend at the equilibrium interest rate.
The line AB in Figure 4A.1 shows all of the consumption possibilities open to the person
through borrowing or lending, and the shaded area contains all of the feasible choices. Let’s
look at this figure more closely to see exactly why points in the shaded area are available.
We will use the letter r to denote the interest rate—the equilibrium rate—in this market.
The rate is risk-free because we assume that no default can take place. Look at point A on
the vertical axis of Figure 4A.1. Point A is a height of
A $60,000 [$50,000 (1 r)]
For example, if the rate of interest is 10 percent, then point A would be
A $60,000 [$50,000 (1 0.1)]
$60,000 $55,000
$115,000
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
5. How to Value Bonds and
Stocks
Chapter 5
EXECUTIVE
SUMMARY
How to Value Bonds
and Stocks
The previous chapter discussed the mathematics of compounding, discounting, and present value. We also showed how to value a
firm. We now use the mathematics of compounding and discounting to determine the
present values of financial obligations of the
firm, beginning with a discussion of how bonds
are valued. Since the future cash flows of
bonds are known, application of net-presentvalue techniques is fairly straightforward.
The uncertainty of future cash flows makes
the pricing of stocks according to NPV more
difficult.
5.1 Definition and Example of a Bond
A bond is a certificate showing that a borrower owes a specified sum. In order to repay the
money, the borrower has agreed to make interest and principal payments on designated
dates. For example, imagine that Kreuger Enterprises just issued 100,000 bonds for $1,000
each, where the bonds have a coupon rate of 5 percent and a maturity of two years. Interest
on the bonds is to be paid yearly. This means that:
1. $100 million (100,000 $1,000) has been borrowed by the firm.
2. The firm must pay interest of $5 million (5% $100 million) at the end of one year.
3. The firm must pay both $5 million of interest and $100 million of principal at the end of
two years.
We now consider how to value a few different types of bonds.
5.2 How to Value Bonds
Pure Discount Bonds
The pure discount bond is perhaps the simplest kind of bond. It promises a single payment,
say $1, at a fixed future date. If the payment is one year from now, it is called a one-year discount bond; if it is two years from now, it is called a two-year discount bond, and so on. The
date when the issuer of the bond makes the last payment is called the maturity date of the
bond, or just its maturity for short. The bond is said to mature or expire on the date of its final
payment. The payment at maturity ($1 in this example) is termed the bond’s face value.
106
69
70
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
107
Chapter 5 How to Value Bonds and Stocks
FIGURE 5.1
Different Types of
Bonds: C, Coupon
Paid Every 6 Months;
F, Face Value at
Year 4 (maturity for
pure discount and
coupon bonds)
Year 1
Months
6
Year 2
12
18
Year 3
24
30
Year 4
36 42
Pure discount bonds
. . .
48
. . .
F
Coupon bonds
C
C
C
C
C
C
C F+ C
Consols
C
C
C
C
C
C
C
C
C
C
Pure discount bonds are often called zero-coupon bonds or zeros to emphasize the fact
that the holder receives no cash payments until maturity. We will use the terms zero, bullet,
and discount interchangeably to refer to bonds that pay no coupons.
The first row of Figure 5.1 shows the pattern of cash flows from a four-year pure discount bond. Note that the face value, F, is paid when the bond expires in the 48th month.
There are no payments of either interest or principal prior to this date.
In the previous chapter, we indicated that one discounts a future cash flow to determine
its present value. The present value of a pure discount bond can easily be determined by the
techniques of the previous chapter. For short, we sometimes speak of the value of a bond
instead of its present value.
Consider a pure discount bond that pays a face value of F in T years, where the interest
rate is r in each of the T years. (We also refer to this rate as the market interest rate.)
Because the face value is the only cash flow that the bond pays, the present value of this
face amount is
Value of a Pure Discount Bond:
F
PV (1 r) T
The present value formula can produce some surprising results. Suppose that the interest rate is 10 percent. Consider a bond with a face value of $1 million that matures in
20 years. Applying the formula to this bond, its PV is given by
PV $1 million
(1.1) 20
$148,644
or only about 15 percent of the face value.
Level-Coupon Bonds
Many bonds, however, are not of the simple, pure discount variety. Typical bonds issued by
either governments or corporations offer cash payments not just at maturity, but also at regular times in between. For example, payments on U.S. government issues and American
corporate bonds are made every six months until the bond matures. These payments are
called the coupons of the bond. The middle row of Figure 5.1 illustrates the case of a fouryear, level-coupon bond: The coupon, C, is paid every six months and is the same throughout the life of the bond.
Note that the face value of the bond, F, is paid at maturity (end of year 4). F is sometimes called the principal or the denomination. Bonds issued in the United States typically
have face values of $1,000, though this can vary with the type of bond.
Corporate Finance,
Seventh Edition
108
Budgeting
Companies, 2004
Stocks
As we mentioned before, the value of a bond is simply the present value of its cash
flows. Therefore, the value of a level-coupon bond is merely the present value of its stream
of coupon payments plus the present value of its repayment of principal. Because a levelcoupon bond is just an annuity of C each period, together with a payment at maturity of
$1,000, the value of a level-coupon bond is
Value of a Level-Coupon Bond:
C
C
C
$1,000
PV ...
(1 r) T (1 r) T
1 r (1 r) 2
where C is the coupon and the face value, F, is $1,000. The value of the bond can be
rewritten as
Value of a Level-Coupon Bond:
PV C ATr $1,000
(1 r) T
As mentioned in the previous chapter, ATr is the present value of an annuity of $1 per period
for T periods at an interest rate per period of r.
EXAMPLE
Suppose it is November 2003 and we are considering a government bond.We see in The Wall Street
Journal some 13s of November 2007.This is jargon that means the annual coupon rate is 13 percent.1
The face value is $1,000, implying that the yearly coupon is $130 (13% $1,000). Interest is paid
each May and November, implying that the coupon every six months is $65 ($130兾2).The face value
will be paid out in November 2007, four years from now. By this we mean that the purchaser obtains
claims to the following cash flows:
5兾04
$65
11兾04
$65
5兾05
$65
11兾05
$65
5兾06
$65
11兾06
$65
5兾07
$65
11兾07
$65 $1,000
If the stated annual interest rate in the market is 10 percent per year, what is the present value of
the bond?
Our work on compounding in the previous chapter showed that the interest rate over any sixmonth interval is one half of the stated annual interest rate.In the current example,this semiannual rate
is 5 percent (10%兾2). Since the coupon payment in each six-month period is $65, and there are eight
of these six-month periods from November 2003 to November 2007,the present value of the bond is
PV $65
$65
$65
$1,000
...
(1.05)
(1.05) 2
(1.05) 8 (1.05) 8
$65 A80.05 $1,000兾(1.05)8
($65 6.463) ($1,000 0.677)
$420.095 $677
$1,097.095
Traders will generally quote the bond as 109.7095,2 indicating that it is selling at 109.7095 percent of the face value of $1,000.
1
The coupon rate is specific to the bond. The coupon rate indicates what cash flow should appear in the numerator of the NPV
equation. The coupon rate does not appear in the denominator of the NPV equation.
2
Bond prices are actually quoted in 32nds of a dollar, so a quote this precise would not be given.
71
72
Corporate Finance,
Seventh Edition
Budgeting
Stocks
Companies, 2004
109
At this point, it is worthwhile to relate the above example of bond-pricing to the discussion of compounding in the previous chapter. At that time we distinguished between the
stated annual interest rate and the effective annual interest rate. In particular, we pointed
out that the effective annual interest rate is
(1 r兾m)m 1
where r is the stated annual interest rate and m is the number of compounding intervals.
Since r 10% and m 2 (because the bond makes semiannual payments), the effective
annual interest rate is
[1 (0.10兾2)]2 1 (1.05)2 1 10.25%
In other words, because the bond is paying interest twice a year, the bondholder earns a
10.25-percent return when compounding is considered.3
One final note concerning level-coupon bonds: Although the preceding example concerns government bonds, corporate bonds are identical in form. For example, DuPont
Corporation has an 81⁄2-percent bond maturing in 2006. This means that DuPont will make
semiannual payments of $42.50 (81⁄2%兾2 $1,000) between now and 2006 for each face
value of $1,000.
Consols
Not all bonds have a final maturity date. As we mentioned in the previous chapter, consols
are bonds that never stop paying a coupon, have no final maturity date, and therefore never
mature. Thus, a consol is a perpetuity. In the 18th century the Bank of England issued such
bonds, called “English consols.” These were bonds that the Bank of England guaranteed
would pay the holder a cash flow forever! Through wars and depressions, the Bank of
England continued to honor this commitment, and you can still buy such bonds in London
today. The U.S. government also once sold consols to raise money to build the Panama
Canal. Even though these U.S. bonds were supposed to last forever and to pay their
coupons forever, don’t go looking for any. There is a special clause in the bond contract that
gives the government the right to buy them back from the holders, and that is what the government has done. Clauses like that are call provisions, and we study them later.
An important example of a consol, though, is called preferred stock. Preferred stock is
stock that is issued by corporations and that provides the holder a fixed dividend in perpetuity. If there were never any question that the firm would actually pay the dividend on the
preferred stock, such stock would in fact be a consol.
These instruments can be valued by the perpetuity formula of the previous chapter. For
example, if the marketwide interest rate is 10 percent, a consol with a yearly interest payment of $50 is valued at
$50
$500
0.10
Concept
Questions
1. Define pure discount bonds, level-coupon bonds, and consols.
2. Contrast the stated interest rate and the effective annual interest rate for bonds
paying semiannual interest.
3
For an excellent discussion of how to value semiannual payments, see J. T. Lindley, B. P. Helms, and M. Haddad,
“A Measurement of the Errors in Intra-Period Compounding and Bond Valuation,” The Financial Review 22 (February 1987).
We benefited from several conversations with the authors of this article.
Corporate Finance,
Seventh Edition
110
Budgeting
Stocks
Companies, 2004
5.3 Bond Concepts
We complete our discussion on bonds by considering two concepts concerning them. First,
we examine the relationship between interest rates and bond prices. Second, we define the
concept of yield to maturity.
Interest Rates and Bond Prices
The above discussion on level-coupon bonds allows us to relate bond prices to interest rates.
Consider the following example.
EXAMPLE
The interest rate is 10 percent. A two-year bond with a 10-percent coupon pays interest of
$100 ($1,000 10%). For simplicity, we assume that the interest is paid annually. The bond is priced
at its face value of $1,000:
$1,000 $100 $1,000 $100
(1.10) 2
1.10
If the interest rate unexpectedly rises to 12 percent, the bond sells at
$966.20 $100 $1,000 $100
(1.12) 2
1.12
Because $966.20 is below $1,000, the bond is said to sell at a discount. This is a sensible result.
Now that the interest rate is 12 percent, a newly issued bond with a 12-percent coupon rate will sell
at $1,000.This newly issued bond will have coupon payments of $120 (0.12 $1,000). Because our
bond has interest payments of only $100, investors will pay less than $1,000 for it.
If interest rates fell to 8 percent, the bond would sell at
$1,035.67 $100 $1,000 $100
(1.08) 2
1.08
Because $1,035.67 is above $1,000, the bond is said to sell at a premium.
Thus, we find that bond prices fall with a rise in interest rates and rise with a fall in
interest rates. Furthermore, the general principle is that a level-coupon bond sells in the
following ways.
1. At the face value of $1,000 if the coupon rate is equal to the marketwide interest rate.
2. At a discount if the coupon rate is below the marketwide interest rate.
3. At a premium if the coupon rate is above the marketwide interest rate.
Yield to Maturity
Let’s now consider the previous example in reverse. If our bond is selling at $1,035.67,
what return is a bondholder receiving? This can be answered by considering the following
equation:
$1,035.67 $100 $1,000 $100
(1 y) 2
1y
The unknown, y, is the discount rate that equates the price of the bond with the discounted
value of the coupons and face value. Our earlier work implies that y 8%. Thus, traders
73
74
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
111
The Present Value Formulas for Bonds
Pure Discount Bonds
PV F
(1 r) T
Level-Coupon Bonds
PV C
冤 r r (1 r) 冥 (1 r)
1
1
F
T
T
C ATr F
(1 r) T
where F is typically $1,000 for a level-coupon bond.
Consols
PV C
r
state that the bond is yielding an 8-percent return. Bond traders also state that the bond has
a yield to maturity of 8 percent. The yield to maturity is frequently called the bond’s yield
for short. So we would say the bond with its 10-percent coupon is priced to yield 8 percent
at $1,035.67.
Bond Market Reporting
Almost all corporate bonds are traded by institutional investors and are traded on the
over-the-counter market (OTC for short). There is a corporate bond market associated
with the New York Stock Exchange. This bond market is mostly a retail market for individual investors for smaller trades. It represents a very small fraction of total corporate
bond trading.
Table 5.1 reproduces some bond data that can be found in The Wall Street Journal on any
particular day. At the bottom of the list you will find AT&T and an entry AT&T 81⁄8兾22. This
entry represents AT&T bonds that mature in the year 2022 and have a coupon rate of 81⁄8.
The coupon rate means 81⁄8 percent of the par value (or face value) of $1,000. Therefore, the
annual coupon for AT&T bonds is $81.25.
TABLE 5.1
Bond Market
Reporting
Bonds
7
AMF 10 ⁄8 06
AMR 9s16
ATT 51⁄8 01
ATT 71⁄8 02
ATT 61⁄2 02
ATT 63⁄4 04
ATT 55⁄8 04
ATT 71⁄2 06
ATT 73⁄4 07
ATT 6s09
ATT 81⁄8 22
Cur. Yld.
Vol.
Close
25.3
8.8
5.2
7.1
6.6
6.9
6.0
7.4
7.6
6.7
8.1
10
25
30
55
50
52
138
60
83
40
97
43
102
98.50
100.13
99
97.75
94.38
100.75
101.50
89
100
Net Chg.
.38
.13
.13
.88
.38
.50
.50
.63
.38
Corporate Finance,
Seventh Edition
112
Budgeting
Stocks
75
Companies, 2004
Under the heading “Close,” you will find the last price for the AT&T bonds at the close
of this particular day. The price is quoted as a percentage of the par value. So the last price
for the AT&T bonds on this particular day was 100 percent of $1,000 or $1,000.00. This
bond is trading at a price less than its par value, and so it is trading at a “discount.” The last
column is “Net Chg.” AT&T bonds traded up from the day before by .38 of 1 percent
(a rounded .375, or 1⁄8). The AT&T bonds have a current yield of 8.1 percent. The current
yield is simply the current coupon divided by the current price, or 81.25 divided by 1,000,
equal to 8.1 percent (rounded to one decimal place).
You should know from our discussion of bond yields that the current yield is not the
same thing as the bonds’ yield to maturity. The yield to maturity is not usually reported
on a daily basis by the financial press. The “Vol” column is the daily volume of 97. This
is the number of bonds that were traded on the New York Stock Exchange on this particular day.
Concept
Questions
1. What is the relationship between interest rates and bond prices?
2. How does one calculate the yield to maturity on a bond?
5.4 The Present Value of Common Stocks
Dividends versus Capital Gains
Our goal in this section is to value common stocks. We learned in the previous chapter that
an asset’s value is determined by the present value of its future cash flows. A stock provides
two kinds of cash flows. First, most stocks pay dividends on a regular basis. Second, the
stockholder receives the sale price when she sells the stock. Thus, in order to value common stocks, we need to answer an interesting question: Is the value of a stock equal to
1. The discounted present value of the sum of next period’s dividend plus next period’s
stock price, or
2. The discounted present value of all future dividends?
This is the kind of question that students would love to see on a multiple-choice exam, because both (1) and (2) are right.
To see that (1) and (2) are the same, let’s start with an individual who will buy the stock
and hold it for one year. In other words, she has a one-year holding period. In addition, she
is willing to pay P0 for the stock today. That is, she calculates
P0 Div1
P
1
1r 1r
(5.1)
Div1 is the dividend paid at year’s end and P1 is the price at year’s end. P0 is the PV of the
common-stock investment. The term in the denominator, r, is the discount rate of the stock.
It will be equal to the interest rate in the case where the stock is riskless. It is likely to be
greater than the interest rate in the case where the stock is risky.
That seems easy enough, but where does P1 come from? P1 is not pulled out of thin air.
Rather, there must be a buyer at the end of year 1 who is willing to purchase the stock
for P1. This buyer determines price by
P1 Div2
P
2
1r 1r
(5.2)
76
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
113
Substituting the value of P1 from (5.2) into equation (5.1) yields
1
Div2 P2
Div1 1r
1r
Div2
Div1
P2
1 r (1 r) 2 (1 r) 2
冤
P0 冢
冣冥
(5.3)
We can ask a similar question for formula (5.3): Where does P2 come from? An investor
at the end of year 2 is willing to pay P2 because of the dividend and stock price at year 3.
This process can be repeated ad nauseam.4 At the end, we are left with
P0 Div1
Divt
Div2
Div3
.. . 2
3
(1
(1
(1
1r
r)
r)
r) t
t1
兺
(5.4)
Thus the value of a firm’s common stock to the investor is equal to the present value of all
of the expected future dividends.
This is a very useful result. A common objection to applying present value analysis to
stocks is that investors are too shortsighted to care about the long-run stream of dividends.
These critics argue that an investor will generally not look past his or her time horizon.
Thus, prices in a market dominated by short-term investors will reflect only near-term dividends. However, our discussion shows that a long-run dividend-discount model holds
even when investors have short-term time horizons. Although an investor may want to cash
out early, she must find another investor who is willing to buy. The price this second investor pays is dependent on dividends after his date of purchase.
Valuation of Different Types of Stocks
The above discussion shows that the value of the firm is the present value of its future dividends. How do we apply this idea in practice? Equation (5.4) represents a very general
model and is applicable regardless of whether the level of expected dividends is growing,
fluctuating, or constant. The general model can be simplified if the firm’s dividends are
expected to follow some basic patterns: (1) zero growth, (2) constant growth, and (3) differential growth. These cases are illustrated in Figure 5.2.
Case 1 (Zero Growth)
The value of a stock with a constant dividend is given by
P0 Div1
Div2
Div
...
1 r (1 r) 2
r
Here it is assumed that Div1 Div2 . . . Div. This is just an application of the perpetuity formula of the previous chapter.
Case 2 (Constant Growth)
End of Year
Dividend
Dividends grow at rate g, as follows:
1
2
3
4
Div
Div(1 g)
Div(1 g)
2
...
Div(1 g)
3
Note that Div is the dividend at the end of the first period.
4
This procedure reminds us of the physicist lecturing on the origins of the universe. He was approached by an elderly gentleman
in the audience who disagreed with the lecture. The attendee said that the universe rests on the back of a huge turtle. When the
physicist asked what the turtle rested on, the gentleman said another turtle. Anticipating the physicist’s objections, the attendee
said, “Don’t tire yourself out, young fellow. It’s turtles all the way down.”
Corporate Finance,
Seventh Edition
114
Budgeting
Companies, 2004
Stocks
FIGURE 5.2
Dividends per share
Low growth
g2
Zero-Growth,
Constant-Growth,
and DifferentialGrowth Patterns
Differential growth
g1 g2
Constant growth
High growth
g1
Zero growth
g=0
Years
1
2
3
4
5
6
7
8
9
10
Dividend-growth models
Div
r
Div
Constant growth: P0 rg
Zero growth: P0 T
Differential growth: P0 兺
t1
EXAMPLE
DivT1
Div(1 g1 ) t
r g2
(1 r) t
(1 r) T
Hampshire Products will pay a dividend of $4 per share a year from now. Financial analysts believe
that dividends will rise at 6 percent per year for the foreseeable future. What is the dividend per
share at the end of each of the first five years?
End of Year
Dividend
1
2
3
4
5
$4.00
$4 (1.06)
$4.24
$4 (1.06)2
$4.4944
$4 (1.06)3
$4.7641
$4 (1.06)4
$5.0499
The value of a common stock with dividends growing at a constant rate is
P0 Div
Div(1 g) Div(1 g) 2 Div(1 g) 3 . . .
(1 r) 2
(1 r) 3
(1 r) 4
1r
Div
rg
where g is the growth rate. Div is the dividend on the stock at the end of the first period. This is the
formula for the present value of a growing perpetuity, which we derived in the previous chapter.
EXAMPLE
Suppose an investor is considering the purchase of a share of the Utah Mining Company. The stock
will pay a $3 dividend a year from today. This dividend is expected to grow at 10 percent per year
(g 10%) for the foreseeable future. The investor thinks that the required return (r) on this stock
is 15 percent, given her assessment of Utah Mining’s risk. (We also refer to r as the discount rate of
the stock.) What is the value of a share of Utah Mining Company’s stock?
77
78
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
115
Using the constant growth formula of case 2, we assess the value to be $60:
$60 $3
0.15 0.10
P0 is quite dependent on the value of g. If g had been estimated to be 121⁄2 percent, the value of
the share would have been
$120 $3
0.15 0.125
The stock price doubles (from $60 to $120) when g only increases 25 percent (from 10 percent to
12.5 percent). Because of P0’s dependency on g, one must maintain a healthy sense of skepticism
when using this constant growth of dividends model.
Furthermore, note that P0 is equal to infinity when the growth rate, g, equals the discount rate, r.
Because stock prices do not grow infinitely, an estimate of g greater than r implies an error in estimation. More will be said of this point later.
Case 3 (Differential Growth) In this case, an algebraic formula would be too unwieldy.
Instead, we present examples.
EXAMPLE
FIGURE 5.3
Consider the stock of Elixir Drug Company, which has a new back-rub ointment and is enjoying
rapid growth.The dividend for a share of stock a year from today will be $1.15. During the next four
years, the dividend will grow at 15 percent per year (g1 15%). After that, growth (g2) will be equal
to 10 percent per year. Can you calculate the present value of the stock if the required return (r) is
15 percent?
Figure 5.3 displays the growth in the dividends.We need to apply a two-step process to discount
these dividends.We first calculate the net present value of the dividends growing at 15 percent per
annum.That is, we first calculate the present value of the dividends at the end of each of the first five
years. Second, we calculate the present value of the dividends beginning at the end of year 6.
Dividends
Growth in Dividends
for Elixir Drug
Company
10% growth rate
15% growth rate
$2.9449
$2.6772
$2.4338
$2.0114 $2.2125
$1.7490
$1.5209
$1.3225
$1.15
End of year
1
2
3
4
5
6
7
8
9
10
Corporate Finance,
Seventh Edition
116
Budgeting
Companies, 2004
Stocks
Calculate Present Value of First Five Dividends
years 1 through 5 is as follows:
Future
Year
Growth
Rate (g1)
1
2
3
4
5
Years 1–5
The present value of dividend payments in
Expected
Dividend
Present
Value
0.15
$1.15
$1
0.15
1.3225
1
0.15
1.5209
1
0.15
1.7490
1
0.15
2.0114
1
The present value of dividends $5
The growing-annuity formula of the previous chapter could normally be used in this step. However,
note that dividends grow at 15 percent, which is also the discount rate. Since g r, the growingannuity formula cannot be used in this example.
Calculate Present Value of Dividends Beginning at End of Year 6 This is the procedure
for deferred perpetuities and deferred annuities that we mentioned in the previous chapter. The
dividends beginning at the end of year 6 are
End of Year
Dividend
6
7
8
Div5 (1 g2)
$2.0114 1.10
$2.2125
Div5 (1 g2)
2.0114 (1.10)2
$2.4338
2
9
Div5 (1 g2)
2.0114 (1.10)3
$2.6772
3
Div5 (1 g2)4
2.0114 (1.10)4
$2.9449
As stated in the previous chapter, the growing-perpetuity formula calculates present value as of one
year prior to the first payment. Because the payment begins at the end of year 6, the present value
formula calculates present value as of the end of year 5.
The price at the end of year 5 is given by
P5 Div6
$2.2125
r g2 0.15 0.10
$44.25
The present value of P5 at the end of year 0 is
P5
$44.25
$22
(1 r) 5 (1.15) 5
The present value of all dividends as of the end of year 0 is $27 ($22 $5).
5.5 Estimates of Parameters in the Dividend-Discount Model
The value of the firm is a function of its growth rate, g, and its discount rate, r. How does
one estimate these variables?
Where Does g Come From?
The previous discussion on stocks assumed that dividends grow at the rate g. We now want
to estimate this rate of growth. This section extends the discussion of growth contained in
Chapter 3. Consider a business whose earnings next year are expected to be the same as
earnings this year unless a net investment is made. This situation is likely to occur, because
79
80
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
117
net investment is equal to gross, or total, investment less depreciation. A net investment of
zero occurs when total investment equals depreciation. If total investment is equal to depreciation, the firm’s physical plant is maintained, consistent with no growth in earnings.
Net investment will be positive only if some earnings are not paid out as dividends, that
is, only if some earnings are retained.5 This leads to the following equation:
Earnings
next
year
Earnings
this
year
Retained
Return on
earnings
retained
this year
earnings
Increase in earnings
(5.5)
The increase in earnings is a function of both the retained earnings and the return on the
retained earnings.
We now divide both sides of (5.5) by earnings this year, yielding
冢
Earnings next year Earnings this year
Retained earnings this year
Earnings this year
Earnings this year
Earnings this year
Return on retained earnings
冣
(5.6)
The left-hand side of (5.6) is simply one plus the growth rate in earnings, which we write
as 1 g.6 The ratio of retained earnings to earnings is called the retention ratio. Thus, we
can write
1 g 1 Retention ratio Return on retained earnings
(5.7)
It is difficult for a financial analyst to determine the return to be expected on currently
retained earnings, because the details on forthcoming projects are not generally public information. However, it is frequently assumed that the projects selected in the current year
have an anticipated return equal to returns from projects in other years. Here, we can estimate the anticipated return on current retained earnings by the historical return on equity,
or ROE. After all, ROE is simply the return on the firm’s entire equity, which is the return
on the cumulation of all the firm’s past projects.7
From (5.7), we have a simple way to estimate growth:
Formula for Firm’s Growth Rate:
g Retention ratio Return on retained earnings
EXAMPLE
(5.8)
Pagemaster Enterprises just reported earnings of $2 million. It plans to retain 40 percent of its
earnings.The historical return on equity (ROE) has been 0.16, a figure that is expected to continue
into the future. How much will earnings grow over the coming year?
We first perform the calculation without reference to equation (5.8).Then we use (5.8) as a check.
5
We ignore the possibility of the issuance of stocks or bonds in order to raise capital. These possibilities are considered in later
chapters.
6
Previously g referred to growth in dividends. However, the growth in earnings is equal to the growth rate in dividends in this
context, because as we will presently see, the ratio of dividends to earnings is held constant. In fact, you have probably figured
out that g is the sustainable growth rate introduced in Chapter 3.
7
Students frequently wonder whether return on equity (ROE) or return on assets (ROA) should be used here. ROA and ROE
are identical in our model because debt financing is ignored. However, most real-world firms have debt. Because debt is treated in
later chapters, we are not yet able to treat this issue in depth now. Suffice it to say that ROE is the appropriate rate, because both
ROE for the firm as a whole and the return to equityholders from a future project are calculated after interest has been deducted.
Corporate Finance,
Seventh Edition
118
Budgeting
Stocks
81
Companies, 2004
Calculation without Reference to Equation (5.8) The firm will retain $800,000 (40% $2 million). Assuming that historical ROE is an appropriate estimate for future returns, the anticipated increase in earnings is
$800,000 0.16 $128,000
The percentage growth in earnings is
Change in earnings $128,000
0.064
Total earnings
$2 million
This implies that earnings in one year will be $2,128,000 ($2,000,000 1.064).
Check Using Equation (5.8)
We use g Retention ratio ROE. We have
g 0.4 0.16 0.064
Where Does r Come From?
In this section, we want to estimate r, the rate used to discount the cash flows of a particular stock. There are two methods developed by academics. We present one method below
but must defer the second until we give it extensive treatment in later chapters.
The first method begins with the concept that the value of a growing perpetuity is
P0 Div
rg
Solving for r, we have
r
Div
g
P0
(5.9)
As stated earlier, Div refers to the dividend to be received one year hence.
Thus, the discount rate can be broken into two parts. The ratio, Div兾P0, places the dividend return on a percentage basis, frequently called the dividend yield. The second term, g,
is the growth rate of dividends.
Because information on both dividends and stock price is publicly available, the first
term on the right-hand side of equation (5.9) can be easily calculated. The second term on
the right-hand side, g, can be estimated from (5.8).
EXAMPLE
Pagemaster Enterprises, the company examined in the previous example, has 1,000,000 shares of
stock outstanding. The stock is selling at $10.What is the required return on the stock?
Because the retention ratio is 40 percent, the payout ratio is 60 percent (1 Retention ratio).
The payout ratio is the ratio of dividends/earnings. Because earnings a year from now will be
$2,128,000 ($2,000,000 1.064), dividends will be $1,276,800 (0.60 $2,128,000). Dividends per
share will be $1.28 ($1,276,800兾1,000,000). Given our previous result that g 0.064, we calculate
r from (5.9) as follows:
0.192 $1.28
0.064
$10.00
A Healthy Sense of Skepticism
It is important to emphasize that our approach merely estimates g; our approach does not
determine g precisely. We mentioned earlier that our estimate of g is based on a number of
82
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
119
assumptions. For example, we assume that the return on reinvestment of future retained
earnings is equal to the firm’s past ROE. We assume that the future retention ratio is equal to
the past retention ratio. Our estimate for g will be off if these assumptions prove to be wrong.
Unfortunately, the determination of r is highly dependent on g. For example, if g is estimated to be 0, r equals 12.8 percent ($1.28兾$10.00). If g is estimated to be 12 percent,
r equals 24.8 percent ($1.28兾$10.00 12%). Thus, one should view estimates of r with a
healthy sense of skepticism.
Because of the preceding, some financial economists generally argue that the estimation
error for r or a single security is too large to be practical. Therefore, they suggest calculating the average r for an entire industry. This r would then be used to discount the dividends
of a particular stock in the same industry.
One should be particularly skeptical of two polar cases when estimating r for individual
securities. First, consider a firm currently paying no dividend. The stock price will be above
zero because investors believe that the firm may initiate a dividend at some point or the firm
may be acquired at some point. However, when a firm goes from no dividends to a positive
number of dividends, the implied growth rate is infinite. Thus, equation (5.9) must be used
with extreme caution here, if at all—a point we emphasize later in this chapter.
Second, we mentioned earlier that the value of the firm is infinite when g is equal to r.
Because prices for stocks do not grow infinitely, an analyst whose estimate of g for a particular firm is equal to or above r must have made a mistake. Most likely, the analyst’s high
estimate for g is correct for the next few years. However, firms simply cannot maintain an
abnormally high growth rate forever. The analyst’s error was to use a short-run estimate
of g in a model requiring a perpetual growth rate.
5.6 Growth Opportunities
We previously spoke of the growth rate of dividends. We now want to address the related
concept of growth opportunities. Imagine a company with a level stream of earnings per
share in perpetuity. The company pays all of these earnings out to stockholders as dividends. Hence,
EPS Div
where EPS is earnings per share and Div is dividends per share. A company of this type is
frequently called a cash cow.
From the perpetuity formula of the previous chapter, the value of a share of stock is:
Value of a Share of Stock When Firm Acts as a Cash Cow:
EPS Div
r
r
where r is the discount rate on the firm’s stock.
This policy of paying out all earnings as dividends may not be the optimal one. Many
firms have growth opportunities, that is, opportunities to invest in profitable projects.
Because these projects can represent a significant fraction of the firm’s value, it would be
foolish to forgo them in order to pay out all earnings as dividends.
Although firms frequently think in terms of a set of growth opportunities, let’s focus on
only one opportunity, that is, the opportunity to invest in a single project. Suppose the firm
retains the entire dividend at date 1 in order to invest in a particular capital budgeting project. The net present value per share of the project as of date 0 is NPVGO, which stands for
the net present value (per share) of the growth opportunity.
Corporate Finance,
Seventh Edition
120
Budgeting
Stocks
83
Companies, 2004
What is the price of a share of stock at date 0 if the firm decides to take on the project at
date 1? Because the per share value of the project is added to the original stock price, the
stock price must now be:
Stock Price after Firm Commits to New Project:
EPS
NPVGO
r
(5.10)
Thus, equation (5.10) indicates that the price of a share of stock can be viewed as the
sum of two different items. The first term (EPS兾r) is the value of the firm if it rested on its
laurels, that is, if it simply distributed all earnings to the stockholders. The second term is
the additional value if the firm retains earnings in order to fund new projects.
EXAMPLE
Sarro Shipping, Inc., expects to earn $1 million per year in perpetuity if it undertakes no new investment opportunities. There are 100,000 shares of stock outstanding, so earnings per share equal
$10 ($1,000,000兾100,000).The firm will have an opportunity at date 1 to spend $1,000,000 in a new
marketing campaign.The new campaign will increase earnings in every subsequent period by $210,000
(or $2.10 per share).This is a 21-percent return per year on the project.The firm’s discount rate is
10 percent. What is the value per share before and after deciding to accept the marketing campaign?
The value of a share of Sarro Shipping before the campaign is
Value of a Share of Sarro When Firm Acts as a Cash Cow:
EPS $10
$100
r
0.1
The value of the marketing campaign as of date 1 is:
Value of Marketing Campaign at Date 1:
$1,000,000 $210,000
$1,100,000
0.1
(5.11)
Because the investment is made at date 1 and the first cash inflow occurs at date 2, equation (5.11)
represents the value of the marketing campaign as of date 1.We determine the value at date 0 by
discounting back one period as follows:
Value of Marketing Campaign at Date 0:
$1,100,000
$1,000,000
1.1
Thus, NPVGO per share is $10 ($1,000,000兾100,000).
The price per share is
EPS兾r NPVGO $100 $10 $110
The calculation can also be made on a straight net-present-value basis. Because all the
earnings at date 1 are spent on the marketing effort, no dividends are paid to stockholders
at that date. Dividends in all subsequent periods are $1,210,000 ($1,000,000 $210,000).
In this case, $1,000,000 is the annual dividend when Sarro is a cash cow. The additional
contribution to the dividend from the marketing effort is $210,000. Dividends per share are
$12.10 ($1,210,000兾100,000). Because these dividends start at date 2, the price per share
at date 1 is $121 ($12.10兾0.1). The price per share at date 0 is $110 ($121兾1.1).
84
Corporate Finance,
Seventh Edition
Budgeting
Stocks
Companies, 2004
121
Note that value is created in this example because the project earned a 21-percent rate
of return when the discount rate was only 10 percent. No value would have been created
had the project earned a 10-percent rate of return. The NPVGO would have been zero, and
value would have been negative had the project earned a percentage return below 10 percent. The NPVGO would be negative in that case.
Two conditions must be met in order to increase value.
1. Earnings must be retained so that projects can be funded.8
2. The projects must have positive net present value.
Surprisingly, a number of companies seem to invest in projects known to have negative
net present values. For example, Jensen has pointed out that, in the late 1970s, oil companies
and tobacco companies were flush with cash.9 Due to declining markets in both industries,
high dividends and low investment would have been the rational action. Unfortunately, a
number of companies in both industries reinvested heavily in what were widely perceived
to be negative-NPVGO projects. A study by McConnell and Muscarella documents this perception.10 They find that, during the 1970s, the stock prices of oil companies generally
decreased on the days that announcements of increases in exploration and development
were made.
Given that NPV analysis (such as that presented in the previous chapter) is common
knowledge in business, why would managers choose projects with negative NPVs? One
conjecture is that some managers enjoy controlling a large company. Because paying dividends in lieu of reinvesting earnings reduces the size of the firm, some managers find it
emotionally difficult to pay high dividends.
Growth in Earnings and Dividends versus Growth
Opportunities
As mentioned earlier, a firm’s value increases when it invests in growth opportunities with
positive NPVGOs. A firm’s value falls when it selects opportunities with negative NPVGOs.
However, dividends grow whether projects with positive NPVs or negative NPVs are
selected. This surprising result can be explained by the following example.
EXAMPLE
Lane Supermarkets, a new firm, will earn $100,000 a year in perpetuity if it pays out all its earnings
as dividends. However, the firm plans to invest 20 percent of its earnings in projects that earn 10 percent per year. The discount rate is 18 percent. An earlier formula tells us that the growth rate of
dividends is
g Retention ratio Return on retained earnings 0.2 0.10 2%
For example, in this first year of the new policy, dividends are $80,000 [(1 0.2) $100,000]. Dividends next year are $81,600 ($80,000 1.02). Dividends the following year are $83,232 [$80,000 (1.02)2] and so on. Because dividends represent a fixed percentage of earnings, earnings must grow
at 2 percent a year as well.
8
Later in the text we speak of issuing stock or debt in order to fund projects.
9
M. C. Jensen, “Agency Costs of Free Cash Flows, Corporate Finance and Takeovers,” American Economic Review
(May 1986).
10
J. J. McConnell and C. J. Muscarella, “Corporate Capital Expenditure Decisions and the Market Value of the Firm,” Journal of
Corporate Finance,
Seventh Edition
122
Budgeting
Stocks
Companies, 2004
However, note that the policy reduces value because the rate of return on the projects of 10 percent is less than the discount rate of 18 percent.That is, the firm would have had a higher value at
date 0 if it had a policy of paying all its earnings out as dividends.Thus, a policy of investing in projects with negative NPVs rather than paying out earnings as dividends will lead to growth in dividends and earnings, but will reduce value.
Dividends or Earnings: Which to Discount?
As mentioned earlier, this chapter applied the growing-perpetuity formula to the valuation
of stocks. In our application, we discounted dividends, not earnings. This is sensible since
investors select a stock for what they can get out of it. They only get two things out of a
stock: dividends and the ultimate sales price, which is determined by what future investors
expect to receive in dividends.
The calculated stock price would be too high were earnings to be discounted instead of
dividends. As we saw in our estimation of a firm’s growth rate, only a portion of earnings
goes to the stockholders as dividends. The remainder is retained to generate future dividends. In our model, retained earnings are equal to the firm’s investment. To discount earnings instead of dividends would be to ignore the investment that a firm must make today in
order to generate future returns.
The No-Dividend Firm
Students frequently ask the following questions: If the dividend-discount model is correct,
why aren’t no-dividend stocks selling at zero? This is a good question and gets at the goals of
the firm. A firm with many growth opportunities is faced with a dilemma. The firm can pay
out dividends now, or it can forgo dividends now so that it can make investments that will
generate even greater dividends in the future.11 This is often a painful choice, because a strategy of dividend deferment may be optimal yet unpopular among certain stockholders.
Many firms choose to pay no dividends—and these firms sell at positive prices.12 Rational shareholders believe that they will either receive dividends at some point or they will
receive something just as good. That is, the firm will be acquired in a merger, with the
stockholders receiving either cash or shares of stock at that time.
Of course, the actual application of the dividend-discount model is difficult for firms of
this type. Clearly, the model for constant growth of dividends does not apply. Though the
differential growth model can work in theory, the difficulties of estimating the date of first
dividend, the growth rate of dividends after that date, and the ultimate merger price make
application of the model quite difficult in reality.
Empirical evidence suggests that firms with high growth rates are likely to pay lower
dividends, a result consistent with the above analysis. For example, consider McDonald’s
Corporation. The company started in the 1950s and grew rapidly for many years. It paid its
first dividend in 1975, though it was a billion-dollar company (in both sales and market
value of stockholder’s equity) prior to that date. Why did it wait so long to pay a dividend?
It waited because it had so many positive growth opportunities, that is, additional locations
for new hamburger outlets, to take advantage of.
Utilities are an interesting contrast because, as a group, they have few growth opportunities. Because of this, they pay out a large fraction of their earnings in dividends. For example, Consolidated Edison, Sempra Energy, and Kansas City Power and Light have had
payout ratios of over 70 percent in many recent years.
11
A third alternative is to issue stock so that the firm has enough cash both to pay dividends and to invest. This possibility is
explored in a later chapter.
12
For example, most Internet firms, such as Amazon.com, Earthlink, Inc., and Ebay, Inc., pay no dividends.
85
86
Corporate Finance,
Seventh Edition
Budgeting
Stocks
Companies, 2004
123
5.7 The Dividend-Growth Model and the NPVGO
Model (Advanced)
This chapter has revealed that the price of a share of stock is the sum of its price as a cash
cow plus the per-share value of its growth opportunities. The Sarro Shipping example
illustrated this formula using only one growth opportunity. We also used the growingperpetuity formula to price a stock with a steady growth in dividends. When the formula is
applied to stocks, it is typically called the dividend-growth model. A steady growth in dividends results from a continual investment in growth opportunities, not just investment in
a single opportunity. Therefore, it is worthwhile to compare the dividend-growth model
with the NPVGO model when growth occurs through continual investing.
EXAMPLE
Cumberland Book Publishers has EPS of $10 at the end of the first year, a dividend-payout ratio
of 40 percent, a discount rate of 16 percent, and a return on its retained earnings of 20 percent.
Because the firm retains some of its earnings each year, it is selecting growth opportunities each
year. This is different from Sarro Shipping, which had a growth opportunity in only one year. We
wish to calculate the price per share using both the dividend-growth model and the NPVGO
model.
The Dividend-Growth Model
The dividends at date 1 are 0.40 $10 $4 per share. The retention ratio is 0.60
(1 0.40), implying a growth rate in dividends of 0.12 (0.60 0.20).
From the dividend-growth model, the price of a share of stock is
Div
$4
$100
r g 0.16 0.12
The NPVGO Model
Using the NPVGO model, it is more difficult to value a firm with growth opportunities each
year (like Cumberland) than a firm with growth opportunities in only one year (like Sarro).
In order to value according to the NPVGO model, we need to calculate on a per-share basis
(1) the net present value of a single growth opportunity, (2) the net present value of all growth
opportunities, and (3) the stock price if the firm acts as a cash cow, that is, the value of the firm
without these growth opportunities. The value of the firm is the sum of (2) (3).
1. Value per Share of a Single Growth Opportunity Out of the earnings per share of
$10 at date 1, the firm retains $6 (0.6 $10) at that date. The firm earns $1.20 ($6 0.20) per
year in perpetuity on that $6 investment. The NPV from the investment is
Per-Share NPV Generated from Investment at Date 1:
$1.20
$6 $1.50
0.16
(5.12)
That is, the firm invests $6 in order to reap $1.20 per year on the investment. The earnings
are discounted at 0.16, implying a value per share from the project of $1.50. Because the
investment occurs at date 1 and the first cash flow occurs at date 2, $1.50 is the value of the
investment at date 1. In other words, the NPV from the date 1 investment has not yet been
brought back to date 0.
Corporate Finance,
Seventh Edition
124
Budgeting
Stocks
Companies, 2004
2. Value per Share of All Opportunities As pointed out earlier, the growth rate of
earnings and dividends is 12 percent. Because retained earnings are a fixed percentage of
total earnings, retained earnings must also grow at 12 percent a year. That is, retained earnings at date 2 are $6.72 ($6 1.12), retained earnings at date 3 are $7.5264 [$6 (1.12)2],
and so on.
Let’s analyze the retained earnings at date 2 in more detail. Because projects will always
earn 20 percent per year, the firm earns $1.344 ($6.72 0.20) in each future year on the
$6.72 investment at date 2.
The NPV from the investment is
NPV per Share Generated from Investment at Date 2:
$6.72 $1.344
$1.68
0.16
(5.13)
$1.68 is the NPV as of date 2 of the investment made at date 2. The NPV from the date 2
investment has not yet been brought back to date 0.
Now consider the retained earnings at date 3 in more detail. The firm earns $1.5053
($7.5264 0.20) per year on the investment of $7.5264 at date 3.
The NPV from the investment is
NPV per Share Generated from Investment at Date 3:
$7.5264 $1.5053
$1.882
0.16
(5.14)
From equations (5.12), (5.13), and (5.14), the NPV per share of all of the growth opportunities, discounted back to date 0, is
$1.68
$1.50
$1.882
...
(1.16) 2 (1.16) 3
1.16
(5.15)
Because it has an infinite number of terms, this expression looks quite difficult to compute. However, there is an easy simplification. Note that retained earnings are growing at
12 percent per year. Because all projects earn the same rate of return per year, the NPVs in
(5.12), (5.13), and (5.14) are also growing at 12 percent per year. Hence, we can write
equation (5.15) as
$1.50 $1.50 1.12 $1.50 (1.12) 2 . . .
(1.16) 2
(1.16) 3
1.16
This is a growth perpetuity whose value is
NPVGO $
1.50
$37.50
0.16 0.12
Because the first NPV of $1.50 occurs at date 1, the NPVGO is $37.50 as of date 0. In other
words, the firm’s policy of investing in new projects from retained earnings has an NPV
of $37.50.
3. Value per Share if Firm Is a Cash Cow We now assume that the firm pays out all
of its earnings as dividends. The dividends would be $10 per year in this case. Since there
would be no growth, the value per share would be evaluated by the perpetuity formula:
Div $10
$62.50
r
0.16
87
88
Corporate Finance,
Seventh Edition
Budgeting
Stocks
Companies, 2004
125
Summation
Formula (5.10) states that value per share is the value of a cash cow plus the value of the
growth opportunities. This is
$100 $62.50 $37.50
Hence, value is the same whether calculated by a discounted-dividend approach or a growthopportunities approach. The share prices from the two approaches must be equal, because
the approaches are different yet equivalent methods of applying concepts of present value.
5.8 Price-Earnings Ratio
We argued earlier that one should not discount earnings in order to determine price per
share. Nevertheless, financial analysts frequently relate earnings and price per share, as made
evident by their heavy reliance on the price-earnings (or P/E) ratio.
Our previous discussion stated that
EPS
Price per share NPVGO
r
Dividing by EPS yields
Price per share 1 NPVGO
EPS
r
EPS
The left-hand side is the formula for the price-earnings ratio. The equation shows that the
P/E ratio is related to the net present value of growth opportunities. As an example, consider two firms, each having just reported earnings per share of $1. However, one firm has
many valuable growth opportunities while the other firm has no growth opportunities at all.
The firm with growth opportunities should sell at a higher price, because an investor is buying both current income of $1 and growth opportunities. Suppose that the firm with growth
opportunities sells for $16 and the other firm sells for $8. The $1 earnings per share number appears in the denominator of the P/E ratio for both firms. Thus, the P/E ratio is 16 for
the firm with growth opportunities, but only 8 for the firm without the opportunities.
This explanation seems to hold fairly well in the real world. Electronic and other hightech stocks generally sell at very high P/E ratios (or multiples, as they are often called) because they are perceived to have high growth rates. In fact, some technology stocks sell at
high prices even though the companies have never earned a profit. The P/E ratios of these
companies are infinite. Conversely, railroads, utilities, and steel companies sell at lower
multiples because of the prospects of lower growth.
Of course, the market is merely pricing perceptions of the future, not the future itself.
We will argue later in the text that the stock market generally has realistic perceptions of a
firm’s prospects. However, this is not always true. In the late 1960s, many electronics firms
were selling at multiples of 200 times earnings. The high perceived growth rates did not
materialize, causing great declines in stock prices during the early 1970s. In earlier
decades, fortunes were made in stocks like IBM and Xerox because the high growth rates
were not anticipated by investors. Most recently we have experienced the dot-com collapse
when many Internet stocks were trading at multiples of thousands of times annual earnings.
In fact, most Internet stocks had no earnings.
One of the most puzzling phenomena to American investors has been the high P/E ratios in the Japanese stock market. The average P/E ratio for the Tokyo Stock Exchange has
varied between 40 and 100 in recent years, while the average American stock had a multiple
of around 25 during this time. Our formula indicates that Japanese companies have been
Corporate Finance,
Seventh Edition
126
Budgeting
89
Companies, 2004
Stocks
TABLE 5.2
Country Composite
International P/E
Ratios
United States
Japan
Germany
Britain
France
Canada
Sweden
Italy
1994
1997
2000
24
101
35
18
29
45
52
29
21
44
31
18
25
25
17
22
30
38
31
20
27
21
20
28
SOURCE: Abstracted from “The Global 1000,” Business Week, July 11, 1994, July 7, 1997, and Forbes, July 24, 2000.
perceived to have great growth opportunities. However, American commentators have
frequently suggested that investors in the Japanese markets have been overestimating these
growth prospects.13 This enigma (at least to American investors) can only be resolved with
the passage of time. Some selected country average P/E ratios appear in Table 5.2. You can
see Japan’s P/E ratio has trended down, and today is about the same as for U.S. stocks.
There are two additional factors explaining the P/E ratio. The first is the discount rate, r.
The above formula shows that the P/E ratio is negatively related to the firm’s discount rate. We
have already suggested that the discount rate is positively related to the stock’s risk or variability. Thus, the P/E ratio is negatively related to the stock’s risk. To see that this is a sensible
result, consider two firms, A and B, behaving as cash cows. The stock market expects both
firms to have annual earnings of $1 per share forever. However, the earnings of firm A are
known with certainty while the earnings of firm B are quite variable. A rational stockholder is
likely to pay more for a share of firm A because of the absence of risk. If a share of firm A sells
at a higher price and both firms have the same EPS, the P/E ratio of firm A must be higher.
The second additional factor concerns the firm’s choice of accounting methods. Under current accounting rules, companies are given a fair amount of leeway. For example, consider inventory accounting where either FIFO or LIFO may be used. In an inflationary environment,
FIFO (first in–first out) accounting understates the true cost of inventory and hence inflates reported earnings. Inventory is valued according to more recent costs under LIFO (last in–first
out), implying that reported earnings are lower here than they would be under FIFO. Thus,
LIFO inventory accounting is a more conservative method than FIFO. Similar accounting leeway exists for construction costs (completed-contracts versus percentage-of-completion
methods) and depreciation (accelerated depreciation versus straight-line depreciation).
As an example, consider two identical firms, C and D. Firm C uses LIFO and reports earnings of $2 per share. Firm D uses the less conservative accounting assumptions of FIFO and
reports earnings of $3 per share. The market knows that both firms are identical and prices
both at $18 per share. This price-earnings ratio is 9 ($18兾$2) for firm C and 6 ($18兾$3) for
firm D. Thus, the firm with the more conservative principles has the higher P/E ratio.
This last example depends on the assumption that the market sees through differences in
accounting treatments. A significant portion of the academic community believes that the
market sees through virtually all accounting differences. These academics are adherents of
the hypothesis of efficient capital markets, a theory that we explore in great detail later
in the text. Though many financial people might be more moderate in their beliefs regarding this issue, the consensus view is certainly that many of the accounting differences are
seen through. Thus, the proposition that firms with conservative accountants have high P/E
ratios is widely accepted.
13
It has been suggested that Japanese companies use more conservative accounting practices, thereby creating higher P/E ratios.
This point, which will be examined shortly for firms in general, appears to explain only a small part of Japan’s high multiples.
90
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
127
This discussion argued that the P/E ratio is a function of three different factors. A company’s ratio or multiple is likely to be high if (1) it has many growth opportunities, (2) it
has low risk, and (3) it is accounted for in a conservative manner. While each of the three
factors is important, it is our opinion that the first factor is much more so. Thus, our discussion of growth is quite relevant in understanding price-earnings multiples.
1. What are the three factors determining a firm’s P/E ratio?
Concept
Question
5.9 Stock Market Reporting
The Wall Street Journal, the New York Times, or your own local newspaper provides useful
information on a large number of stocks in several stock exchanges. Table 5.3 reproduces
what has been reported on a particular day for several stocks listed on the New York Stock
Exchange. In Table 5.3, you can easily find the line for General Electric (i.e., “GenElec”).
Reading left to right, the first two numbers are the high and low share prices over the last
52 weeks. For example, the highest price that General Electric traded for at the end of any
particular day over the last 52 weeks was $6050. This is read as 60 and the decimal .50. The
stock symbol for General Electric is GE. Its annual dividend is $0.55. Most dividend-paying
companies such as General Electric pay dividends on a quarterly basis. So the annual dividend is actually the last quarterly dividend of .138 multiplied by 4 (i.e., .138 4 $0.55).
Some firms like GenenTech do not pay dividends. The Div column for GenenTech is
blank. The “Yld” column stands for dividend yield. General Electric’s dividend yield is the
current annual dividend, $0.55, divided by the current closing daily price, which is $5663
(you can find the closing price for this particular day in the next to last column). Note that
$0.55兾5663 ⬵ 1.0 percent. The next column is labeled PE, which is the symbol for the priceearnings ratio. The price-earnings ratio is the closing price divided by the current earnings
per share (based upon the latest quarterly earnings per share multiplied by 4). General
Electric’s price-earnings ratio is 51. If we were financial analysts or investment bankers, we
would say General Electric “sells for 51 times earnings.” The next column is the volume of
shares traded on this particular day (in hundreds). For General Electric, 18,305,100 shares
traded. This was a heavy trading day for General Electric. The last columns are the High, the
Low, and the Last (Close) share prices on this day. The “Net Chg” tells us that the General
Electric closing price of $5663 was lower than its closing price on the previous day by 144. In
other words, the price of General Electric dropped from $5807 to $5663, in one day.
TABLE 5.3
Stock Market Reporting of NYSE-Listed Securities
52 Weeks
Hi
Lo
Stock
Sym
Div
5375
2225
84
245
1544
6494
6050
4394
9463
1906
956
43
6688
250
3625
3821
2938
5694
Gap Inc
GartnerGp
Gateway
Genentech
GenDatacm
GenDynam
GenElec
GenMills
GenMotor
GPS
IT
GTW
DNA
GDC
GD
GE
GIS
GM
.09
1.04
.55
1.10
2.00
Yld
%
PE
Vol
100s
Hi
Lo
Close
.5
...
...
...
...
1.6
1.0
2.9
3.4
15
22
31
dd
dd
17
51
18
7
65172
2331
23354
21468
456
23318
183051
5054
22653
2050
1094
4740
159
425
6481
5769
3794
6113
19
1031
4215
147
4
6344
5531
3731
5838
1925
1094
4462
149
406
6456
5663
3769
5863
Net
Chg
175
...
129
431
025
1
144
013
106
Corporate Finance,
Seventh Edition
128
Concept
Questions
Budgeting
Companies, 2004
Stocks
From Table 5.3:
1. What is the closing price of Gateway, Inc.?
2. What is the PE of Gateway, Inc.?
3. What is the annual dividend of General Motors?
In this chapter we use general present-value formulas from the previous chapter to price bonds and
stock.
1. Pure discount bonds and perpetuities can be viewed as the polar cases of bonds.The value of a
pure discount bond (also called a zero-coupon bond, or simply a zero) is
PV F
(1 r) T
The value of a perpetuity (also called a consol) is
PV C
r
2. Level-payment bonds can be viewed as an intermediate case.The coupon payments form an annuity and the principal repayment is a lump sum.The value of this type of bond is simply the sum
of the values of its two parts.
3. The yield to maturity on a bond is that single rate that discounts the payments on the bond to
its purchase price.
4. A stock can be valued by discounting its dividends.We mention three types of situations:
a. The case of zero growth of dividends.
b. The case of constant growth of dividends.
c. The case of differential growth.
5. An estimate of the growth rate of a stock is needed for formulas (4b) or (4c) above. A useful
estimate of the growth rate is
g Retention ratio Return on retained earnings
6. It is worthwhile to view a share of stock as the sum of its worth, if the company behaves like a
cash cow (the company does no investing), and the value per share of its growth opportunities.
We write the value of a share as
EPS
NPVGO
r
We show that, in theory, share price must be the same whether the dividend-growth model or
the above formula is used.
7. From accounting, we know that earnings are divided into two parts: dividends and retained
earnings. Most firms continually retain earnings in order to create future dividends. One should
not discount earnings to obtain price per share since part of earnings must be reinvested.
Only dividends reach the stockholders and only they should be discounted to obtain share
price.
8. We suggest that a firm’s price-earnings ratio is a function of three factors:
a. The per-share amount of the firm’s valuable growth opportunities.
b. The risk of the stock.
c. The type of accounting method used by the firm.
91
Corporate Finance,
Seventh Edition
Budgeting
Stocks
Companies, 2004
129
premium, 110
pure discount bond, 106
retention ratio, 117
return on equity, 117
yield to maturity, 111
KEY TERMS
coupons, 107
discount, 110
face value, 106
maturity date, 106
payout ratio, 118
SUGGESTED
READING
The best place to look for additional information is in investment textbooks. A good one is:
Bodie, Z.,A. Kane, and A. Marcus. Investments. 5th ed. Burr Ridge, Ill.: Irwin/McGraw-Hill, 2002.
QUESTIONS
& PROBLEMS
5.1
What is the present value of a 10-year, pure discount bond paying $1,000 at maturity if the
appropriate interest rate is:
a. 5 percent
b. 10 percent
c. 15 percent
5.2
Microhard has issued a bond with the following characteristics:
Principal: $1,000
Time to maturity: 20 years
Coupon rate: 8 percent, compounded semiannually
Semiannual payments
Calculate the price of this bond if the stated annual interest rate, compounded semiannually, is:
a. 8 percent
b. 10 percent
c. 6 percent
5.3
Consider a bond with a face value of $1,000.The coupon payment is made semiannually and the
yield on the bond is 12 percent (effective annual yield).How much would you pay for the bond if:
a. The coupon rate is 8 percent and the remaining time to maturity is 20 years?
b. The coupon rate is 10 percent and the remaining time to maturity is 15 years?
5.4
Jay’s Trucking, Inc., has issued an 8 percent, 20-year bond paying interest semiannually. The
bond has a face value of $1,000. If the yield on the bond is 10 percent (effective annual yield),
what is the price of the bond?
5.5
A bond is sold at $923.14 (below its par value of $1,000).The bond matures in 15 years and has
a 10-percent yield, expressed as a stated annual interest rate, compounded semiannually.
What is the coupon rate on the bond if the coupon is paid semiannually? The next payment
occurs six months from today.
5.6
You have just purchased a newly issued $1,000 five-year Vanguard Company bond at par.This
five-year bond pays $60 in interest semiannually. You are also considering the purchase of
another Vanguard Company bond that pays $30 in semiannual interest payments and has six
years remaining before maturity.This bond has a face value of $1,000.
a. What is the yield on the five-year bond (expressed as an effective annual yield)?
b. Assume that the five-year bond and the six-year bond have the same yield.What should
you be willing to pay for the six-year bond?
c. How will your answer in part (b) change if the five-year bond pays $40 in semiannual interest instead of $60? Assume that the five-year bond paying $40 semiannually is purchased at par.
5.7
Consider two bonds, A and B.The coupon rates are 10 percent and the face values are $1,000
for both bonds. Both bonds have annual coupons. Bond A has 20 years to maturity while
bond B has 10 years to maturity.
a. What are the prices of the two bonds if the relevant market interest rate for both bonds
is 10 percent?
b. If the market interest rate increases to 12 percent,what will be the prices of the two bonds?
c. If the market interest rate decreases to 8 percent, what will be the prices of the two bonds?
HOW TO VALUE
BONDS
BOND CONCEPTS
92
Corporate Finance,
Seventh Edition
130
Budgeting
Companies, 2004
Stocks
5.8
a. If the market interest rate unexpectedly increases, what would be the effect on the prices
of long-term bonds? Why?
b. How would a rise in the interest rate affect the general level of stock prices? Why?
5.9
Consider a bond paying an annual coupon of $80 with a face value of $1,000. Calculate the
yield to maturity if the bond has:
a. 20 years remaining to maturity and is priced at $1,200.
b. 10 years remaining to maturity and is priced at $950.
5.10 HexCorp Inc. has two different bonds currently outstanding. Bond A has a face value of
$40,000 and matures in 20 years. The bond makes no payments for the first six years, pays
$2,000 semiannually for the subsequent eight years, and finally pays $2,500 semiannually for
the last six years. Bond B also has a face value of $40,000 and matures in 20 years. However,
it makes no coupon payments over the life of the bond. If the stated annual interest rate is
12 percent, compounded semiannually,
a. What is the current price of Bond A?
b. What is the current price of Bond B?
5.11 Use the following February 11, 2002, Wall Street Journal quotation for AT&T Corp.Which of
the following statement are false?
a. The closing price of the bond with the shortest time to maturity is $1,000.
b. The annual coupon for the bond maturing in 2018 is $90.
c. The price on the day before this quotation (February 9) for the AT&T bond maturing in
2024 is $1,075 per bond contract.
d. The current yield on the AT&T bond maturing in 2004 is 7.125 percent.
e. The AT&T bond maturing in 2004 has a yield to maturity of less than 7.125 percent.
Bonds
ATT 9s 18
ATT 5 1兾8 03
ATT 7 1兾8 04
ATT 8 1兾8 24
Current Yield
Volume
Close
Net Change
?
?
?
?
10
5
193
39
117
100
104.125
107.375
.25
.75
.25
.13 (1兾8)
5.12 The following are selected quotations from The Wall Street Journal on Friday, April 23, 2002.
Which of the following statements about Wilson’s bond are false?
a. The bond maturing in 2003 has a yield to maturity greater than 63兾8 percent.
b. The closing price of the bond with the shortest time to maturity on the day before the
quotation is $1,003.25.
c. The annual coupon payment for the bond maturing in 2016 is $75.
d. The current yield on the Wilson’s bond with the longest time to maturity is 7.29 percent.
e. None of the above.
Bonds
6 3兾8
WILSON
02
WILSON 6 3兾8 03
WILSON 7 1兾4 05
WILSON 7 1兾2 16
THE PRESENT
VALUE OF
COMMON STOCKS
Current Yield
Volume
Close
Net Change
?
?
?
?
76
9
39
225
100.375
98
103.625
102.825
.13 (1兾8)
.5
.13 (1兾8)
.13 (1兾8)
5.13 A common stock just paid an annual dividend of $2 yesterday. The dividend is expected to
grow at 8 percent annually for the next three years, after which it will grow at 4 percent in
perpetuity.The appropriate discount rate is 12 percent.What is the price of the stock?
5.14 Use the following February 12, 2002, Wall Street Journal quotation for Merck & Co. to answer
the next question.
93
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Stocks
131
52 Weeks
Hi
Low
Stock
Sym
Div
120 80.19
Merck
MRK
1.80
Yield
%
PE
?
30
Vol.
100s
Hi
Low
Close
Net
Change
195111
115.9
114.5
115
1.25
Which of the following statements are false?
a. The dividend yield is approximately 1.6 percent.
b. The closing price per share on February 10, 2002, was $113.75.
c. The closing price per share on February 11, 2002, was $115.
d. The earnings per share were about $3.83.
5.15 Examine the following stock quote for Citigroup:
52 Weeks
Hi
Low
Stock
Sym
Div
Yield
%
PE
Vol.
100s
Hi
Low
Close
Net
Change
126.25
72.50
Citigroup
CCI
1.30
1.32
16
20925
98.4
97.8
98.13
.13
The expected growth rate of Citigroup’s dividends is 7 percent per year. According to the
constant-growth dividend model, what is the stock’s required return? Assume that the annual
dividend of $1.30 was paid yesterday.
5.16 You own $100,000 worth of Smart Money stock. One year from now, you will receive a dividend of $2 per share. You will receive a $4 dividend two years from now. You will sell the
stock for $50 per share three years from now. Dividends are taxed at the rate of 28 percent.
Assume there is no capital gains tax. The required rate of return is 15 percent. How many
shares of stock do you own?
5.17 Consider the stock of Davidson Company, which will pay an annual dividend of $2 one year
from today.The dividend will grow at a constant annual rate of 5 percent, forever.The market
requires a 12-percent return on the company’s stock.
a. What is the current price of a share of the stock?
b. What will the stock price be 10 years from today?
5.18 Scubaland, Inc., is experiencing a period of rapid growth. Earnings and dividends per share are
expected to grow at a rate of 18 percent during the next two years, 15 percent in the third
year, and 6 percent thereafter.Yesterday, Scubaland paid a dividend of $1.15. If the required
rate of return on the stock is 12 percent, what is the price of a share of the stock today?
5.19 Calamity Mining Company’s iron ore reserves are being depleted, and its costs of recovering
a declining quantity of ore are rising each year.As a result, the company’s earnings are declining at a rate of 10 percent per year. If the dividend per share to be paid tomorrow is $5 and
the required rate of return is 14 percent, what is the value of the firm’s stock? Assume that
the dividend payments are based on a fixed percentage of the firm’s earnings.
5.20 Pasqually Mineral Water, Inc., will pay a quarterly dividend per share of $1 at the end of each
of the next 12 quarters.Thereafter, the dividend will grow at a quarterly rate of 0.5 percent,
forever. The appropriate rate of return on the stock is 10 percent, compounded quarterly.
What is the current stock price?
5.21 Suppose Amsterdam Foods, Inc., has just paid a dividend of $1.40 per share. Its dividend is expected to grow at 5 percent per year in perpetuity. If the required return is 10 percent, what
is the value of a share of Amsterdam Foods?
5.22 In order to buy back its own shares, Pennzoil Co. has decided to suspend its dividends for the
next two years. It will resume its annual cash dividend of $2.00 in year 3 and year 4.Thereafter, its dividend payments will grow at an annual growth rate of 6 percent, forever. The
required rate of return on Pennzoil’s stock is 16 percent. According to the discounteddividend model, what should Pennzoil’s current share price be?
94
Corporate Finance,
Seventh Edition
132
Budgeting
Stocks
Companies, 2004
5.23 The Webster Co. has just paid a dividend of $5.25 per share. The company will increase its
dividend by 14 percent next year.The company will then reduce its dividend growth rate by
3 percent each year until the dividend reaches the industry average of 5 percent growth.The
company will maintain that dividend growth rate, forever.The required rate of return for the
Webster Co. is 14 percent.What is the price of the stock?
ESTIMATES OF
PARAMETERS IN
THE DIVIDENDDISCOUNT MODEL
5.24 Allen, Inc., is expected to pay equal dividends at the end of each of the next two years.Thereafter, the dividend will grow at a constant annual rate of 4 percent, forever. The current
stock price is $30. What is next year’s dividend payment if the required rate of return is
12 percent?
5.25 The newspaper reported last week that Bradley Enterprises earned $20 million this year.The
report also stated that the firm’s return on equity is 14 percent. Bradley retains 60 percent of
its earnings.
a. What is the firm’s earnings growth rate?
b. What will next year’s earnings be?
5.26 Juggernaut Satellite Corporation earned $10 million for the fiscal year ending yesterday.The
firm also paid out 25 percent of its earnings as dividends yesterday.The firm will continue to
pay out 25 percent of its earnings as annual, end-of-year dividends.The remaining 75 percent
of earnings is retained by the company for use in projects. The company has 1.25 million
shares of common stock outstanding.The current stock price is $30.The historical return on
equity (ROE) of 12 percent is expected to continue in the future.What is the required rate
of return on the stock?
5.27 Four years ago, Bling Diamond, Inc., paid a dividend of $.80 per share. Bling paid a dividend of
$1.66 per share yesterday. Dividends will grow over the next five years at the same rate they
grew over the last four years. Thereafter, dividends will grow at 8 percent per year. The required return on the stock is 18 percent.What will Bling Diamond’s cash dividend be in seven
years?
GROWTH
OPPORTUNITIES
5.28 Rite Bite Enterprises sells toothpicks. Gross revenues last year were $3 million, and total costs
were $1.5 million. Rite Bite has 1 million shares of common stock outstanding. Gross
revenues and costs are expected to grow at 5 percent per year. Rite Bite pays no income
taxes. All earnings are paid out as dividends.
a. If the appropriate discount rate is 15 percent and all cash flows are received at year’s end,
what is the price per share of Rite Bite stock?
b. Rite Bite has decided to produce toothbrushes.The project requires an immediate outlay
of $15 million. In one year, another outlay of $5 million will be needed.The year after that,
net cash inflows will be $6 million.That profit level will be maintained in perpetuity.What
effect will undertaking this project have on the price per share of the stock?
5.29 California Real Estate, Inc., expects to earn $100 million per year in perpetuity if it does not undertake any new projects.The firm has an opportunity to invest $15 million today and $5 million in one year in real estate.The new investment will generate annual earnings of $10 million
in perpetuity, beginning two years from today.The firm has 20 million shares of common stock
outstanding, and the required rate of return on the stock is 15 percent. Land investments are
not depreciable. Ignore taxes.
a. What is the price of a share of stock if the firm does not undertake the new investment?
b. What is the value of the investment?
c. What is the per-share stock price if the firm undertakes the investment?
5.30 The annual earnings of Avalanche Skis Inc. will be $4 per share in perpetuity if the firm makes
no new investments. Under such a situation, the firm would pay out all of its earnings as dividends.Assume the first dividend will be received exactly one year from now.
Alternatively, assume that three years from now, and in every subsequent year in perpetuity, the company can invest 25 percent of its earnings in new projects. Each project will earn
40 percent at year-end, in perpetuity.The firm’s discount rate is 14 percent.
95
Corporate Finance,
Seventh Edition
Budgeting
Stocks
Companies, 2004
133
a. What is the price per share of Avalanche Skis Inc. stock today without the company making the new investment?
b. If Avalanche announces that the new investment will be made, what will the per-share
stock price be today?
PRICE-EARNINGS
RATIO
5.31 Consider Pacific Energy Company and U.S. Bluechips, Inc., both of which reported cash flows
of $800,000 and have 500,000 shares of common stock outstanding.Without new projects,
both firms will continue to generate cash flows of $800,000 in perpetuity. Assume that the
cash flows are equal to earnings.Assume both firms require a 15 percent rate of return.
a. Pacific Energy Company has a new project that will generate additional cash flows of
$100,000 each year in perpetuity. Calculate the P/E ratio of the company.
b. U.S. Bluechips has a new project that will increase cash flows by $200,000 in perpetuity.
Calculate the P/E ratio of the firm.
5.32 (Challenge Question) Lewin Skis Inc. (today) expects to earn $4 per share for each of the
future operating periods (beginning at time 1) if the firm makes no new investments (and returns the earnings as dividends to the shareholders). However, Clint Williams, president and
CEO, has discovered an opportunity to retain (and invest) 25 percent of the earnings beginning three years from today (starting at time 3).This opportunity to invest will continue (for
each period) indefinitely. He expects to earn 40 percent (per year) on this new equity investment (ROE of 40), the return beginning one year after each investment is made. The firm’s
equity discount rate is 14 percent throughout.
a. What is the price per share (now at time 0) of Lewin Skis Inc. stock without making the
new investment?
b. If the new investment is expected to be made, per the preceding information, what would
the value of the stock (per share) be now (at time 0)?
c. What is the expected capital gain yield for the second period, assuming the proposed investment is made? What is the expected capital gain yield for the second period if the proposed investment is not made?
d. What is the expected dividend yield for the second period if the new investment is made?
What is the expected dividend yield for the second period if the new investment is not
made?
VALUATION
OF STOCKS
5.33 ABC Inc. has a P/E ratio of 12 and maintains a dividend payout ratio of 40 percent.The stock
price of ABC Inc. on January 1 is $32.What would the value of stock be if the dividend payout ratio was 60 percent?
5.34 XYZ Inc. has earnings of $10 million and is projected to grow at a constant rate of 5 percent
forever because of the benefits gained from the learning curve. Currently all earnings are paid
out as dividends. The company plans to launch a new project two years from now which
would be completely internally funded and require 20 percent of the earnings that year.The
project would start generating revenues one year after the launch of the project and the earnings from the new project in any year are estimated to be constant at $0.5 million.The company has 10 million shares of stock outstanding. Estimate the value of XYZ stock.The discount
rate is 10 percent.
S&P
PROBLEMS
5.35 Enter the ticker symbol “WMT” for Wal-Mart. Using the most recent balance sheet and income statement under the “Excel Analytics” link, calculate the sustainable growth rate for
Wal-Mart. Now download the “Mthly.Adj. Price” and find the closing stock price for the same
month as the balance sheet and income statement you used.What is the implied required return on Wal-Mart according to the dividend growth model? Does this number make sense?
Why or why not?
5.36 Assume that investors require an 11 percent return on Harley-Davidson (HDI) stock. Under
the “Excel Analytics” link find the “Mthly.Adj. Price” and find the closing price for the month
of the most recent fiscal year-end for HDI. Using this stock price and the EPS for the most recent year, calculate the NPVGO for Harley-Davidson. What is the appropriate P/E ratio for
Harley-Davidson using these calculations?
96
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
7. Net Present Value and
Capital Budgeting
Chapter 7
EXECUTIVE
SUMMARY
Net Present Value and
Capital Budgeting
In late 1990, the Boeing Company announced
its intention to build the Boeing 777, a commercial airplane that could carry up to 390 passengers and fly 7,600 miles.This was expected
to be an enormous undertaking. Analysts believed the up-front investment and research
and development expenditures necessary to
manufacture the Boeing 777 would be as much
as $8 billion. Delivery of the planes was expected to begin in 1995 and to continue for at
least 35 years.Was the 777 a good project for
Boeing? This chapter shows you how to answer this important question.
The previous chapter discussed the basics
of capital budgeting. We now move beyond
these basics into real-world application. We
show you how to use the net present value
(NPV) method and the internal rate of return
(IRR) method for real-world capital budgeting
decisions.
In this chapter, we identify the relevant
cash flows of a project, including initial investment outlays, requirements for working capital, and operating cash flows. We look at the
effects of depreciation and taxes.We examine
the impact of inflation on interest rates and
on a project’s discount rate, and we show why
inflation must be handled consistently in NPV
analysis.
7.1 Incremental Cash Flows
Cash Flows—Not Accounting Income
You may not have thought about it, but there is a big difference between corporate finance
courses and financial accounting courses. Techniques in corporate finance generally use cash
flows, whereas financial accounting generally stresses income or earnings numbers. Certainly, our text has followed this tradition since our net present value techniques discounted
cash flows, not earnings. When considering a single project, we discounted the cash flows
that the firm receives from the project. When valuing the firm as a whole, we discounted
dividends—not earnings—because dividends are the cash flows that an investor receives.
EXAMPLE
178
The Weber-Decker Co. just paid $1 million in cash for a building, as part of a new capital budgeting
project.This entire $1 million is an immediate cash outflow. However, assuming straight-line depreciation over 20 years, only $50,000 ($1 million/20) is considered an accounting expense in the current
year. Current earnings are thereby reduced by only $50,000. The remaining $950,000 is expensed
over the following 19 years. For capital budgeting purposes, the relevant cash outflow at date 0 is the
full $1 million, not the reduction in earnings of only $50,000.
97
98
Corporate Finance,
Seventh Edition
Budgeting
Capital Budgeting
Chapter 7 Net Present Value and Capital Budgeting
Companies, 2004
179
Always discount cash flows, not earnings, when performing a capital budgeting calculation. Earnings do not represent real money. You can’t spend out of earnings, you can’t eat
out of earnings, and you can’t pay dividends out of earnings. You can only do these things
out of cash flow.
In addition, it is not enough to use cash flows. In calculating the NPV of a project, only
cash flows that are incremental to the project should be used. These cash flows are the
changes in the firm’s cash flows that occur as a direct consequence of accepting the project.
That is, we are interested in the difference between the cash flows of the firm with the
project and the cash flows of the firm without the project.
The use of incremental cash flows sounds easy enough, but pitfalls abound in the real
world. We describe below how to avoid some of the pitfalls of determining incremental
cash flows.
Sunk Costs
A sunk cost is a cost that has already occurred. Because sunk costs are in the past, they cannot be changed by the decision to accept or reject the project. Just as we “let bygones be
bygones,” we should ignore such costs. Sunk costs are not incremental cash outflows.
EXAMPLE
The General Milk Company is currently evaluating the NPV of establishing a line of chocolate milk.
As part of the evaluation the company had paid a consulting firm $100,000 to perform a testmarketing analysis.This expenditure was made last year. Is this cost relevant for the capital budgeting
decision now confronting the management of General Milk Company?
The answer is no.The $100,000 is not recoverable, so the $100,000 expenditure is a sunk cost,
or spilled milk. Of course, the decision to spend $100,000 for a marketing analysis was a capital
budgeting decision itself and was perfectly relevant before it was sunk. Our point is that once the
company incurred the expense, the cost became irrelevant for any future decision.
Opportunity Costs
Your firm may have an asset that it is considering selling, leasing, or employing elsewhere
in the business. If the asset is used in a new project, potential revenues from alternative
uses are lost. These lost revenues can meaningfully be viewed as costs. They are called
opportunity costs because, by taking the project, the firm forgoes other opportunities for
using the assets.
EXAMPLE
Suppose the Weinstein Trading Company has an empty warehouse in Philadelphia that can be used
to store a new line of electronic pinball machines. The company hopes to sell these machines to
affluent northeastern consumers. Should the warehouse be considered a cost in the decision to
sell the machines?
The answer is yes.The company could sell the warehouse, if the firm decides not to market the
pinball machines.Thus, the sales price of the warehouse is an opportunity cost in the pinball machine
decision.
Side Effects
Another difficulty in determining incremental cash flows comes from the side effects of
the proposed project on other parts of the firm. A side effect is classified as either erosion
or synergy. Erosion occurs when a new product reduces the sales and, hence, the cash
Corporate Finance,
Seventh Edition
180
Budgeting
Capital Budgeting
Companies, 2004
flows, of existing products. Synergy occurs when a new project increases the cash flows of
existing projects.
EXAMPLE
Suppose the Innovative Motors Corporation (IMC) is determining the NPV of a new convertible
sports car. Some of the customers who would purchase the car are owners of IMC’s compact sedan.
Are all sales and profits from the new convertible sports car incremental?
The answer is no because some of the cash flow represents transfers from other elements of
IMC’s product line.This is erosion, which must be included in the NPV calculation.Without taking
erosion into account, IMC might erroneously calculate the NPV of the sports car to be, say,
$100 million. If half the customers are transfers from the sedan and lost sedan sales have an NPV of
$150 million, the true NPV is $50 million ($100 million $150 million).
IMC is also contemplating the formation of a racing team.The team is forecasted to lose money
for the foreseeable future, with perhaps the best projection showing an NPV of $35 million for the
operation. However, IMC’s managers are aware that the team will likely generate great publicity for
all of IMC’s products. A consultant estimates that the increase in cash flows elsewhere in the firm
has a present value of $65 million. Assuming that the consultant’s estimates of synergy are trustworthy, the net present value of the team is $30 million ($65 million $35 million).The managers
should form the team.
Allocated Costs
Frequently a particular expenditure benefits a number of projects. Accountants allocate this
cost across the different projects when determining income. However, for capital budgeting purposes, this allocated cost should be viewed as a cash outflow of a project only if it
is an incremental cost of the project.
EXAMPLE
Concept
Questions
The Voetmann Consulting Corp. devotes one wing of its suite of offices to a library requiring a cash
outflow of $100,000 a year in upkeep. A proposed capital budgeting project is expected to generate
revenue equal to 5 percent of the overall firm’s sales.An executive at the firm, H. Sears, argues that
$5,000 (5% 100,000) should be viewed as the proposed project’s share of the library’s costs. Is
this appropriate for capital budgeting?
The answer is no. One must ask the question:What is the difference between the cash flows of
the entire firm with the project and the cash flows of the entire firm without the project? The firm
will spend $100,000 on library upkeep whether or not the proposed project is accepted. Since
acceptance of the proposed project does not affect this cash flow, the cash flow should be ignored
when calculating the NPV of the project.
1. What are the four difficulties in determining incremental cash flows?
2. Define sunk costs, opportunity costs, side effects, and allocated costs.
7.2 The Baldwin Company: An Example
We next consider the example of a proposed investment in machinery and related items.
Our example involves the Baldwin Company and colored bowling balls.
The Baldwin Company, originally established in 1965 to make footballs, is now a leading producer of tennis balls, baseballs, footballs, and golf balls. In 1973 the company
99
100
Corporate Finance,
Seventh Edition
Budgeting
Capital Budgeting
Companies, 2004
181
introduced “High Flite,” its first line of high-performance golf balls. The Baldwin management has sought opportunities in whatever businesses seem to have some potential for
cash flow. In 2002 W. C. Meadows, vice president of the Baldwin Company, identified another segment of the sports ball market that looked promising and that he felt was not adequately served by larger manufacturers. That market was for brightly colored bowling
balls, and he believed a large number of bowlers valued appearance and style above performance. He also believed that it would be difficult for competitors to take advantage of
the opportunity because of both Baldwin’s cost advantages and its highly developed marketing skills.
As a result, in late 2003 the Baldwin Company investigated the marketing potential of
brightly colored bowling balls. Baldwin sent a questionnaire to consumers in three markets:
Philadelphia, Los Angeles, and New Haven. The results of the three questionnaires were
much better than expected and supported the conclusion that the brightly colored bowling
ball could achieve a 10- to 15-percent share of the market. Of course, some people at
Baldwin complained about the cost of the test marketing, which was $250,000. (As we
shall see later, this is a sunk cost and should not be included in project evaluation.)
In any case, the Baldwin Company is now considering investing in a machine to produce bowling balls. The bowling balls would be manufactured in a building owned by the
firm and located near Los Angeles. This building, which is vacant, and the land can be sold
for $150,000 after taxes.
Working with his staff, Meadows is preparing an analysis of the proposed new product.
He summarizes his assumptions as follows: The cost of the bowling ball machine is
$100,000. The machine has an estimated market value at the end of five years of $30,000.
Production by year during the five-year life of the machine is expected to be as follows:
5,000 units, 8,000 units, 12,000 units, 10,000 units, and 6,000 units. The price of bowling
balls in the first year will be $20. The bowling ball market is highly competitive, so
Meadows believes that the price of bowling balls will increase at only 2 percent per year,
as compared to the anticipated general inflation rate of 5 percent. Conversely, the plastic
used to produce bowling balls is rapidly becoming more expensive. Because of this, production cash outflows are expected to grow at 10 percent per year. First-year production
costs will be $10 per unit. Meadows has determined, based upon Baldwin’s taxable income, that the appropriate incremental corporate tax rate in the bowling ball project is
34 percent.
Net working capital is defined as the difference between current assets and current liabilities. Like any other manufacturing firm, Baldwin finds that it must maintain an investment in working capital. It will purchase raw materials before production and sale, giving
rise to an investment in inventory. It will maintain cash as a buffer against unforeseen expenditures. And, its credit sales will generate accounts receivable. Management determines
that an immediate (year 0) investment in the different items of working capital of $10,000
is required. Working capital is forecasted to rise in the early years of the project but to fall
to $0 by the project’s end. In other words, the investment in working capital is completely
recovered by the end of the project’s life.
Projections based on these assumptions and Meadows’s analysis appear in Tables 7.1
through 7.4. In these tables all cash flows are assumed to occur at the end of the year.
Because of the large amount of information in these tables, it is important to see how the
tables are related. Table 7.1 shows the basic data for both investment and income. Supplementary schedules on operations and depreciation, as presented in Tables 7.2 and 7.3, help
explain where the numbers in Table 7.1 come from. Our goal is to obtain projections of
cash flow. The data in Table 7.1 are all that are needed to calculate the relevant cash flows,
as shown in Table 7.4.
Corporate Finance,
Seventh Edition
182
TABLE 7.1
Budgeting
Companies, 2004
Capital Budgeting
The Worksheet for Cash Flows of the Baldwin Company (in $ thousands)
(All cash flows occur at the end of the year.)
Year 0
Investments:
(1) Bowling ball machine
(2) Accumulated depreciation
(3) Adjusted basis of machine
after depreciation (end-of-year)
(4) Opportunity cost (warehouse)
(5) Net working capital (end-of-year)
(6) Change in net working capital
(7) Total cash flow of investment
[(1) (4) (6)]
Income:
(8) Sales revenues
(9) Operating costs
(10) Depreciation
(11) Income before taxes
[(8) (9) (10)]
(12) Tax at 34 percent
(13) Net income
Year 1
Year 2
Year 3
Year 4
Year 5
$20.00
80.00
$52.00
48.00
$71.20
28.80
$82.72
17.28
$21.76*
94.24
5.76
10.00
16.32
6.32
6.32
24.97
8.65
8.65
21.22
3.75
3.75
150.00
0
21.22
192.98
$100.00
50.00
20.00
30.00
$163.20
88.00
32.00
43.20
$249.72
145.20
19.20
85.32
$212.20
133.10
11.52
67.58
$129.90
87.84
11.52
30.54
10.20
19.80
14.69
28.51
29.01
56.31
22.98
44.60
10.38
20.16
$100.00
150.00
10.00
10.00
260.00
*We assume that the ending market value of the capital investment at year 5 is $30 (in thousands). Capital gain is the difference between the ending market
value and the adjusted basis of the machine.The adjusted basis is the original purchase price of the machine less depreciation.The capital gain is $24.24
($30 $5.76). Capital gains for corporations are taxed at the ordinary income rate (34% in this example), so the capital gains tax here is $8.24 [0.34 ($30 $5.76)].The after-tax capital gain is $30 [0.34 ($30 $5.76)] $21.76.
TABLE 7.2
Operating Revenues
and Costs of the
Baldwin Company
(1)
(2)
(3)
Price
(4)
Sales
Revenues
(5)
Cost
per Unit
(6)
Operating
Costs
Year
Production
1
2
3
4
5
5,000
8,000
12,000
10,000
6,000
$20.00
20.40
20.81
21.22
21.65
$100,000
163,200
249,720
212,200
129,900
$10.00
11.00
12.10
13.31
14.64
$ 50,000
88,000
145,200
133,100
87,840
Prices rise at 2% a year.
Unit costs rise at 10% a year.
An Analysis of the Project
Investments
The investment outlays for the project are summarized in the top segment
of Table 7.1. They consist of three parts:
1. The Bowling Ball Machine. The purchase requires an immediate (year 0) cash outflow of $100,000. The firm realizes a cash inflow when the machine is sold in year 5. These
cash flows are shown in line 1 of Table 7.1. As indicated in the footnote to the table, taxes
are incurred when the asset is sold.
2. The Opportunity Cost of Not Selling the Warehouse. If Baldwin accepts the bowlingball project, it will use a warehouse and land that could otherwise be sold. The estimated
sales price of the warehouse and land is therefore included as an opportunity cost in year 0,
as presented in line 4. Opportunity costs are treated as cash outflows for purposes of capital
budgeting. However, note that if the project is accepted, management assumes that the
warehouse will be sold for $150,000 (after taxes) in year 5.
101
102
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
183
TABLE 7.3
Depreciation
(in percent) under
Modified Accelerated
Cost Recovery
System (MACRS)
Recovery Period Class
Year
3 Years
5 Years
7 Years
10 Years
15 Years
20 Years
1
2
3
4
5
6
7
8
9
10
11
12–15
16
17–20
21
0.333
0.444
0.148
0.074
0.200
0.320
0.192
0.115
0.115
0.058
0.143
0.245
0.175
0.125
0.089
0.089
0.089
0.045
0.100
0.180
0.144
0.115
0.092
0.074
0.066
0.066
0.066
0.066
0.033
0.050
0.095
0.086
0.077
0.069
0.062
0.059
0.059
0.059
0.059
0.059
0.059
0.030
0.038
0.072
0.067
0.062
0.057
0.053
0.049
0.045
0.045
0.045
0.045
0.045
0.045
0.045
0.022
Depreciation is expressed as a percent of the asset’s cost.These schedules are based on the IRS publication Depreciation.
Details on depreciation are presented in the appendix.Three-year depreciation actually carries over four years because the
IRS assumes purchase is made in midyear.
TABLE 7.4
Incremental Cash Flows for the Baldwin Company (in $ thousands)
Year 0
(1)
(2)
(3)
(4)
Sales revenue [line 8,Table 7.1]
Operating costs [line 9,Table 7.1]
Taxes [line 12,Table 7.1]
Cash flow from operations
[(1) (2) (3)]
(5) Total cash flow of investment
[line 7,Table 7.1]
(6) Total cash flow of project
[(4) (5)]
NPV @
4%
123.641
10%
51.588
15%
5.472
15.67%
0
20%
31.351
Year 1
Year 2
Year 3
Year 4
Year 5
$100.00
50.00
10.20
39.80
$163.20
88.00
14.69
60.51
$249.72
145.20
29.01
75.51
$212.20
133.10
22.98
56.12
$129.90
87.84
10.38
31.68
6.32
8.65
3.75
192.98
54.19
66.86
59.87
224.66
$260.00
260.00
39.80
The test marketing cost of $250,000 is not included. The tests occurred in the past and
should be viewed as a sunk cost.
3. The Investment in Working Capital. Required working capital appears in line 5.
Working capital rises over the early years of the project as expansion occurs. However, all
working capital is assumed to be recovered at the end, a common assumption in capital
budgeting. In other words, all inventory is sold by the end, the cash balance maintained as
a buffer is liquidated, and all accounts receivable are collected. Increases in working capital in the early years must be funded by cash generated elsewhere in the firm. Hence, these
increases are viewed as cash outflows. To reiterate, it is the increase in working capital over
a year that leads to a cash outflow in that year. Even if working capital is at a high level,
there will be no cash outflow over a year if working capital stays constant over that year.
Conversely, decreases in working capital in the later years are viewed as cash inflows. All
Corporate Finance,
Seventh Edition
184
Budgeting
Capital Budgeting
Companies, 2004
of these cash flows are presented in line 6. A more complete discussion of working capital
is provided later in this section.
To recap, there are three investments in this example: the bowling ball machine (line 1
in Table 7.1), the opportunity cost of the warehouse (line 4), and the changes in working
capital (line 6). The total cash flow from the above three investments is shown in line 7.
Income and Taxes
Next, the determination of income is presented in the bottom segment of Table 7.1. While we are ultimately interested in cash flow—not income—we need
the income calculation in order to determine taxes. Lines 8 and 9 of Table 7.1 show sales
revenues and operating costs, respectively. The projections in these lines are based on the
sales revenues and operating costs computed in columns 4 and 6 of Table 7.2. The estimates of revenues and costs follow from assumptions made by the corporate planning staff
at Baldwin. In other words, the estimates critically depend on the fact that product prices
are projected to increase at 2 percent per year and costs per unit are projected to increase at
10 percent per year.
Depreciation of the $100,000 capital investment is shown in line 10 of Table 7.1. Where
do these numbers come from? Depreciation for tax purposes for U.S. companies is based
on the Modified Accelerated Cost Recovery System (MACRS).1 Each asset is assigned a
useful life under MACRS, with an accompanying depreciation schedule as shown in
Table 7.3.2 The IRS ruled that Baldwin is to depreciate its capital investment over five
years, so the second column of the table applies in this case. Since depreciation in the table
is expressed as a percentage of the asset’s cost, multiply the percentages in this column by
$100,000 to arrive at depreciation in dollars.
Income before taxes is calculated in line 11 of Table 7.1. Taxes are provided in line 12
of this table, and net income is calculated in line 13.
Cash Flow
Cash flow is finally determined in Table 7.4. We begin by reproducing lines 8,
9, and 12 in Table 7.1 as lines 1, 2, and 3 in Table 7.4. Cash flow from operations, which is
sales minus both operating costs and taxes, is provided in line 4 of Table 7.4. Total investment cash flow, taken from line 7 of Table 7.1, appears as line 5 of Table 7.4. Cash flow
from operations plus total cash flow of the investment equals total cash flow of the project,
which is displayed as line 6 of Table 7.4.
Net Present Value
The NPV of the Baldwin bowling ball project can be calculated
from the cash flows in line 6. As can be seen at the bottom of Table 7.4, the NPV is $51,588
if 10 percent is the appropriate discount rate and $31,351 if 20 percent is the appropriate
discount rate. If the discount rate is 15.67 percent, the project will have a zero NPV. In
other words, the project’s internal rate of return is 15.67 percent. If the discount rate of the
Baldwin bowling ball project is above 15.67 percent, it should not be accepted because its
NPV would be negative.
Which Set of Books?
It should be noted that the firm’s management generally keeps two sets of books, one for
the IRS (called the tax books) and another for its annual report (called the stockholders’
books). The tax books follow the rules of the IRS. The stockholders’ books follow the rules
1
2
Depreciation rules are discussed in detail in the appendix to this chapter.
Under current IRS rules, 30 percent of the value of the asset may be depreciated in the first year. This is referred to as bonus
depreciation. The depreciation percentages in the table then apply to the 70 percent of the asset that remains. Bonus depreciation
does not apply to real estate. We have not included bonus depreciation in the Baldwin example since, at the time this textbook
went to press, the relevant rule was scheduled to expire on January 1, 2005.
103
104
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
185
of the Financial Accounting Standards Board (FASB), the governing body in accounting.
The two sets of rules differ widely in certain areas. For example, income on municipal
bonds is ignored for tax purposes while being treated as income by the FASB. The differences almost always benefit the firm, because the rules permit income on the stockholders’
books to be higher than income on the tax books. That is, management can look profitable
to the stockholders without needing to pay taxes on all of the reported profit. In fact, there
are plenty of large companies that consistently report positive earnings to the stockholders
while reporting losses to the IRS.
We present a synopsis of the IRS rules on depreciation in the appendix. The rules on
depreciation for the stockholders’ books differ, as they do in many other accounting areas.
Which of the two sets of rules on depreciation do we use to create the previous tables for
Baldwin? Clearly, we are interested in the IRS rules. Our purpose is to calculate net cash
flow, and tax payments are cash outflows. The FASB regulations determine accounting income, not cash flow.
A Note on Net Working Capital
The investment in net working capital is an important part of any capital budgeting analysis.
While we explicitly considered net working capital in lines 5 and 6 of Table 7.1, students
may be wondering where the numbers in these lines came from. An investment in net working capital arises whenever (1) inventory is purchased, (2) cash is kept in the project as a
buffer against unexpected expenditures, and (3) credit sales are made, generating accounts
receivable rather than cash. (The investment in net working capital is reduced by credit purchases, which generate accounts payables.) This investment in net working capital represents a cash outflow, because cash generated elsewhere in the firm is tied up in the project.
To see how the investment in net working capital is built from its component parts, we
focus on year 1. We see in Table 7.1 that Baldwin’s managers predict sales in year 1 to be
$100,000 and operating costs to be $50,000. If both the sales and costs were cash transactions, the firm would receive $50,000 ($100,000 $50,000). As stated earlier, this cash
flow would occur at the end of year 1.
Now let’s give you more information. The managers:
1. Forecast that $9,000 of the sales will be on credit, implying that cash receipts at the end
of year 1 will be only $91,000 ($100,000 $9,000). The accounts receivable of $9,000
will be collected at the end of year 2.
2. Believe that they can defer payment on $3,000 of the $50,000 of costs, implying that
cash disbursements at the end of year 1 will be only $47,000 ($50,000 $3,000). Baldwin
will pay off the $3,000 of accounts payable at the end of year 2.
3. Decide that inventory of $2,500 should be left on hand at the end of year 1 to avoid
stockouts (that is, running out of inventory).
4. Decide that cash of $1,500 should be earmarked for the project at the end of year 1 to
avoid running out of cash.
Thus, net working capital at the end of year 1 is
$9,000
Accounts
receivable
$3,000
Accounts
payable
$2,500
$1,500 Inventory
Cash
$10,000
Net working
capital
Because $10,000 of cash generated elsewhere in the firm must be used to offset this requirement for net working capital, Baldwin’s managers correctly view the investment in net
working capital as a cash outflow of the project. As the project grows over time, needs for
net working capital increase. Changes in net working capital from year to year represent
Corporate Finance,
Seventh Edition
186
Budgeting
Capital Budgeting
Companies, 2004
further cash flows, as indicated by the negative numbers for the first few years of line 6 of
Table 7.1. However, in the declining years of the project, net working capital is reduced—
ultimately to zero. That is, accounts receivable are finally collected, the project’s cash buffer
is returned to the rest of the corporation, and all remaining inventory is sold off. This frees
up cash in the later years, as indicated by positive numbers in years 4 and 5 on line 6.
Typically, corporate worksheets (such as Table 7.1) treat net working capital as a whole.
The individual components of working capital (receivables, inventory, etc.) do not generally appear in the worksheets. However, the reader should remember that the working capital numbers in the worksheets are not pulled out of thin air. Rather, they result from a
meticulous forecast of the components, just as we illustrated for year 1.
Interest Expense
It may have bothered you that interest expense was ignored in the Baldwin example. After
all, many projects are at least partially financed with debt, particularly a bowling ball machine that is likely to increase the debt capacity of the firm. As it turns out, our approach of
assuming no debt financing is rather standard in the real world. Firms typically calculate a
project’s cash flows under the assumption that the project is financed only with equity. Any
adjustments for debt financing are reflected in the discount rate, not the cash flows. The treatment of debt in capital budgeting will be covered in depth later in the text. Suffice it to say at
this time that the full ramifications of debt financing are well beyond our current discussion.
Concept
Questions
1. What are the items leading to cash flow in any year?
2. Why did we determine income when NPV analysis discounts cash flows, not
income?
3. Why is working capital viewed as a cash outflow?
7.3 The Boeing 777: A Real-World Example
Will the principles discussed in the previous sections of this chapter allow us to perform
capital budgeting in the real world? Let’s see by examining the Boeing 777 project, which
we mentioned in the executive summary of this chapter. As stated there, the Boeing Company announced in late 1990 its intention to build the 777. The company anticipated selling several thousand of these planes over a 35-year period, beginning in 1995.
The relevant projected information is presented in Table 7.5, with the determination of
annual net cash flow being the ultimate goal of the table. Net cash flow can be determined
in three steps:
1. Taxes. In order to determine taxes each year, we begin with taxable income, which can
be expressed as:
Taxable income Sales revenue Operating costs Depreciation
Choosing a representative year, say, 2005, we have:
Taxable income $19,468.56 $17,911.07 $116.83 $1440.66
Boeing forecasts a tax rate of 34 percent, implying taxes in 2005 of:
0.34 $1440.66 $489.82
2. Investment. Investment is the sum of the change in net working capital and the amount
of capital expenditures, which is $450.88 ($431.41 $19.47) for 2005.
105
14
145
140
111
107
102
92
92
105
89
111
130
118
94
123
125
125
98
84
89
89
89
89
89
89
89
89
89
89
89
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
$ 1,847.55
19,418.96
19,244.23
15,737.95
16,257.35
15,333.42
14,289.29
14,717.97
17,233.97
15,066.42
19,468.56
23,307.53
21,911.40
17,944.00
24,103.23
25,316.97
26,076.48
21,133.07
18,550.25
20,321.64
20,931.29
21,559.23
22,206.00
22,872.18
23,558.35
24,265.10
24,993.05
25,742.85
26,515.13
$27,310.58
Sales
Revenue
$ 865.00
1,340.00
1,240.00
840.00
1,976.69
17,865.45
16,550.04
13,377.26
13,656.17
12,726.74
11,860.11
12,068.74
14,131.85
12,354.47
17,911.07
20,510.63
18,843.81
15,252.40
22,174.98
22,278.94
22,425.77
17,963.10
15,582.21
16,866.97
17,372.97
17,894.16
18,430.98
18,983.92
19,553.43
20,140.03
20,744.23
21,366.56
22,007.56
$22,667.78
Operating
Costs
$ 40.00
96.00
116.40
124.76
112.28
101.06
90.95
82.72
77.75
75.63
75.00
75.00
99.46
121.48
116.83
112.65
100.20
129.20
96.99
76.84
65.81
61.68
57.96
54.61
52.83
52.83
52.83
52.83
47.52
35.28
28.36
28.36
28.36
$ 16.05
Depreciation
Incremental Cash Flows: Boeing 777
$ (905.00)
(1,436.00)
(1,356.40)
(964.76)
(241.42)
1,452.45
2,603.24
2,277.97
2,523.43
2,531.05
2,354.18
2,574.23
3,002.66
2,590.47
1,440.66
2,684.25
2,967.39
2,562.40
1,831.26
2,961.19
3,584.90
3,108.29
2,910.08
3,400.06
3,505.49
3,612.24
3,722.19
3,835.43
3,957.40
4,089.79
4,220.46
4,347.93
4,479.21
$ 4,626.75
Income
before
Taxes
$ (307.70)
(488.24)
(461.18)
(328.02)
(82.08)
493.83
885.10
774.51
857.97
860.56
800.42
875.24
1,020.90
880.76
489.82
912.65
1,008.91
871.22
622.63
1,006.80
1,218.87
1,056.82
989.43
1,156.02
1,191.87
1,228.16
1,265.54
1,304.05
1,345.52
1,390.53
1,434.96
1,478.30
1,522.93
$1,573.10
Taxes
$ 181.06
1,722.00
(17.12)
(343.62)
50.90
90.54
(102.33)
42.01
246.57
(212.42)
431.41
376.22
(136.82)
(388.81)
603.60
118.95
74.43
(484.45)
(253.12)
173.60
59.75
61.54
63.38
65.29
67.24
69.26
71.34
73.48
75.68
$ 77.95
Change in
Net Working
Capital
$400.00
600.00
300.00
200.00
1.85
19.42
19.42
15.74
16.26
15.33
14.29
14.72
244.64
244.64
19.47
23.31
21.91
567.22
24.10
25.32
26.08
21.13
18.55
20.32
20.93
21.56
22.21
22.87
23.56
24.27
24.99
25.74
26.52
$ 27.31
Capital
Expenditures
$ 400.00
600.00
300.00
200.00
182.91
1,741.42
2.30
(327.88)
67.16
105.87
(88.04)
56.73
491.21
32.22
450.88
399.53
(114.91)
178.41
627.70
144.27
100.51
(463.32)
(234.57)
193.92
80.68
83.10
85.59
88.16
90.80
93.53
96.33
99.22
102.20
$ 105.26
Investment
$ (957.30)
(1,451.76)
(1,078.82)
(711.98)
(229.97)
681.74
1,806.79
1,914.06
1,676.05
1,640.25
1,716.80
1,717.26
1,590.01
1,798.97
616.79
1,484.73
2,173.59
1,641.97
677.92
1,886.96
2,331.33
2,576.47
2,213.18
2,104.73
2,285.77
2,353.81
2,423.89
2,496.05
2,568.60
2,641.01
2,717.53
2,798.77
2,882.44
$ 2,964.45
Net
Cash Flow
Corporate Finance,
Seventh Edition
Budgeting
Capital Budgeting
NOTES:
Tax rate is 34 percent.
Net Cash Flow for a given year can be determined by adding across the columns. Recall that Net Cash Flow is equal to Sales Revenue Operating Costs Taxes Investment.
SOURCE: Robert Bruner, Case Studies in Finance, 4th edition (Burr Ridge, Ill.: McGraw-Hill/Irwin, 2003).
Number
of Planes
Delivered
TABLE 7.5
106
Companies, 2004
187
Corporate Finance,
Seventh Edition
188
Budgeting
Capital Budgeting
Companies, 2004
3. Final calculation. We calculate net cash flow as:
Sales revenue Operating costs Taxes Investment
which for 2005 is
$19,468.56 $17,911.07 $489.82 $450.88 $616.79
The last column in Table 7.5 provides net cash flow for each of the 35 years.
In addition to the items in the table, Boeing invested several hundred million dollars in
research and development prior to late 1990. Since these outflows were incurred prior to
the decision to build the plane, they are sunk costs and should properly be excluded from
the table.
The net present value (NPV) of the Boeing 777 project is calculated by discounting the
net cash flows in the last column of the table. Of course, the NPV of any project is dependent on the discount rate. Figure 7.1 graphs NPV as a function of the discount rate. NPV
must be negatively related to this rate, since there is only one change in the signs of the
cash flows. The net present value of the project is 0 for a discount rate of 21 percent. Hence,
the internal rate of return (IRR) of the project is 21 percent. Boeing should accept the project if their discount rate is less than 21 percent but should reject the project if their discount
rate is above 21 percent.
It should be mentioned that the analysis in Table 7.5, as well as the analysis for any
project, is entirely based on forecasts. The subsequent reality may be much different, as
was the case with the 777. Though the table shows delivery of 711 planes by the end of
1999, only 282 planes had actually been delivered through May 2000.
FIGURE 7.1
NPV of the Boeing 777 Project as a Function of the Discount Rate
$54,000.00
$50,000.00
$46,000.00
$42,000.00
Net present value
$38,000.00
$34,000.00
$30,000.00
$26,000.00
$22,000.00
$18,000.00
$14,000.00
$10,000.00
$2,000.00
0
$2,000.00
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
66
69
72
75
78
81
84
87
90
93
96
99
$6,000.00
Discount rate %
The internal rate of return (IRR) of the project is 21%.
107
108
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
189
7.4 Inflation and Capital Budgeting
Inflation is an important fact of economic life, and it must be considered in capital budgeting. We begin our examination of inflation by considering the relationship between interest
rates and inflation.
Interest Rates and Inflation
Suppose that a bank offers a one-year interest rate of 10 percent. This means that an individual who deposits $1,000 will receive $1,100 ($1,000 1.10) in one year. While 10 percent may seem like a handsome return, one can only put it in perspective after examining
the rate of inflation.
Imagine that the rate of inflation is 6 percent over the year and it affects all goods
equally. For example, a restaurant that charges $1.00 for a hamburger today will charge
$1.06 for the same hamburger at the end of the year. You can use your $1,000 to buy 1,000
hamburgers today (date 0). Alternatively, if you put your money in the bank, you can buy
1,038 ($1,100兾$1.06) hamburgers at date 1. Thus, lending increases your hamburger consumption by only 3.8 percent.
Since the prices of all goods rise at this 6-percent rate, lending lets you increase your
consumption of any single good or any combination of goods by only 3.8 percent. Thus,
3.8 percent is what you are really earning through your savings account, after adjusting for
inflation. Economists refer to the 3.8-percent number as the real interest rate. Economists
refer to the 10-percent rate as the nominal interest rate or simply the interest rate. This
discussion is illustrated in Figure 7.2.
We have used an example with a specific nominal interest rate and a specific inflation
rate. In general, the formula between real and nominal interest rates can be written as
1 Nominal interest rate (1 Real interest rate) (1 Inflation rate)
Rearranging terms, we have
Real interest rate 1 Nominal interest rate
1
1 Inflation rate
(7.1)
The formula indicates that the real interest rate in our example is 3.8 percent (1.10兾1.06 1).
The above formula determines the real interest rate precisely. The following formula is
an approximation:
Real interest rate ⬵ Nominal interest rate Inflation rate
(7.2)
The symbol ⬵ indicates that the equation is approximately true. This latter formula calculates the real rate in our example as:
4% 10% 6%
FIGURE 7.2
Calculation of Real
Rate of Interest
Today (Date 0)
Individual invests
$1,000 in bank
(Because hamburgers sell
for $1 at date 0, $1,000
would have purchased
1,000 hamburgers.)
10%
Interest rate
3.8%
Date 1
Individual receives
$1,100 from bank
Inflation rate has
been 6% over year
Because each hamburger
sells for $1.06 at date 1,
1,038 (= $1,100/$1.06)
hamburgers can be purchased.
Hamburger is used as illustrative good. 1,038 hamburgers can be purchased on date 1
instead of 1,000 hamburgers at date 0. Real interest rate = 1,038/1,000 – 1 = 3.8%.
Corporate Finance,
Seventh Edition
190
Budgeting
Companies, 2004
Capital Budgeting
The student should be aware that, while equation (7.2) may seem more intuitive than equation (7.1), (7.2) is only an approximation.
This approximation is reasonably accurate for low rates of interest and inflation. In our
example, the difference between the approximate calculation and the exact one is only
0.2 percent (4 percent 3.8 percent). Unfortunately, the approximation becomes poor
when rates are higher.
EXAMPLE
The little-known monarchy of Gerberovia recently had a nominal interest rate of 300 percent and
an inflation rate of 280 percent. According to equation (7.2), the real interest rate is:
300% 280% 20%
(Approximate formula)
However, according to equation (7.1), this rate is:
1 300%
1 5.26%
1 280%
(Exact formula)
How do we know that the second formula is indeed the exact one? Let’s think in terms of hamburgers again. Had you deposited $1,000 in a Gerberovian bank a year ago, the account would be
worth $4,000 [$1,000 (1 300%)] today. However, while a hamburger cost $1 a year ago, it costs
$3.80 (1 280%) today. Therefore, you would now be able to buy 1052.6 (4,000兾3.80) hamburgers,
implying a real interest rate of 5.26 percent.
The recent real and nominal interest rates for the United States are presented in Figure 7.3.
The figure suggests that the nominal rate of interest exhibits more variability from year to
year than does the real rate, a finding that seems to hold over most time periods.
FIGURE 7.3
Nominal and Real Interest Rates and Inflation for the United States
20
U.S. Treasury bills rate
Inflation (CPI)
U.S. real risk-free return
15
Percentage
10
5
0
–5
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02
–10
Year (1950–2002)
Nominal interest rates are based on three-month Treasury bills (or equivalent). The measure of inflation used is
the Consumer Price Index. Real rates are calculated according to equation (7.1).
109
110
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
191
Cash Flow and Inflation
The above analysis defines two types of interest rates, nominal rates and real rates, and
relates them through equation (7.1). Capital budgeting requires data on cash flows as well
as on interest rates. Like interest rates, cash flows can be expressed in either nominal or
real terms.
A nominal cash flow refers to the actual dollars to be received (or paid out). A real cash
flow refers to the cash flow’s purchasing power. Like most definitions, these definitions are
best explained by examples.
EXAMPLE
Burrows Publishing has just purchased the rights to the next book of famed romantic novelist
Barbara Musk. Still unwritten, the book should be available to the public in four years. Currently, romantic novels sell for $10.00 in softcover. The publishers believe that inflation will be 6 percent a
year over the next four years. Since romantic novels are so popular, the publishers anticipate that
their prices will rise about 2 percent per year more than the inflation rate over the next four years.
Burrows Publishing plans to sell the novel at $13.60 [(1.08)4 $10.00] four years from now, anticipating sales of 100,000 copies.
The expected cash flow in the fourth year of $1.36 million ($13.60 100,000) is a nominal cash
flow. That is, the firm expects to receive $1.36 million at that time. In other words, a nominal cash
flow refers to the actual dollars to be received in the future.
The purchasing power of $1.36 million in four years is
$1.08 million $1.36 million
(1.06) 4
The figure, $1.08 million, is a real cash flow since it is expressed in terms of purchasing power.
Extending our hamburger example, the $1.36 million to be received in four years will only buy
1.08 million hamburgers because the price of a hamburger will rise from $1 to $1.26 [$1 (1.06)4]
over the period.
EXAMPLE
EOBII Publishers, a competitor of Burrows, recently bought a printing press for $2,000,000 to be
depreciated by the straight-line method over five years.This implies yearly depreciation of $400,000
($2,000,000兾5). Is this $400,000 figure a real or a nominal quantity?
Depreciation is a nominal quantity because $400,000 is the actual tax deduction over each of the
next four years. Depreciation becomes a real quantity if it is adjusted for purchasing power. Hence,
$316,837 [$400,000兾(1.06)4] is depreciation in the fourth year, expressed as a real quantity.
Discounting: Nominal or Real?
Our previous discussion showed that interest rates can be expressed in either nominal or
real terms. Similarly, cash flows can be expressed in either nominal or real terms. Given
these choices, how should one express interest rates and cash flows when performing capital budgeting?
Financial practitioners correctly stress the need to maintain consistency between cash
flows and discount rates. That is,
Nominal cash flows must be discounted at the nominal rate.
Real cash flows must be discounted at the real rate.
As long as one is consistent, either approach is correct. In order to minimize computational
error, it is generally advisable in practice to choose the approach that is easiest. This idea is
illustrated in the following two examples.
Corporate Finance,
Seventh Edition
192
EXAMPLE
Budgeting
Companies, 2004
Capital Budgeting
Shields Electric forecasts the following nominal cash flows on a particular project:
Date
Cash flow
0
1
2
$1,000
$600
$650
The nominal interest rate is 14 percent, and the inflation rate is forecast to be 5 percent.What is the
value of the project?
Using Nominal Quantities
The NPV can be calculated as
$26.47 $1,000 $600
$650
(1.14) 2
1.14
The project should be accepted.
Using Real Quantities
The real cash flows are
Date
Cash flow
0
1
2
$1,000
$571.43
$600
1.05
$589.57
$650
(1.05) 2
冢
冣
冢
冣
The real interest rate is 8.57143 percent (1.14兾1.05 1).
The NPV can be calculated as
$26.47 $1,000 $571.43
$589.57
1.0857143 (1.0857143) 2
The NPV is the same whether cash flows are expressed in nominal or in real quantities. It
must always be the case that the NPV is the same under the two different approaches.
Because both approaches always yield the same result, which one should be used? As
mentioned above, use the approach that is simpler, since the simpler approach generally
leads to fewer computational errors. Because the Shields Electric example begins with
nominal cash flows, nominal quantities produce a simpler calculation here.
EXAMPLE
Altshuler, Inc., generated the following forecast for a capital budgeting project:
Year
0
Capital expenditure
Revenues (in real terms)
Cash expenses (in real terms)
Depreciation (straight line)
1
2
$1,900
950
605
$2,000
1,000
605
$1,210
The president, David Altshuler, estimates inflation to be 10 percent per year over the next two years.
In addition, he believes that the cash flows of the project should be discounted at the nominal rate
of 15.5 percent. His firm’s tax rate is 40 percent.
111
112
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
193
Mr. Altshuler forecasts all cash flows in nominal terms, leading to the following spreadsheet:
Year
0
Capital expenditure
Revenues
Expenses
Depreciation
________________
Taxable income
Taxes (40%)
________________
Income after taxes
Depreciation
________________
Cash flow
$1,210
1
2
$2,090 ( 1,900 1.10)
1,045 ( 950 1.10)
605 ( 1,210兾2)
_____
440
176
_____
264
605
_____
$ 869
$2,420 [ 2,000 (1.10)2]
1,210 [ 1,000 (1.10)2]
605
_____
605
242
_____
363
605
_____
$ 968
NPV $1,210 $968
$869
$268
1.155 (1.155) 2
Mr. Altshuler’s sidekick, Stuart Weiss, prefers working in real terms. He first calculates the real rate
to be 5 percent (1.155兾1.10 1). Next, he generates the following spreadsheet in real quantities:
Year
0
Capital expenditure
Revenues
Expenses
Depreciation
________________
Taxable income
Taxes (40%)
________________
Income after taxes
Depreciation
________________
Cash flow
1
2
$1,210
$1,900
950
550
_____ ( 605兾1.1)
400
160
_____
240
550
_____
$ 790
NPV $1,210 $2,000
1,000
500 [ 605兾(1.1)2]
______
500
200
______
300
500
______
$ 800
$790
$800
$268
(1.05) 2
1.05
In explaining his calculations to Mr. Altshuler, Mr. Weiss points out:
1. Since the capital expenditure occurs at date 0 (today),its nominal value and its real value are equal.
2. Because yearly depreciation of $605 is a nominal quantity, one converts it to a real quantity by
discounting at the inflation rate of 10 percent.
3. It is no coincidence that both Mr. Altshuler and Mr. Weiss arrive at the same NPV number.
Both methods must always generate the same NPV.
Concept
Questions
1. What is the difference between the nominal and the real interest rate?
2. What is the difference between nominal and real cash flows?
7.5 Investments of Unequal Lives: The Equivalent
Annual Cost Method
Suppose a firm must choose between two machines of unequal lives. Both machines can do
the same job, but they have different operating costs and will last for different time periods.
A simple application of the NPV rule suggests taking the machine whose costs have the
Corporate Finance,
Seventh Edition
194
Budgeting
113
Companies, 2004
Capital Budgeting
lower present value. This choice might be a mistake, however, because the lower-cost machine may need to be replaced before the other one.
EXAMPLE
The Downtown Athletic Club must choose between two mechanical tennis ball throwers. Machine A
costs less than machine B but will not last as long. The cash outflows from the two machines are:
Date
Machine
0
1
2
3
4
A
B
$500
$600
$120
$100
$120
$100
$120
$100
$100
Machine A costs $500 and lasts three years.There will be maintenance expenses of $120 to be paid at
the end of each of the three years.Machine B costs $600 and lasts four years.There will be maintenance
expenses of $100 to be paid at the end of each of the four years.We place all costs in real terms, an assumption greatly simplifying the analysis. Revenues per year are assumed to be the same, regardless of
machine, so they are ignored in the analysis. Note that all numbers in the above chart are outflows.
To get a handle on the decision, let’s take the present value of the costs of each of the
two machines. Assuming a discount rate of 10 percent, we have:
$120
1.1
$100
Machine B: $916.99 $600 1.1
Machine A: $798.42 $500 $120
$120
2
(1.1)
(1.1) 3
(7.3)
$100
$100
$100
2
3
(1.1)
(1.1)
(1.1) 4
Machine B has a higher present value of outflows. A naive approach would be to select
machine A because of its lower present value. However, machine B has a longer life so perhaps its cost per year is actually lower.
How might one properly adjust for the difference in useful life when comparing the two
machines? Perhaps the easiest approach involves calculating something called the equivalent annual cost of each machine. This approach puts costs on a per-year basis.
Equation (7.3) showed that payments of ($500, $120, $120, $120) are equivalent to a
single payment of $798.42 at date 0. We now wish to equate the single payment of $798.42
at date 0 with a three-year annuity. Using techniques of previous chapters, we have
$798.42 C A30.10
A30.10 is an annuity of $1 a year for three years, discounted at 10 percent. C is the
unknown—the annuity payment per year such that the present value of all payments equals
$798.42. Because A30.10 equals 2.4869, C equals $321.05 ($798.42兾2.4869). Thus, a payment stream of ($500, $120, $120, $120) is equivalent to annuity payments of $321.05
made at the end of each year for three years. We refer to $321.05 as the equivalent annual
cost of machine A.
This idea is summarized in the little chart below:
Date
Cash outflows of Machine A
Equivalent annual cost of Machine A
0
1
2
3
$500
$120
$321.05
$120
$321.05
$120
$321.05
114
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
195
The Downtown Athletic Club should be indifferent between cash outflows of ($500, $120,
$120, $120) and cash outflows of ($0, $321.05, $321.05, $321.05). Alternatively, one can
say that the purchase of the machine is financially equivalent to a rental agreement calling
for annual lease payments of $321.05.
Now let’s turn to machine B. We calculate its equivalent annual cost from
$916.99 C A40.10
Because A40.10 equals 3.1699, C equals $916.99兾3.1699, or $289.28.
As we did above for machine A, the following chart can be created for machine B:
Date
Cash outflows of Machine B
Equivalent annual cost of Machine B
0
1
2
3
4
$600
$100
$289.28
$100
$289.28
$100
$289.28
$100
$289.28
The decision is easy once the charts of the two machines are compared. Would you
rather make annual lease payments of $321.05 or $289.28? Put this way, the problem becomes a no-brainer. Clearly, a rational person would rather pay the lower amount. Thus,
machine B is the preferred choice.
Two final remarks are in order. First, it is no accident that we specified the costs of the
tennis ball machines in real terms. While B would still have been the preferred machine had
the costs been stated in nominal terms, the actual solution would have been much more difficult. As a general rule, always convert cash flows to real terms when working through
problems of this type.
Second, the above analysis applies only if one anticipates that both machines can be replaced. The analysis would differ if no replacement were possible. For example, imagine that
the only company that manufactured tennis ball throwers just went out of business and no
new producers are expected to enter the field. In this case, machine B would generate revenues in the fourth year whereas machine A would not. Here, simple net present value analysis for mutually exclusive projects including both revenues and costs would be appropriate.
The General Decision to Replace (Advanced)
The previous analysis concerned the choice between machine A and machine B, both of
which were new acquisitions. More typically, firms must decide when to replace an existing
machine with a new one. This decision is actually quite straightforward. One should replace
if the annual cost of the new machine is less than the annual cost of the old machine. As with
much else in finance, an example clarifies this approach better than further explanation.
EXAMPLE
Consider the situation of BIKE, which must decide whether to replace an existing machine. BIKE currently pays no taxes.The replacement machine costs $9,000 now and requires maintenance of $1,000
at the end of every year for eight years. At the end of eight years the machine would be sold for $2,000.
The existing machine requires increasing amounts of maintenance each year, and its salvage value
falls each year, as shown:
Year
Maintenance
Salvage
Present
1
2
3
4
$
0
1,000
2,000
3,000
4,000
$4,000
2,500
1,500
1,000
0
Corporate Finance,
Seventh Edition
196
Budgeting
Companies, 2004
Capital Budgeting
This chart tells us that the existing machine can be sold for $4,000 now. If it is sold one year from
now, the resale price will be $2,500, and $1,000 must be spent on maintenance during the year to
keep it running. For ease of calculation, we assume that this maintenance fee is paid at the end of the
year.The machine will last for four more years before it falls apart. In other words, salvage value will
be zero at the end of year 4. If BIKE faces an opportunity cost of capital of 15 percent, when should
it replace the machine?
As we said above, our approach is to compare the annual cost of the replacement machine with
the annual cost of the old machine.The annual cost of the replacement machine is simply its equivalent annual cost (EAC). Let’s calculate that first.
Equivalent Annual Cost of New Machine
ment machine is as follows:
The present value of the cost of the new replace-
PVcosts $9,000 $1,000 A80.15 $2,000
(1.15) 8
$9,000 $1,000 (4.4873) $2,000 (0.3269)
$12,833
Notice that the $2,000 salvage value is an inflow. It is treated as a negative number in the above equation because it offsets the cost of the machine.
The EAC of a new replacement machine equals
PV兾8-year annuity factor at 15% PV
$12,833
$2,860
A80.15
4.4873
This calculation implies that buying a replacement machine is financially equivalent to renting this
machine for $2,860 per year.
Cost of Old Machine This calculation is a little trickier. If BIKE keeps the old machine for one
year, the firm must pay maintenance costs of $1,000 a year from now. But this is not BIKE’s only cost
from keeping the machine for one year. BIKE will receive $2,500 at date 1 if the old machine is kept
for one year but would receive $4,000 today if the old machine were sold immediately.This reduction in sales proceeds is clearly a cost as well.
Thus, the PV of the costs of keeping the machine one more year before selling it equals
$4,000 $1,000 $2,500
$2,696
1.15
1.15
That is, if BIKE holds the old machine for one year, BIKE does not receive the $4,000 today. This
$4,000 can be thought of as an opportunity cost. In addition, the firm must pay $1,000 a year from
now. Finally, BIKE does receive $2,500 a year from now.This last item is treated as a negative number because it offsets the other two costs.
While we normally express cash flows in terms of present value, the analysis to come is made
easier if we express the cash flow in terms of its future value one year from now.This future value is
$2,696 1.15 $3,100
In other words, the cost of keeping the machine for one year is equivalent to paying $3,100 at the
end of the year.
Making the Comparison Now let’s review the cash flows. If we replace the machine immediately,
we can view our annual expense as $2,860,beginning at the end of the year. This annual expense occurs
115
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
197
forever, if we replace the new machine every eight years.This cash flow stream can be written as
Expenses from replacing
machine immediately
Year 1
Year 2
Year 3
Year 4
...
$2,860
$2,860
$2,860
$2,860
...
If we replace the old machine in one year, our expense from using the old machine for that final
year can be viewed as $3,100, payable at the end of the year.After replacement, our annual expense
is $2,860, beginning at the end of two years. This annual expense occurs forever, if we replace the
new machine every eight years.This cash flow stream can be written as
Expenses from using old machine for
one year and then replacing it
Year 1
Year 2
Year 3
Year 4
...
$3,100
$2,860
$2,860
$2,860
...
Put this way, the choice is a no-brainer. Anyone would rather pay $2,860 at the end of the year than
$3,100 at the end of the year.Thus, BIKE should replace3 the old machine immediately in order to
minimize the expense at year 1.
Two final points should be made on the decision to replace. First, we have examined a situation
where both the old machine and the replacement machine generate the same revenues. Because
revenues are unaffected by the choice of machine, revenues do not enter our analysis.This situation
is common in business. For example, the decision to replace either the heating system or the air conditioning system in one’s home office will likely not affect firm revenues. However, sometimes revenues will be greater with a new machine.The above approach can easily be amended to handle differential revenues.
Second, we want to stress the importance of the above approach. Applications of the above
approach are pervasive in business, since every machine must be replaced at some point.
Concept
Question
1. What is the equivalent annual cost method of capital budgeting?
This chapter discusses a number of practical applications of capital budgeting.
1. Capital budgeting must be placed on an incremental basis. This means that sunk costs must be
ignored, while both opportunity costs and side effects must be considered.
2. In the Baldwin case, we computed NPV using the following two steps:
a. Calculate the net cash flow from all sources for each period.
b. Calculate the NPV using the cash flows calculated above.
3
One caveat is in order. Perhaps the old machine’s maintenance is high in the first year but drops after that. A decision to replace
immediately might be premature in that case. Therefore, we need to check the cost of the old machine in future years.
The cost of keeping the existing machine a second year is
PV of costs at time 1 $2,500 $2,000 $1,500
$2,935
1.15
1.15
which has future value of $3,375 ($2,935 1.15).
The costs of keeping the existing machine for years 3 and 4 are also greater than the EAC of buying a new machine. Thus,
BIKE’s decision to replace the old machine immediately is still valid.
116
Corporate Finance,
Seventh Edition
198
Budgeting
Companies, 2004
Capital Budgeting
3. Inflation must be handled consistently. One approach is to express both cash flows and the discount rate in nominal terms.The other approach is to express both cash flow and the discount rate
in real terms.Because either approach yields the same NPV calculation,the simpler method should
be used.The simpler method will generally depend on the type of capital budgeting problem.
4. A firm should use the equivalent annual cost approach when choosing between two machines of
unequal lives.
opportunity cost, 179
real cash flow, 191
real interest rate, 189
sunk cost, 179
synergy, 179
KEY TERMS
allocated cost, 180
erosion, 179
net working capital, 181
nominal cash flow, 191
nominal interest rate, 189
SUGGESTED
READING
An excellent in-depth examination of the capital budgeting decision is contained in:
Copeland,T.,T. Koller, and J. Murrin. Valuation: Measuring and Managing the Value of Companies, 3rd ed.
The McKinsey Company, 1996.
QUESTIONS
& PROBLEMS
7.1
Which of the following should be treated as incremental cash flows when computing the NPV
of an investment?
a. A reduction in the sales of a company’s other products caused by the investment.
b. An expenditure on plant and equipment that has not yet been made and will be made only
if the project is accepted.
c. Costs of research and development undertaken in connection with the product during the
past three years.
d. Annual depreciation expense from the investment.
e. Dividend payments by the firm.
f. The resale value of plant and equipment at the end of the project’s life.
g. Salary and medical costs for production personnel who will be employed only if the
project is accepted.
7.2
Your company currently produces and sells steel-shaft golf clubs.The board of directors wants
you to consider the introduction of a new line of titanium bubble woods with graphite shafts.
Which of the following costs are not relevant?
I. Land you already own that will be used for the project, but otherwise will be sold for
$700,000, its market value.
II. A $300,000 drop in your sales of steel-shaft clubs if the titanium woods with graphite
shafts are introduced.
III. $200,000 spent on research and development last year on graphite shafts.
a. I only
b. II only
c. III only
d. I and III only
e. II and III only
7.3
The Best Manufacturing Company is considering a new investment. Financial projections for
the investment are tabulated below. Cash flows are in $ thousands, and the corporate tax rate
is 34 percent. Assume all sales revenue is received in cash, all operating costs and income
taxes are paid in cash, and all cash flows occur at the end of the year.
NPV AND CAPITAL
BUDGETING
Investment
Sales revenue
Operating costs
Depreciation
Net working capital
(end of year)
Year 0
Year 1
Year 2
Year 3
Year 4
$10,000
—
—
—
200
—
$7,000
2,000
2,500
250
—
$7,000
2,000
2,500
300
—
$7,000
2,000
2,500
200
—
$7,000
2,000
2,500
—
117
Corporate Finance,
Seventh Edition
Budgeting
Capital Budgeting
Companies, 2004
199
a. Compute the incremental net income of the investment for each year.
b. Compute the incremental cash flows of the investment for each year.
c. Suppose the appropriate discount rate is 12 percent.What is the NPV of the project?
7.4
According to the February 7, 2002, issue of The Sports Universe, the Seattle Mariner’s designated runner, Andy Schneider, signed a three-year contract in January 2002 with the following
provisions:
a. $1,400,000 signing bonus
b. $2,500,000 salary per year for three years
c. 10 years of deferred payments of $1,250,000 per year (these payments begin in year 4)
d. Several bonus provisions that total as much as $750,000 per year for the three years of
the contract
Assume that Schneider has a 60-percent probability of receiving the bonuses each year, and
that he signed the contract on January 1, 2002. Use the expected value of the bonuses as
incremental cash flows. Assume that expected cash flows are discounted at 12.36 percent.
Ignore taxes. Schneider’s signing bonus was paid on January 1, 2002. Schneider’s salary and
bonuses other than the signing bonus are paid at the end of the year.What was the present
value of this contract in January when Schneider signed it?
7.5
Benson Enterprises is evaluating alternative uses for a three-story manufacturing and warehousing building that it has purchased for $225,000. The company can continue to rent the
building to the present occupants for $12,000 per year.The present occupants have indicated
an interest in staying in the building for at least another 15 years. Alternatively, the company
could modify the existing structure to use for its own manufacturing and warehousing needs.
Benson’s production engineer feels the building could be adapted to handle one of two new
product lines.The cost and revenue data for the two product alternatives are as follows:
Initial cash outlay for building modifications
Initial cash outlay for equipment
Annual pretax cash revenues (generated for 15 years)
Annual pretax expenditures (generated for 15 years)
Product A
Product B
$ 36,000
144,000
105,000
60,000
$ 54,000
162,000
127,500
75,000
The building will be used for only 15 years for either Product A or Product B.After 15 years,
the building will be too small for efficient production of either product line. At that time,
Benson plans to rent the building to firms similar to the current occupants.To rent the building again, Benson will need to restore the building to its present layout. The estimated cash
cost of restoring the building if Product A has been undertaken is $3,750. If Product B has
been manufactured, the cash cost will be $28,125.These cash costs can be deducted for tax
purposes in the year the expenditures occur.
Benson will depreciate the original building shell (purchased for $225,000) over a 30-year
life to zero, regardless of which alternative it chooses.The building modifications and equipment purchases for either product are estimated to have a 15-year life.They will be depreciated by the straight-line method.The firm’s tax rate is 34 percent, and its required rate of return on such investments is 12 percent.
For simplicity, assume all cash flows occur at the end of the year. The initial outlays for
modifications and equipment will occur today (year 0), and the restoration outlays will occur
at the end of year 15. Benson has other profitable ongoing operations that are sufficient to
cover any losses.Which use of the building would you recommend to management?
7.6
Dickinson Brothers, Inc., is considering investing in a machine to produce computer keyboards. The price of the machine will be $400,000 and its economic life is five years. The
machine will be fully depreciated by the straight-line method. The machine will produce
10,000 keyboards each year.The price of each keyboard will be $40 in the first year and will
increase by 5 percent per year.The production cost per keyboard will be $20 in the first year
and will increase by 10 percent per year.The corporate tax rate for the company is 34 percent. If the appropriate discount rate is 15 percent, what is the NPV of the investment?
118
Corporate Finance,
Seventh Edition
200
Budgeting
Capital Budgeting
Companies, 2004
7.7
Scott Investors, Inc., is considering the purchase of a $500,000 computer with an economic life
of five years. The computer will be fully depreciated over five years using the straight-line
method.The market value of the computer will be $100,000 in five years.The computer will replace five office employees whose combined annual salaries are $120,000.The machine will also
immediately lower the firm’s required net working capital by $100,000. This amount of net
working capital will need to be replaced once the machine is sold.The corporate tax rate is
34 percent.Is it worthwhile to buy the computer if the appropriate discount rate is 12 percent?
7.8
The Gap is considering buying cash register software from Microsoft so that it can more effectively deal with its retail sales. The software package costs $750,000 and will be depreciated down to zero using the straight-line method over its five-year economic life.The marketing department predicts that sales will be $600,000 per year for the next three years, after
which the market will cease to exist. Cost of goods sold and operating expenses are predicted to be 25 percent of sales.After three years the software can be sold for $40,000.The
Gap also needs to add net working capital of $25,000 immediately.The additional net working capital will be recovered in full at the end of the project life.The corporate tax rate for the
Gap is 35 percent and the required rate of return relevant to the project is 17 percent.What
is the NPV of the new software?
7.9
Commercial Real Estate, Inc., is considering the purchase of a $4 million building. The company will enter into a long-term lease to commercial tenants, with payments made annually.
The building will be fully depreciated over 20 years via the straight-line method. In addition,
the market value of the building will be zero at that time.The annual lease payments will increase at 3 percent per year.The appropriate discount rate for all cash flows is 12 percent.
The corporate tax rate is 34 percent. What is the least amount of money that Commercial
Real Estate should ask for the first-year lease payment? Assume that the first lease payment
is made immediately after the signing of the contract.
7.10 Royal Dutch Petroleum is considering a new project that complements its existing business.
The machine required for the project costs $2 million. The marketing department predicts
that sales related to the project will be $1.2 million per year for the next four years, after
which the market will cease to exist.The machine will be depreciated down to zero over its
five-year economic life using the straight-line method. Cost of goods sold and operating expenses related to the project are predicted to be 25 percent of sales. After four years the
machine can be sold for $150,000. Royal Dutch also needs to add net working capital of
$100,000 immediately.The additional net working capital will be recovered in full at the end
of the project’s life.The corporate tax rate is 35 percent.The required rate of return for Royal
Dutch Petroleum is 16.55 percent. Should Royal Dutch proceed with the project?
7.11 Majestic Mining Corporation (MMC) is negotiating the purchase of a new piece of equipment
for its current operations. MMC wants to know the maximum price that it should be willing
to pay for the equipment.You are given the following facts:
a. The new equipment would replace existing equipment with a current market value of $20,000.
b. The new equipment would not affect revenues, but before-tax operating costs would be
reduced by $10,000 per year for eight years.These savings in cost occur at year-end.
c. The old equipment is now five years old. It is expected to last for another eight years, and
will have no resale value at that time. It was purchased for $40,000 and is being depreciated to zero by the straight-line method over 10 years.
d. The new equipment will be depreciated to zero by the straight-line method over five
years. MMC expects to sell the equipment for $5,000 at the end of eight years.The proceeds from this sale will be subject to taxes at the ordinary corporate income tax rate of
34 percent.
e. MMC has profitable ongoing operations.
f. The appropriate discount rate is 8 percent.
7.12 A firm is considering an investment of $28 million (purchase price) in new equipment to replace old equipment with a book value of $12 million and a market value of $20 million. If the
firm replaces the old equipment with the new equipment, it expects to save $17.5 million in
119
Corporate Finance,
Seventh Edition
Budgeting
Capital Budgeting
Companies, 2004
201
operating costs the first year.The amount of these savings will grow at a rate of 12 percent
per year for each of the following three years.The old equipment has a remaining life of four
years. It is being depreciated by the straight-line method. 33.3 percent of the original book
value of the new equipment will be depreciated in the first year, 39.9 percent will be depreciated in the second year, 14.8 percent will be depreciated in the third year, and 12.0 percent
will be depreciated in the final year.The salvage value of both the old equipment and the new
equipment at the end of four years is 0. In addition, replacement of the old equipment with
the new equipment requires an immediate increase in net working capital of $5 million, which
will not be recovered until the end of the four-year investment. Assume that the purchase and
sale of equipment occurs today and all other cash flows occur at the end of their respective
years. If the firm’s cost of capital is 14 percent and is subject to a 40 percent tax rate, find:
a. The net investment.
b. The after-tax incremental cash flow at the end of each year.
c. The internal rate of return on the investment.
d. The net present value of the investment.
7.13 Shoe-tek, Inc., is a leading manufacturer of running shoes. With the baby boomers getting
older, they realized the potential market in shoes specifically designed for walking rather than
running. Market research suggests that the walking shoe market will be $100 million and
Shoe-tek could capture 20 percent of this market because of its strong brand. However, it is
estimated that 10 percent of Shoe-tek’s current sales of running shoes are already being used
by baby boomers for walking. If Shoe-tek introduces a walking shoe, half of these consumers
would switch from Shoe-tek’s running shoe to walking shoes. Shoe-tek has already spent
$10 million on R&D for its running shoes and could leverage this and produce a totally new
walking shoe for an additional $1 million in R&D. Shoe-tek would also need to construct an
extension to their warehouse to accommodate the additional materials and inventory. This
extension would cost $1 million. If annual revenues for Shoe-tek are $80 million, what is the
amount to use as the annual sales figure when evaluating this project? Why?
7.14 Carson Palmer, the 2002 Heisman Trophy winner, was the #1 draft pick in the NFL. His agent
was asking for a five-year contract with the following provisions:
• $5 million signing bonus
• $2 million a year salary
• Several bonus provisions that total as much as $2 million a year, for each of the five years
Assume that Carson has a 50 percent probability of receiving the entire bonus each year and
that he signs the contract on January 1. Also, assume an effective annual interest rate of
12 percent and ignore taxes. Carson’s salary and bonus are paid at the end of the year.What
is the present value of Carson’s contract in January?
7.15 With the growing popularity of casual surf print clothing, two recent MBA graduates decided
to broaden this casual surf concept to encompass a “surf lifestyle for the home.” With limited
capital,they decided to focus on surf print table and floor lamps to accent people’s homes.They
projected unit sales of these lamps to be 5,000 in the first year, with growth of 15 percent each
year, for the next five years. Production of these lamps will require $28,000 in net working
capital to start, and additional net working capital investments each year equal to 40 percent
of the projected sales increase for that year. Total fixed costs are $75,000 per year, variable
production costs are $20 per unit, and the units are priced at $45 each.The equipment needed
to begin production will cost $60,000.The equipment will be depreciated using a straight-line
method over a five-year life and is not expected to have a salvage value.The effective tax rate
is 34 percent and the required rate of return is 25 percent.What is the NPV of this project?
7.16 The Big Burrito is planning to purchase a touch screen order system for its drive-thru window that would allow customers to select their order as soon as they arrive.This would reduce customer wait time and increase order accuracy.The touch screen and software would
cost the Big Burrito $150,000 and would last five years.There would also be an annual maintenance cost of $5,000. In addition to improved customer service, the Big Burrito would gain
two benefits. First, they could totally eliminate the full-time worker who used to accept and
120
Corporate Finance,
Seventh Edition
202
Budgeting
Companies, 2004
Capital Budgeting
enter these orders. His annual salary plus benefits total $30,000 per year. Second, they expect
drive-thru sales to increase by $15,000 a year due to improved customer perception and increased through-put. Cost of goods sold is 25 percent of the incremental sales. Net working
capital (NWC) is expected to increase by $5,000 in the first year and be recovered at the end
of five years. If the appropriate discount rate is 15 percent and you ignore taxes, should the
Big Burrito go ahead with this investment?
7.17 A new basketball star, Jun, is coming from Seoul, Korea! The following are the provisions of his
four-year deal with the San Francisco Golden Gates!
$500,000 signing bonus
$800,000 salary per year for four years.
8 years of deferred payments of $100,000 per year beginning year 5.
Several bonus provisions that total about $150,000 per year for the four years of the contract.
Assuming that Jun has a 55 percent chance of receiving the bonus each year, and that he signed
the contract on January 1, what is the present value of his contract at signing? Jun’s salary and
bonus are paid at the end of each year. The effective annual interest rate is at 10.5 percent.
Please ignore taxes.
7.18 Maruta is considering the purchase of a $1.5 million automation machine for its popular
Kamury sedan line. The automation machine will have a useful life of five years and will depreciate based on the system enacted by the Tax Reform Act of 1986. (See Table 7.3 for the
depreciation schedules.) The market value of the automation machine will be $0.4 million in
five years. On the benefit side, the automation machine will replace 20 factory workers,
whose annual salaries are $0.3 million. In addition, the use of the machine will lower net working capital requirements by $0.5 million, although that requirement will return to normal after
the five years.The corporate tax rate is 34 percent.
Is it worthwhile to purchase the automation machine if the discount rate is 15 percent?
7.19 Raphael Restaurant is considering the purchase of a $10,000 souffle maker.The souffle maker
has an economic life of five years and will be fully depreciated by the straight-line method.The
machine will produce 2,000 souffles per year, with each costing $2 to make and priced at $5.
As for additional cost, the increase in net working capital requirements is $1,000, which will
be fully recovered at the end of year 5. Assume that the discount rate is 17 percent and the
tax rate is 34 percent.
Is it worthwhile for Raphael to make the purchase?
7.20 Galweiser Glass is considering adding a machine that will make 2.0 liter glass bottles.The machine will cost $1 million and will produce 2 million bottles per year with each bottle costing
$0.10.The useful economic life of the machine is five years, which will be depreciated straightline with no salvage value.The increase in net working capital requirements is $10,000, which
will be fully recovered at the end of year 5. Assume that the discount rate is 13 percent and
the tax rate is 34 percent.
a. At what price per bottle will the NPV of the machine be 0?
b. If the market value per bottle is $0.25,is it worthwhile for Galweiser to make the investment?
CAPITAL
BUDGETING
WITH INFLATION
7.21 Consider the following cash flows on two mutually exclusive projects.
Year
Project A
Project B
0
1
2
3
$40,000
20,000
15,000
15,000
$50,000
10,000
20,000
40,000
The cash flows of Project A are expressed in real terms while those of Project B are expressed in nominal terms.The appropriate nominal discount rate is 15 percent and the inflation rate is 4 percent.Which project should you choose?
121
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
203
7.22 Etonic Inc. is considering an investment of $250,000 in an asset with an economic life of five
years.The firm estimates that the nominal annual cash revenues and expenses at the end of
the first year will be $200,000 and $50,000, respectively. Both revenues and expenses will
grow thereafter at the annual inflation rate of 3 percent. Etonic will use the straight-line
method to depreciate its asset to zero over five years.The salvage value of the asset is estimated to be $30,000 in nominal terms at that time.The one-time net working capital investment of $10,000 is required immediately and will be recovered at the end of the project.The
nominal discount rate for all cash flows is 15 percent.All corporate cash flows are subject to
a 34 percent tax rate.What is the project’s total nominal cash flow from assets in year 5?
7.23 Sanders Enterprises, Inc. has been considering the purchase of a new manufacturing facility for
$120,000.The facility is to be fully depreciated on a straight-line basis over seven years. It is
expected to have no resale value after the seven years. Operating revenues from the facility
are expected to be $50,000, in nominal terms, at the end of the first year.The revenues are
expected to increase at the inflation rate of 5 percent. Production costs at the end of the first
year will be $20,000, in nominal terms, and they are expected to increase at 7 percent per
year.The real discount rate is 14 percent.The corporate tax rate is 34 percent. Sanders has
other ongoing, profitable operations. Should the company accept the project?
7.24 Phillips Industries runs a small manufacturing operation. For this fiscal year, it expects real net
cash flows of $120,000. Phillips is an ongoing operation, but it expects competitive pressures
to erode its real net cash flows at 6 percent per year in perpetuity. The appropriate real
discount rate for Phillips is 11 percent. All net cash flows are received at year-end. What is
the present value of the net cash flows from Phillips’s operations?
7.25 The Biological Insect Control Corporation (BICC) has hired you as a consultant to evaluate
the NPV of their proposed toad ranch. BICC plans to breed toads and sell them as ecologically desirable insect-control mechanisms.They anticipate that the business will continue into
perpetuity. Following the negligible start-up costs, BICC expects the following nominal cash
flows at the end of the year.
Revenues
Labor costs
Other costs
$150,000
80,000
40,000
The company will lease machinery for $20,000 per year.The lease payments start at the end
of year 1 and are expressed in nominal terms. Revenues will increase by 5 percent per year in
real terms. Labor costs will increase by 3 percent per year in real terms. Other costs will decrease by 1 percent per year in real terms.The rate of inflation is expected to be 6 percent
per year. BICC’s required rate of return is 10 percent in real terms. There are no taxes.
All cash flows occur at year-end.What is the NPV of BICC’s proposed toad ranch today?
7.26 Sony International has an investment opportunity to produce a new stereo color TV. The
required investment on January 1 of this year is $32 million.The firm will depreciate the investment to zero using the straight-line method over four years.The investment has no resale value
after completion of the project.The firm is in the 34 percent tax bracket.The price of the product will be $400 per unit, in real terms, and will not change over the life of the project. Labor
costs forYear 1 will be $15.30 per hour, in real terms, and will increase at 2 percent per year in
real terms. Energy costs forYear 1 will be $5.15 per physical unit, in real terms, and will increase
at 3 percent per year in real terms.The inflation rate is 5 percent per year. Revenues are received and costs are paid at year-end. Refer to the table below for the production schedule.
Physical production, in units
Labor input, in hours
Energy input, physical units
Year 1
Year 2
Year 3
Year 4
100,000
2,000,000
200,000
200,000
2,000,000
200,000
200,000
2,000,000
200,000
150,000
2,000,000
200,000
The real discount rate for Sony is 8 percent. Calculate the NPV of this project.
122
Corporate Finance,
Seventh Edition
204
Budgeting
Companies, 2004
Capital Budgeting
7.27 Sparkling Water, Inc., expects to sell 2 million bottles of drinking water each year in perpetuity.This year, each bottle will sell for $2.50 in real terms and will cost $0.70 in real terms. Sales
income and costs occur at year-end. Revenues will rise at a real rate of 7 percent annually,
while real costs will rise at a real rate of 5 percent annually.The real discount rate is 10 percent.The corporate tax rate is 34 percent.What is Sparkling worth today?
7.28 International Buckeyes is building a factory that can make 1 million buckeyes a year for five
years, after which the market will cease to exist. The factory costs $6 million, paid immediately. In year 1, each buckeye will sell for $3.15 in nominal terms.The price will increase 5 percent each year in real terms.Variable costs will be $0.2625 per buckeye in nominal terms in
year 1 and will rise by 2 percent each subsequent year in real terms. International Buckeyes
will fully depreciate the factory over five years by the straight-line method.The firm will be
able to sell the factory for $638,140.78 in nominal terms at the end of year 5.The nominal discount rate for cash flows is 20 percent.The rate of inflation is 5 percent. Cash flows, except
for the initial investment, occur at the end of each year.The corporate tax rate is 34 percent.
What is the NPV of the project?
7.29 After extensive medical and marketing research, Pill, Inc. believes it can penetrate the pain
reliever market. It is considering two alternative products.The first is to produce a medication for headache pain. The second is a pill for headache and arthritis pain. Both products
would be introduced at a price of $4 per package in real terms.The headache-only medication is projected to sell 5 million packages a year, while the headache and arthritis remedy
would sell 10 million packages a year. Cash costs of production in the first year are expected
to be $1.50 per package in real terms for the headache-only brand. Production costs are expected to be $1.70 in real terms for the headache and arthritis pill. All prices and costs are
expected to rise at the general inflation rate of 5 percent.
Either product requires further investment. The headache-only pill could be produced
using equipment costing $10.2 million.That equipment would last three years and have no resale value. The machinery required to produce the broader remedy would cost $12 million
and last three years.The firm expects that equipment to have a $1 million resale value (in real
terms) at the end of year 3.
Pill, Inc., uses straight-line depreciation.The firm faces a corporate tax rate of 34 percent
and believes that the appropriate real discount rate is 13 percent.Which pain reliever should
the firm produce?
EQUIVALENT
ANNUAL COST AND
REPLACEMENT
WITH UNEQUAL
LIVES
7.30 A machine with a four-year life is purchased for $12,000.The annual year-end operating cost
is $6,000. At the end of four years, the machine is sold for $2,000.The cash outflows each year
can be represented as follows:
C0
C1
C2
C3
C4
$12,000
$6,000
$6,000
$6,000
$4,000
The cost of capital is 6 percent. Ignore taxes.What is the present value of the cost of operating a series of such machines in perpetuity?
7.31 A machine costs $60,000 and requires $5,000 maintenance for each year of its three-year life.
The maintenance costs are paid at the end of each year. After three years, the machine will be
replaced. Assume a tax rate of 34 percent and a discount rate of 14 percent. If the machine is
depreciated over three years using the straight-line method, with no salvage value, what is the
equivalent annual cost (EAC)?
7.32 United Healthcare, Inc., needs a new admitting system. The system costs $60,000, requires
$2,000 in maintenance for each year of its five-year economic life, and has no salvage value.
The maintenance costs are paid at the end of each year. The system will be fully depreciated using the straight-line method over five years. Assume a tax rate of 35 percent and
an annual discount rate of 18 percent. What is the equivalent annual cost of this admitting
system?
123
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Capital Budgeting
205
7.33 Bridgton Golf Academy is evaluating different golf practice equipment. The “Dimple-Max”
equipment costs $45,000, has a three-year life, and costs $5,000 per year to operate.The relevant discount rate is 12 percent.Assume that the straight-line depreciation method is used
and that the equipment is fully depreciated to zero. Furthermore, assume the equipment has
a salvage value of $10,000 at the end of the project’s life.The relevant tax rate for income and
capital gains is 34 percent.All cash flows occur at the end of the year.What is the equivalent
annual cost (EAC) of this equipment?
7.34 Office Automation, Inc., must choose between two copiers, the XX40 or the RH45. The
XX40 costs less than the RH45, but its economic life is shorter.The costs and maintenance
expenses of these two copiers, expressed in real terms, are given as follows:
Copier
XX40
RH45
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
$700
$900
$100
$110
$100
$110
$100
$110
—
$110
—
$110
All cash flows occur at year-end.The inflation rate is 5 percent, and the nominal discount rate
is 14 percent. Assume that revenues are the same regardless of the copier, and assume that
whichever copier the company chooses, it will continue to buy that model forever. Which
copier should the company choose? Ignore taxes and depreciation.
7.35 Plexi Glasses, Inc., must choose between two facilities. Facility 1 costs $2.1 million and has an
economic life of seven years.The maintenance costs for Facility 1 are $60,000 per year. Facility 2 costs $2.8 million and has an economic life of 10 years.The annual maintenance costs for
Facility 2 are $100,000 per year. Both facilities will be fully depreciated to zero by the straightline method. The facilities will have no resale values at the end of their economic lives. The
corporate tax rate is 34 percent. Revenues from the facilities are the same.The company is
assumed to earn sufficient revenues to generate tax shields from depreciation. Assume all
cash flows besides the initial investment occur at the end of the year. If the appropriate discount rate is 10 percent, which facility should Plexi Glasses, Inc., choose?
7.36 Pilot Plus Pens is deciding when to replace its old machine.The old machine’s current salvage
value is $2 million. Its current book value is $1 million. If not sold, the old machine will require
maintenance costs of $400,000 at the end of the year for the next five years. Depreciation on
the old machine is $200,000 per year.At the end of five years, the old machine will have a salvage value of $200,000 and a book value of $0.A replacement machine costs $3 million now
and requires maintenance costs of $500,000 at the end of each year during its economic life
of five years. At the end of the five years, the new machine will have a salvage value of
$500,000. It will be fully depreciated by the straight-line method. In five years, a replacement
machine will cost $3,500,000. Pilot will need to purchase this machine regardless of what
choice it makes today.The corporate tax rate is 34 percent and the appropriate discount rate
is 12 percent.The company is assumed to earn sufficient revenues to generate tax shields from
depreciation. Should Pilot Plus Pens replace the old machine now or at the end of five years?
7.37 Gold Star Industries is contemplating a purchase of computers. The firm has narrowed its
choices to the SAL 5000 and the DET 1000. Gold Star would need 10 SALs, where each SAL
costs $3,750 and requires $500 of maintenance each year. At the end of the computer’s eightyear life, Gold Star expects to sell each one for $500.Alternatively, Gold Star could buy eight
DETs. Each DET costs $5,250 and requires $700 of maintenance every year. Each DET lasts
for six years and has a resale value of $600 at the end of its economic life. Gold Star will continue to purchase the model that it chooses today into perpetuity. Ignore tax effects and assume that the maintenance costs occur at year-end.Which model should Gold Star buy if the
appropriate discount rate is 11 percent?
7.38 Harwell University must purchase word processors for its typing lab.The university can buy
10 EVF word processors that cost $8,000 each and have annual, year-end maintenance costs
124
Corporate Finance,
Seventh Edition
206
Budgeting
Companies, 2004
Capital Budgeting
of $2,000 per machine.The EVF word processors will be replaced at the end of year 4 and
have no value at that time.Alternatively, Harwell can buy 11 AEH word processors to accomplish the same work.The AEH word processors will be replaced after three years.They each
cost $5,000, and have annual, year-end maintenance costs of $2,500 per machine. Each AEH
word processor will have a resale value of $500 at the end of three years. The university’s
opportunity cost of funds for this type of investment is 14 percent. Because the university is
a nonprofit institution, it does not pay taxes. It is anticipated that whichever manufacturer
is chosen now will be the supplier of future machines. Would you recommend purchasing
10 EVF word processors or 11 AEH machines?
7.39 DJ Party, Inc., is considering the replacement of its old, fully depreciated sound mixer.Two new
models are available. Mixer X costs $400,000, has a five-year economic life, and yields cash
flow savings of $120,000 per year. Mixer Y costs $600,000, has an eight-year economic life, and
yields cash flow savings of $130,000 per year. No new technological developments are expected. Ignore taxes. The cost of capital is 11 percent. Should DJ Party, Inc., replace the old
mixer with X or Y?
7.40 KZD Construction must choose between two pieces of equipment.Tamper A costs $600,000
and lasts five years.This tamper requires $110,000 of maintenance each year.Tamper B costs
$750,000, but lasts 7 years. Maintenance costs for Tamper B are $90,000 per year.All maintenance costs occur at the end of the year.The appropriate discount rate for KZD Construction is 12 percent. Ignore taxes.Which machine should KZD purchase?
7.41 Klious Pharmaceuticals must decide when to replace its autoclave. Klious’s current autoclave
will require increasing amounts of maintenance at the end of each year.The resale value of the
equipment falls every year. For example, if the firm replaces the old machine today, it will incur
no maintenance costs related to the old machine and will be able to sell it immediately for $900.
If the firm replaces the old machine at the end of the first year, it will incur maintenance costs
of $200 and be able to sell the machine for $850.Refer to the following table for complete data:
Year
Maintenance Costs
Resale Value
0 (Today)
1
2
3
4
5
$ 0
200
275
325
450
500
$900
850
775
700
600
500
In any year, Klious can purchase a new autoclave for $3,000.The equipment has an economic
life of five years. At the end of each year, the equipment requires $20 of maintenance. Klious
expects to sell the machine for $1,200 at the end of five years. Klious pays no taxes and employs a discount rate of 10 percent. Maintenance costs and the realization of the resale value
occur at the end of each year. (Note: the forgone resale value occurs at the beginning of each
year.) When should Klious replace its current machine?
MINICASES Goodweek Tires, Inc.
After extensive research and development, Goodweek Tires, Inc., has recently developed a
new tire, the SuperTread, and must decide whether to make the investment necessary to
produce and market the SuperTread. The tire would be ideal for drivers doing a large
amount of wet weather and off-road driving in addition to its normal freeway usage. The
research and development costs so far total about $10 million. The SuperTread would be
put on the market beginning this year and Goodweek expects it to stay on the market for
125
Corporate Finance,
Seventh Edition
Budgeting
Capital Budgeting
Companies, 2004
207
a total of four years. Test marketing costing $5 million shows that there is a significant
market for a SuperTread-type tire.
As a financial analyst at Goodweek Tires, you are asked by your CFO, Mr. Adam Smith,
to evaluate the SuperTread project and provide a recommendation on whether to go ahead
with the investment. You are informed that all previous investments in the SuperTread are
sunk costs and only future cash flows should be considered. Except for the initial investment which will occur immediately, assume all cash flows will occur at year-end.
Goodweek must initially invest $120 million in production equipment to make the
SuperTread. The equipment is expected to have a seven-year useful life. This equipment
can be sold for $51,428,571 at the end of four years. Goodweek intends to sell the
SuperTread to two distinct markets:
1. The Original Equipment Manufacturer (OEM) Market The OEM market consists primarily of the large automobile companies (e.g., General Motors) who buy tires for new
cars. In the OEM market, the SuperTread is expected to sell for $36 per tire. The variable
cost to produce each tire is $18.
2. The Replacement Market The replacement market consists of all tires purchased after
the automobile has left the factory. This market allows higher margins and Goodweek
expects to sell the SuperTread for $59 per tire there. Variable costs are the same as in the
OEM market.
Goodweek Tires intends to raise prices at 1 percent above the inflation rate. Variable
costs will also increase 1 percent above the inflation rate. In addition, the SuperTread project will incur $25 million in marketing and general administration costs the first year (this
figure is expected to increase at the inflation rate in the subsequent years).
Goodweek’s corporate tax rate is 40 percent. Annual inflation is expected to remain
constant at 3.25 percent. The company uses a 15.9 percent discount rate to evaluate new
product decisions.
The Tire Market
Automotive industry analysts expect automobile manufacturers to produce 2 million new
cars this year and production to grow at 2.5 percent per year thereafter. Each new car needs
four tires (the spare tires are undersized and are in a different category). Goodweek Tires
expects the SuperTread to capture 11 percent of the OEM market.
Industry analysts estimate that the replacement tire market size will be 14 million tires
this year and that it will grow at 2 percent annually. Goodweek expects the SuperTread to
capture an 8 percent market share.
You decide to use the MACRS depreciation schedule (seven-year property class). You
also decide to consider net working capital (NWC) requirements in this scenario. The immediate initial working capital requirement is $11 million, and thereafter the net working
capital requirements will be 15 percent of sales. What will be the NPV, payback period, discounted payback period, AAR, IRR, and PI on this project?
I.Q., Inc.
In order to maintain its leadership position in the computer peripherals industry, particularly inkjet printers and accessories, I.Q. has begun to develop a new ink for its 8xx line of
inkjet printers. As a marketing manager of the 8xx line of inkjet printers and accessories,
you are in the position to make a decision whether or not to continue the development. The
project is codenamed IQ8Ink.
126
Corporate Finance,
Seventh Edition
208
Budgeting
Capital Budgeting
Companies, 2004
Research efforts for the IQ8Ink has cost I.Q., Inc., $1 million so far, in addition to a positive test marketing effort costing $0.5 million. However, these are sunk costs and will not
impact your decision making. What should be considered are the new investment and
future cash inflows. From your observation, you know that you can invest immediately and
start production now. You also know that the economic life of this effort is only four years,
meaning potentially four years of production.
I.Q.’s CEO K. Fione is very pleased with the progress of the 8xx line so far and wishes to
congratulate you on a job well done. So, the decision on the development of IQ8Ink is critical. From engineering, you know that you will need to invest another $1 million in production equipment to make this new ink. The equipment will have a useful life of five years and
will depreciate by the straight-line method. At year 4, you expect to sell the equipment for
$0.3 million. Furthermore, the net working capital requirement will increase by $1 million
immediately and will be recaptured at year 4.
As for the potential customers, there are two distinct segments:
1. New 8xx printers—For every new 8xx printer, one unit of this new ink will be used. (Assume complete retirement of old ink models with no costs associated.) Internal transfer
price is at $2 now. The variable cost to produce per unit is $0.50.
2. Existing 8xx printers—While competitors exist, offering generic ink, IQ8Ink is superior
and will take a large percentage of market share. Wholesale price is at $10 now. The
variable cost to produce per unit is the same as above.
Note that on average, ink price and cost rise at 2 percent above the inflation rate. In addition, marketing and administration efforts will cost $0.5 million the first year and increase
at inflation each subsequent year.
From economic data, inflation is expected to remain constant at 3 percent. I.Q.’s corporate tax rate is 34 percent and the division has a discount rate of 15 percent.
Last, you know that production of new 8xx printers will be 300,000 units in the first year
and will increase by 10 percent per year. Additionally, the demand for ink from existing
8xx printers is 1 million units in the first year and increases by 10 percent per year. Out of the
demand for ink from existing 8xx printers, I.Q. expects to capture 80 percent.
Jimmy’s Hot Dog Stands
Jimmy Levitin owns a popular hot dog stand on a trendy section of Melrose Boulevard.
Following the success of his first hot dog stand, “Jimmy’s,” which has been in operations
for five years, Jimmy is now considering opening a second hot dog stand in another trendy
location, on Sunset Boulevard in the Silver Lake area. Jimmy’s market research shows that
the clientele in both areas is similar: young professionals, typically without children, who
like the traditional aspect of eating hot dogs, but also relish his gourmet, specially manufactured low-fat dogs and the healthy side dishes his stand also sells. Jimmy’s overall plan
is to get the second stand up and running for five years, and then sell both stands off to a
new owner and retire to Santa Barbara.
Jimmy estimates that the cost of starting up a second stand will be as follows:
Purchase of real estate (retail food outlet)
Installation of specialized kitchen equipment
Furniture and fittings
$400,000
40,000
25,000
Jimmy estimates that net working capital will increase by $20,000 for the first year for the
new outlet. He also estimates that yearly operating costs of the new location would be
127
Corporate Finance,
Seventh Edition
Budgeting
Capital Budgeting
Companies, 2004
209
almost identical to those of his current stand:
Labor costs, inclusive of all overhead costs:
Kitchen and service staff (4 persons)
Raw materials:
Hot dogs: 200 per day 7 days 52 weeks
Drinks
Other food supplies
Nonfood supplies
Total raw materials
The revenues at his current location are as follows:
Sales of hot dogs and other food items
Drinks
Total revenues
$ 96,000
54,600
18,400
72,800
22,200
________
$168,000
$418,000
92,000
________
$510,000
In addition to contributing profits, Jimmy expects that opening a second stand will decrease
the cost of purchasing gourmet hot dogs from 75 cents to 60 cents in both locations. This
is due to economies of scale, since the new outlet would double output over the current
level of demand. Jimmy also expects that he will be able to manage both locations himself,
avoiding hiring a second manager for the new location.
Assume that:
• The marginal tax rate is 34 percent.
• The required rate of return is 10 percent.
• Depreciate over five years using the straight-line method.
What is the NPV of this investment?
Appendix 7A
Depreciation
The Baldwin case made some assumptions about depreciation. Where did these assumptions come from? Assets are currently depreciated for tax purposes according to the provisions of the 1986 Tax Reform Act. There are seven classes of depreciable property.
• The three-year class includes certain specialized short-lived property. Tractor units and
•
•
•
•
•
racehorses over two years old are among the very few items fitting into this class.
The five-year class includes (a) cars and trucks; (b) computers and peripheral equipment, as well as calculators, copiers, and typewriters; and (c) specific items used for
research purposes.
The seven-year class includes office furniture, equipment, books, and single-purpose
agricultural structures. It is also a catch-all category, because any asset not designated
to be in another class is included here.
The 10-year class includes vessels, barges, tugs, and similar equipment related to
water transportation.
The 15-year class encompasses a variety of specialized items. Included are equipment
of telephone distribution plants and similar equipment used for voice and data communications, and sewage treatment plants.
The 20-year class includes farm buildings, sewer pipe, and other very long-lived
equipment.
128
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
8. Risk Analysis, Real
Options, and Capital
Budgeting
129
Chapter 8
EXECUTIVE
SUMMARY
Risk Analysis, Real Options,
and Capital Budgeting
Chapters 6 and 7 covered the basic principles of capital budgeting, with particular emphasis on the net present value (NPV)
approach. However, this is not the end of the
story. Real-world practitioners often wonder
how much confidence they should place in
NPV calculations.This chapter examines sensitivity analysis, scenario analysis, break-even
analysis, and Monte Carlo simulations, all of
which help the practitioner determine the
degree of confidence to be placed in a capital budgeting calculation.
Information is uncovered as a project unfolds, allowing a manager to make sequential
decisions over the life of the project. This
chapter covers decision trees and real options,
capital budgeting techniques that specifically
take the sequential nature of decision-making
into account.
8.1 Decision Trees
There is usually a sequence of decisions in NPV project analysis. This section introduces
the device of decision trees for identifying these sequential decisions.
Imagine you are the treasurer of the Solar Electronics Corporation (SEC), and the engineering group has recently developed the technology for solar-powered jet engines. The jet
engine is to be used with 150-passenger commercial airplanes. The marketing staff has proposed that SEC develop some prototypes and conduct test marketing of the engine. A
corporate planning group, including representatives from production, marketing, and engineering, estimates that this preliminary phase will take a year and will cost $100 million.
Furthermore, the group believes there is a 75-percent chance that the marketing tests will
prove successful.
If the initial marketing tests are successful, SEC can go ahead with full-scale production. This investment phase will cost $1,500 million. Production and sales will occur over
the next five years. The preliminary cash flow projection appears in Table 8.1. Should SEC
go ahead with investment and production on the jet engine, the NPV at a discount rate of
15 percent (in millions) is
5
NPV $1,500 $900
兺 (1.15)
t
t1
$1,500 $900 A50.15
$1,517
211
130
Corporate Finance,
Seventh Edition
212
Budgeting
Companies, 2004
Budgeting
TABLE 8.1
Investment
Cash Flow Forecasts
for Solar Electronics
Corporation’s Jet
Engine Base Case
(millions)*
Revenues
Variable costs
Fixed costs
Depreciation
Pretax profit
Tax (Tc 0.34)
Year 1
Years 2–6
$6,000
(3,000)
(1,791)
(300)
______
_
909
(309)
____
___
_____
__
$ 600
$ 900
Net profit
Cash flow
Initial investment costs
$1,500
*Assumptions: (1) Investment is depreciated in years 2 through 6 using the straight-line method; (2) tax rate is 34 percent;
(3) the company receives no tax benefits on initial development costs.
FIGURE 8.1
Decision Tree
($ millions) for SEC
Now
Year 1
Development
and test
Initial investment
$1,500
NPV $1,517
Invest
Success
(75% probability)
Do not invest
Test results
revealed
NPV 0
NPV $3,611
Test
Invest
Failure
(25% probability)
No test
Do not invest
NPV 0
Squares represent decision points. Circle represents receipt of information.
SEC must make 2 decisions:
1. Whether to develop and test engine
2. Whether to invest for full-scale production
Note that the NPV is calculated as of date 1, the date at which the investment of $1,500 million is made. Later we bring this number back to date 0.
If the initial marketing tests are unsuccessful, SEC’s $1,500 million investment has an
NPV of $3,611 million. This figure is also calculated as of date 1. (To save space, we will
not provide the raw numbers leading to this calculation.)
Figure 8.1 displays the problem concerning the jet engine as a decision tree. If SEC decides to conduct test marketing, there is a 75-percent probability that the test marketing will
be successful. If the tests are successful, the firm faces a second decision: whether to invest
Corporate Finance,
Seventh Edition
Budgeting
131
Companies, 2004
Budgeting
213
Chapter 8 Risk Analysis, Real Options, and Capital Budgeting
$1,500 million in a project that yields $1,517 million NPV or to stop. If the tests are unsuccessful, the firm faces a different decision: whether to invest $1,500 million in a project
that yields $3,611 million NPV or to stop.
To review, SEC has the following two decisions to make:
1. Whether to develop and test the solar-powered jet engine.
2. Whether to invest for full-scale production following the results of the test.
One makes decisions in reverse order with decision trees. Thus we analyze the secondstage investment of $1,500 million first. If the tests are successful, should SEC make the
second-stage investment? The answer is obviously yes, since $1,517 million is greater than
zero. If the tests are unsuccessful, should the second-stage investment be made? Just as obviously, the answer is no, since $3,611 million is below zero.
Now we move back to the first stage, where the decision boils down to the question:
Should SEC invest $100 million now to obtain a 75-percent chance of $1,517 million one
year later? The expected payoff evaluated at date 1 (in millions) is
Expected
payoff
冢
冣冢
Probability
Payoff
Probability Payoff
of
if
of
if
success
successful
failure
failure
(0.75
$1,138
$1,517)
(0.25
冣
$0)
The NPV of testing computed at date 0 (in millions) is
NPV $100 $1,138
1.15
$890
Since the NPV is a positive number, the firm should test the market for solar-powered jet
engines.
Warning We have used a discount rate of 15 percent for both the testing and the investment decisions. Perhaps a higher discount rate should have been used for the initial testmarketing decision, which is likely to be riskier than the investment decision.
Concept
Questions
1. What is a decision tree?
2. How do decision trees handle sequential decisions?
8.2 Sensitivity Analysis, Scenario Analysis,
and Break-Even Analysis
One thrust of this book is that NPV analysis is a superior capital budgeting technique. In
fact, because the NPV approach uses cash flows rather than profits, uses all the cash flows,
and discounts the cash flows properly, it is hard to find any theoretical fault with it. However, in our conversations with practical businesspeople, we hear the phrase “a false sense
of security” frequently. These people point out that the documentation for capital budgeting proposals is often quite impressive. Cash flows are projected down to the last thousand
dollars (or even the last dollar) for each year (or even each month). Opportunity costs and
side effects are handled quite properly. Sunk costs are ignored—also quite properly. When
132
214
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Budgeting
a high net present value appears at the bottom, one’s temptation is to say yes immediately.
Nevertheless, the projected cash flow often goes unmet in practice, and the firm ends up
with a money loser.
Sensitivity Analysis and Scenario Analysis
How can the firm get the net-present-value technique to live up to its potential? One approach is sensitivity analysis (a.k.a. what-if analysis and bop analysis1), which examines
how sensitive a particular NPV calculation is to changes in underlying assumptions. We
illustrate the technique with Solar Electronics’ solar-powered jet engine from the previous
section. As pointed out earlier, the cash flow forecasts for this project appear in Table 8.1.
We begin by considering the assumptions underlying revenues, costs, and after-tax cash flows
shown in the table.
Revenues
Sales projections for the proposed jet engine have been estimated by the marketing department as
Number of jet
Size of jet
Market Share engines sold
engine market
3,000
Sales revenues 0.30
10,000
Number of jet
engines sold
Price per
engine
$2 million
$6,000 million 3,000
Thus, it turns out that the revenue estimates depend on three assumptions.
1. Market share.
2. Size of jet engine market.
3. Price per engine.
Costs
Financial analysts frequently divide costs into two types: variable costs and fixed
costs. Variable costs change as the output changes, and they are zero when production is
zero. Costs of direct labor and raw materials are usually variable. It is common to assume that
a variable cost is constant per unit of output, implying that total variable costs are proportional to the level of production. For example, if direct labor is variable and one unit of final
output requires $10 of direct labor, then 100 units of final output should require $1,000 of
direct labor.
Fixed costs are not dependent on the amount of goods or services produced during the
period. Fixed costs are usually measured as costs per unit of time, such as rent per month
or salaries per year. Naturally, fixed costs are not fixed forever. They are only fixed over a
predetermined time period.
The engineering department has estimated variable costs to be $1 million per engine.
Fixed costs are $1,791 million per year. The cost breakdowns are
Variable
cost
$3,000 million
Variable cost
Number of jet
engines sold
per unit
$1 million 3,000
Total cost before taxes Variable cost Fixed cost
$4,791 million
$3,000 million $1,791 million
1
Bop stands for best, optimistic, pessimistic.
Corporate Finance,
Seventh Edition
Budgeting
133
Companies, 2004
Budgeting
215
TABLE 8.2
Different Estimates
for Solar Electronics’
Solar Plane
Variable
Pessimistic
Expected
or Best
Optimistic
Market size (per year)
Market share
Price
Variable cost (per plane)
Fixed cost (per year)
Investment
5,000
20%
$1.9 million
$1.2 million
$1,891 million
$1,900 million
10,000
30%
$2 million
$1 million
$1,791 million
$1,500 million
20,000
50%
$2.2 million
$0.8 million
$1,741 million
$1,000 million
TABLE 8.3
NPV Calculations
as of Date 1
(in $ millions) for the
Solar Plane Using
Sensitivity Analysis
Market size
Market share
Price
Variable cost
Fixed cost
Investment
Pessimistic
Expected
or Best
Optimistic
$1,802*
696*
853
189
1,295
1,208
$1,517
1,517
1,517
1,517
1,517
1,517
$8,154
5,942
2,844
2,844
1,628
1,903
Under sensitivity analysis, one input is varied while all other inputs are assumed to meet their
expectation. For example, an NPV of $1,802 occurs when the pessimistic forecast of 5,000 is
used for market size. However, the expected forecasts from Table 8.2 are used for all other
variables when $1,802 is generated.
*We assume that the other divisions of the firm are profitable, implying that a loss on this project can offset income elsewhere
in the firm, thereby reducing the overall taxes of the firm.
The above estimates for market size, market share, price, variable cost, and fixed cost, as
well as the estimate of initial investment, are presented in the middle column of Table 8.2.
These figures represent the firm’s expectations or best estimates of the different parameters.
For purposes of comparison, the firm’s analysts prepared both optimistic and pessimistic
forecasts for the different variables. These are also provided in the table.
Standard sensitivity analysis calls for an NPV calculation for all three possibilities of a
single variable, along with the expected forecast for all other variables. This procedure is
illustrated in Table 8.3. For example, consider the NPV calculation of $8,154 million
provided in the upper right-hand corner of this table. This occurs when the optimistic forecast of 20,000 units per year is used for market size. However, the expected forecasts from
Table 8.2 are employed for all other variables when the $8,154 million figure is generated.
Note that the same number of $1,517 million appears in each row of the middle column
of Table 8.3. This occurs because the expected forecast is used for the variable that was
singled out, as well as for all other variables.
Table 8.3 can be used for a number of purposes. First, taken as a whole, the table can indicate whether NPV analysis should be trusted. In other words, it reduces the false sense of
security we spoke of earlier. Suppose that NPV is positive when the expected forecast for
each variable is used. However, further suppose that every number in the pessimistic column is highly negative and every number in the optimistic column is highly positive. Even
a single error in this forecast greatly alters the estimate, making one leery of the net present
value approach. A conservative manager might well scrap the entire NPV analysis in this
situation. Fortunately, this does not seem to be the case in Table 8.3, because all but two of
the numbers are positive. Managers viewing the table will likely consider NPV analysis to
be useful for the solar-powered jet engine.
134
216
Corporate Finance,
Seventh Edition
Budgeting
Budgeting
Companies, 2004
Second, sensitivity analysis shows where more information is needed. For example,
error in the estimate of investment appears to be relatively unimportant because, even
under the pessimistic scenario, the NPV of $1,208 million is still highly positive. By contrast, the pessimistic forecast for market share leads to a negative NPV of $696 million,
and a pessimistic forecast for market size leads to a substantially negative NPV of
$1,802 million. Since the effect of incorrect estimates on revenues is so much greater
than the effect of incorrect estimates on costs, more information on the factors determining
revenues might be needed.
Because of these advantages, sensitivity analysis is widely used in practice. Graham and
Harvey2 report that slightly over 50 percent of the 392 firms in their sample subject their capital budgeting calculations to sensitivity analysis. This number is particularly large when one
considers that only about 75 percent of the firms in their sample use NPV analysis.
Unfortunately, sensitivity analysis also suffers from some drawbacks. For example, sensitivity analysis may unwittingly increase the false sense of security among managers.
Suppose all pessimistic forecasts yield positive NPVs. A manager might feel that there is
no way the project can lose money. Of course, the forecasters may simply have an optimistic view of a pessimistic forecast. To combat this, some companies do not treat optimistic and pessimistic forecasts subjectively. Rather, their pessimistic forecasts are always,
say, 20 percent less than expected. Unfortunately, the cure in this case may be worse than
the disease, because a deviation of a fixed percentage ignores the fact that some variables
are easier to forecast than others.
In addition, sensitivity analysis treats each variable in isolation when, in reality, the different variables are likely to be related. For example, if ineffective management allows
costs to get out of control, it is likely that variable costs, fixed costs, and investment will all
rise above expectation at the same time. If the market is not receptive to a solar plane, both
market share and price should decline together.
Managers frequently perform scenario analysis, a variant of sensitivity analysis, to
minimize this problem. Simply put, this approach examines a number of different likely
scenarios, where each scenario involves a confluence of factors. As a simple example, consider the effect of a few airline crashes. These crashes are likely to reduce flying in total,
thereby limiting the demand for any new engines. Furthermore, even if the crashes did not
involve solar-powered aircraft, the public could become more averse to any innovative and
controversial technologies. Hence, SEC’s market share might fall as well. Perhaps the cash
flow calculations would look like those in Table 8.4 under the scenario of a plane crash.
Given the calculations in the table, the NPV (in millions) would be
$2,023 $1,500 $156 A50.15
A series of scenarios like this might illuminate issues concerning the project better than the
standard application of sensitivity analysis would.
Break-Even Analysis
Our discussion of sensitivity analysis and scenario analysis suggests that there are many
ways to examine variability in forecasts. We now present another approach, break-even
analysis. As its name implies, this approach determines the sales needed to break even. The
approach is a useful complement to sensitivity analysis, because it also sheds light on the
severity of incorrect forecasts. We calculate the break-even point in terms of both accounting profit and present value.
2
See Figure 2 of John Graham and Campbell Harvey, “The Theory and Practice of Corporate Finance: Evidence from the
Field,” Journal of Financial Economics (May/June 2001).
Corporate Finance,
Seventh Edition
Budgeting
217
TABLE 8.4
Year 1
Cash Flow Forecast
(in $ millions) under
the Scenario of a
Plane Crash*
Revenues
Variable costs
Fixed costs
Depreciation
Pretax profit
Tax (Tc 0.34)†
Net profit
Cash flow
Initial investment cost
135
Companies, 2004
Budgeting
Years 2–6
$2,800
1,400
1,791
300
691
235
456
156
$1,500
*Assumptions are
Market size
Market share
7,000 (70 percent of expectation)
20% (2兾3 of expectation)
Forecasts for all other variables are the expected forecasts as given in Table 8.2.
†
Tax loss offsets income elsewhere in firm.
TABLE 8.5
Revenues and Costs of Project under Different Sales Assumptions (in $ millions, except unit sales)
Year 1
Years 2–6
Initial
Investment
Annual
Unit
Sales Revenues
$1,500
1,500
1,500
1,500
0
1,000
3,000
10,000
$
0
2,000
6,000
20,000
Variable
Costs
Fixed
Costs
0 $1,791
1,000
1,791
3,000
1,791
10,000
1,791
$
DepreciTaxes*
ation
(Tc ⴝ 0.34)
$300
300
300
300
$ 711
371
309
2,689
Net
Profit
$1,380
720
600
5,220
Operating
NPV
Cash
(evaluated
Flows
date 1)
$1,080
420
900
5,520
$5,120
2,908
1,517
17,004
*Loss is incurred in the first two rows. For tax purposes, this loss offsets income elsewhere in the firm.
Accounting Profit
Net profit under four different sales forecasts is
Unit Sales
Net Profit (in $ millions)
0
1,000
3,000
10,000
$1,380
720
600
5,220
A more complete presentation of costs and revenues appears in Table 8.5.
We plot the revenues, costs, and profits under the different assumptions about sales in
Figure 8.2. The revenue and cost curves cross at 2,091 jet engines. This is the break-even
point, i.e., the point where the project generates no profits or losses. As long as sales are
above 2,091 jet engines, the project will make a profit.
This break-even point can be calculated very easily. Because the sales price is $2 million per engine and the variable cost is $1 million per engine,3 the after-tax difference per
engine is
(Sales price Variable cost) (1 Tc) ($2 million $1 million) (1 0.34)
$0.66 million
3
Though the previous section considered both optimistic and pessimistic forecasts for sales price and variable cost, break-even
analysis uses just the expected or best estimates of these variables.
136
Corporate Finance,
Seventh Edition
218
Budgeting
Companies, 2004
Budgeting
FIGURE 8.2
$ millions
Break-Even Point
Using Accounting
Numbers
Total revenues
Total costs
Variable costs
$4,182
Fixed costs
2,091
$2,091 (including depreciation)
Output (in terms of sales units)
where Tc is the corporate tax rate of 34 percent. This after-tax difference is called the contribution margin because each additional engine contributes this amount to after-tax profit.
Fixed costs are $1,791 million and depreciation is $300 million, implying that the aftertax sum of these costs is
(Fixed costs Depreciation) (1 Tc) ($1,791 million $300 million)
(1 0.34) $1,380 million
That is, the firm incurs costs of $1,380 million, regardless of the number of sales. Because
each engine contributes $0.66 million, sales must reach the following level to offset the
above costs:
Accounting Profit Break-Even Point:
(Fixed costs Depreciation) (1 Tc ) $1,380 million
2,091
(Sales price Variable costs) (1 Tc )
$0.66 million
Thus, 2,091 engines is the break-even point required for an accounting profit.
Present Value
As we stated many times in the text, we are more interested in present
value than we are in net profits. Therefore, we must calculate the present value of the cash
flows. Given a discount rate of 15 percent, we have
Unit Sales
NPV ($ millions)
0
1,000
3,000
10,000
5,120
2,908
1,517
17,004
These NPV calculations are reproduced in the last column of Table 8.5. We can see that the
NPV is negative if SEC produces 1,000 jet engines and positive if it produces 3,000 jet
engines. Obviously, the zero NPV point occurs between 1,000 and 3,000 jet engines.
The present value break-even point can be calculated very easily. The firm originally invested $1,500 million. This initial investment can be expressed as a five-year equivalent
annual cost (EAC), determined by dividing the initial investment by the appropriate five-year
annuity factor:
Initial investment
Initial investment
5-year annuity factor at 15%
A50.15
$1,500 million
$447.5 million
3.3522
EAC Ross−Westerfield−Jaffe:
Corporate Finance,
Seventh Edition
Budgeting
Budgeting
Companies, 2004
137
219
Note that the EAC of $447.5 million is greater than the yearly depreciation of $300 million.
This must occur since the calculation of EAC implicitly assumes that the $1,500 million investment could have been invested at 15 percent.
After-tax costs, regardless of output, can be viewed as
$1,528 $447.5 $1,791
$300
0.66 0.34
million million million
million
Fixed
Depreci EAC (1 Tc) Tc
costs
ation
That is, in addition to the initial investment’s equivalent annual cost of $447.5 million, the
firm pays fixed costs each year and receives a depreciation tax shield each year. The
depreciation tax shield is written as a negative number since it offsets the costs in the equation. Because each plane contributes $0.66 million to after-tax profit, it will take the following sales to offset the above costs:
Present Value Break-Even Point:
EAC Fixed costs ( 1 Tc ) Depreciation Tc $1,528 million
2,315
(Sales price Variable costs) (1 Tc )
$0.66 million
Thus, 2,315 planes is the break-even point from the perspective of present value.
Why is the accounting break-even point different from the financial break-even point?
When we use accounting profit as the basis for the break-even calculation, we subtract depreciation. Depreciation for the solar-jet-engines project is $300 million. If 2,091 solar jet
engines are sold, SEC will generate sufficient revenues to cover the $300 million depreciation expense plus other costs. Unfortunately, at this level of sales SEC will not cover the
economic opportunity costs of the $1,500 million laid out for the investment. If we take
into account that the $1,500 million could have been invested at 15 percent, the true annual
cost of the investment is $447.5 million and not $300 million. Depreciation understates the
true costs of recovering the initial investment. Thus, companies that break even on an accounting basis are really losing money. They are losing the opportunity cost of the initial
investment.
Concept
Questions
1.
2.
3.
4.
What is a sensitivity analysis?
Why is it important to perform a sensitivity analysis?
What is a break-even analysis?
Describe how sensitivity analysis interacts with break-even analysis.
8.3 Monte Carlo Simulation
Both sensitivity analysis and scenario analysis attempt to answer the question, “What if?”
However, while both analyses are frequently used in the real world, each has its own limitations. Sensitivity analysis allows only one variable to change at a time. By contrast, many
variables are likely to move at the same time in the real world. Scenario analysis follows
specific scenarios, such as changes in inflation, government regulation, or the number of
competitors. While this methodology is often quite helpful, it cannot cover all sources of
variability. In fact, projects are likely to exhibit a lot of variability under just one economic
scenario.
Monte Carlo simulation is a further attempt to model real-world uncertainty. This approach takes its name from the famous European casino, because it analyzes projects the
way one might analyze gambling strategies. Imagine a serious blackjack player who wonders if he should take a third card whenever his first two cards total 16. Most likely, a
138
220
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Budgeting
formal mathematical model would be too complex to be practical here. However, he could
play thousands of hands in a casino, sometimes drawing a third card when his first two
cards add to 16 and sometimes not drawing that third card. He could compare his winnings
(or losings) under the two strategies in order to determine which was better. Of course,
since he would probably lose a lot of money performing this test in a real casino, simulating the results from the two strategies on a computer might be cheaper. Monte Carlo simulation of capital budgeting projects is in this spirit.
Imagine that Backyard Barbeques, Inc. (BBI), a manufacturer of both charcoal and gas
grills, has the blueprint for a new grill that cooks with compressed hydrogen. The CFO,
Edward H. Comiskey, being dissatisfied with simpler capital budgeting techniques, wants
a Monte Carlo simulation for this new grill. A consultant specializing in the Monte Carlo
approach, Lester Mauney, takes him through the five basic steps of the method.
Step 1: Specify the Basic Model
Les Mauney breaks up cash flow into three components: annual revenue, annual costs, and
initial investment. The revenue in any year is viewed as:
Price per
Number of grills sold
Market share of BBI’s
hydrogen grill
by entire industry
hydrogen grill (in percent)
(8.1)
The cost in any year is viewed as:
Fixed manufacturing costs Variable manufacturing costs Marketing costs
Selling costs
Initial investment is viewed as:
Cost of patent Test-marketing costs Cost of production facility
Step 2: Specify a Distribution for Each Variable in the Model
Here comes the hard part. Let’s start with revenue, which has three components in (8.1).
The consultant first models overall market size, that is, the number of grills sold by the
entire industry. The trade publication, Outdoor Food (OF), reported that 10 million grills
of all types were sold in the continental United States last year and it forecasts sales of
10.5 million next year. Mr. Mauney, using OF’s forecast and his own intuition, creates the
following distribution for next year’s sales of grills by the entire industry:
Probability
Next year’s industrywide unit sales
20%
60%
20%
10 million
10.5 million
11 million
The tight distribution here reflects the slow but steady historical growth in the grill market.
Lester Mauney realizes that estimating the market share of BBI’s hydrogen grill is more
difficult. Nevertheless, after a great deal of analysis, he determines the distribution of next
year’s market share to be:
Probability
Market share of BBI’s hydrogen
grill next year
10%
20%
30%
25%
10%
5%
1%
2%
3%
4%
5%
8%
While the consultant assumed a symmetrical distribution for industrywide unit sales, he believes a skewed distribution makes more sense for the project’s market share. In his mind,
there is always the small possibility that sales of the hydrogen grill will really take off.
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Budgeting
139
221
The above forecasts assume that unit sales for the overall industry are unrelated to the
project’s market share. In other words, the two variables are independent of each other.
Mr. Mauney reasons that, while an economic boom might increase industrywide grill sales
and a recession might decrease them, the project’s market share is unlikely to be related to
economic conditions.
Now Mr. Mauney must determine the distribution of price per grill. Mr. Comiskey, the
CFO, informs him that the price will be in the area of $200 per grill, given what other competitors are charging. However, the consultant believes that the price per hydrogen grill
will almost certainly depend on the size of the overall market for grills. As in any business,
you can usually charge more if demand is high.
After rejecting a number of complex models for price, Mr. Mauney settles on the following specification:
Next year’s price
$190 $1 Industrywide unit sales (in millions) 兾 $3
per hydrogen grill
(8.2)
The grill price in (8.2) is dependent on the unit sales of the industry. In addition, random
variation is modeled via the term “兾 $3,” where a drawing of $3 and a drawing of
$3 each occur 50 percent of the time. For example, if industrywide unit sales are 11 million, the price per share would be either:
$190 $11 $3 $203
$190 $11 $3 $197
(50% probability)
(50% probability)
The consultant now has distributions for each of the three components of next year’s
revenue. However, he needs distributions for future years as well. Using forecasts from
Outdoor Food and other publications, Mr. Mauney forecasts the distribution of growth
rates for the entire industry over the second year to be:
Probability
Growth rate of industrywide unit sales in second year
20%
60%
20%
1%
3%
5%
Given both the distribution of next year’s industrywide unit sales and the distribution of
growth rates for this variable over the second year, we can generate the distribution of industrywide unit sales for the second year. A similar extension should give Mr. Mauney a
distribution for later years as well, though we won’t go into the details here. And, just as the
consultant extended the first component of revenue (industrywide unit sales) to later years,
he would want to do the same thing for market share and unit price.
The above discussion shows how the three components of revenue can be modeled.
Step 2 would be complete once the components of cost and of investment are modeled in a
similar way. Special attention must be paid to the interactions between variables here, since
ineffective management will likely allow the different cost components to rise together.
However, since you are probably getting the idea now, we will skip the rest of this step.
Step 3: The Computer Draws One Outcome
As we said above, next year’s revenue in our model is the product of three components.
Imagine that the computer randomly picks industrywide unit sales of 10 million, a market
share for BBI’s hydrogen grill of 2 percent and a $3 random price variation. Given these
drawings, next year’s price per hydrogen grill will be:
$190 $10 $3 $203
140
Corporate Finance,
Seventh Edition
222
Budgeting
Companies, 2004
Budgeting
and next year’s revenue for BBI’s hydrogen grill will be:
10 million 0.02 $203 $40.6 million
Of course, we are not done with the entire outcome yet. We would have to perform drawings for revenue in each future year. In addition, we would perform drawings for costs in each
future year. Finally, a drawing for initial investment would have to be made as well. In this
way, a single outcome would generate a cash flow from the project in each future year.
How likely is it that the specific outcome above would be drawn? We can answer this
because we know the probability of each component. Since industry sales of $10 million
has a 20 percent probability, a market share of 2 percent also has a 20 percent probability,
and a random price variation of $3 has a 50 percent probability, the probability of these
three drawings together in the same outcome is:
0.02 0.20 0.20 0.50
(8.3)
Of course, the probability would get even smaller once drawings for future revenues, future
costs, and the initial investment are included in the outcome.
This step generates the cash flow for each year from a single outcome. What we are
ultimately interested in is the distribution of cash flow each year across many outcomes.
We ask the computer to randomly draw over and over again to give us this distribution,
which is just what is done in the next step.
Step 4: Repeat the Procedure
While the above three steps generate one outcome, the essence of Monte Carlo simulation is
repeated outcomes. Depending on the situation, the computer may be called on to generate
thousands or even millions of outcomes. The result of all these drawings is a distribution of
cash flow for each future year. This distribution is the basic output of Monte Carlo simulation.
Consider Figure 8.3. Here, repeated drawings have produced the simulated distribution
of the third year’s cash flow. There would be, of course, a distribution like the one in this
figure for each future year. This leaves us with just one more step.
Step 5: Calculate NPV
Given the distribution of cash flow for the third year in Figure 8.3, one can determine the
expected cash flow for this year. In a similar manner, one can also determine the expected
Simulated
Distribution of the
Third Year’s Cash
Flow for BBI’s New
Hydrogen Grill
Number of outcomes
FIGURE 8.3
0
Cash f low
In Monte Carlo simulations, repeated sampling of all the variables from a
specific model generates a statistical distribution
Corporate Finance,
Seventh Edition
Budgeting
Budgeting
141
Companies, 2004
223
cash flow for each future year and can then calculate the net present value of the project by
discounting these expected cash flows at an appropriate rate.
Monte Carlo simulation is often viewed as a step beyond either sensitivity analysis or scenario analysis. Interactions between the variables are explicitly specified in Monte Carlo so,
at least in theory, this methodology provides a more complete analysis. And, as a by-product,
having to build a precise model deepens the forecaster’s understanding of the project.
Since Monte Carlo simulations have been around for at least 35 years, you might think
that most firms would be performing them by now. Surprisingly, this does not seem to be
the case. In our experience, executives are frequently skeptical of all the complexity. It is
difficult to model either the distributions of each variable or the interactions between variables. In addition, the computer output is often devoid of economic intuition. Thus, while
Monte Carlo simulations are used in certain real-world situations,4 the approach is not
likely to be “the wave of the future.” In fact, Graham and Harvey5 report that only about
15 percent of the firms in their sample use capital budgeting simulations.
8.4 Real Options
In Chapter 6, we stressed the superiority of net present value (NPV) analysis over other
approaches when valuing capital budgeting projects. However, both scholars and practitioners have pointed out problems with NPV. The basic idea here is that NPV analysis, as well
as all the other approaches in Chapter 6, ignores the adjustments that a firm can make after
a project is accepted. These adjustments are called real options. In this respect, NPV underestimates the true value of a project. NPV’s conservatism here is best explained through
a series of examples.
The Option to Expand
Conrad Willig, an entrepreneur, recently learned of a chemical treatment causing water to
freeze at 100 degrees Fahrenheit, rather than 32 degrees. Of all the many practical applications for this treatment, Mr. Willig liked the idea of hotels made of ice more than anything
else. Conrad estimated the annual cash flows from a single ice hotel to be $2 million, based
on an initial investment of $12 million. He felt that 20 percent was an appropriate discount
rate, given the risk of this new venture. Assuming that the cash flows were perpetual,
Mr. Willig determined the NPV of the project to be:
$12,000,000 $2,000,000兾0.20 $2 million
Most entrepreneurs would have rejected this venture, given its negative NPV. But
Conrad was not your typical entrepreneur. He reasoned that NPV analysis missed a hidden
source of value. While he was pretty sure that the initial investment would cost $12 million,
there was some uncertainty concerning annual cash flows. His cash flow estimate of
$2 million per year actually reflected his belief that there was a 50 percent probability that
annual cash flows will be $3 million and a 50 percent probability that annual cash flows
will be $1 million.
The NPV calculations for the two forecasts are:
Optimistic forecast: $12 million $3 million兾0.20 $3 million
Pessimistic forecast: $12 million $1 million兾0.20 $7 million
4
More than perhaps any other, the pharmaceutical industry has pioneered applications of this methodology. For example, see,
Nancy A. Nichols, “Scientific Management at Merck: An Interview with CFO Judy Lewent,” Harvard Business Review
(January/February 1994).
5
See Figure 2 of Graham and Harvey, op. cit.
142
Corporate Finance,
Seventh Edition
224
Budgeting
Companies, 2004
Budgeting
FIGURE 8.4
If successful
Decision Tree for Ice
Hotel
Expand
Build first
ice hotel
If unsuccessful
Do not expand
On the surface, this new calculation doesn’t seem to help Mr. Willig very much since an
average of the two forecasts yields an NPV for the project of:
50% $3 million 50% ($7 million) $2 million
just the value he calculated in the first place.
However, if the optimistic forecast turns out to be correct, Mr. Willig would want to
expand. If he believes that there are, say, 10 locations in the country that can support an ice
hotel, the true NPV of the venture would be:
50% 10 $3 million 50% ($7 million) $11.5 million
The idea here, which is represented in Figure 8.4, is both basic and universal. The entrepreneur has the option to expand if the pilot location is successful. For example, think of
all the people that start restaurants, most of them ultimately failing. These individuals are
not necessarily overly optimistic. They may realize the likelihood of failure but go ahead
anyway because of the small chance of starting the next McDonald’s or Burger King.
The Option to Abandon
Managers also have the option to abandon existing projects. While abandonment may seem
cowardly, it can often save companies a great deal of money. Because of this, the option to
abandon increases the value of any potential project.
The above example on ice hotels, which illustrated the option to expand, can also illustrate the option to abandon. To see this, imagine that Mr. Willig now believes that there is
a 50 percent probability that annual cash flows will be $6 million and a 50 percent probability that annual cash flows will be $2 million. The NPV calculations under the two forecasts become:
Optimistic forecast: $12 million $6 million兾0.2 $18 million
Pessimistic forecast: $12 million $2 million兾0.2 $22 million
yielding an NPV for the project of:
50% $18 million 50% ($22 million) $2 million
(8.4)
Furthermore, now imagine that Mr. Willig wants to own, at most, just one ice hotel, implying that there is no option to expand. Since the NPV in (8.4) is negative, it looks as if he
will not build the hotel.
But things change when we consider the abandonment option. As of date 1, the entrepreneur will know which forecast has come true. If cash flows equal those under the optimistic
forecast, Conrad will keep the project alive. If, however, cash flows equal those under the
Corporate Finance,
Seventh Edition
Budgeting
143
Companies, 2004
Budgeting
225
FIGURE 8.5
High box
office revenue
The Abandonment
Option in the Movie
Industry
Cost
containment
Good script
Commission
script
Produce
movie
Large
cost overrun
Bad script
More
advertising
Release upon
completion
Low box
office revenue
No further
advertising
Abandon
prior to
completion
Abandon
Movie studios have abandonment options throughout the production of a movie.
pessimistic forecast, he will abandon the hotel. Knowing these possibilities ahead of time,
the NPV of the project becomes:
50% $18 million 50% ($12 million $2 million兾1.20) $2.17 million
Since Mr. Willig abandons after experiencing the cash flow of $2 million at date 1, he
does not have to endure this outflow in any of the later years. Because the NPV is now positive, Conrad will accept the project.
The example here is clearly a stylized one. While many years may pass before a project
is abandoned in the real world, our ice hotel was abandoned after just one year. And, while
salvage values generally accompany abandonment, we assumed no salvage value for the
ice hotel. Nevertheless, abandonment options are pervasive in the real world.
For example, consider the movie-making industry. As shown in Figure 8.5, movies
begin with either the purchase or development of a script. A completed script might cost a
movie studio a few million dollars and potentially lead to actual production. However, the
great majority of scripts (perhaps well in excess of 80 percent) are abandoned. Why would
studios abandon scripts that they had commissioned in the first place? While the studios
know ahead of time that only a few scripts will be promising, they don’t know which ones.
Thus, they cast a wide net, commissioning many scripts to get a few good ones. And, the
studios must be ruthless with the bad scripts, since the expenditure here pales in comparison to the huge losses from producing a bad movie.
The few lucky scripts will then move into production, where costs might be budgeted in
the tens of millions of dollars, if not much more. At this stage, the dreaded phrase is that onlocation production gets “bogged down,” creating cost overruns. But the studios are
equally ruthless here. Should these overruns become excessive, production is likely to be
abandoned in midstream. Interestingly, abandonment almost always occurs due to high
costs, not due to the fear that the movie won’t be able to find an audience. Little information on that score will be obtained until the movie is actually released.
Release of the movie is accompanied by significant advertising expenditures, perhaps in
the range of $10 to $20 million. Box office success in the first few weeks is likely to lead
144
Corporate Finance,
Seventh Edition
226
Budgeting
Companies, 2004
Budgeting
to further advertising expenditures. Again, the studio has the option, but not the obligation,
to increase advertising here.
Movie-making is one of the riskiest businesses around, with studios receiving hundreds
of millions of dollars in a matter of weeks from a blockbuster while receiving practically
nothing during this period from a flop. The above abandonment options contain costs that
might otherwise bankrupt the industry.
Timing Options
One often finds urban land that has been vacant for many years. Yet this land is bought and
sold from time to time. Why would anyone pay a positive price for land that has no source
of revenue? Certainly one could not arrive at this positive value through NPV analysis.
However, the paradox can easily be explained in terms of real options.
Suppose that the land’s highest and best use is as an office building. Total construction
costs for the building are estimated to be $1 million. Currently, net rents (after all costs) are
estimated to be $90,000 per year in perpetuity and the discount rate is 10 percent. The NPV
of this proposed building would be:
$1 million $90,000兾.10 $100,000
Since this NPV is negative, one would not currently want to build. In addition, it appears
as if the land is worthless. However, suppose that the federal government is planning various urban revitalization programs for the city. Office rents will likely increase if the
programs succeed. In this case, the property’s owner might want to erect the office building after all. Conversely, office rents will remain the same, or even fall, if the programs fail.
The owner will not build in this case.
We say that the property owner has a timing option. While he does not currently want to
build, he will want to build in the future should rents in the area rise substantially. This timing option explains why vacant land often has value. While there are costs, such as taxes,
from holding raw land, the value of an office building after a substantial rise in rents may
more than offset these holding costs. Of course, the exact value of the vacant land depends
on both the probability of success in the revitalization program and the extent of the rent
increase. Figure 8.6 illustrates this timing option.
Mining operations almost always provide timing options as well. Suppose you own a
copper mine where the cost of mining each ton of copper exceeds the sales revenue. It’s a
no-brainer to say that you would not want to mine the copper currently. And since there are
costs of ownership such as property taxes, insurance, and security, you might actually want
to pay someone to take the mine off your hands. However, we would caution you not to do
FIGURE 8.6
Rents rise substantially
Decision Tree for
Vacant Land
Erect office building
Do not build yet, since
rents are too low
Rents either stay
the same or fall
Do not build yet
Vacant land may have value today, since the owner can erect a profitable office
building if rents rise.
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Budgeting
145
227
so hastily. Copper prices in the future might very well increase enough so that production
is profitable. Given that possibility, you could likely find someone to pay a positive price
for the property today.
Concept
Questions
1. What are the different types of real options?
2. Why does traditional NPV analysis tend to underestimate the true value of a
capital project?
1. Though NPV is the best capital budgeting approach conceptually, it has been criticized in practice
for providing managers with a false sense of security. Sensitivity analysis shows NPV under varying assumptions, giving managers a better feel for the project’s risks. Unfortunately, sensitivity
analysis modifies only one variable at a time, while many variables are likely to vary together in
the real world. Scenario analysis examines a project’s performance under different scenarios (e.g.,
war breaking out or oil prices skyrocketing). Finally, managers want to know how bad forecasts
must be before a project loses money. Break-even analysis calculates the sales figure at which the
project breaks even.Though break-even analysis is frequently performed on an accounting profit
basis, we suggest that a net present value basis is more appropriate.
2. Monte Carlo simulation begins with a model of the firm’s cash flows, based on both the interactions between different variables and the movement of each individual variable over time.
Random sampling generates a distribution of these cash flows for each period, leading to a net
present value calculation.
3. We analyze the hidden options in capital budgeting, such as the option to expand, the option to
abandon, and timing options.
KEY TERMS
break-even analysis, 216
contribution margin, 218
decision trees, 211
fixed costs, 214
Monte Carlo simulation, 219
SUGGESTED
READINGS
The classic article on break-even analysis is:
Reinhart, U. E.“Breakeven Analysis for Lockheed’s Tristar:An Application of Financial Theory.” Journal
of Finance (September 1977).
An excellent book on real options is:
Amram, Martha, and Nalin Kulatilaka. Real Options: Managing Strategic Investment in an Uncertain World.
Boston: Harvard Business School Press (1999).
A fascinating discussion of real options in the movie business can be found in:
Martin, Laura,“Film Studio Reel Options.” Unpublished manuscript, Credit Suisse First Boston (CSFB)
(May 11, 2001). Obtainable at www.valuesweep.com
QUESTIONS
& PROBLEMS
8.1
DECISION TREES
real options, 223
scenario analysis, 216
sensitivity analysis, 214
variable costs, 214
Sony Electronics, Inc., has developed a new VCR. If the VCR is successful, the present value of
the payoff (at the time the product is brought to market) is $20 million. If the VCR fails, the
present value of the payoff is $5 million. If the product goes directly to market, there is a
50 percent chance of success.Alternatively, Sony can delay the launch by one year and spend
$2 million to test market the VCR.Test marketing allows the firm to improve the product and
increase the probability of success to 75 percent.The appropriate discount rate is 15 percent.
Should the firm conduct test marketing?
This chapter discusses a number of practical applications of capital budgeting.
146
Corporate Finance,
Seventh Edition
228
ACCOUNTING
BREAK-EVEN
ANALYSIS
Budgeting
Companies, 2004
Budgeting
8.2
The manager for a growing firm is considering the launch of a new product. If the product goes
directly to market, there is a 50 percent chance of success. For $120,000, the manager can conduct a focus group that will increase the product’s chance of success to 70 percent. Alternatively,
the manager has the option to pay a consulting firm $400,000 to research the market and refine
the product.The consulting firm successfully launches new products 90 percent of the time. If the
firm successfully launches the product, the payoff will be $1.2 million. If the product is a failure,
the firm will receive $0.Which action will result in the highest expected payoff to the firm?
8.3
The sales of Tandem Bicycles, Inc., are decreasing because of foreign competition.The firm’s
chief financial officer (CFO) is considering the following mutually exclusive options to maintain market share this year:
• Price the products more aggressively.With this option, there is a 55 percent chance that
Tandem will only lose $1.3 million in cash flow due to the decreased revenue. However,
there is a 45 percent probability that Tandem’s pricing strategy will fail, and the firm will
lose a total of $1,850,000 in cash flow.
• Pay $800,000 for a lobbyist to convince the regulators to impose tariffs on overseas bicycle manufacturers.With the lobbyists, there is a 75 percent chance that Tandem will lose
no cash flow to the foreign competition. If the lobbyists do not succeed,Tandem Bicycles
will lose $2 million in cash flow.
Assume all cash flows occur today, and that Tandem Bicycles will cease operations after this
year. As the assistant to the CFO, which strategy would you recommend to maximize expected cash flow?
8.4
B&B has a new baby powder ready to market. If the firm goes directly to the market with the
product, there is only 55 percent chance of success. However, the firm can conduct customer segment research, which will take a year and cost $1 million. By going through research, B&B will be
able to better target potential customers and will increase the probability of success to 70 percent.If successful,the baby powder will bring a present value profit (at time of initial selling) of $30
million. If unsuccessful, the present value payoff is only $3 million. Should the firm conduct customer segment research or go directly to market? The appropriate discount rate is 15 percent.
8.5
Young screenwriter Carl Draper has just finished his first script. It has action, drama, humor,
and he thinks it will be a blockbuster. He takes the script to every motion picture studio in
town and tries to sell it but to no avail. Finally, ACME studios offers to buy the script, for either a) $5,000 or b) 1 percent of the movie’s profits.There are two decisions that will take
place for the studio. First is if the script is good or bad, and second if the movie is good or
bad. First, there is a 90 percent chance that the script is bad. If it is bad, the studio does nothing more and throws the script out. If the script is good, they will shoot the movie.After the
movie is shot, the studio will review it and there is a 70 percent chance that the movie is bad.
If the movie is bad, the movie will not be promoted and will not turn a profit. If the movie is
good, the studio will promote heavily and the average profit is $10 million. Carl rejects the
$5,000 and says he wants the 1 percent of profits.Was this a good decision by Carl?
8.6
Samuelson, Inc., has just purchased a $600,000 machine to produce calculators.The machine
will be fully depreciated by the straight-line method over its economic life of five years and
will produce 20,000 calculators each year.The variable production cost per calculator is $15
and total fixed costs are $900,000 per year.The corporate tax rate for the company is 30 percent. For the firm to break even (in terms of accounting profit), how much should the firm
charge per calculator?
8.7
Consider the following information for a big-screen television distributor:
Sales price per TV
Variable costs per TV
Fixed costs per year
Depreciation per year
Tax rate
$1,500
$1,100
$120,000
$20,000
35%
Corporate Finance,
Seventh Edition
Budgeting
Companies, 2004
Budgeting
147
229
How many units must the distributor sell in a given year to break even (in terms of accounting profit)?
8.8
You are considering investing in a company that cultivates abalone for sale to local restaurants. Use the following information:
Sales price per abalone
Variable costs per abalone
Depreciation per year
Tax rate
$2.00
$0.72
$340,000
$20,000
35%
a. How many abalone must be harvested and sold per year for you to receive any profit
(accounting break-even point)?
b. How much profit will you receive if he sells 300,000 abalone per year?
What is the minimum number of times that a video arcade must be played in a given period
to break even?
Game price
Variable cost
Fixed costs
Depreciation
Tax rate
$0.50
$0.02
$1,000
$50
34%
8.10 Your buddy comes to you with a sure fire way to make some quick money and help pay off
your student loans. His idea is to sell T-shirts with the words “I get” on them.“You get it?” He
says, “You see all those bumper stickers and T-shirts that say, ‘got milk’ or ‘got surf.’ So this
says,‘I get.’ It’s funny! All we have to do is buy a used silk screen press for $2,000 and we are
in business!” Assume there are no fixed costs, and you depreciate the $2,000 in the first period. Further, taxes are 30 percent.
a. How many shirts would you need to sell to break even if each shirt costs $8 to make, and
you can sell them for $10 a piece?
Now assume one year has passed and you have sold 5,000 shirts! You find out that the Dairy
Farmers of America have copyrighted the “got milk” slogan and are requiring you to pay
$10,000 to continue operations.You expect this craze will last for another three years and
that your discount rate is 12 percent.
b. What is the present value break-even point for you enterprise now?
PRESENT VALUE
BREAK-EVEN
ANALYSIS
8.11 Using the information in Problem 8.8, calculate the present value break-even point if the discount rate is 15 percent, the initial investment is $140,000, and the project’s economic life is
seven years. Assume the initial investment is fully depreciated by the straight-line method
over its economic life.
8.12 L.J.’s Toys Inc. just purchased a $200,000 machine to produce toy cars. The machine will be
fully depreciated by the straight-line method over its five-year economic life. Each toy sells
for $25.The variable cost per toy is $5, and the firm incurs fixed costs of $350,000 each year.
The corporate tax rate for the company is 25 percent. The appropriate discount rate is
12 percent.What is the present value break-even point for the project?
8.13 The Cornchopper Company is considering the purchase of a new harvester. Cornchopper
has hired you to determine the break-even purchase price (in terms of present value) of the
harvester. This break-even purchase price is the price at which the project’s NPV is zero. Base
your analysis on the following facts:
• The new harvester is not expected to affect revenues, but pretax operating expenses will
be reduced by $10,000 per year for 10 years.
8.9
148
Corporate Finance,
Seventh Edition
230
Budgeting
Companies, 2004
Budgeting
•
•
•
•
•
•
•
•
The old harvester is now 5 years old, with 10 years of its scheduled life remaining. It was
originally purchased for $45,000 and has been depreciated by the straight-line method.
The old harvester can be sold for $20,000 today.
The new harvester will be depreciated by the straight-line method over its 10-year life.
The corporate tax rate is 34 percent.
The firm’s required rate of return is 15 percent.
The initial investment, the proceeds from selling the old harvester, and any resulting tax
effects occur immediately. Capital gains and losses are taxed at the corporate rate of
34 percent when they are realized.
All other cash flows occur at year-end.
The market value of each harvester at the end of its economic life is zero.
8.14 Niko has purchased a brand new machine to produce its High Flight line of shoes. The machine has an economic life of five years. The depreciation schedule for the machine is straightline with no salvage value.The machine costs $300,000.
The sales price per pair of shoes is $60, while the variable cost is $8. $100,000 of fixed
cost per year is attributed to the machine.
Assume that the corporate tax rate is 34 percent and the appropriate discount rate is
8 percent.What is the present value break-even point?
SCENARIO
ANALYSIS
8.15 The CFO of Mercer, Inc., is considering an investment of $420,000 in a machine that will be
depreciated by the straight-line method over its seven-year economic life. The appropriate
discount rate is 13 percent, and the corporate tax rate for the company is 35 percent. Assume
all revenues and expenses, which are presented below, are received and paid in cash.
Unit sales
Price
Variable costs per unit
Pessimistic
Expected
Optimistic
23,000
$
38
$
21
$320,000
25,000
$
40
$
20
$300,000
27,000
$
42
$
19
$280,000
a. Calculate the NPV of the project in each of the above scenarios.
b. If each scenario is equally likely, is the machine a worthwhile investment?
8.16 You are the financial analyst for a tennis racket manufacturer. The company is considering a
project using a graphite-like material in its rackets. Given the following information about the
market for a racket with the new material, will you recommend the project?
Market size
Market share
Selling price
Variable costs per year
Initial investment
Pessimistic
Expected
Optimistic
110,000
22%
$
115
$
72
$ 850,000
$1,500,000
120,000
25%
$
120
$
70
$ 800,000
$1,500,000
130,000
27%
$
125
$
68
$ 750,000
$1,500,000
Assume the appropriate discount rate is 13 percent.The corporate tax rate is 40 percent.The
firm will fully depreciate the initial investment over the next five years by the straight-line
method. Each of the three scenarios is equally likely. Assume all revenues and expenses are
received and paid in cash.
8.17 Xrco Petroleum has identified a new type of fuel additive and is considering launching this
new product. As a marketing manager, you have come up with the following scenarios for the
Corporate Finance,
Seventh Edition
Budgeting
149
Companies, 2004
Budgeting
231
launch. From finance, you know that the tax rate for the company is 34 percent and the
effective discount rate is 10 percent.You also know that the depreciation is $100,000 per year
and that production will occur over the next five years only. Will you undertake the project?
Expected
Optimistic
100,000
20%
$
100
$
80
$ 300,000
$1,000,000
150,000
25%
120
75
250,000
1,000,000
200,000
30%
140
70
200,000
1,000,000
* Per year
* Per year
8.18 The Big Burrito is planning to purchase a touch screen order system for its drive-thru window that would allow customers to select their order as soon as they arrive. This would reduce customer wait time and increase order accuracy. The touch screen and software would
cost the Big Burrito $150,000 and would last five years. There would also be an annual maintenance cost of $5,000. In addition to improved customer service, the Big Burrito would gain
two benefits. First, it could totally eliminate the full-time worker who used to accept and
enter these orders. His annual salary plus benefits total $30,000 per year. Second, it expects
drive-thru sales to increase but it doesn’t know how much.The estimates are:
Revenue increase (decrease)
COGS, 25% of rev increase
Pessimistic
Expected
Optimistic
$(5,000)
(1,250)
$15,000
3,750
$20,000
5,000
Net working capital (NWC) is expected to increase by $5,000 in the first year and be recovered at the end of year 5. If the appropriate discount rate is 15 percent and you ignore taxes,
should the Big Burrito go ahead with this investment?
Pessimistic
Year
0
Investments:
Touch screen system
Annual maintenance
Change in NWC
Wages saved
Total cash flow from
investments
Year
2
Year
3
Year
4
Year
5
NPV
$(150,000)
$(150,000)
Income:
Revenue
COGS
Cash flow from
operations
Total cash flow from
project
PV 15% (CF)
Year
1
$(150,000)
CF
(150,000)
$ (5,000)
(5,000)
30,000
$ (5,000)
$ (5,000)
$ (5,000)
30,000
30,000
30,000
$ (5,000)
5,000
30,000
$20,000
$25,000
$25,000
$25,000
$30,000
$ (5,000)
1,250
$ (5,000)
1,250
$ (5,000)
1,250
$ (5,000)
1,250
$ (5,000)
1,250
$ (3,750)
$ (3,750)
$ (3,750)
$ (3,750)
$ (3,750)
$16,250
CF兾1.15
14,130
$21,250
CF兾(1.15)2
16,068
$21,250
CF兾(1.15)3
13,972
$21,250
CF兾(1.15)4
12,150
$26,250
CF兾(1.15)5
13,051 ($80,629)
Market size
Market share
Price
Variable cost
Fixed cost
Investment
Pessimistic
150
Corporate Finance,
Seventh Edition
Budgeting
Budgeting
Companies, 2004
232
THE OPTION TO
ABANDON
8.19 M.V.P. Games, Inc., has hired you to perform a feasibility study of a new video game that requires a $4 million initial investment. M.V.P. expects total annual operating cash flow of
$750,000 for the next 10 years. The relevant discount rate is 10 percent. Ignore depreciation
and taxes. Cash flows occur at year-end.
a. What is the NPV of the new video game?
b. After one year, the estimate of remaining annual cash flows will either be revised upward
to $1.5 million or revised downward to $0. Each revision has an equal probability of occurring. At that time, the video game project can be sold for $200,000. What is the revised
NPV, given that the firm can abandon the project after one year?
c. What is the option value of abandonment?
8.20 Allied Products, Inc., is considering a new product launch. The firm expects to have annual operating cash flow of $200 million for the next ten years. Allied Products uses a discount rate
of 20 percent for new product launches. The initial investment is $100 million. Ignore taxes
and assume that the project has no salvage value at the end of its economic life.
a. What is the NPV of the new product?
b. After the first year, the project can be dismantled and sold for $50 million. If the estimate
of remaining cash flows can be revised based on the first year’s experience, at what level
of expected cash flows does it make sense to abandon the project?
8.21 Applied Nanotech is thinking about introducing a new surface cleaning machine.The marketing department has come up with the estimate that Applied Nanotech can sell 10 units per
year at $0.3 million net cash flow per unit for the next five years.The engineering department
has come up with the estimate that developing the machine will take $10 million initial investment. The finance department has estimated that 25 percent discount rate should be
used.
a. What is the base case NPV?
b. If unsuccessful, after the first year the project can be dismantled and sold for scrap for
$5 million. Also, after the first year, expected cash flows will be revised up to 20 units per
year or to 0 units, with equal probability. If so, what is the option value of abandonment?
What is the revised NPV?
8.22 Snapple is planning to enter the bottled water market. They expect to sell 5 million bottles
per year at a net cash flow of $.50 a piece for the next five years but they are unsure about
the market. At the end of the first year, they will learn if the product is a success or failure. If
it is a success, they can revise their forecast to 8 million bottles per year. If it is a failure, unit
sales will be 1 million. Success and failure are equally likely. The relevant discount rate is 15
percent and the initial investment required is $3 million. If they abandon the project after year
1, they can recover $1.5 million of the initial investment.
a. What is the base case NPV?
b. What is the value of the option to abandon?
Corporate Finance,
Seventh Edition
III: Risk
10. Return and Risk: The
Capital−Asset−Pricing
Model (CAPM)
Companies, 2004
151
Chapter 10
Return and Risk: The Capital-AssetEXECUTIVE SUMMARY
Pricing Model (CAPM)
The previous chapter achieved two purposes.
First, we acquainted you with the history of
U.S. capital markets. Second, we presented statistics such as expected return, variance, and
standard deviation. Our ultimate goal in the
next three chapters is to determine the appropriate discount rate for capital budgeting projects. Because the discount rate on a project is
a function of its risk, the discussion in the previous chapter on standard deviation is a necessary first step. However, we shall see that standard deviation is not the final word on risk.
Our next step is to investigate the relationship between the risk and the return of
individual securities when these securities are
part of a large portfolio.This task is taken up
in Chapter 10.The actual treatment of the appropriate discount rate for capital budgeting
is reserved for Chapter 12.
The crux of the current chapter can be
summarized as follows: An individual who
holds one security should use expected return as the measure of the security’s return.
Standard deviation or variance is the proper
measure of the security’s risk. An individual
who holds a diversified portfolio cares about
the contribution of each security to the expected return and the risk of the portfolio. It
turns out that a security’s expected return is
the appropriate measure of the security’s contribution to the expected return on the portfolio. However, neither the security’s variance
nor the security’s standard deviation is an appropriate measure of a security’s contribution
to the risk of a portfolio.The contribution of a
security to the risk of a portfolio is best measured by beta.
10.1 Individual Securities
In the first part of Chapter 10 we will examine the characteristics of individual securities.
In particular, we will discuss:
1. Expected Return. This is the return that an individual expects a stock to earn over the
next period. Of course, because this is only an expectation, the actual return may be either
higher or lower. An individual’s expectation may simply be the average return per period a
security has earned in the past. Alternatively, it may be based on a detailed analysis of a
firm’s prospects, on some computer-based model, or on special (or inside) information.
2. Variance and Standard Deviation. There are many ways to assess the volatility of a
security’s return. One of the most common is variance, which is a measure of the squared
deviations of a security’s return from its expected return. Standard deviation is the square
root of the variance.
3. Covariance and Correlation. Returns on individual securities are related to one another.
Covariance is a statistic measuring the interrelationship between two securities.Alternatively,
255
152
256
Corporate Finance,
Seventh Edition
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
this relationship can be restated in terms of the correlation between the two securities.
Covariance and correlation are building blocks to an understanding of the beta coefficient.
10.2 Expected Return, Variance, and Covariance
Expected Return and Variance
Suppose financial analysts believe that there are four equally likely states of the economy:
depression, recession, normal, and boom times. The returns on the Supertech Company are
expected to follow the economy closely, while the returns on the Slowpoke Company are
not. The return predictions are as follows:
Supertech Returns
RAt
Slowpoke Returns
RBt
20%
10
30
50
5%
20
12
9
Depression
Recession
Normal
Boom
Variance can be calculated in four steps. An additional step is needed to calculate standard
deviation. (The calculations are presented in Table 10.1.) The steps are:
1. Calculate the expected return:
Supertech
0.20 0.10 0.30 0.50
0.175 17.5% RA
4
Slowpoke
0.05 0.20 0.12 0.09
0.055 5.5% RB
4
2. For each company, calculate the deviation of each possible return from the company’s
expected return given previously. This is presented in the third column of Table 10.1.
3. The deviations we have calculated are indications of the dispersion of returns. However,
because some are positive and some are negative, it is difficult to work with them in this
form. For example, if we were to simply add up all the deviations for a single company,
we would get zero as the sum.
To make the deviations more meaningful, we multiply each one by itself. Now all the
numbers are positive, implying that their sum must be positive as well. The squared
deviations are presented in the last column of Table 10.1.
4. For each company, calculate the average squared deviation, which is the variance:1
Supertech
0.140625 0.005625 0.015625 0.105625
0.066875
4
1
In this example, the four states give rise to four possible outcomes for each stock. Had we used past data, the outcomes would
have actually occurred. In that case, statisticians argue that the correct divisor is N 1, where N is the number of observations.
Thus the denominator would be 3 ( (4 1)) in the case of past data, not 4. Note that the example in Section 9.5 involved past
data and we used a divisor of N 1. While this difference causes grief to both students and textbook writers, it is a minor point
in practice. In the real world, samples are generally so large that using N or N 1 in the denominator has virtually no effect on
the calculation of variance.
Corporate Finance,
Seventh Edition
III: Risk
257
Chapter 10 Return and Risk: The Capital-Asset-Pricing Model (CAPM)
TABLE 10.1
Calculating Variance
and Standard
Deviation
(1)
State of
Economy
(2)
Rate of
Return
(3)
Deviation from
Expected Return
Depression
Supertech*
RAt
0.20
(Expected return ⴝ 0.175)
(RAt RA )
0.375
( 0.20 0.175)
0.075
0.125
0.325
Recession
Normal
Boom
0.10
0.30
0.50
Slowpoke†
RBt
Depression
* RA (4)
Squared Value
of Deviation
(RAt RA ) 2
0.140625
[ (0.375)2]
0.005625
0.015625
0.105625
___________
0.267500
(Expected return ⴝ 0.055)
(RBt RB )
0.005
( 0.05 0.055)
0.145
0.175
0.035
0.05
Recession
Normal
Boom
153
Companies, 2004
Model (CAPM)
0.20
0.12
0.09
(RBt RB ) 2
0.000025
[ (0.005)2]
0.021025
0.030625
0.001225
___________
0.052900
0.20 0.10 0.30 0.50
0.175 17.5%
4
Var(RA ) A2 0.2675
0.066875
4
SD(RA) A 兹0.066875 0.2586 25.86%
† RB 0.05 0.20 0.12 0.09
0.055 5.5%
4
Var(RB ) B2 0.0529
0.013225
4
SD(RB) B 兹0.013225 0.1150 11.50%
Slowpoke
0.000025 0.021025 0.030625 0.001225
0.013225
4
Thus, the variance of Supertech is 0.066875, and the variance of Slowpoke is 0.013225.
5. Calculate standard deviation by taking the square root of the variance:
Supertech
兹0.066875 0.2586 25.86%
Slowpoke
兹0.013225 0.1150 11.50%
Algebraically, the formula for variance can be expressed as
Var(R) Expected value of (R R) 2
where R is the security’s expected return and R is the actual return.
A look at the four-step calculation for variance makes it clear why it is a measure of the
spread of the sample of returns. For each observation, one squares the difference between the
actual return and the expected return. One then takes an average of these squared differences.
154
Corporate Finance,
Seventh Edition
258
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
Squaring the differences makes them all positive. If we used the differences between each return and the expected return and then averaged these differences, we would get zero because
the returns that were above the mean would cancel the ones below.
However, because the variance is still expressed in squared terms, it is difficult to
interpret. Standard deviation has a much simpler interpretation, which was provided in
Section 9.5. Standard deviation is simply the square root of the variance. The general formula for the standard deviation is
SD(R) 兹Var(R)
Covariance and Correlation
Variance and standard deviation measure the variability of individual stocks. We now wish
to measure the relationship between the return on one stock and the return on another. Enter
covariance and correlation.
Covariance and correlation measure how two random variables are related. We explain
these terms by extending the Supertech and Slowpoke example presented earlier in this
chapter.
EXAMPLE
We have already determined the expected returns and standard deviations for both Supertech and
Slowpoke. (The expected returns are 0.175 and 0.055 for Supertech and Slowpoke, respectively.The
standard deviations are 0.2586 and 0.1150, respectively.) In addition, we calculated the deviation of
each possible return from the expected return for each firm. Using these data, covariance can be
calculated in two steps. An extra step is needed to calculate correlation.
1. For each state of the economy, multiply Supertech’s deviation from its expected return and
Slowpoke’s deviation from its expected return together. For example, Supertech’s rate of return
in a depression is 0.20, which is 0.375 (0.20 0.175) from its expected return. Slowpoke’s
rate of return in a depression is 0.05, which is 0.005 (0.05 0.055) from its expected return.
Multiplying the two deviations together yields 0.001875 [(0.375) (0.005)].The actual calculations are given in the last column of Table 10.2.This procedure can be written algebraically as
(RAt RA ) (RBt RB )
(10.1)
where RAt and RBt are the returns on Supertech and Slowpoke in state t. RA and RB are the expected returns on the two securities.
2. Calculate the average value of the four states in the last column.This average is the covariance.
That is,2
AB Cov(RA, RB ) 0.0195
0.004875
4
Note that we represent the covariance between Supertech and Slowpoke as either Cov(RA, RB) or
AB. Equation (10.1) illustrates the intuition of covariance. Suppose Supertech’s return is generally
above its average when Slowpoke’s return is above its average, and Supertech’s return is generally
below its average when Slowpoke’s return is below its average. This is indicative of a positive
dependency or a positive relationship between the two returns.Note that the term in equation (10.1)
will be positive in any state where both returns are above their averages. In addition, (10.1) will still be
positive in any state where both terms are below their averages.Thus, a positive relationship between
the two returns will give rise to a positive value for covariance.
2
As with variance, we divided by N (4 in this example) because the four states give rise to four possible outcomes. However,
had we used past data, the correct divisor would be N 1 (3 in this example).
Corporate Finance,
Seventh Edition
III: Risk
259
TABLE 10.2
State of
Economy
Depression
Calculating Covariance and Correlation
Rate of
Return of
Supertech
RAt
0.20
Deviation
from
Expected
Return
(RAt RA)
(Expected return
0.175)
0.375
( 0.20 0.175)
0.075
Rate of
Return of
Slowpoke
RBt
0.05
(Expected return
0.055)
0.005
( 0.05 0.055)
0.145
0.10
Normal
0.30
0.125
0.12
0.175
0.50
____
0.70
0.325
0.09
____
0.22
0.035
AB Cov (RA, RB ) 0.0195
0.004875
4
AB Corr(RA, RB ) Cov (RA, RB )
0.004875
0.1639
SD (RA ) SD(RB ) 0.2586 0.1150
0.20
Deviation
from
Expected
Return
(RBt RB)
Recession
Boom
155
Companies, 2004
Model (CAPM)
Product of
Deviations
(RAt RA) (RBt RB)
0.001875
( 0.375 0.005)
0.010875
( 0.075 0.145)
0.021875
( 0.125 0.175)
0.011375
( 0.325 0.035)
________________
0.0195
Conversely, suppose Supertech’s return is generally above its average when Slowpoke’s return is
below its average, and Supertech’s return is generally below its average when Slowpoke’s return is
above its average.This is indicative of a negative dependency or a negative relationship between the
two returns. Note that the term in equation (10.1) will be negative in any state where one return is
above its average and the other return is below its average.Thus, a negative relationship between the
two returns will give rise to a negative value for covariance.
Finally, suppose there is no relation between the two returns. In this case, knowing whether the
return on Supertech is above or below its expected return tells us nothing about the return on
Slowpoke. In the covariance formula, then, there will be no tendency for the deviations to be positive or negative together. On average, they will tend to offset each other and cancel out, making the
covariance zero.
Of course, even if the two returns are unrelated to each other, the covariance formula will not
equal zero exactly in any actual history.This is due to sampling error; randomness alone will make
the calculation positive or negative. But for a historical sample that is long enough, if the two returns
are not related to each other, we should expect the covariance to come close to zero.
The covariance formula seems to capture what we are looking for. If the two returns are positively related to each other, they will have a positive covariance, and if they are negatively related
to each other, the covariance will be negative. Last, and very important, if they are unrelated, the
covariance should be zero.
The formula for covariance can be written algebraically as
AB Cov(RA, RB ) Expected value of 关(RA RA ) (RB RB ) 兴
where RA and RB are the expected returns for the two securities, and RA and RB are the actual returns.The ordering of the two variables is unimportant.That is, the covariance of A with B is equal
to the covariance of B with A. This can be stated more formally as Cov(RA, RB) Cov(RB, RA) or
AB BA.
156
Corporate Finance,
Seventh Edition
260
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
The covariance we calculated is 0.004875. A negative number like this implies that the return
on one stock is likely to be above its average when the return on the other stock is below its
average, and vice versa. However, the size of the number is difficult to interpret. Like the variance figure, the covariance is in squared deviation units. Until we can put it in perspective, we don’t know
what to make of it.
We solve the problem by computing the correlation:
3. To calculate the correlation, divide the covariance by the standard deviations of both of the two
securities. For our example, we have:
AB Corr(RA, RB ) Cov(RA, RB )
0.004875
0.1639
A B
0.2586 0.1150
(10.2)
where A and B are the standard deviations of Supertech and Slowpoke, respectively. Note that
we represent the correlation between Supertech and Slowpoke either as Corr(RA, RB) or AB. As
with covariance, the ordering of the two variables is unimportant.That is, the correlation of A with
B is equal to the correlation of B with A. More formally, Corr(RA, RB) Corr(RB, RA) or AB BA.
Because the standard deviation is always positive, the sign of the correlation between two variables must be the same as that of the covariance between the two variables. If the correlation is positive, we say that the variables are positively correlated; if it is negative, we say that they are negatively
FIGURE 10.1
Examples of Different
Correlation
Coefficients—the
Graphs in the Figure
Plot the Separate
Returns on the Two
Securities through
Time
Perfect negative correlation
Corr(RA, RB) = –1
Perfect positive correlation
Corr(RA, RB) = 1
Returns
Returns
0
0
A
B
Time
Both the return on security A and the return on
security B are higher than average at the same
time. Both the return on security A and the
return on security B are lower than average at
the same time.
B
A
Time
Security A has a higher-than-average return
when security B has a lower-than-average
return, and vice versa.
Zero correlation
Corr(RA, RB) = 0
Returns
0
A
B
Time
The return on security A is completely
unrelated to the return on security B.
Corporate Finance,
Seventh Edition
III: Risk
157
Companies, 2004
Model (CAPM)
261
correlated; and if it is zero, we say that they are uncorrelated. Furthermore, it can be proved that the
correlation is always between 1 and 1.This is due to the standardizing procedure of dividing by
the two standard deviations.
We can compare the correlation between different pairs of securities. For example, it turns out
that the correlation between General Motors and Ford is much higher than the correlation between
General Motors and IBM. Hence, we can state that the first pair of securities is more interrelated
than the second pair.
Figure 10.1 shows the three benchmark cases for two assets, A and B. The figure shows two
assets with return correlations of 1, 1, and 0. This implies perfect positive correlation, perfect
negative correlation, and no correlation, respectively. The graphs in the figure plot the separate
returns on the two securities through time.
10.3 The Return and Risk for Portfolios
Suppose that an investor has estimates of the expected returns and standard deviations on
individual securities and the correlations between securities. How then does the investor
choose the best combination or portfolio of securities to hold? Obviously, the investor
would like a portfolio with a high expected return and a low standard deviation of return.
It is therefore worthwhile to consider:
1. The relationship between the expected return on individual securities and the expected
return on a portfolio made up of these securities.
2. The relationship between the standard deviations of individual securities, the correlations between these securities, and the standard deviation of a portfolio made up of these
securities.
The Example of Supertech and Slowpoke
In order to analyze the above two relationships, we will use the same example of Supertech
and Slowpoke that was presented previously. The relevant calculations are as follows.
The Expected Return on a Portfolio
The formula for expected return on a portfolio is very simple:
The expected return on a portfolio is simply a weighted average of the expected
returns on the individual securities.
Relevant Data from Example of Supertech
and Slowpoke
Item
Symbol
Value
Expected return on Supertech
Expected return on Slowpoke
Variance of Supertech
Variance of Slowpoke
Standard deviation of Supertech
Standard deviation of Slowpoke
Covariance between Supertech and Slowpoke
Correlation between Supertech and Slowpoke
RSuper
RSlow
2Super
2Slow
Super
Slow
Super, Slow
Super, Slow
0.175 17.5%
0.055 5.5%
0.066875
0.013225
0.2586 25.86%
0.1150 11.50%
0.004875
0.1639
158
Corporate Finance,
Seventh Edition
262
EXAMPLE
III: Risk
Model (CAPM)
Companies, 2004
Part III Risk
Consider Supertech and Slowpoke. From the preceding box, we find that the expected returns on
these two securities are 17.5 percent and 5.5 percent, respectively.
The expected return on a portfolio of these two securities alone can be written as
Expected return on portfolio XSuper (17.5%) XSlow (5.5%) RP
where XSuper is the percentage of the portfolio in Supertech and XSlow is the percentage of the portfolio in Slowpoke. If the investor with $100 invests $60 in Supertech and $40 in Slowpoke, the expected return on the portfolio can be written as
Expected return on portfolio 0.6 17.5% 0.4 5.5% 12.7%
Algebraically, we can write
Expected return on portfolio XARA XBRB RP
(10.3)
where XA and XB are the proportions of the total portfolio in the assets A and B, respectively.
(Because our investor can only invest in two securities, XA XB must equal 1 or 100 percent.)
RA and RB are the expected returns on the two securities.
Now consider two stocks, each with an expected return of 10 percent. The expected
return on a portfolio composed of these two stocks must be 10 percent, regardless of the
proportions of the two stocks held. This result may seem obvious at this point, but it will
become important later. The result implies that you do not reduce or dissipate your expected return by investing in a number of securities. Rather, the expected return on your
portfolio is simply a weighted average of the expected returns on the individual assets in
the portfolio.
Variance and Standard Deviation of a Portfolio
The Variance
The formula for the variance of a portfolio composed of two securities, A
and B, is
The Variance of the Portfolio
Var(portfolio) X2A A2 2XAXB
A, B X2B 2B
Note that there are three terms on the right-hand side of the equation. The first term involves the variance of A(
A2 ), the second term involves the covariance between the two securities (
A,B), and the third term involves the variance of B(
B2 ). (As stated earlier in this
chapter, A,B B, A. That is, the ordering of the variables is not relevant when expressing
the covariance between two securities.)
The formula indicates an important point. The variance of a portfolio depends on both
the variances of the individual securities and the covariance between the two securities.
The variance of a security measures the variability of an individual security’s return.
Covariance measures the relationship between the two securities. For given variances of
the individual securities, a positive relationship or covariance between the two securities
increases the variance of the entire portfolio. A negative relationship or covariance between
the two securities decreases the variance of the entire portfolio. This important result seems
to square with common sense. If one of your securities tends to go up when the other goes
down, or vice versa, your two securities are offsetting each other. You are achieving what
we call a hedge in finance, and the risk of your entire portfolio will be low. However, if
both your securities rise and fall together, you are not hedging at all. Hence, the risk of your
entire portfolio will be higher.
Corporate Finance,
Seventh Edition
III: Risk
159
Companies, 2004
Model (CAPM)
263
The variance formula for our two securities, Super and Slow, is
2
2
2
2
Var(portfolio) X Super
Super
2XSuper XSlow
Super, Slow XSlow
Slow
(10.4)
Given our earlier assumption that an individual with $100 invests $60 in Supertech and
$40 in Slowpoke, XSuper 0.6 and XSlow 0.4. Using this assumption and the relevant data
from the previous box, the variance of the portfolio is
0.023851 0.36 0.066875 2 [0.6 0.4 (0.004875)] 0.16 0.013225
(10.4)
The Matrix Approach
Alternatively, equation (10.4) can be expressed in the following
matrix format:
Supertech
Slowpoke
Supertech
Slowpoke
2
2
X Super
Super
XSuper XSlow
Super, Slow
0.024075 0.36 0.066875
0.00117 0.6 0.4 (0.004875)
XSuper XSlow
Super, Slow
2
2
X Slow
Slow
0.00117 0.6 0.4 (0.004875)
0.002116 0.16 0.013225
There are four boxes in the matrix. We can add the terms in the boxes to obtain equation (10.4), the variance of a portfolio composed of the two securities. The term in the
upper left-hand corner involves the variance of Supertech. The term in the lower right-hand
corner involves the variance of Slowpoke. The other two boxes contain the term involving
the covariance. These two boxes are identical, indicating why the covariance term is multiplied by 2 in equation (10.4).
At this point, students often find the box approach to be more confusing than equation (10.4). However, the box approach is easily generalized to more than two securities, a
task we perform later in this chapter.
Standard Deviation of a Portfolio Given (10.4), we can now determine the standard
deviation of the portfolio’s return. This is
P SD(portfolio) 兹Var冠portfolio冡兹0.023851
0.1544 15.44%
(10.5)
The interpretation of the standard deviation of the portfolio is the same as the interpretation
of the standard deviation of an individual security. The expected return on our portfolio is
12.7 percent. A return of 2.74 percent (12.7% 15.44%) is one standard deviation below
the mean and a return of 28.14 percent (12.7% 15.44%) is one standard deviation above
the mean. If the return on the portfolio is normally distributed, a return between 2.74 percent and 28.14 percent occurs about 68 percent of the time.3
The Diversification Effect
It is instructive to compare the standard deviation of the
portfolio with the standard deviation of the individual securities. The weighted average of
the standard deviations of the individual securities is
Weighted average of standard deviations XSuper
Super XSlow
Slow
0.2012 0.6 0.2586 0.4 0.115
(10.6)
3
There are only four equally probable returns for Supertech and Slowpoke, so neither security possesses a normal distribution.
Thus, probabilities would be slightly different in our example.
160
264
Corporate Finance,
Seventh Edition
III: Risk
Model (CAPM)
Companies, 2004
Part III Risk
One of the most important results in this chapter concerns the difference between equations (10.5) and (10.6). In our example, the standard deviation of the portfolio is less than
a weighted average of the standard deviations of the individual securities.
We pointed out earlier that the expected return on the portfolio is a weighted average of
the expected returns on the individual securities. Thus, we get a different type of result for
the standard deviation of a portfolio than we do for the expected return on a portfolio.
It is generally argued that our result for the standard deviation of a portfolio is due to
diversification. For example, Supertech and Slowpoke are slightly negatively correlated
( 0.1639). Supertech’s return is likely to be a little below average if Slowpoke’s return is above average. Similarly, Supertech’s return is likely to be a little above average if
Slowpoke’s return is below average. Thus, the standard deviation of a portfolio composed
of the two securities is less than a weighted average of the standard deviations of the two
securities.
The above example has negative correlation. Clearly, there will be less benefit from diversification if the two securities exhibit positive correlation. How high must the positive
correlation be before all diversification benefits vanish?
To answer this question, let us rewrite (10.4) in terms of correlation rather than covariance. The covariance can be rewritten as4
Super, Slow Super, Slow
Super
Slow
(10.7)
The formula states that the covariance between any two securities is simply the correlation
between the two securities multiplied by the standard deviations of each. In other words,
covariance incorporates both (1) the correlation between the two assets and (2) the variability of each of the two securities as measured by standard deviation.
From our calculations earlier in this chapter we know that the correlation between the
two securities is 0.1639. Given the variances used in equation (10.4), the standard
deviations are 0.2586 and 0.115 for Supertech and Slowpoke, respectively. Thus, the variance of a portfolio can be expressed as
Variance of the Portfolio’s Return
2
2XSuper XSlowSuper, Slow
Super
Slow X 2Slow
Slow
2
2
X Super
Super
(10.8)
0.023851 0.36 0.066875 2 0.6 0.4 (0.1639)
0.2586 0.115 0.16 0.013225
The middle term on the right-hand side is now written in terms of correlation, , not
covariance.
Suppose Super, Slow 1, the highest possible value for correlation. Assume all the other
parameters in the example are the same. The variance of the portfolio is
Variance of the 0.040466 0.36 0.066875 2 (0.6 0.4 1 0.2586
portfolio’s return
0.115) 0.16 0.013225
The standard deviation is
Standard variation of portfolio’s return 兹0.040466 0.2012 20.12%
(10.9)
Note that equations (10.9) and (10.6) are equal. That is, the standard deviation of a portfolio’s return is equal to the weighted average of the standard deviations of the individual
returns when 1. Inspection of (10.8) indicates that the variance and hence the standard
4
As with covariance, the ordering of the two securities is not relevant when expressing the correlation between the two securities.
That is, Super,Slow Slow,Super.
Corporate Finance,
Seventh Edition
III: Risk
Model (CAPM)
265
TABLE 10.3
Asset
Standard Deviations
for Standard & Poor’s
500 Index and for
Selected Stocks in
the Index
S&P 500 Index
Bell Atlantic
Ford Motor Co.
Walt Disney Co.
General Electric
IBM
McDonald’s Corp.
Sears, Roebuck & Co.
Toys “R” Us Inc.
Amazon.com
161
Companies, 2004
Standard Deviation
13.33%
28.60
31.39
41.05
29.54
32.18
32.38
29.76
32.23
59.21
As long as the correlations between pairs of securities are less than 1, the standard deviation of an index is less than the
weighted average of the standard deviations of the individual securities within the index.
deviation of the portfolio must fall as the correlation drops below 1. This leads to:
As long as 1, the standard deviation of a portfolio of two securities is less than
the weighted average of the standard deviations of the individual securities.
In other words, the diversification effect applies as long as there is less than perfect correlation (as long as 1). Thus, our Supertech-Slowpoke example is a case of overkill.
We illustrated diversification by an example with negative correlation. We could have
illustrated diversification by an example with positive correlation—as long as it was not
perfect positive correlation.
An Extension to Many Assets
The preceding insight can be extended to the case of
many assets. That is, as long as correlations between pairs of securities are less than 1, the
standard deviation of a portfolio of many assets is less than the weighted average of the
standard deviations of the individual securities.
Now consider Table 10.3, which shows the standard deviation of the Standard & Poor’s
500 Index and the standard deviations of some of the individual securities listed in the index
over a recent 10-year period. Note that all of the individual securities in the table have higher
standard deviations than that of the index. In general, the standard deviations of most of the
individual securities in an index will be above the standard deviation of the index itself,
though a few of the securities could have lower standard deviations than that of the index.
Concept
Questions
1. What are the formulas for the expected return, variance, and standard deviation of a portfolio of two assets?
2. What is the diversification effect?
3. What are the highest and lowest possible values for the correlation coefficient?
10.4 The Efficient Set for Two Assets
Our results on expected returns and standard deviations are graphed in Figure 10.2. In the
figure, there is a dot labeled Slowpoke and a dot labeled Supertech. Each dot represents
both the expected return and the standard deviation for an individual security. As can be
seen, Supertech has both a higher expected return and a higher standard deviation.
The box or “䊐” in the graph represents a portfolio with 60 percent invested in Supertech
and 40 percent invested in Slowpoke. You will recall that we have previously calculated
both the expected return and the standard deviation for this portfolio.
162
Corporate Finance,
Seventh Edition
266
FIGURE 10.2
Expected Returns and
Standard Deviations
for Supertech,
Slowpoke, and a
Portfolio Composed
of 60 Percent in
Supertech and
40 Percent in
Slowpoke
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
Expected return (%)
Supertech
17.5
12.7
5.5
Slowpoke
11.50
15.44
25.86
Standard
deviation (%)
The choice of 60 percent in Supertech and 40 percent in Slowpoke is just one of an infinite number of portfolios that can be created. The set of portfolios is sketched by the
curved line in Figure 10.3.
Consider portfolio 1. This is a portfolio composed of 90 percent Slowpoke and 10 percent Supertech. Because it is weighted so heavily toward Slowpoke, it appears close to the
Slowpoke point on the graph. Portfolio 2 is higher on the curve because it is composed of
50 percent Slowpoke and 50 percent Supertech. Portfolio 3 is close to the Supertech point
on the graph because it is composed of 90 percent Supertech and 10 percent Slowpoke.
There are a few important points concerning this graph.
1. We argued that the diversification effect occurs whenever the correlation between
the two securities is below 1. The correlation between Supertech and Slowpoke is
0.1639. The diversification effect can be illustrated by comparison with the straight line
between the Supertech point and the Slowpoke point. The straight line represents points
that would have been generated had the correlation coefficient between the two securities
been 1. The diversification effect is illustrated in the figure since the curved line is always
to the left of the straight line. Consider point 1. This represents a portfolio composed of
90 percent in Slowpoke and 10 percent in Supertech if the correlation between the two
were exactly 1. We argue that there is no diversification effect if 1. However, the diversification effect applies to the curved line, because point 1 has the same expected return
as point 1 but has a lower standard deviation. (Points 2 and 3 are omitted to reduce the
clutter of Figure 10.3.)
Though the straight line and the curved line are both represented in Figure 10.3, they do
not simultaneously exist in the same world. Either 0.1639 and the curve exists or
1 and the straight line exists. In other words, though an investor can choose between
different points on the curve if 0.1639, she cannot choose between points on the
curve and points on the straight line.
2. The point MV represents the minimum variance portfolio. This is the portfolio with
the lowest possible variance. By definition, this portfolio must also have the lowest possible
standard deviation. (The term minimum variance portfolio is standard in the literature, and
we will use that term. Perhaps minimum standard deviation would actually be better, because standard deviation, not variance, is measured on the horizontal axis of Figure 10.3.)
Corporate Finance,
Seventh Edition
III: Risk
Companies, 2004
Model (CAPM)
267
FIGURE 10.3
Set of Portfolios
Composed of
Holdings in
Supertech and
Slowpoke
(correlation between
the two securities is
0.1639)
163
Expected return
on portfolio (%)
XSupertech = 60%
XSlowpoke = 40%
Supertech
3
17.5
2
MV
1
1
5.5
Slowpoke
11.50
25.86
Standard
deviation
of portfolio’s
return (%)
Portfolio 1 is composed of 90 percent Slowpoke and 10 percent Supertech ( 0.1639).
Portfolio 1' is composed of 90 percent Slowpoke and 10 percent Supertech ( 1).
Point MV denotes the minimum variance portfolio. This is the portfolio with the lowest
possible variance. By definition, the same portfolio must also have the lowest possible standard deviation.
3. An individual contemplating an investment in a portfolio of Slowpoke and Supertech
faces an opportunity set or feasible set represented by the curved line in Figure 10.3. That
is, he can achieve any point on the curve by selecting the appropriate mix between the two
securities. He cannot achieve any point above the curve because he cannot increase the return on the individual securities, decrease the standard deviations of the securities, or decrease the correlation between the two securities. Neither can he achieve points below the
curve because he cannot lower the returns on the individual securities, increase the standard deviations of the securities, or increase the correlation. (Of course, he would not want
to achieve points below the curve, even if he were able to do so.)
Were he relatively tolerant of risk, he might choose portfolio 3. (In fact, he could even
choose the end point by investing all his money in Supertech.) An investor with less tolerance for risk might choose portfolio 2. An investor wanting as little risk as possible would
choose MV, the portfolio with minimum variance or minimum standard deviation.
4. Note that the curve is backward bending between the Slowpoke point and MV. This
indicates that, for a portion of the feasible set, standard deviation actually decreases as one
increases expected return. Students frequently ask, “How can an increase in the proportion
of the risky security, Supertech, lead to a reduction in the risk of the portfolio?”
This surprising finding is due to the diversification effect. The returns on the two securities are negatively correlated with each other. One security tends to go up when the other
goes down and vice versa. Thus, an addition of a small amount of Supertech acts as a hedge
to a portfolio composed only of Slowpoke. The risk of the portfolio is reduced, implying
backward bending. Actually, backward bending always occurs if 0. It may or may not
occur when 0. Of course, the curve bends backward only for a portion of its length. As
164
Corporate Finance,
Seventh Edition
268
FIGURE 10.4
Opportunity Sets
Composed of
Holdings in
Supertech and
Slowpoke
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
Expected return
on portfolio
=–1
= – 0.1639
=0
= 0.5
=1
Standard
deviation
of portfolio’s
return
Each curve represents a different correlation. The lower the correlation, the more
bend in the curve.
one continues to increase the percentage of Supertech in the portfolio, the high standard deviation of this security eventually causes the standard deviation of the entire portfolio to rise.
5. No investor would want to hold a portfolio with an expected return below that of the
minimum variance portfolio. For example, no investor would choose portfolio 1. This
portfolio has less expected return but more standard deviation than the minimum variance
portfolio has. We say that portfolios such as portfolio 1 are dominated by the minimum
variance portfolio. Though the entire curve from Slowpoke to Supertech is called the
feasible set, investors only consider the curve from MV to Supertech. Hence, the curve
from MV to Supertech is called the efficient set or the efficient frontier.
Figure 10.3 represents the opportunity set where 0.1639. It is worthwhile to examine Figure 10.4, which shows different curves for different correlations. As can be seen,
the lower the correlation, the more bend there is in the curve. This indicates that the
diversification effect rises as declines. The greatest bend occurs in the limiting case where
1. This is perfect negative correlation. While this extreme case where 1 seems
to fascinate students, it has little practical importance. Most pairs of securities exhibit positive correlation. Strong negative correlation, let alone perfect negative correlation, are unlikely occurrences indeed.5
Note that there is only one correlation between a pair of securities. We stated earlier
that the correlation between Slowpoke and Supertech is 0.1639. Thus, the curve in
Figure 10.4 representing this correlation is the correct one, and the other curves should be
viewed as merely hypothetical.
The graphs we examined are not mere intellectual curiosities. Rather, efficient sets can
easily be calculated in the real world. As mentioned earlier, data on returns, standard deviations, and correlations are generally taken from past observations, though subjective notions
can be used to determine the values of these parameters as well. Once the parameters have
5
A major exception occurs with derivative securities. For example, the correlation between a stock and a put on the stock is
generally strongly negative. Puts will be treated later in the text.
Corporate Finance,
Seventh Edition
III: Risk
FIGURE 10.5
Return/Risk Trade-off
for World Stocks:
Portfolio of U.S. and
Foreign Stocks
Total return
on portfolio (%)
0.2
0.19
Minimum
0.18
variance
0.17
portfolio
0.16
269
0 % U.S., 100% Foreign
10%
30%
0.15
0.14
165
Companies, 2004
Model (CAPM)
20% U.S., 80% Foreign
40%
50%
0.13
0.12
0.11
0.1
0.09
0.08
60%
70%
80% U.S., 20% Foreign
90%
100% U.S.
0.07
0.06
0.15
0.17
0.19
0.21
Risk (standard
deviation of
0.23 portfolio’s
return) (%)
been determined, any one of a whole host of software packages can be purchased to generate an efficient set. However, the choice of the preferred portfolio within the efficient set is
up to you. As with other important decisions like what job to choose, what house or car to
buy, and how much time to allocate to this course, there is no computer program to choose
the preferred portfolio.
An efficient set can be generated where the two individual assets are portfolios themselves. For example, the two assets in Figure 10.5 are a diversified portfolio of American
stocks and a diversified portfolio of foreign stocks. Expected returns, standard deviations,
and the correlation coefficient were calculated over the recent past. No subjectivity entered
the analysis. The U.S. stock portfolio with a standard deviation of about 0.173 is less risky
than the foreign stock portfolio, which has a standard deviation of about 0.222. However,
combining a small percentage of the foreign stock portfolio with the U.S. portfolio actually
reduces risk, as can be seen by the backward-bending nature of the curve. In other words,
the diversification benefits from combining two different portfolios more than offset the introduction of a riskier set of stocks into one’s holdings. The minimum variance portfolio
occurs with about 80 percent of one’s funds in American stocks and about 20 percent in
foreign stocks. Addition of foreign securities beyond this point increases the risk of one’s
entire portfolio.
The backward-bending curve in Figure 10.5 is important information that has not
bypassed American money managers. In recent years, pension-fund and mutual-fund
managers in the United States have sought out investment opportunities overseas. Another
point worth pondering concerns the potential pitfalls of using only past data to estimate
future returns. The stock markets of many foreign countries have had phenomenal growth
in the past 25 years. Thus, a graph like Figure 10.5 makes a large investment in these foreign
markets seem attractive. However, because abnormally high returns cannot be sustained
forever, some subjectivity must be used when forecasting future expected returns.
Concept
Question
1. What is the relationship between the shape of the efficient set for two assets
and the correlation between the two assets?
166
Corporate Finance,
Seventh Edition
270
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
10.5 The Efficient Set for Many Securities
The previous discussion concerned two securities. We found that a simple curve sketched
out all the possible portfolios. Because investors generally hold more than two securities,
we should look at the same graph when more than two securities are held. The shaded area
in Figure 10.6 represents the opportunity set or feasible set when many securities are considered. The shaded area represents all the possible combinations of expected return and
standard deviation for a portfolio. For example, in a universe of 100 securities, point 1
might represent a portfolio of, say, 40 securities. Point 2 might represent a portfolio of
80 securities. Point 3 might represent a different set of 80 securities, or the same 80 securities held in different proportions, or something else. Obviously, the combinations are virtually endless. However, note that all possible combinations fit into a confined region. No
security or combination of securities can fall outside of the shaded region. That is, no one
can choose a portfolio with an expected return above that given by the shaded region. Furthermore, no one can choose a portfolio with a standard deviation below that given in the
shady area. Perhaps more surprisingly, no one can choose an expected return below that
given in the curve. In other words, the capital markets actually prevent a self-destructive
person from taking on a guaranteed loss.6
So far, Figure 10.6 is different from the earlier graphs. When only two securities are involved, all the combinations lie on a single curve. Conversely, with many securities the
combinations cover an entire area. However, notice that an individual will want to be
somewhere on the upper edge between MV and X. The upper edge, which we indicate in
Figure 10.6 by a thick curve, is called the efficient set. Any point below the efficient set
would receive less expected return and the same standard deviation as a point on the efficient set. For example, consider R on the efficient set and W directly below it. If W contains
the risk you desire, you should choose R instead in order to receive a higher expected return.
FIGURE 10.6
The Feasible Set
of Portfolios
Constructed from
Many Securities
Expected return
on portfolio
X
2
1
R
3
W
MV
Standard
deviation
of portfolio’s
return
6
Of course, someone dead set on parting with his money can do so. For example, he can trade frequently without purpose, so
that commissions more than offset the positive expected returns on the portfolio.
Corporate Finance,
Seventh Edition
III: Risk
167
Companies, 2004
Model (CAPM)
271
TABLE 10.4
Matrix Used to
Calculate the
Variance of a
Portfolio
Stock
1
2
3
1
X12 12
X1X2Cov(R1,R2)
X1X3Cov(R1,R3)
X1XNCov(R1,RN)
X2X3Cov(R2,R3)
X2XNCov(R2,RN)
2
3
X2X1Cov(R2,R1)
X 22
22
X3X1Cov(R3,R1)
X3X2Cov(R3,R2)
XNX1Cov(RN,R1)
XNX2Cov(RN,R2)
X 23
23
...
N
X3XNCov(R3,RN)
.
.
.
N
XNX3Cov(RN,R3)
X N2 N2
The variance of the portfolio is the sum of the terms in all the boxes.
i is the standard deviation of stock i.
Cov(Ri, Rj) is the covariance between stock i and stock j.
Terms involving the standard deviation of a single security appear on the diagonal.Terms involving covariance between two
securities appear off the diagonal.
In the final analysis, Figure 10.6 is quite similar to Figure 10.3. The efficient set in
Figure 10.3 runs from MV to Supertech. It contains various combinations of the securities
Supertech and Slowpoke. The efficient set in Figure 10.6 runs from MV to X. It contains
various combinations of many securities. The fact that a whole shaded area appears in
Figure 10.6 but not in Figure 10.3 is just not an important difference; no investor would
choose any point below the efficient set in Figure 10.6 anyway.
We mentioned before that an efficient set for two securities can be traced out easily in
the real world. The task becomes more difficult when additional securities are included
because the number of observations grows. For example, using subjective analysis to estimate expected returns and standard deviations for, say, 100 or 500 securities may very well
become overwhelming, and the difficulties with correlations may be greater still. There are
almost 5,000 correlations between pairs of securities from a universe of 100 securities.
Though much of the mathematics of efficient-set computation had been derived in the
1950s,7 the high cost of computer time restricted application of the principles. In recent
years, the cost has been drastically reduced. A number of software packages allow the calculation of an efficient set for portfolios of moderate size. By all accounts these packages
sell quite briskly, so that our discussion above would appear to be important in practice.
Variance and Standard Deviation in a Portfolio of Many Assets
We earlier calculated the formulas for variance and standard deviation in the two-asset
case. Because we considered a portfolio of many assets in Figure 10.6, it is worthwhile to
calculate the formulas for variance and standard deviation in the many-asset case. The formula for the variance of a portfolio of many assets can be viewed as an extension of the
formula for the variance of two assets.
To develop the formula, we employ the same type of matrix that we used in the twoasset case. This matrix is displayed in Table 10.4. Assuming that there are N assets, we
write the numbers 1 through N on the horizontal axis and 1 through N on the vertical axis.
This creates a matrix of N N N2 boxes. The variance of the portfolio is the sum of the
terms in all the boxes.
7
The classic treatise is Harry Markowitz, Portfolio Selection (New York: John Wiley & Sons, 1959). Markowitz won the Nobel
Prize in economics in 1990 for his work on modern portfolio theory.
168
Corporate Finance,
Seventh Edition
272
III: Risk
Part III Risk
TABLE 10.5
Number of Variance
and Covariance
Terms as a Function
of the Number of
Stocks in the
Portfolio
Companies, 2004
Model (CAPM)
Number of
Stocks in
Portfolio
Total
Number
of Terms
Number of
Variance Terms
(number of terms
on diagonal)
Number of
Covariance Terms
(number of terms
off diagonal)
1
2
3
10
100
.
.
.
N
1
4
9
100
10,000
.
.
.
N2
1
2
3
10
100
.
.
.
N
0
2
6
90
9,900
.
.
.
N2 N
In a large portfolio, the number of terms involving covariance between two securities is much greater than the number of
terms involving variance of a single security.
Consider, for example, the box in the second row and the third column. The term in the
box is X2X3 Cov(R2, R3). X2 and X3 are the percentages of the entire portfolio that are invested in the second asset and the third asset, respectively. For example, if an individual
with a portfolio of $1,000 invests $100 in the second asset, X2 10% ($100兾$1,000).
Cov(R3, R2) is the covariance between the returns on the third asset and the returns on the
second asset. Next, note the box in the third row and the second column. The term in this
box is X3X2 Cov(R3, R2). Because Cov(R3, R2) Cov(R2, R3), both boxes have the same
value. The second security and the third security make up one pair of stocks. In fact, every
pair of stocks appears twice in the table, once in the lower left-hand side and once in the
upper right-hand side.
Now consider boxes on the diagonal. For example, the term in the first box on the diagonal is X 12 12 . Here, 12 is the variance of the return on the first security.
Thus, the diagonal terms in the matrix contain the variances of the different stocks. The
off-diagonal terms contain the covariances. Table 10.5 relates the numbers of diagonal
and off-diagonal elements to the size of the matrix. The number of diagonal terms (number
of variance terms) is always the same as the number of stocks in the portfolio. The number
of off-diagonal terms (number of covariance terms) rises much faster than the number of
diagonal terms. For example, a portfolio of 100 stocks has 9,900 covariance terms. Since
the variance of a portfolio’s returns is the sum of all the boxes, we have:
The variance of the return on a portfolio with many securities is more dependent on
the covariances between the individual securities than on the variances of the
individual securities.
Concept
Questions
1. What is the formula for the variance of a portfolio for many assets?
2. How can the formula be expressed in terms of a box or matrix?
10.6 Diversification: An Example
The preceding point can be illustrated by altering the matrix in Table 10.4 slightly. Suppose
that we make the following three assumptions:
1. All securities possess the same variance, which we write as var. In other words,
2i var for every security.
Corporate Finance,
Seventh Edition
III: Risk
169
Companies, 2004
Model (CAPM)
273
TABLE 10.6
Stock
1
2
3
1
(1兾N2 ) var
(1兾N2 ) cov
(1兾N2 ) cov
(1兾N2 )cov
2
(1兾N2 ) cov
(1兾N2 ) var
(1兾N2 ) cov
(1兾N2 )cov
3
(1兾N2 ) cov
(1兾N2 ) cov
(1兾N2 ) var
(1兾N2 )cov
(1兾N2 ) cov
(1兾N2 ) cov
(1兾N2 ) cov
(1兾N2 )var
Matrix Used to Calculate the Variance of a
Portfolio When (a) All
Securities Possess the
Same Variance, Which
___
We Represent as var ;
(b) All Pairs of Securities Possess the Same
Covariance, Which
___ We
Represent as cov ;
(c) All Securities Are
Held in the Same Proportion, Which Is 1兾N
...
N
N
2. All covariances in Table 10.4 are the same. We represent this uniform covariance as
cov. In other words, Cov(Ri, Rj ) cov for every pair of securities. It can easily be
shown that var cov.
3. All securities are equally weighted in the portfolio. Because there are N assets, the
weight of each asset in the portfolio is 1兾N. In other words, Xi 1兾N for each security i.
Table 10.6 is the matrix of variances and covariances under these three simplifying
assumptions. Note that all of the diagonal terms are identical. Similarly, all of the offdiagonal terms are identical. As with Table 10.4, the variance of the portfolio is the sum of
the terms in the boxes in Table 10.6. We know that there are N diagonal terms involving
variance. Similarly, there are N (N 1) off-diagonal terms involving covariance. Summing across all the boxes in Table 10.6 we can express the variances of the portfolio as
Variance of portfolio N
冢N 冣var N(N 1)
1
2
Number of
Each
Number of
diagonal
diagonal
off-diagonal
terms
term
terms
2
1
N N
var cov
N
N2
1
1
var 1 cov
N
N
冢冣
冢冣
冢
冢
冢N 冣cov
1
2
(10.10)
Each
off-diagonal
term
冣
冣
Equation (10.10) expresses the variance of our special portfolio as a weighted sum of the
average security variance and the average covariance.8
Now, let’s increase the number of securities in the portfolio without limit. The variance
of the portfolio becomes
Variance of portfolio (when N S q) cov
(10.11)
This occurs because (1) the weight on the variance term, 1兾N, goes to 0 as N goes to infinity, and (2) the weight on the covariance term, 1 1兾N, goes to 1 as N goes to infinity.
Equation (10.10) is actually a weighted average of the variance and covariance terms because the weights, 1兾N and 1 1兾N,
sum to 1.
8
170
Corporate Finance,
Seventh Edition
274
III: Risk
Model (CAPM)
Companies, 2004
Part III Risk
FIGURE 10.7
Variance
of
portfolio’s
return
Relationship between
the Variance of a
Portfolio’s Return
and the Number of
Securities in the
Portfolio*
Diversifiable risk,
unique risk, or
unsystematic risk
var
cov
Portfolio risk,
market risk, or
systematic risk
1
2
3
4
Number of
securities
*This graph assumes
a. All securities have constant variance, var.
b. All securities have constant covariance, cov.
c. All securities are equally weighted in portfolio.
The variance of a portfolio drops as more securities are added to the portfolio.
However, it does not drop to zero. Rather, cov serves as the floor.
Formula (10.11) provides an interesting and important result. In our special portfolio,
the variances of the individual securities completely vanish as the number of securities
becomes large. However, the covariance terms remain. In fact, the variance of the portfolio
becomes the average covariance, cov. One often hears that one should diversify. In other
words, you should not put all your eggs in one basket. The effect of diversification on the risk
of a portfolio can be illustrated in this example. The variances of the individual securities are
diversified away, but the covariance terms cannot be diversified away.
The fact that part, but not all, of one’s risk can be diversified away should be explored.
Consider Mr. Smith, who brings $1,000 to the roulette table at a casino. It would be very
risky if he put all his money on one spin of the wheel. For example, imagine that he put the
full $1,000 on red at the table. If the wheel showed red, he would get $2,000, but if the
wheel showed black, he would lose everything. Suppose, instead, he divided his money
over 1,000 different spins by betting $1 at a time on red. Probability theory tells us that he
could count on winning about 50 percent of the time. This means that he could count on
pretty nearly getting all his original $1,000 back.9 In other words, risk is essentially eliminated with 1,000 different spins.
Now, let’s contrast this with our stock market example, which we illustrate in Figure 10.7. The variance of the portfolio with only one security is, of course, var because the
variance of a portfolio with one security is the variance of the security. The variance of the
portfolio drops as more securities are added, which is evidence of the diversification
effect. However, unlike Mr. Smith’s roulette example, the portfolio’s variance can never
9
This example ignores the casino’s cut.
Corporate Finance,
Seventh Edition
III: Risk
Model (CAPM)
Companies, 2004
171
275
drop to zero. Rather it reaches a floor of cov, which is the covariance of each pair of
securities.10
Because the variance of the portfolio asymptotically approaches cov, each additional
security continues to reduce risk. Thus, if there were neither commissions nor other transactions costs, it could be argued that one can never achieve too much diversification. However, there is a cost to diversification in the real world. Commissions per dollar invested fall
as one makes larger purchases in a single stock. Unfortunately, one must buy fewer shares
of each security when buying more and more different securities. Comparing the costs and
benefits of diversification, Meir Statman argues that a portfolio of about 30 stocks is needed
to achieve optimal diversification.11
We mentioned earlier that var must be greater than cov. Thus, the variance of a security’s return can be broken down in the following way:
Total risk of
Unsystematic or
individual security Portfolio risk diversifiable risk
(var)
(cov)
(var cov)
Total risk, which is var in our example, is the risk that one bears by holding onto one security only. Portfolio risk is the risk that one still bears after achieving full diversification,
which is cov in our example. Portfolio risk is often called systematic or market risk as
well. Diversifiable, unique, or unsystematic risk is that risk that can be diversified away
in a large portfolio, which must be ( var cov) by definition.
To an individual who selects a diversified portfolio, the total risk of an individual security is not important. When considering adding a security to a diversified portfolio, the
individual cares about only that portion of the risk of a security that cannot be diversified
away. This risk can alternatively be viewed as the contribution of a security to the risk of
an entire portfolio. We will talk later about the case where securities make different contributions to the risk of the entire portfolio.
Risk and the Sensible Investor
Having gone to all this trouble to show that unsystematic risk disappears in a well-diversified
portfolio, how do we know that investors even want such portfolios? Suppose they like risk
and don’t want it to disappear?
We must admit that, theoretically at least, this is possible, but we will argue that it does
not describe what we think of as the typical investor. Our typical investor is risk averse.
Risk-averse behavior can be defined in many ways, but we prefer the following example:
A fair gamble is one with zero expected return; a risk-averse investor would prefer to avoid
fair gambles.
Why do investors choose well-diversified portfolios? Our answer is that they are risk
averse, and risk-averse people avoid unnecessary risk, such as the unsystematic risk on a
stock. If you do not think this is much of an answer, consider whether you would take on
such a risk. For example, suppose you had worked all summer and had saved $5,000,
which you intended to use for your college expenses. Now, suppose someone came up to
you and offered to flip a coin for the money: heads, you would double your money, and
tails, you would lose it all.
10
Though it is harder to show, this risk reduction effect also applies to the general case where variances and covariances are not
equal.
11
Meir Statman, “How Many Stocks Make a Diversified Portfolio?” Journal of Financial and Quantitative Analysis (September
1987).
172
Corporate Finance,
Seventh Edition
276
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
Would you take such a bet? Perhaps you would, but most people would not. Leaving
aside any moral question that might surround gambling and recognizing that some people
would take such a bet, it’s our view that the average investor would not.
To induce the typical risk-averse investor to take a fair gamble, you must sweeten the
pot. For example, you might need to raise the odds of winning from 50–50 to 70–30 or
higher. The risk-averse investor can be induced to take fair gambles only if they are sweetened so that they become unfair to the investor’s advantage.
Concept
Questions
1. What are the two components of the total risk of a security?
2. Why doesn’t diversification eliminate all risk?
10.7 Riskless Borrowing and Lending
Figure 10.6 assumes that all the securities on the efficient set are risky. Alternatively, an
investor could combine a risky investment with an investment in a riskless or risk-free
security, such as an investment in United States Treasury bills. This is illustrated in the following example.
EXAMPLE
Ms. Bagwell is considering investing in the common stock of Merville Enterprises. In addition,
Ms. Bagwell will either borrow or lend at the risk-free rate.The relevant parameters are
Expected return
Standard deviation
Common Stock
of Merville
Risk-Free
Asset
14%
0.20
10%
0
Suppose Ms. Bagwell chooses to invest a total of $1,000, $350 of which is to be invested in Merville
Enterprises and $650 placed in the risk-free asset.The expected return on her total investment is
simply a weighted average of the two returns:
Expected return on portfolio composed
0.114 (0.35 0.14) (0.65 0.10)
of one riskless and one risky asset
(10.12)
Because the expected return on the portfolio is a weighted average of the expected return on the
risky asset (Merville Enterprises) and the risk-free return, the calculation is analogous to the way we
treated two risky assets. In other words, equation (10.3) applies here.
Using equation (10.4), the formula for the variance of the portfolio can be written as
2
2
2
2
XMerville
Merville
2X Merville XRisk-free
Merville, Risk-free XRisk-free
Risk-free
However, by definition, the risk-free asset has no variability. Thus, both Merville, Risk-free and 2Risk-free
are equal to zero, reducing the above expression to
Variance of portfolio composed
2
2
Merville
XMerville
(0.35) 2 (0.20) 2
0.0049
(10.13)
Corporate Finance,
Seventh Edition
III: Risk
Companies, 2004
Model (CAPM)
277
FIGURE 10.8
Expected Return and
Risk for a Portfolio of
One Risky Asset and
One Riskless Asset
173
Expected return
on portfolio (%)
120% in Merville Enterprises
–20% in risk-free assets
(borrowing at risk-free
rate)
Merville Enterprises
14
10 = RF
35% in Merville Enterprises
65% in risk-free assets
Borrowing to invest in
Merville when the
borrowing rate is greater
than the lending rate
20
Standard
deviation
of portfolio’s
return (%)
The standard deviation of the portfolio is
Standard deviation of portfolio composed
XMerville
Merville
0.35 0.20
(10.14)
0.07
The relationship between risk and expected return for one risky and one riskless asset can be
seen in Figure 10.8. Ms. Bagwell’s split of 35–65 percent between the two assets is represented on a
straight line between the risk-free rate and a pure investment in Merville Enterprises. Note that,
unlike the case of two risky assets, the opportunity set is straight, not curved.
Suppose that, alternatively, Ms. Bagwell borrows $200 at the risk-free rate. Combining this with
her original sum of $1,000, she invests a total of $1,200 in Merville. Her expected return would be
Expected return on portfolio
formed by borrowing
14.8% 1.20 0.14 (0.2 0.10)
to invest in risky asset
Here, she invests 120 percent of her original investment of $1,000 by borrowing 20 percent of her
original investment. Note that the return of 14.8 percent is greater than the 14-percent expected
return on Merville Enterprises. This occurs because she is borrowing at 10 percent to invest in a
security with an expected return greater than 10 percent.
The standard deviation is
Standard deviation of portfolio formed
0.24 1.20 0.2
by borrowing to invest in risky asset
The standard deviation of 0.24 is greater than 0.20, the standard deviation of the Merville investment, because borrowing increases the variability of the investment.This investment also appears in
Figure 10.8.
174
Corporate Finance,
Seventh Edition
278
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
So far, we have assumed that Ms. Bagwell is able to borrow at the same rate at which she can
lend.12 Now let us consider the case where the borrowing rate is above the lending rate.The dotted line in Figure 10.8 illustrates the opportunity set for borrowing opportunities in this case.The
dotted line is below the solid line because a higher borrowing rate lowers the expected return on
the investment.
The Optimal Portfolio
The previous section concerned a portfolio formed between one riskless asset and one risky
asset. In reality, an investor is likely to combine an investment in the riskless asset with a
portfolio of risky assets. This is illustrated in Figure 10.9.
Consider point Q, representing a portfolio of securities. Point Q is in the interior of the
feasible set of risky securities. Let us assume the point represents a portfolio of 30 percent in AT&T, 45 percent in General Motors (GM), and 25 percent in IBM. Individuals
combining investments in Q with investments in the riskless asset would achieve points
along the straight line from RF to Q. We refer to this as line I. For example, point 1 on the
line represents a portfolio of 70 percent in the riskless asset and 30 percent in stocks represented by Q. An investor with $100 choosing point 1 as his portfolio would put $70
in the risk-free asset and $30 in Q. This can be restated as $70 in the riskless asset, $9
(0.3 $30) in AT&T, $13.50 (0.45 $30) in GM, and $7.50 (0.25 $30) in IBM.
Point 2 also represents a portfolio of the risk-free asset and Q, with more (65%) being
invested in Q.
Point 3 is obtained by borrowing to invest in Q. For example, an investor with $100 of
his own would borrow $40 from the bank or broker in order to invest $140 in Q. This can
FIGURE 10.9
Expected return
on portfolio
Expected Return and
Standard Deviation
for an Investment in
a Combination of
Risky Securities and
the Riskless Asset
Line (capital market line)
II
5
Y
A
4
2
Risk-free
rate (RF)
1
Q
3
Line
I
X
35% in risk-free asset – 40% in risk-free asset
140% in stocks
65% in stocks
represented by Q
represented by Q
70% in risk-free asset
30% in stocks
represented by Q
Standard
deviation
of portfolio’s
return
Portfolio Q is composed of 30 percent AT&T, 45 percent GM, 25 percent IBM.
12
Surprisingly, this appears to be a decent approximation because a large number of investors are able to borrow from a
stockbroker (called going on margin) when purchasing stocks. The borrowing rate here is very near the riskless rate of interest,
particularly for large investors. More will be said about this in a later chapter.
Corporate Finance,
Seventh Edition
III: Risk
175
Companies, 2004
Model (CAPM)
279
be stated as borrowing $40 and contributing $100 of one’s money in order to invest
$42 (0.3 $140) in AT&T, $63 (0.45 $140) in GM, and $35 (0.25 $140) in IBM.
The above investments can be summarized as:
Point Q
AT&T
GM
IBM
Risk-free
Total investment
Point 1
(lending $70)
Point 3
(borrowing $40)
$ 30
45
25
____0
$
9
13.50
7.50
70.00
______
$ 42
63
35
40
____
$100
$100
$100
Though any investor can obtain any point on line I, no point on the line is optimal. To
see this, consider line II, a line running from RF through A. Point A represents a portfolio
of risky securities. Line II represents portfolios formed by combinations of the risk-free
asset and the securities in A. Points between RF and A are portfolios in which some money
is invested in the riskless asset and the rest is placed in A. Points past A are achieved by
borrowing at the riskless rate to buy more of A than one could with one’s original funds
alone.
As drawn, line II is tangent to the efficient set of risky securities. Whatever point an individual can obtain on line I, he can obtain a point with the same standard deviation and a
higher expected return on line II. In fact, because line II is tangent to the efficient set of
risky assets, it provides the investor with the best possible opportunities. In other words,
line II can be viewed as the efficient set of all assets, both risky and riskless. An investor
with a fair degree of risk aversion might choose a point between RF and A, perhaps point 4.
An individual with less risk aversion might choose a point closer to A or even beyond A.
For example, point 5 corresponds to an individual borrowing money to increase his investment in A.
The graph illustrates an important point. With riskless borrowing and lending, the portfolio of risky assets held by any investor would always be point A. Regardless of the investor’s tolerance for risk, he would never choose any other point on the efficient set of
risky assets (represented by curve XAY) nor any point in the interior of the feasible region.
Rather, he would combine the securities of A with the riskless assets if he had high aversion to risk. He would borrow the riskless asset to invest more funds in A had he low aversion to risk.
This result establishes what financial economists call the separation principle. That is,
the investor’s investment decision consists of two separate steps:
1. After estimating (a) the expected returns and variances of individual securities, and
(b) the covariances between pairs of securities, the investor calculates the efficient set of
risky assets, represented by curve XAY in Figure 10.9. He then determines point A, the tangency between the risk-free rate and the efficient set of risky assets (curve XAY). Point A
represents the portfolio of risky assets that the investor will hold. This point is determined
solely from his estimates of returns, variances, and covariances. No personal characteristics, such as degree of risk aversion, are needed in this step.
2. The investor must now determine how he will combine point A, his portfolio of risky
assets, with the riskless asset. He might invest some of his funds in the riskless asset and
some in portfolio A. He would end up at a point on the line between RF and A in this case.
Alternatively, he might borrow at the risk-free rate and contribute some of his own funds
176
Corporate Finance,
Seventh Edition
280
III: Risk
Model (CAPM)
Companies, 2004
Part III Risk
as well, investing the sum in portfolio A. He would end up at a point on line II beyond A.
His position in the riskless asset, that is, his choice of where on the line he wants to be, is
determined by his internal characteristics, such as his ability to tolerate risk.
Concept
Questions
1. What is the formula for the standard deviation of a portfolio composed of one
riskless and one risky asset?
2. How does one determine the optimal portfolio among the efficient set of risky
assets?
10.8 Market Equilibrium
Definition of the Market-Equilibrium Portfolio
The above analysis concerns one investor. His estimates of the expected returns and variances for individual securities and the covariances between pairs of securities are his and
his alone. Other investors would obviously have different estimates of the above variables.
However, the estimates might not vary much because all investors would be forming
expectations from the same data on past price movements and other publicly available
information.
Financial economists often imagine a world where all investors possess the same estimates on expected returns, variances, and covariances. Though this can never be literally
true, it can be thought of as a useful simplifying assumption in a world where investors
have access to similar sources of information. This assumption is called homogeneous
expectations.13
If all investors had homogeneous expectations, Figure 10.9 would be the same for all
individuals. That is, all investors would sketch out the same efficient set of risky assets
because they would be working with the same inputs. This efficient set of risky assets is
represented by the curve XAY. Because the same risk-free rate would apply to everyone, all
investors would view point A as the portfolio of risky assets to be held.
This point A takes on great importance because all investors would purchase the risky
securities that it represents. Those investors with a high degree of risk aversion might combine A with an investment in the riskless asset, achieving point 4, for example. Others with
low aversion to risk might borrow to achieve, say, point 5. Because this is a very important
conclusion, we restate it:
In a world with homogeneous expectations, all investors would hold the portfolio
of risky assets represented by point A.
If all investors choose the same portfolio of risky assets, it is possible to determine what
that portfolio is. Common sense tells us that it is a market-value-weighted portfolio of all
existing securities. It is the market portfolio.
In practice, financial economists use a broad-based index such as the Standard & Poor’s
(S&P) 500 as a proxy for the market portfolio. Of course all investors do not hold the same
portfolio in practice. However, we know that a large number of investors hold diversified
portfolios, particularly when mutual funds or pension funds are included. A broad-based
index is a good proxy for the highly diversified portfolios of many investors.
13
The assumption of homogeneous expectations states that all investors have the same beliefs concerning returns, variances, and
covariances. It does not say that all investors have the same aversion to risk.
Corporate Finance,
Seventh Edition
III: Risk
177
Companies, 2004
Model (CAPM)
281
Definition of Risk When Investors Hold the Market Portfolio
The previous section states that many investors hold diversified portfolios similar to broadbased indices. This result allows us to be more precise about the risk of a security in the
context of a diversified portfolio.
Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta of the security. We illustrate beta by an example.
EXAMPLE
Consider the following possible returns on both the stock of Jelco, Inc., and on the market:
State
Type of
Economy
Return on
Market
(percent)
Return on
Jelco, Inc.
(percent)
I
II
III
IV
Bull
Bull
Bear
Bear
15
15
5
5
25
15
5
15
Though the return on the market has only two possible outcomes (15% and 5%), the return on
Jelco has four possible outcomes. It is helpful to consider the expected return on a security for a
given return on the market. Assuming each state is equally likely, we have
Return on
Market
(percent)
Expected Return
on Jelco, Inc.
(percent)
Bull
15%
20% 25% 21 15% 12
Bear
5%
10% 5% 12 (15%) 12
Type of
Economy
Jelco, Inc., responds to market movements because its expected return is greater in bullish states
than in bearish states. We now calculate exactly how responsive the security is to market movements. The market’s return in a bullish economy is 20 percent [15% (5%)] greater than the
market’s return in a bearish economy. However, the expected return on Jelco in a bullish economy
is 30 percent [20% (10%)] greater than its expected return in a bearish state.Thus, Jelco, Inc.,
has a responsiveness coefficient of 1.5 (30%兾20%).
This relationship appears in Figure 10.10.The returns for both Jelco and the market in each state
are plotted as four points. In addition, we plot the expected return on the security for each of
the two possible returns on the market.These two points, each of which we designate by an X, are
joined by a line called the characteristic line of the security.The slope of the line is 1.5, the number calculated in the previous paragraph.This responsiveness coefficient of 1.5 is the beta of Jelco.
The interpretation of beta from Figure 10.10 is intuitive. The graph tells us that the returns of
Jelco are magnified 1.5 times over those of the market.When the market does well, Jelco’s stock is
expected to do even better. When the market does poorly, Jelco’s stock is expected to do even
worse. Now imagine an individual with a portfolio near that of the market who is considering the
addition of Jelco to his portfolio. Because of Jelco’s magnification factor of 1.5, he will view this stock
as contributing much to the risk of the portfolio. (We will show shortly that the beta of the average
security in the market is 1.) Jelco contributes more to the risk of a large, diversified portfolio than
does an average security because Jelco is more responsive to movements in the market.
178
Corporate Finance,
Seventh Edition
282
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
FIGURE 10.10
Return on security (%)
Performance of Jelco,
Inc., and the Market
Portfolio
Characteristic line
I
25
20
X (15%, 20%)*
II
10
– 15
III
–5
(–5%, – 10%) X
Slope = = 1.5
5
15
25
Return on
market (%)
– 10
IV
– 20
The two points marked X represent the expected return on Jelco for each possible outcome of the market portfolio. The expected return on Jelco is positively related to the
return on the market. Because the slope is 1.5, we say that Jelco’s beta is 1.5. Beta
measures the responsiveness of the security’s return to movement in the market.
*(15%, 20%) refers to the point where the return on the market is 15 percent and the
return on the security is 20 percent.
TABLE 10.7
Stock
Estimates of Beta for
Selected Individual
Stocks
High-beta stocks
Oracle, Inc.
Inprise Corporation
Citicorp
Average-beta stocks
Du Pont
Kimberly-Clark Corp.
Ford Motor Co.
Low-beta stocks
Green Mountain Power
Homestake Mining
Bell Atlantic
Beta
1.63
1.58
2.29
1.08
0.80
0.96
0.26
0.22
0.37
The beta is defined as Cov(Ri, RM)兾 Var(RM), where Cov(Ri, RM) is the covariance of the return on an individual stock, Ri, and the
return on the market, RM.Var(RM) is the variance of the return on the market, RM.
Further insight can be gleaned by examining securities with negative betas. One should
view these securities as either hedges or insurance policies. The security is expected to do
well when the market does poorly and vice versa. Because of this, adding a negative-beta
security to a large, diversified portfolio actually reduces the risk of the portfolio.14
Table 10.7 presents empirical estimates of betas for individual securities. As can be
seen, some securities are more responsive to the market than others. For example, Oracle
has a beta of 1.63. This means that, for every 1 percent movement in the market,15 Oracle
14
Unfortunately, empirical evidence shows that virtually no stocks have negative betas.
15
In Table 10.7, we use the Standard & Poor’s 500 Index as the proxy for the market portfolio.
Corporate Finance,
Seventh Edition
III: Risk
179
Companies, 2004
Model (CAPM)
283
is expected to move 1.63 percent in the same direction. Conversely, Green Mountain Power
has a beta of only 0.26. This means that, for every 1 percent movement in the market,
Green Mountain is expected to move 0.26 percent in the same direction.
We can summarize our discussion of beta by saying:
Beta measures the responsiveness of a security to movements in the market portfolio.
The Formula for Beta
Our discussion so far has stressed the intuition behind beta. The actual definition of beta is
i Cov(Ri, RM )
2 (RM )
(10.15)
where Cov(Ri, RM) is the covariance between the return on asset i and the return on the market portfolio and 2(RM) is the variance of the market.
One useful property is that the average beta across all securities, when weighted by the
proportion of each security’s market value to that of the market portfolio, is 1. That is,
N
兺 X 1
i i
(10.16)
i1
where Xi is the proportion of security i’s market value to that of the entire market and N is
the number of securities in the market.
Equation (10.16) is intuitive, once you think about it. If you weight all securities by their
market values, the resulting portfolio is the market. By definition, the beta of the market
portfolio is 1. That is, for every 1 percent movement in the market, the market must move
1 percent—by definition.
A Test
We have put these questions on past corporate finance examinations:
1. What sort of investor rationally views the variance (or standard deviation) of an individual security’s return as the security’s proper measure of risk?
2. What sort of investor rationally views the beta of a security as the security’s proper measure of risk?
A good answer might be something like the following:
A rational, risk-averse investor views the variance (or standard deviation) of her portfolio’s
return as the proper measure of the risk of her portfolio. If for some reason or another the
investor can hold only one security, the variance of that security’s return becomes the variance
of the portfolio’s return. Hence, the variance of the security’s return is the security’s proper
measure of risk.
If an individual holds a diversified portfolio, she still views the variance (or standard deviation) of her portfolio’s return as the proper measure of the risk of her portfolio. However, she
is no longer interested in the variance of each individual security’s return. Rather, she is interested in the contribution of an individual security to the variance of the portfolio.
Under the assumption of homogeneous expectations, all individuals hold the market
portfolio. Thus, we measure risk as the contribution of an individual security to the variance of the market portfolio. This contribution, when standardized properly, is the beta of
the security. While very few investors hold the market portfolio exactly, many hold reasonably diversified portfolios. These portfolios are close enough to the market portfolio so
that the beta of a security is likely to be a reasonable measure of its risk.
180
Corporate Finance,
Seventh Edition
284
Concept
Questions
III: Risk
Model (CAPM)
Companies, 2004
Part III Risk
1. If all investors have homogeneous expectations, what portfolio of risky assets do
they hold?
2. What is the formula for beta?
3. Why is beta the appropriate measure of risk for a single security in a large
portfolio?
10.9 Relationship between Risk and Expected Return (CAPM)
It is commonplace to argue that the expected return on an asset should be positively related
to its risk. That is, individuals will hold a risky asset only if its expected return compensates
for its risk. In this section, we first estimate the expected return on the stock market as a
whole. Next, we estimate expected returns on individual securities.
Expected Return on Market
Financial economists frequently argue that the expected return on the market can be represented as:
RM RF Risk premium
In words, the expected return on the market is the sum of the risk-free rate plus some compensation for the risk inherent in the market portfolio. Note that the equation refers to the
expected return on the market, not the actual return in a particular month or year. Because
stocks have risk, the actual return on the market over a particular period can, of course, be
below RF, or can even be negative.
Since investors want compensation for risk, the risk premium is presumably positive.
But exactly how positive is it? It is generally argued that the place to start looking for the
risk premium in the future is the average risk premium in the past. As reported in Chapter 9,
Ibbotson and Sinquefield found that the average return on large-company common stocks
was 12.2 percent over 1926–2002. The average risk-free rate over the same time interval
was 3.8 percent. Thus, the average difference between the two was 8.4 percent (12.2% 3.8%). Financial economists find this to be a useful estimate of the difference to occur in
the future.16
For example, if the risk-free rate, estimated by the current yield on a one-year Treasury
bill, is 1 percent, the expected return on the market is
9.4% 1% 8.4%
Of course, the future equity risk premium could be higher or lower than the historical equity risk premium. This could be true if future risk is higher or lower than past risk or if
individual risk aversions are higher or lower than those of the past.
Expected Return on Individual Security
Now that we have estimated the expected return on the market as a whole, what is the
expected return on an individual security? We have argued that the beta of a security is the
appropriate measure of risk in a large, diversified portfolio. Since most investors are diversified, the expected return on a security should be positively related to its beta. This is
illustrated in Figure 10.11.
16
This is not the only way to estimate the market-risk premium. In fact, there are several useful ways to estimate the market-risk
premium. For example, refer to Table 9.2 and note the average return on common stocks (12.2%) and long-term government
bonds (5.8%). As noted in footnote 9 in Chapter 9, one could argue that the long-term government bond return is the best
measure of the long-term historical risk-free rate. If so, a good estimate of the historical market risk premium would be
12.2% 5.8% 7.4%. With this empirical version of the CAPM, one would use the current long-term government bond return
to estimate the current risk-free rate.
Corporate Finance,
Seventh Edition
III: Risk
Companies, 2004
Model (CAPM)
285
FIGURE 10.11
181
Expected return
on security (%)
Expected Return
on an Individual
Security and Beta
of the Security
Security market line (SML)
M
T
RM
S
RF
0
0.8
Beta of
security
1
The Security Market Line (SML) is the graphical depiction of the capital-asset-pricing
model (CAPM).
The expected return on a stock with a beta of 0 is equal to the risk-free rate.
The expected return on a stock with a beta of 1 is equal to the expected return on the market.
Actually, financial economists can be more precise about the relationship between
expected return and beta. They posit that, under plausible conditions, the relationship
between expected return and beta can be represented by the following equation.17
R
RF
Expected
return on
a security
Riskfree rate
Capital-Asset-Pricing Model
Beta of
the security
(RM RF )
(10.17)
Difference between
expected return
on market and
risk-free rate
This formula, which is called the capital-asset-pricing model (or CAPM for short),
implies that the expected return on a security is linearly related to its beta. Since the average return on the market has been higher than the average risk-free rate over long periods
of time, RM RF is presumably positive. Thus, the formula implies that the expected
return on a security is positively related to its beta. The formula can be illustrated by
assuming a few special cases:
• Assume that 0. Here R RF, that is, the expected return on the security is equal
•
to the risk-free rate. Because a security with zero beta has no relevant risk, its expected
return should equal the risk-free rate.
Assume that 1. Equation (10.17) reduces to R RM . That is, the expected return
on the security is equal to the expected return on the market. This makes sense since
the beta of the market portfolio is also 1.
Formula (10.17) can be represented graphically by the upward-sloping line in Figure 10.11. Note that the line begins at RF and rises to RM when beta is 1. This line is frequently called the security market line (SML).
17
This relationship was first proposed independently by John Lintner and William F. Sharpe.
182
Corporate Finance,
Seventh Edition
286
III: Risk
Model (CAPM)
Companies, 2004
Part III Risk
As with any line, the SML has both a slope and an intercept. RF, the risk-free rate, is the
intercept. Because the beta of a security is the horizontal axis, RM RF is the slope. The
line will be upward-sloping as long as the expected return on the market is greater than
the risk-free rate. Because the market portfolio is a risky asset, theory suggests that its
expected return is above the risk-free rate. As mentioned, the empirical evidence of the previous chapter showed that the average return per year on the market portfolio (e.g., largecompany stocks) over the past 77 years was 8.4 percent above the risk-free rate.
EXAMPLE
The stock of Aardvark Enterprises has a beta of 1.5 and that of Zebra Enterprises has a beta of 0.7.
The risk-free rate is assumed to be 3 percent, and the difference between the expected return on
the market and the risk-free rate is assumed to be 8.0 percent.The expected returns on the two securities are:
Expected Return for Aardvark
15.0% 3% 1.5 8.0%
(10.18)
Expected Return for Zebra
8.6% 3% 0.7 8.0%
Three additional points concerning the CAPM should be mentioned:
1. Linearity. The intuition behind an upwardly sloping curve is clear. Because beta is
the appropriate measure of risk, high-beta securities should have an expected return above
that of low-beta securities. However, both Figure 10.11 and equation (10.17) show something more than an upwardly sloping curve; the relationship between expected return and
beta corresponds to a straight line.
It is easy to show that the line of Figure 10.11 is straight. To see this, consider security S
with, say, a beta of 0.8. This security is represented by a point below the security market
line in the figure. Any investor could duplicate the beta of security S by buying a portfolio
with 20 percent in the risk-free asset and 80 percent in a security with a beta of 1. However,
the homemade portfolio would itself lie on the SML. In other words, the portfolio dominates security S because the portfolio has a higher expected return and the same beta.
Now consider security T with, say, a beta greater than 1. This security is also below the
SML in Figure 10.11. Any investor could duplicate the beta of security T by borrowing to
invest in a security with a beta of 1. This portfolio must also lie on the SML, thereby dominating security T.
Because no one would hold either S or T, their stock prices would drop. This price adjustment would raise the expected returns on the two securities. The price adjustment would continue until the two securities lay on the security market line. The preceding example considered
two overpriced stocks and a straight SML. Securities lying above the SML are underpriced.
Their prices must rise until their expected returns lie on the line. If the SML is itself curved,
many stocks would be mispriced. In equilibrium, all securities would be held only when prices
changed so that the SML became straight. In other words, linearity would be achieved.
2. Portfolios as well as securities. Our discussion of the CAPM considered individual
securities. Does the relationship in Figure 10.11 and equation (10.17) hold for portfolios as
well?
Yes. To see this, consider a portfolio formed by investing equally in our two securities,
Aardvark and Zebra. The expected return on the portfolio is
Expected Return on Portfolio
11.8% 0.5 15.0% 0.5 8.6%
(10.19)
Corporate Finance,
Seventh Edition
III: Risk
Model (CAPM)
Companies, 2004
183
287
The beta of the portfolio is simply a weighted average of the betas of the two securities.
Thus we have
Beta of Portfolio
1.1 0.5 1.5 0.5 0.7
Under the CAPM, the expected return on the portfolio is
(10.20)
Because the expected return in (10.19) is the same as the expected return in (10.20), the
example shows that the CAPM holds for portfolios as well as for individual securities.
3. A potential confusion. Students often confuse the SML in Figure 10.11 with line II in
Figure 10.9. Actually, the lines are quite different. Line II traces the efficient set of portfolios formed from both risky assets and the riskless asset. Each point on the line represents
an entire portfolio. Point A is a portfolio composed entirely of risky assets. Every other
point on the line represents a portfolio of the securities in A combined with the riskless
asset. The axes on Figure 10.9 are the expected return on a portfolio and the standard deviation of a portfolio. Individual securities do not lie along line II.
The SML in Figure 10.11 relates expected return to beta. Figure 10.11 differs from Figure 10.9 in at least two ways. First, beta appears in the horizontal axis of Figure 10.11, but
standard deviation appears in the horizontal axis of Figure 10.9. Second, the SML in Figure 10.11 holds both for all individual securities and for all possible portfolios, whereas
line II in Figure 10.9 holds only for efficient portfolios.
We stated earlier that, under homogeneous expectations, point A in Figure 10.9
becomes the market portfolio. In this situation, line II is referred to as the capital market
line (CML).
Concept
Questions
1. Why is the SML a straight line?
2. What is the capital-asset-pricing model?
3. What are the differences between the capital market line and the security
market line?
This chapter sets forth the fundamentals of modern portfolio theory. Our basic points are these:
1. This chapter shows us how to calculate the expected return and variance for individual securities, and the covariance and correlation for pairs of securities. Given these statistics, the expected
return and variance for a portfolio of two securities A and B can be written as
Expected return on portfolio XARA XBRB
Var(portfolio) X A2 A2 2XAXB
AB X B2 B2
2. In our notation, X stands for the proportion of a security in one’s portfolio. By varying X, one can
trace out the efficient set of portfolios.We graphed the efficient set for the two-asset case as a
curve, pointing out that the degree of curvature or bend in the graph reflects the diversification
effect:The lower the correlation between the two securities, the greater the bend.The same general shape of the efficient set holds in a world of many assets.
11.8% 3% 1.1 8.0%
184
Corporate Finance,
Seventh Edition
288
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
3. Just as the formula for variance in the two-asset case is computed from a 22 matrix, the variance formula is computed from an NN matrix in the N-asset case.We show that, with a large
number of assets, there are many more covariance terms than variance terms in the matrix. In
fact, the variance terms are effectively diversified away in a large portfolio but the covariance
terms are not.Thus, a diversified portfolio can only eliminate some, but not all, of the risk of the
individual securities.
4. The efficient set of risky assets can be combined with riskless borrowing and lending. In this case,
a rational investor will always choose to hold the portfolio of risky securities represented by
point A in Figure 10.9.Then he can either borrow or lend at the riskless rate to achieve any desired point on line II in the figure.
5. The contribution of a security to the risk of a large, well-diversified portfolio is proportional to
the covariance of the security’s return with the market’s return. This contribution, when standardized, is called the beta.The beta of a security can also be interpreted as the responsiveness
of a security’s return to that of the market.
6. The CAPM states that
R RF (RM RF )
In other words, the expected return on a security is positively (and linearly) related to the security’s beta.
homogeneous expectations, 280
market portfolio, 280
opportunity (feasible) set, 267
portfolio, 261
risk averse, 275
security market line, 285
separation principle, 279
systematic (market) risk, 275
KEY TERMS
beta, 281
capital-asset-pricing model, 285
capital market line, 287
characteristic line, 281
correlation, 258
covariance, 258
diversifiable (unique)
(unsystematic) risk, 275
efficient set (efficient frontier), 268
SUGGESTED
READINGS
The capital-asset-pricing model was originally published in these two classic articles:
Lintner, J. “Security Prices, Risk and Maximal Gains from Diversification.” Journal of Finance
(December 1965).
Sharpe,W. F. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance (September 1964). (William F. Sharpe won the Nobel Prize in Economics in 1990 for
his development of CAPM.)
The seminal influence of Harry Markowitz is described in:
Markowitz, H. “Travels along the Efficient Frontier.” Dow Jones Asset Management (May/June 1997).
QUESTIONS
& PROBLEMS
10.1
EXPECTED RETURN,
VARIANCE,AND
COVARIANCE
Ms. Sharp thinks that the distribution of rates of return on Q-mart stock is as follows:
State of
Economy
Probability of
State Occurring
Q-Mart Stock
Return (%)
Depression
Recession
Normal
Boom
0.1
0.2
0.5
0.2
4.5
4.4
12.0
20.7
a. What is the expected return on the stock?
b. What is the standard deviation of returns on the stock?
Corporate Finance,
Seventh Edition
III: Risk
185
Companies, 2004
Model (CAPM)
289
10.2
Suppose you have invested only in two stocks, A and B.The returns on the two stocks depend on the following three states of the economy, which are equally likely to happen:
State of
Economy
Bear
Normal
Bull
Return on
Stock A (%)
Return on
Stock B (%)
6.30
10.50
15.60
3.70
6.40
25.30
a. Calculate the expected return on each stock.
b. Calculate the standard deviation of returns on each stock.
c. Calculate the covariance and correlation between the returns on the two stocks.
Mr. Henry can invest in Highbull stock and Slowbear stock. His projection of the returns on
these two stocks is as follows:
State of
Economy
Probability of
State Occurring
Return on
Highbull Stock (%)
Return on
Slowbear Stock (%)
Recession
Normal
Boom
0.25
0.60
0.15
2.00
9.20
15.40
5.00
6.20
7.40
b. Calculate the standard deviation of returns on each stock.
c. Calculate the covariance and correlation between the returns on the two stocks.
PORTFOLIOS
10.4
A portfolio consists of 120 shares of Atlas stock, which sell for $50 per share, and 150 shares
of Babcock stock, which sell for $20 per share.What are the weights of the two stocks in
this portfolio?
10.5
Security F has an expected return of 12 percent and a standard deviation of 9 percent per
year. Security G has an expected return of 18 percent and a standard deviation of 25 percent
per year.
a. What is the expected return on a portfolio composed of 30 percent of security F and
70 percent of security G?
b. If the correlation between the returns of security F and security G is 0.2, what is the standard deviation of the portfolio described in part (a)?
10.6
Suppose the expected returns and standard deviations of stocks A and B are E(RA) 0.15,
E(RB) 0.25, A 0.1, and B 0.2, respectively.
a. Calculate the expected return and standard deviation of a portfolio that is composed of
40 percent A and 60 percent B when the correlation between the returns on A and B is 0.5.
b. Calculate the standard deviation of a portfolio that is composed of 40 percent A and
60 percent B when the correlation coefficient between the returns on A and B is 0.5.
c. How does the correlation between the returns on A and B affect the standard deviation
of the portfolio?
10.7
Suppose Janet Smith holds 100 shares of Macrosoft stock and 300 shares of Intelligence
stock. Macrosoft’s stock currently sells at $80 per share, while Intelligence’s stock sells at
$40 per share.The expected return on Macrosoft’s stock is 15 percent, while the expected
return on Intelligence’s stock is 20 percent.The correlation between the returns on the two
stocks is 0.38.
a. Calculate the expected return and standard deviation of her portfolio.
b. Today she sold 200 shares of Intelligence stock in order to pay her tuition. Calculate the
expected return and standard deviation of her new portfolio.
10.3
186
290
Corporate Finance,
Seventh Edition
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
10.8
Consider the possible rates of return on stocks A and B over the next year:
State of
Economy
Probability of
State Occurring
Stock A Return
If State Occurs (%)
Stock B Return
If State Occurs (%)
Recession
Normal
Boom
0.2
0.5
0.3
7
7
7
5
10
25
a. Determine the expected returns, variances, and standard deviations for stock A and
stock B.
b. Determine the covariance and correlation between the returns of stock A and stock B.
c. Determine the expected return and standard deviation of an equally weighted portfolio
of stock A and stock B.
10.9
Suppose there are only two stocks in the world: stock A and stock B.The expected returns
on these two stocks are 10 percent and 20 percent, while the standard deviations of the
stocks are 5 percent and 15 percent, respectively.The correlation between the returns on
the two stocks is 0.
a. Calculate the expected return and standard deviation of a portfolio that is composed of
30 percent A and 70 percent B.
b. Calculate the expected return and standard deviation of a portfolio that is composed of
90 percent A and 10 percent B.
c. Suppose you are risk averse. Would you hold 100 percent in stock A? How about
100 percent stock B? Explain.
10.10 If a portfolio has a positive weight for each asset, can the expected return on the portfolio
be greater than the expected return on the asset in the portfolio with the highest expected
return? Can the expected return on the portfolio be less than the expected return on the
asset in the portfolio with the lowest expected return? Explain.
10.11 Miss Maple is considering two securities, A and B, with the relevant information given below:
State of
Economy
Probability
Return on
Security A (%)
Return on
Security B (%)
0.4
0.6
3.0
15.0
6.5
6.5
Bear
Bull
a. Calculate the expected return and standard deviation of each of the two securities.
b. Suppose Miss Maple invested $2,500 in security A and $3,500 in security B. Calculate the
expected return and standard deviation of her portfolio.
10.12 A broker has advised you not to invest in oil industry stocks because they have high standard deviations. Is the broker’s advice sound for a risk-averse investor like yourself? Why or
why not?
10.13 There are three securities in the market. The following chart shows their possible payoffs.
State
Probability
of Outcome
Return on
Security 1 (%)
Return on
Security 2 (%)
Return on
Security 3 (%)
1
2
3
4
0.1
0.4
0.4
0.1
0.25
0.20
0.15
0.10
0.25
0.15
0.20
0.10
0.10
0.15
0.20
0.25
III: Risk
187
Companies, 2004
Model (CAPM)
291
a. What is the expected return and standard deviation of each security?
b. What are the covariances and correlations between the pairs of securities?
c. What is the expected return and standard deviation of a portfolio with half of its funds
invested in security 1 and half in security 2?
d. What is the expected return and standard deviation of a portfolio with half of its funds
e. What is the expected return and standard deviation of a portfolio with half of its funds
f. What do your answers in parts (a), (c), (d), and (e) imply about diversification?
10.14 The return on Stock A is uncorrelated with the return on stock B. Stock A has a 40 percent chance of having a return of 15 percent and a 60 percent chance of a return of 10 percent.
Stock B has a one-half chance of a 35 percent return and a one-half chance of a 5 percent
return.
a. Write a list of all of the possible outcomes and their probabilities.
b. What is the expected return on a portfolio with 50 percent invested in stock A and
50 percent invested in stock B?
10.15 Assume there are N securities in the market. The expected return on every security is
10 percent. All securities also have the same variance of 0.0144. The covariance between any
pair of securities is 0.0064.
a. What is the expected return and variance of an equally weighted portfolio containing all
N securities? Note: the weight of each security in the portfolio is 1兾N.
b. What will happen to the variance of the portfolio as N approaches infinity?
c. What characteristics of a security are most important in the determination of the variance of a well-diversified portfolio?
10.16 Is the following statement true or false? Explain.
The most important characteristic in determining the variance of a well-diversified portfolio is
the variance of each of the individual stocks.
10.17 Briefly explain why the covariance of a security with the rest of a well-diversified portfolio
is a more appropriate measure of the risk of the security than the security’s variance.
10.18 Consider the following quotation from a leading investment manager:
The shares of Southern Co. have traded close to $12 for most of the past three years. Since
Southern’s stock has demonstrated very little price movement, the stock has a low beta.Texas
Instruments, on the other hand, has traded as high as $150 and as low as its current $75. Since
TI’s stock has demonstrated a large amount of price movement, the stock has a very high
beta.
Do you agree with this analysis? Explain.
10.19 The market portfolio has an expected return of 12 percent and a standard deviation of
10 percent.The risk-free rate is 5 percent.
a. What is the expected return on a well-diversified portfolio with a standard deviation of
7 percent?
b. What is the standard deviation of a well-diversified portfolio with an expected return of
20 percent?
10.20 Consider the following information on the returns on the market and Fuji stock.
Type of Economy
Bear
Bull
Calculate the beta of Fuji.
Return
on Market (%)
Expected Return
on Fuji (%)
2.50
16.3
3.40
12.8
Corporate Finance,
Seventh Edition
188
Corporate Finance,
Seventh Edition
III: Risk
Companies, 2004
Model (CAPM)
292
Part III Risk
CAPM
10.21 William Shakespeare’s character Polonius in Hamlet says,“Neither a borrower nor a lender
be.” Under the assumptions of the capital-asset-pricing model, what would be the composition of Polonius’s portfolio?
10.22 Securities A, B, and C have the following characteristics:
Security
Expected Return (%)
Beta
A
B
C
10
14
20
0.7
1.2
1.8
a. What is the expected return on a portfolio with equal weights?
b. What is the beta of a portfolio with equal weights?
c. Are the three securities priced correctly according to the capital-asset-pricing model?
10.23 Holup, Inc., makes pneumatic equipment.The beta of Holup’s stock is 1.2. The expected market risk premium is 8.5 percent, and the current risk-free rate is 6 percent. Assume the
capital-asset-pricing model holds.What is the expected return on Holup’s stock?
10.24 The beta of stock A is 0.80.The risk-free rate is 6 percent, and the market risk premium is
8.5 percent. Assume the capital-asset-pricing model holds.What is the expected return on
stock A?
10.25 The risk-free rate is 8 percent. The beta of stock B is 1.5, and the expected return on the
market portfolio is 15 percent. Assume the capital-asset-pricing model holds. What is the
expected return on stock B?
10.26 Suppose the expected market risk premium is 7.5 percent and the risk-free rate is 3.7 percent.The expected return on TriStar’s stock is 14.2 percent.Assume the capital-asset-pricing
model holds.What is the beta of TriStar’s stock?
10.27 Consider the following two stocks:
Murck Pharmaceutical
Pizer Drug Corp
Beta
Expected Return
1.4
0.7
25%
14%
Assume the capital-asset-pricing model holds. Based on the CAPM, what is the risk-free
rate? What is the expected return on the market portfolio?
10.28 Suppose you observe the following situation:
State of Economy
Probability of State
Bust
Normal
Boom
0.25
0.5
0.25
Return If State Occurs
Stock A
Stock B
0.1
0.1
0.2
0.3
0.05
0.4
b. Assuming the capital-asset-pricing model holds and stock A’s beta is greater than stock B’s
beta by 0.25, what is the expected market risk premium?
10.29 Assume the capital-asset-pricing model holds.
a. Draw the security market line for the case where the expected market risk premium is
5 percent and the risk-free rate is 7 percent.
b. Suppose that an asset has a beta of 0.8 and an expected return of 9 percent. Does the
expected return of this asset lie above or below the security market line that you drew
in part (a)? Is the security properly priced? If not, explain what will happen in this market.
III: Risk
189
Companies, 2004
Model (CAPM)
293
c. Suppose that an asset has a beta of 3 and an expected return of 25 percent. Does the expected return of this asset lie above or below the security market line that you drew in
part (a)? Is the security properly priced? If not, explain what will happen in this market.
10.30 A stock has a beta of 1.8. A security analyst who specializes in studying this stock expects its
return to be 18 percent. Suppose the risk-free rate is 5 percent and the expected market
risk premium is 8 percent. Is the analyst pessimistic or optimistic about this stock relative to
the market’s expectations?
10.31 Suppose the expected return on the market portfolio is 13.8 percent and the risk-free rate is
6.4 percent. Solomon Inc. stock has a beta of 1.2.Assume the capital-asset-pricing model holds.
a. What is the expected return on Solomon’s stock?
b. If the risk-free rate decreases to 3.5 percent, what is the expected return on Solomon’s
stock?
10.32 A portfolio that combines the risk-free asset and the market portfolio has an expected return of 25 percent and a standard deviation of 4 percent.The risk-free rate is 5 percent, and
the expected return on the market portfolio is 20 percent.Assume the capital-asset-pricing
model holds.What expected rate of return would a security earn if it had a 0.5 correlation
with the market portfolio and a standard deviation of 2 percent?
10.33 The risk-free rate is 7.6 percent. Potpourri Inc. stock has a beta of 1.7 and an expected return of 16.7 percent.Assume the capital-asset-pricing model holds.
a. What is the expected market risk premium?
b. Magnolia Industries stock has a beta of 0.8.What is the expected return on the Magnolia
stock?
c. Suppose you have invested $10,000 in a combination of Potpourri and Magnolia stock.
The beta of the portfolio is 1.07. How much did you invest in each stock? What is the expected return of the portfolio?
10.34 Suppose the risk-free rate is 6.3 percent and the market portfolio has an expected return of
14.8 percent. The market portfolio has a variance of 0.0121. Portfolio Z has a correlation
coefficient with the market of 0.45 and a variance of 0.0169. According to the capital-assetpricing model, what is the expected return on portfolio Z?
10.35 You have access to the following data concerning the Durham Company and the market
portfolio:
Variance of returns on the market portfolio 0.04326
Covariance between the returns on Durham and the market portfolio 0.0635
The expected market risk premium is 9.4 percent and the expected return on Treasury bills
is 4.9 percent.
a. Write the equation of the security market line.
b. What is the required return on Durham Company’s stock?
10.36 Johnson Paint stock has an expected return of 19 percent and a beta of 1.7, while Williamson
Tire stock has an expected return of 14 percent and a beta of 1.2. Assume the capital-assetpricing model holds.What is the expected return on the market? What is the risk-free rate?
10.37 Is the following statement true or false? Explain.
A risky security cannot have an expected return that is less than the risk-free rate because no
risk-averse investor would be willing to hold this asset in equilibrium.
10.38 Suppose you have invested $30,000 in the following four stocks:
Security
Amount Invested
Beta
Stock A
Stock B
Stock C
Stock D
$ 5,000
10,000
8,000
7,000
0.75
1.1
1.36
1.88
Corporate Finance,
Seventh Edition
190
Corporate Finance,
Seventh Edition
294
III: Risk
Companies, 2004
Model (CAPM)
Part III Risk
The risk-free rate is 4 percent and the expected return on the market portfolio is 15 percent. Based on the capital-asset-pricing model, what is the expected return on the above
portfolio?
10.39 You have been provided the following data on the securities of three firms, the market portfolio, and the risk-free asset:
Security
Firm A
Firm B
Firm C
The market portfolio
The risk-free asset
Expected Return
Standard Deviation
Correlation*
Beta
0.13
0.16
0.25
0.15
0.05
0.12
(ii)
0.24
0.1
(vi)
(i)
0.4
0.75
(iv)
(vii)
0.9
1.1
(iii)
(v)
(viii)
*With the market portfolio.
a. Fill in the missing values in the table.
b. Is the stock of Firm A correctly priced according to the capital-asset-pricing model
(CAPM)? What about the stock of Firm B? Firm C? If these securities are not correctly
priced, what is your investment recommendation for someone with a well-diversified
portfolio?
10.40 There are two stocks in the market, stock A and stock B. The price of stock A today is $50.
The price of stock A next year will be $40 if the economy is in a recession, $55 if the economy is normal, and $60 if the economy is expanding.The probabilities of recession, normal
times, and expansion are 0.1, 0.8, and 0.1, respectively. Stock A pays no dividends and has a
correlation of 0.8 with the market portfolio. Stock B has an expected return of 9 percent, a
standard deviation of 12 percent, a correlation with the market portfolio of 0.2, and a correlation with stock A of 0.6. The market portfolio has a standard deviation of 10 percent.
Assume the CAPM holds.
a. If you are a typical, risk-averse investor with a well-diversified portfolio, which stock
would you prefer? Why?
b. What are the expected return and standard deviation of a portfolio consisting of 70 percent of stock A and 30 percent of stock B?
c. What is the beta of the portfolio in part (b)?
ADVANCED
(REQUIRES
CALCULUS)
10.41 Assume stocks A and B have the following characteristics:
Stock
Expected Return (%)
Standard Deviation %
A
B
5
10
10
20
The covariance between the returns on the two stocks is 0.001.
a. Suppose an investor holds a portfolio consisting of only stock A and stock B. Find the
portfolio weights, XA and XB, such that the variance of his portfolio is minimized. (Hint:
Remember that the sum of the two weights must equal 1.)
b. What is the expected return on the minimum variance portfolio?
c. If the covariance between the returns on the two stocks is 0.02, what are the minimum
variance weights?
d. What is the variance of the portfolio in part (c)?
S&P
PROBLEMS
NOTE: While these problems can be calculated manually, it is recommended that a spreadsheet program such as Excel® be used for calculations.
10.42 Go to the “Excel Analytics” link for Johnson and Johnson (JNJ) and Southwest Airlines (LUV)
and download the monthly adjusted stock prices. Copy the monthly returns for each stock
into a new spreadsheet. Calculate the covariance and correlation between the two stock
returns.Would you expect a higher or lower correlation if you had chosen Procter & Gamble
instead of Southwest Airlines? What is the standard deviation of a portfolio 75 percent
Corporate Finance,
Seventh Edition
III: Risk
Model (CAPM)
Companies, 2004
191
295
invested in JNJ and 25 percent in LUV? What about a portfolio equally invested in the two
stocks? What about a portfolio 25 percent in JNJ and 75 percent in LUV?
10.43 Go to the “Excel Analytics” link for Amazon.com (AMZN) and download the monthly adjusted stock prices. Copy the monthly returns for Amazon.com and the monthly S&P 500 returns in a new spreadsheet. Calculate the beta of Amazon.com for the entire period of data
available. Now download the monthly stock prices for Duke Energy (DUK) and calculate the
beta for this company. Are the betas similar? Would you have expected the beta for Amazon
to be higher or lower than the beta for Duke Energy? Why?
Is Beta Dead?
The capital-asset-pricing model represents one of the most important advances in financial
economics. It is clearly useful for investment purposes, since it shows how the expected
return on an asset is related to its beta. In addition, we will show in Chapter 12 that it is useful in corporate finance, since the discount rate on a project is a function of the project’s
beta. However, one must never forget that, as with any other model, the CAPM is not
revealed truth but, rather, a construct to be empirically tested.
The first empirical tests of the CAPM occurred over 20 years ago and were quite supportive. Using data from the 1930s to the 1960s, researchers showed that the average return
on a portfolio of stocks was positively related to the beta of the portfolio,18 a finding consistent with the CAPM. Though some evidence in these studies was less consistent with the
CAPM,19 financial economists were quick to embrace the CAPM following these empirical papers.
While a large body of empirical work developed in the following decades, often with
varying results, the CAPM was not seriously called into question until the 1990s. Two
papers by Fama and French20 (yes, the same Fama whose joint paper in 1973 with James
MacBeth supported the CAPM) present evidence inconsistent with the model. Their work
has received a great deal of attention, both in academic circles and in the popular press,
with newspaper articles displaying headlines such as “Beta Is Dead!” These papers make
two related points. First, they conclude that the relationship between average return and
beta is weak over the period from 1941 to 1990 and virtually nonexistent from 1963 to
1990. Second, they argue that the average return on a security is negatively related to both
the firm’s price-to-earnings (P/E) ratio and the firm’s market value-to-book value (M/B)
ratio. These contentions, if confirmed by other research, would be quite damaging to the
CAPM. After all, the CAPM states that the expected returns on stocks should be related
only to beta, and not to other factors such as P/E and M/B.
However, a number of researchers have criticized the Fama-French papers. While we
avoid an in-depth discussion of the fine points of the debate, we mention a few issues. First,
although Fama and French cannot reject the hypothesis that average returns are unrelated
to beta, one can also not reject the hypothesis that average returns are related to beta exactly
18
Perhaps the two most well-known papers were Fischer Black, Michael C. Jensen, and Myron S. Scholes, “The Capital Asset
Pricing Model: Some Empirical Tests,” in M. Jensen, ed., Studies in the Theory of Capital Markets (New York: Praeger, 1972),
and Eugene F. Fama and James MacBeth, “Risk, Return and Equilibrium: Some Empirical Tests,” Journal of Political Economy
8 (1973), pp. 607–36.
19
For example, the studies suggest that the average return on a zero-beta portfolio is above the risk-free rate, a finding
inconsistent with the CAPM.
20
Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance 47 (1992),
pp. 427–66, and E. F. Fama and K. R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of
Financial Economics 17 (1993), pp. 3–56.
Appendix 10A
Corporate Finance,
Seventh Edition
27. Cash Management
Companies, 2004
Chapter 27
Cash Management
EXECUTIVE SUMMARY
192
The balance sheet of Singapore Airlines
showed total assets of $8.7 billion in March
1994. On this basis, Singapore Airlines was
one of the largest transportation firms in the
world. In addition, Singapore Airlines held
$62.4 million in cash. This cash included currency, demand deposits at commercial banks,
and undeposited checks.1
Since cash earns no interest, why would
Singapore Airlines hold cash? It would seem
more sensible for Singapore Airlines to put its
cash into marketable securities, such as Treasury bills, and get some investment income.
Of course, one reason Singapore Airlines
holds cash is to pay for goods and services.
Singapore Airlines might prefer to pay its
employees in Treasury bills, but the minimum
denomination of Treasury bills is $10,000!
The firm must use cash because cash is more
divisible than Treasury bills.2
This chapter is about how firms manage
cash.The basic objective in cash management
is to keep the investment in cash as low as
possible while still operating the firm’s activities efficiently and effectively. This chapter
separates cash management into three steps:
1. Determining the appropriate target cash
balance.
2. Collecting and disbursing cash efficiently.
3. Investing excess cash in marketable
securities.
Determining the appropriate target cash
balance involves an assessment of the tradeoff between the benefit and cost of liquidity.
The benefit of holding cash is the convenience
in liquidity it gives the firm.The cost of holding cash is the interest income that the firm
could have received from investing in Treasury
bills and other marketable securities. If the
firm has achieved its target cash balance, the
value it gets from the liquidity provided by its
cash will be exactly equal to the value forgone
in interest on an equivalent holding of Treasury bills. In other words, a firm should increase its holding of cash until the net present
value from doing so is zero. The incremental
liquidity value of cash should decline as more
of it is held.
After the optimal amount of cash is determined, the firm must establish procedures so
that cash is collected and disbursed as efficiently as possible.This usually reduces to the
dictum,“collect early and pay late.”
Firms must invest temporarily idle cash in
short-term marketable securities.These securities can be bought and sold in the money
market. Money-market securities have very
little risk of default and are highly marketable.
1
It was somewhat unusual for Singapore Airlines to report cash in this way. Usually, a firm’s reported cash includes cash
equivalents, such as Treasury bills.
2
Cash is liquid. One property of liquidity is divisibility, that is, how easily an asset can be divided into parts.
753
Corporate Finance,
Seventh Edition
754
27. Cash Management
Companies, 2004
Part VII Short-Term Finance
27.1 Reasons for Holding Cash
The term cash is a surprisingly imprecise concept. The economic definition of cash includes currency, checking account deposits at commercial banks, and undeposited checks.
However, financial managers often use the term cash to include short-term marketable
securities. Short-term marketable securities are frequently referred to as “cash equivalents”
and include Treasury bills, certificates of deposit, and repurchase agreements. (Several different types of short-term marketable securities are described at the end of this chapter.)
The balance sheet item “cash” usually includes cash equivalents.
The previous chapter discussed the management of net working capital. Net working
capital includes both cash and cash equivalents. This chapter is concerned with cash, not
net working capital, and it focuses on the narrow economic definition of cash.
The basic elements of net working capital management such as carrying costs, shortage
costs, and opportunity costs are relevant for cash management. However, cash management is more concerned with how to minimize cash balances by collecting and disbursing
cash effectively.
There are two primary reasons for holding cash. First, cash is needed to satisfy the
transactions motive. Transactions-related needs come from normal disbursement and collection activities of the firm. The disbursement of cash includes the payment of wages and
salaries, trade debts, taxes, and dividends. Cash is collected from sales from operations, sales
of assets, and new financing. The cash inflows (collections) and outflows (disbursements)
are not perfectly synchronized, and some level of cash holdings is necessary to serve as a
buffer. If the firm maintains too small a cash balance, it may run out of cash. If so, it must
sell marketable securities or borrow. Selling marketable securities and borrowing involve
trading costs.
Another reason to hold cash is for compensating balances. Cash balances are kept at
commercial banks to compensate for banking services rendered to the firm. A minimum required compensating balance at banks providing credit services to the firm may impose a
lower limit on the level of cash a firm holds.
The cash balance for most firms can be thought of as consisting of transactions balances
and compensating balances. However, it would not be correct for a firm to add the amount
of cash required to satisfy its transactions needs to the amount of cash needed to satisfy its
compensatory balances to produce a target cash balance. The same cash can be used to satisfy both requirements.
The cost of holding cash is, of course, the opportunity cost of lost interest. To determine
the target cash balance, the firm must weigh the benefits of holding cash against the costs.
It is generally a good idea for firms to figure out first how much cash to hold to satisfy the
transactions needs. Next, the firm must consider compensating-balance requirements,
which will impose a lower limit on the level of the firm’s cash holdings. Because compensating balances merely provide a lower limit, we shall ignore compensating balances for
the following discussion of the target cash balance.
Concept
Questions
1. What is the transactions motive, and how does it lead firms to hold cash?
2. What is a compensating balance?
27.2 Determining the Target Cash Balance
The target cash balance involves a trade-off between the opportunity costs of holding too
much cash and the trading costs of holding too little. Figure 27.1 presents the problem
graphically. If a firm tries to keep its cash holdings too low, it will find itself selling
marketable securities (and perhaps later buying marketable securities to replace those sold)
193
194
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
755
Chapter 27 Cash Management
FIGURE 27.1
Cost in dollars
of holding cash
Costs of Holding Cash
Total costs of holding cash
Opportunity costs
Trading costs
Size of cash balance (C)
C*
Optimal size
of cash balance
Trading costs are increased when the firm must sell securities to establish a
cash balance. Opportunity costs are increased when there is a cash balance
because there is no return to cash.
more frequently than if the cash balance was higher. Thus, trading costs will tend to fall as
the cash balance becomes larger. In contrast, the opportunity costs of holding cash rise
as the cash holdings rise. At point C* in Figure 27.1, the sum of both costs, depicted as the
total cost curve, is at a minimum. This is the target or optimal cash balance.
The Baumol Model
William Baumol was the first to provide a formal model of cash management incorporating opportunity costs and trading costs.3 His model can be used to establish the target cash
balance.
Suppose the Golden Socks Corporation began week 0 with a cash balance of C $1.2 million, and outflows exceed inflows by $600,000 per week. Its cash balance will drop to zero at
the end of week 2, and its average cash balance will be C兾2 $1.2 million兾2 $600,000
over the two-week period. At the end of week 2, Golden Socks must replace its cash either by
selling marketable securities or by borrowing. Figure 27.2 shows this situation.
If C were set higher, say, at $2.4 million, cash would last four weeks before the firm
would need to sell marketable securities, but the firm’s average cash balance would increase to $1.2 million (from $600,000). If C were set at $600,000, cash would run out in
one week and the firm would need to replenish cash more frequently, but its average cash
balance would fall from $600,000 to $300,000.
Because transactions costs must be incurred whenever cash is replenished (for example,
the brokerage costs of selling marketable securities), establishing large initial cash balances
will lower the trading costs connected with cash management. However, the larger the average cash balance, the greater the opportunity cost (the return that could have been earned
on marketable securities).
3
W. S. Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics 66
(November 1952).
Corporate Finance,
Seventh Edition
756
Companies, 2004
27. Cash Management
FIGURE 27.2
Starting cash:
C = $1,200,000
Cash Balances for
the Golden Socks
Corporation
$600,000 = C/2
Average cash
Ending cash: 0
Weeks
0
1
2
3
4
The Golden Socks Corporation begins week 0 with cash
of $1,200,000. The balance drops to zero by the second
week. The average cash balance is C兾2 $1,200,000兾2 $600,000 over the period.
To solve this problem, Golden Socks needs to know the following three things:
F The fixed cost of selling securities to replenish cash
T The total amount of new cash needed for transactions purposes over the
relevant planning period, say, one year
and
K The opportunity cost of holding cash; this is the interest rate on marketable
securities
With this information, Golden Socks can determine the total costs of any particular cashbalance policy. It can then determine the optimal cash-balance policy.
The Opportunity Costs
The total opportunity costs of cash balances, in dollars, must
be equal to the average cash balance multiplied by the interest rate, or:
Opportunity costs ($) (C兾2) K
The opportunity costs of various alternatives are given here:
Initial
Cash Balance
Average
Cash Balance
Opportunity
Costs (K 0.10)
C
$4,800,000
2,400,000
1,200,000
600,000
300,000
C兾2
$2,400,000
1,200,000
600,000
300,000
150,000
(C兾2) K
$240,000
120,000
60,000
30,000
15,000
The Trading Costs Total trading costs can be determined by calculating the number of
times that Golden Socks must sell marketable securities during the year. The total amount
of cash disbursement during the year is $600,000 52 weeks $31.2 million. If the initial cash balance is set at $1.2 million, Golden Socks will sell $1.2 million of marketable
securities every two weeks. Thus, trading costs are given by:
$31.2 million
F 26F
$1.2 million
195
196
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
757
The general formula is:
Trading costs ($) (T兾C) F
A schedule of alternative trading costs follows:
Total
Disbursements
during Relevant Period
Initial
Cash
Balance
Trading
Costs
(F $1,000)
T
$31,200,000
31,200,000
31,200,000
31,200,000
31,200,000
C
$4,800,000
2,400,000
1,200,000
600,000
300,000
(T兾C) F
$ 6,500
13,000
26,000
52,000
104,000
The Total Cost
The total cost of cash balances consists of the opportunity costs plus the
trading costs:
Total cost Opportunity costs Trading costs
(C兾2) K (T兾C) F
Cash
Balance
Total
Cost
$4,800,000
2,400,000
1,200,000
600,000
300,000
$246,500
133,000
86,000
82,000
119,000
Opportunity
Costs
Trading
Costs
$240,000
120,000
60,000
30,000
15,000
$
6,500
13,000
26,000
52,000
104,000
The Solution We can see from the preceding schedule that a $600,000 cash balance results in the lowest total cost of the possibilities presented: $82,000. But what about
$700,000 or $500,000 or other possibilities? To determine minimum total costs precisely,
Golden Socks must equate the marginal reduction in trading costs as balances rise with the
marginal increase in opportunity costs associated with cash balance increases. The target
cash balance should be the point where the two offset each other. This can be calculated by
using either numerical iteration or calculus. We will use calculus, but if you are unfamiliar
with such an analysis, you can skip to the solution.
Recall that the total cost equation is:
Total cost (TC) (C兾2) K (T兾C) F
If we differentiate the TC equation with respect to the cash balance and set the derivative
equal to zero, we will find that:
dTC K TF
2 0
dC
2 C
4
Marginal
Marginal
Marginal
total cost opportunity costs trading costs
4
Marginal trading costs are negative because trading costs are reduced when C is increased.
Corporate Finance,
Seventh Edition
758
27. Cash Management
Companies, 2004
The solution for the general cash balance, C*, is obtained by solving this equation for C:
K TF
2 C2
C * 兹2TF兾K
If F $1,000, T $31,200,000, and K 0.10, then C* $789,936.71. Given the value
of C*, opportunity costs are:
(C *兾2) K $789,936.71
0.10 $39,496.84
2
Trading costs are:
(T兾C* ) F $31,200,000
$1,000 $39,496.84
$789,936.71
Hence, total costs are:
$39,496.84 $39,496.84 $78,993.68
Limitations
The Baumol model represents an important contribution to cash management. The limitations of the model include the following:
1. The Model Assumes the Firm Has a Constant Disbursement Rate. In practice, disbursements can be only partially managed, because due dates differ and costs cannot be predicted with certainty.
2. The Model Assumes There Are No Cash Receipts during the Projected Period. In fact,
most firms experience both cash inflows and outflows on a daily basis.
3. No Safety Stock Is Allowed For. Firms will probably want to hold a safety stock of cash
designed to reduce the possibility of a cash shortage or cash-out. However, to the extent
that firms can sell marketable securities or borrow in a few hours, the need for a safety
stock is minimal.
The Baumol model is possibly the simplest and most stripped-down sensible model for
determining the optimal cash position. Its chief weakness is that it assumes discrete, certain
cash flows. We next discuss a model designed to deal with uncertainty.
The Miller-Orr Model
Merton Miller and Daniel Orr developed a cash-balance model to deal with cash inflows
and outflows that fluctuate randomly from day to day.5 In the Miller-Orr model, both cash
inflows and cash outflows are included. The model assumes that the distribution of daily
net cash flows (cash inflow minus cash outflow) is normally distributed. On each day the
net cash flow could be the expected value or some higher or lower value. We will assume
that the expected net cash flow is zero.
Figure 27.3 shows how the Miller-Orr model works. The model operates in terms of
upper (H) and lower (L) control limits, and a target cash balance (Z). The firm allows its
cash balance to wander randomly within the lower and upper limits. As long as the cash
balance is between H and L, the firm makes no transaction. When the cash balance reaches
H, such as at point X, then the firm buys H Z units (or dollars) of marketable securities.
5
M. H. Miller and D. Orr, “A Model of the Demand for Money by Firms,” Quarterly Journal of Economics (August 1966).
197
198
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
759
FIGURE 27.3
Cash ($)
The Miller-Orr Model
H
Z
L
Time
X
Y
H is the upper control limit. L is the lower
control limit. The target cash balance is Z.
As long as cash is between L and H, no
transaction is made.
This action will decrease the cash balance to Z. In the same way, when cash balances fall to
L, such as at point Y (the lower limit), the firm should sell Z L securities and increase the
cash balance to Z. In both situations, cash balances return to Z. Management sets the lower
limit, L, depending on how much risk of a cash shortfall the firm is willing to tolerate.
Like the Baumol model, the Miller-Orr model depends on trading costs and opportunity
costs. The cost per transaction of buying and selling marketable securities, F, is assumed to
be fixed. The percentage opportunity cost per period of holding cash, K, is the daily interest rate on marketable securities. Unlike the Baumol model, the number of transactions per
period is a random variable that varies from period to period, depending on the pattern of
cash inflows and outflows.
As a consequence, trading costs per period are dependent on the expected number of
transactions in marketable securities during the period. Similarly, the opportunity costs of
holding cash are a function of the expected cash balance per period.
Given L, which is set by the firm, the Miller-Orr model solves for the target cash balance,
Z, and the upper limit, H. Expected total costs of the cash-balance–return policy (Z, H) are
equal to the sum of expected transactions costs and expected opportunity costs. The values
of Z (the return-cash point) and H (the upper limit) that minimize the expected total cost
have been determined by Miller and Orr:
3
Z * 兹3F
2兾4K L
H* 3Z* 2L
where * denotes optimal values, and 2 is the variance of net daily cash flows.
The average cash balance in the Miller-Orr model is:
Average cash balance EXAMPLE
4Z L
3
To clarify the Miller-Orr model, suppose F $1,000, the interest rate is 10 percent annually, and the
standard deviation of daily net cash flows is $2,000. The daily opportunity cost, K, is:
(1 K)365 1.0 0.10
365
1 K 兹1.10 1.000261
K 0.000261
Corporate Finance,
Seventh Edition
760
Companies, 2004
27. Cash Management
The variance of daily net cash flows is
2 (2,000)2 4,000,000
Let us assume that L 0:
3
Z * 兹 (3 $1,000 4,000,000)兾 (4 0.000261) 0
3
兹 ($11,493,900,000,000 $22,568
H* 3 $22,568 $67,704
Average cash balance 4 $22,568
$30,091
3
Implications of the Miller-Orr Model
To use the Miller-Orr model, the manager must
do four things.
1. Set the lower control limit for the cash balance. This lower limit can be related to a minimum safety margin decided on by management.
2. Estimate the standard deviation of daily cash flows.
3. Determine the interest rate.
4. Estimate the trading costs of buying and selling marketable securities.
These four steps allow the upper limit and return point to be computed. Miller and Orr
tested their model using nine months of data for cash balances for a large industrial firm.
The model was able to produce average daily cash balances much lower than the averages
actually obtained by the firm.6
The Miller-Orr model clarifies the issues of cash management. First, the model shows
that the best return point, Z*, is positively related to trading costs, F, and negatively related
to K. This finding is consistent with and analogous to the Baumol model. Second, the
Miller-Orr model shows that the best return point and the average cash balance are positively related to the variability of cash flows. That is, firms whose cash flows are subject to
greater uncertainty should maintain a larger average cash balance.
Other Factors Influencing the Target Cash Balance
Borrowing In our previous examples, the firm has obtained cash by selling marketable
securities. Another alternative is to borrow cash. Borrowing introduces additional considerations to cash management.
1. Borrowing is likely to be more expensive than selling marketable securities because the
interest rate is likely to be higher.
2. The need to borrow will depend on management’s desire to hold low cash balances. A
firm is more likely to need to borrow to cover an unexpected cash outflow the greater its
cash flow variability and the lower its investment in marketable securities.
Compensating Balance The costs of trading securities are well below the lost income
from holding cash for large firms. Consider a firm faced with either selling $2 million of
Treasury bills to replenish cash or leaving the money idle overnight. The daily opportunity
6
D. Mullins and R. Hamonoff discuss tests of the Miller-Orr model in “Applications of Inventory Cash Management Models,”
in Modern Developments in Financial Management, ed. by S. C. Myers (New York: Praeger, 1976). They show that the model
works very well when compared to the actual cash balances of several firms. However, simple rules of thumb do as good a job
as the Miller-Orr model.
199
200
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
761
cost of $2 million at a 10-percent annual interest rate is 0.10兾365 0.027 percent per day.
The daily return earned on $2 million is 0.00027 $2 million $540. The cost of selling
$2 million of Treasury bills is much less than $540. As a consequence, a large firm will buy
and sell securities many times a day before it will leave substantial amounts idle overnight.
However, most large firms hold more cash than cash-balance models imply. Here are
some possible reasons.
1. Firms have cash in the bank as a compensating balance in payment for banking services.
2. Large corporations have thousands of accounts with several dozen banks. Sometimes it
makes more sense to leave cash alone than to manage each account on a daily basis.
Concept
Questions
1. What is a target cash balance?
2. What are the strengths and weaknesses of the Baumol model and the Miller-Orr
model?
27.3 Managing the Collection and Disbursement of Cash
A firm’s cash balance as reported in its financial statements (book cash or ledger cash) is
not the same thing as the balance shown in its bank account (bank cash or collected bank
cash). The difference between bank cash and book cash is called float and represents the
net effect of checks in the process of collection.
EXAMPLE
Imagine that General Mechanics, Inc., (GMI) currently has $100,000 on deposit with its bank. It purchases some raw materials, paying its vendors with a check written on July 8 for $100,000. The
company’s books (that is, ledger balances) are changed to show the $100,000 reduction in the cash
balance. But the firm’s bank will not find out about this check until it has been deposited at the vendor’s bank and has been presented to the firm’s bank for payment on, say, July 15. Until the check’s
presentation, the firm’s bank cash is greater than its book cash, and it has positive float.
Position Prior to July 8:
Float Firm’s bank cash Firm’s book cash
$100,000
0
$100,000
Position from July 8 through July 14:
Disbursement float Firm’s bank cash Firm’s book cash
$100,000
0
$100,000
During the period of time that the check is clearing, GMI has a balance with the bank of $100,000. It
can obtain the benefit of this cash while the check is clearing. For example, the bank cash could be
invested in marketable securities. Checks written by the firm generate disbursement float, causing an
immediate decrease in book cash but no immediate change in bank cash.
EXAMPLE
Imagine that GMI receives a check from a customer for $100,000. Assume, as before, that the
company has $100,000 deposited at its bank and has a neutral float position. It deposits the check
and increases its book cash by $100,000 on November 8. However, the cash is not available to GMI
until its bank has presented the check to the customer’s bank and received $100,000 on, say,
November 15. In the meantime, the cash position at GMI will reflect a collection float of $100,000.
Corporate Finance,
Seventh Edition
762
27. Cash Management
Companies, 2004
Position Prior to November 8:
Float Firm’s bank cash Firm’s book cash
$100,000
$100,000
0
Position from November 8 through November 14:
Collection float Firm’s bank cash Firm’s book cash
$100,000
$200,000
$100,000
Checks received by the firm represent collection float, which increases book cash
immediately but does not immediately change bank cash. The firm is helped by disbursement float and is hurt by collection float. The sum of disbursement float and collection float
is net float.
A firm should be more concerned with net float and bank cash than with book cash. If a
financial manager knows that a check will not clear for several days, he or she will be able
to keep a lower cash balance at the bank than might be true otherwise. Good float management can generate a great deal of money. For example, suppose the average daily sales of
Exxon are about $400 million. If Exxon speeds up the collection process or slows down the
disbursement process by one day, it frees up $400 million, which can be invested in marketable securities. With an interest rate of 4 percent, this represents overnight interest of
approximately $44,000 [($400 million兾365) 0.04].
Float management involves controlling the collection and disbursement of cash. The
objective in cash collection is to reduce the lag between the time customers pay their bills
and the time the checks are collected. The objective in cash disbursement is to slow down
payments, thereby increasing the time between when checks are written and when checks
are presented. In other words, collect early and pay late. Of course, to the extent that the
firm succeeds in doing this, the customers and suppliers lose money, and the trade-off is the
effect on the firm’s relationship with them.
Collection float can be broken down into three parts: mail float, in-house processing
float, and availability float:
1. Mail Float is the part of the collection and disbursement process where checks are
trapped in the postal system.
2. In-House Processing Float is the time it takes the receiver of a check to process the payment and deposit it in a bank for collection.
3. Availability Float refers to the time required to clear a check through the banking system.
The clearing process takes place using the Federal Reserve check collection service,
using correspondent banks, or using local clearinghouses.
EXAMPLE
A check for $1,000 is mailed from a customer on Monday, September 1. Because of mail, processing,
and clearing delays, it is not credited as available cash in the firm’s bank until the following Monday,
seven days later. The float for this check is:
Float $1,000 7 days $7,000
Another check for $7,000 is mailed on September 1. It is available on the next day. The float for this
check is:
Float $7,000 1 day $7,000
201
202
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
763
The measurement of float depends on the time lag and the dollars involved.The cost of float is
an opportunity cost, because the cash is unavailable for use during the time checks are tied up in the
collection process.The cost of float can be determined by (1) estimating the average daily receipts,
(2) calculating the average delay in obtaining the receipts, and (3) discounting the average daily
receipts by the delay-adjusted cost of capital.
EXAMPLE
Suppose that Concepts, Inc., has two receipts each month:
Number of
Days’ Delay
Amount
Item 1
Item 2
Total
3
5
$5,000,000
3,000,000
_________
$8,000,000
Float
$15,000,000
15,000,000
__________
$30,000,000
The average daily float over the month is equal to:
Average Daily Float:
Total float $30,000,000
$1,000,000
Total days
30
Another procedure that can be used to calculate average daily float is to determine average daily
receipts and multiply by the average daily delay.
Average Daily Receipts:
Total receipts $8,000,000
$266,666.67
Total days
30
Weighted average delay (5兾8) 3 (3兾8) 5
1.875 1.875 3.75 days
Average daily float Average daily receipts Weighted average delay
$266,666.67 3.75 $1,000,000
EXAMPLE
Suppose Concepts, Inc., has average daily receipts of $266,667.The float results in this amount being
delayed 3.75 days.The present value of the delayed cash flow is:
V
$266,667
1 rB
where rB is the cost of debt capital for Concepts, adjusted to the relevant time frame. Suppose the
annual cost of debt capital is 10 percent.Then:
rB 0.1 (3.75兾365) 0.00103
and:
V
$266,667
$266,392.62
1 0.00103
Thus, the net present value of the delay float is $266,392.62 $266,667 $274.38 per day. For
a year, this is $274.38 365 $100,148.70.
Corporate Finance,
Seventh Edition
764
Companies, 2004
27. Cash Management
Accelerating Collections
The following is a depiction of the basic parts of the cash collection process.
Customer
mails
payment
Company
receives
payment
Company
deposits
payment
Cash
received
Time
Mail
delay
Processing
delay
Clearing
delay
Mail
float
Processing
float
Clearing
float
Collection float
The total time in this process is made up of mailing time, check-processing time, and
check-clearing time. The amount of time cash spends in each part of the cash collection
process depends on where the firm’s customers and banks are located and how efficient the
firm is at collecting cash. Some of the techniques used to accelerate collections and reduce
collection time are lockboxes, concentration banking, and wire transfers.
Lockboxes
The lockbox is the most widely used device to speed up collections of cash.
It is a special post office box set up to intercept accounts receivable payments.
Figure 27.4 illustrates the lockbox system.7 The collection process is started by customers mailing their checks to a post office box instead of sending them to the firm. The
lockbox is maintained by a local bank and is typically located no more than several hundred miles away. Large corporations may maintain more than 20 lockboxes around the
country. In the typical lockbox system, the local bank collects the lockbox checks from the
post office several times a day. The bank deposits the checks directly to the firm’s account.
Details of the operation are recorded (in some computer-usable form) and sent to the firm.
A lockbox system reduces mailing time because checks are received at a nearby post office instead of at corporate headquarters. Lockboxes also reduce the firm’s processing time
because they reduce the time required for a corporation to physically handle receivables
and to deposit checks for collection. A bank lockbox should enable a firm to get its receipts
processed, deposited, and cleared faster than if it were to receive checks at its headquarters
and deliver them itself to the bank for deposit and clearing.
Concentration Banking Using lockboxes is one way firms can collect checks from
customers and get them into deposit banks. Another way to speed up collection is to get the
cash from the deposit banks to the firm’s main bank more quickly. This is done by a method
called concentration banking.
With a concentration-banking system, the firm’s sales offices are usually responsible for
the collection and processing of customer checks. The sales office deposits the checks into
a local deposit bank account. Surplus funds are transferred from the deposit bank to the concentration bank. The purpose of concentration banking is to obtain customer checks from
nearby receiving locations. Concentration banking reduces mailing time because the firm’s
sales office is usually nearer than corporate headquarters to the customer. Furthermore,
bank clearing time will be reduced because the customer’s check is usually drawn on a local
7
Two types of lockboxes are offered by banks. Wholesale lockboxes are used in processing a small number of large-dollar
checks. Retail lockboxes are used for processing a large number of smaller checks.
203
204
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
765
FIGURE 27.4
Overview of Lockbox
Processing
Corporate
customers
Corporate
customers
Corporate
customers
Post office
box 1
Corporate
customers
Post office
box 2
Local bank
collects funds from
post office boxes
Envelopes opened;
separation of
checks and receipts
Details of receivables
go to firm
Deposit of checks
into bank accounts
Firm processes
receivables
Bank clears
checks
The flow starts when a corporate customer mails remittances to a post office box
number instead of to the corporation. Several times a day the bank collects the lockbox receipts from the post office, the checks are then put into the company bank
accounts.
bank. Figure 27.5 illustrates this process, where concentration banks are combined with
lockboxes in a total cash-management system.
The corporate cash manager uses the pools of cash at the concentration bank for shortterm investing or for some other purpose. The concentration banks usually serve as the
source of short-term investments. They also serve as the focal point for transferring funds
to disbursement banks.
Wire Transfers
After the customers’ checks get into the local banking network, the objective is to transfer the surplus funds (funds in excess of required compensating balances)
from the local deposit bank to the concentration bank. The fastest and most expensive way
is by wire transfer.8 Wire transfers take only a few minutes, and the cash becomes available to the firm upon receipt of a wire notice at the concentration bank. Wire transfers take
place electronically, from one computer to another, and eliminate the mailing and checkclearing times associated with other cash-transfer methods.
Two wire services are available—Fedwire, the Federal Reserve wire service (that is
operated by the Federal Reserve bank system), and CHIPS (Clearing House Interbank
8
A slower and cheaper way is a depository transfer check. This is an unsigned, nonnegotiable check drawn on the local collection
bank and payable to the concentration bank.
Corporate Finance,
Seventh Edition
766
Companies, 2004
27. Cash Management
FIGURE 27.5
Lockboxes and
Concentration
Banks in a CashManagement System
Corporate
customers
Corporate
customers
Firm sales
office
Statements are sent by mail to firm
for receivables processing
Corporate
customers
Local bank
deposits
Post office
lockbox receipts
Funds are transferred to concentration
bank by depository checks
and wire transfers
Corporate
customers
Concentration
bank
Cash manager analyzes bank balance and deposit
information and revises cash allocation
Firm cash
manager
Maintenance of
cash reserves
Disbursements
Short-term
investments of cash
Maintenance of
compensating
balance at
creditor bank
Payments System)—as well as the proprietary wire systems of the major investment banks.
A typical wire transfer cost is $10, which is split between the originating bank and the
receiving bank.
EXAMPLE
The decision to use a bank cash-management service incorporating lockboxes and concentration
banks depends on where a firm’s customers are located and the speed of the U.S. postal system. Suppose Atlantic Corporation, located in Philadelphia, is considering a lockbox system. Its collection
delay is currently eight days. It does business in the southwestern part of the country (New Mexico,
Arizona, and California).The proposed lockbox system will be located in Los Angeles and operated
by Pacific Bank. Pacific Bank has analyzed Atlantic’s cash-gathering system and has concluded it
can decrease collection float by two days. Specifically, the bank has come up with the following
information on the proposed lockbox system:
Reduction in mailing time
Reduction in clearing time
Reduction in firm’s processing time
Total reduction
Daily interest on Treasury bills
Average number of daily payments to lockboxes
Average size of payment
1.0 day
0.5 day
0.5
day
_______
2.0 days
0.03%
200
$5,000
205
206
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
767
The cash flows for the current collection are shown in the following cash flow time chart:
Mail
time
Processing
time
Customer
mails
check
Day
0
Check
is
received
1
2
3
4
Availability
time
Deposit
is
made
5
Cash
is
available
6
7
8
The cash flows for the lockbox collection operation will be as follows:
Mail
time
Processing
time
Customer
mails
check
Day
0
Check
is
received
1
2
3
Availability
time
Deposit
is
made
3.5
Cash
is
available
4
5
6
The average daily collections from the southwestern region are $1 million (200 $5,000). The
Pacific Bank has agreed to operate a lockbox system for an annual fee of $20,000 and $0.30 per
check processed.
On this basis the lockbox would increase the collected bank balance by $1 million 2 $2 million.The lockbox, in effect, releases $2 million to the firm by reducing processing, mailing, and clearing
time by two days.
The Atlantic Corporation can expect to realize a daily return of 0.0003 $2 million $600.
The yearly savings would be $600 365 days $219,000 under the lockbox system.
The Pacific Bank’s charge for this lockbox service would be
Annual variable fee
Annual fixed fee
Total
365 days 200 checks $0.30 $21,900
$20,000
_______
$41,900
Because the return on released funds exceeds the lockbox system costs, Atlantic should employ
Pacific Bank. (We should note, however, that this example has ignored the cost of moving funds into
the concentration account.)
Delaying Disbursements
Accelerating collections is one method of cash management; paying more slowly is another. The cash disbursement process is illustrated in Figure 27.6. Techniques to slow down
disbursement will attempt to increase mail time and check-clearing time.
Disbursement Float (“Playing the Float Game”)
Even though the cash balance at the bank may be $1 million, a firm’s books may show only
$500,000 because it has written $500,000 in payment checks. The disbursement float of
Corporate Finance,
Seventh Edition
768
27. Cash Management
Companies, 2004
FIGURE 27.6
Cash Disbursement
Disbursement process
Firm prepares check
to supplier
Post office
processing
Devices to delay
check clearing
1. Write check on distant bank
2. Hold payment for several days after
postmarked in office
3. Call supplier firm to verify statement
accuracy for large amounts
1. Mail from distant post office
2. Mail from post office that requires
a great deal of handling
Delivery of check
to supplier
Deposit goes to
supplier’s bank
Bank collects
funds
$500,000 is available for the corporation to use until the checks are presented for payment. Float in terms of slowing down payment checks comes from mail delivery, checkprocessing time, and collection of funds. This is illustrated in Figure 27.6. Disbursement float
can be increased by writing a check on a geographically distant bank. For example, a New
York supplier might be paid with checks drawn on a Los Angeles bank. This will increase the
time required for the checks to clear through the banking system.
Zero-Balance Accounts
Some firms set up a zero-balance account (ZBA) to handle disbursement activity. The account has a zero balance as checks are written. As checks are presented to the zero-balance
account for payment (causing a negative balance), funds are automatically transferred in
from a central control account. The master account and the ZBA are located in the same
bank. Thus, the transfer is automatic and involves only an accounting entry in the bank.
Drafts
Firms sometimes use drafts instead of checks. Drafts differ from checks because they are
not drawn on a bank but on the issuer (the firm) and are payable by the issuer. The bank acts
only as an agent, presenting the draft to the issuer for payment. When a draft is transmitted
to a firm’s bank for collection, the bank must present the draft to the issuing firm for acceptance before making payment. After the draft has been accepted, the firm must deposit
the necessary cash to cover the payment. The use of drafts rather than checks allows a firm
to keep lower cash balances in its disbursement accounts because cash does not need to be
deposited until the drafts are presented to it for payment.
207
208
Corporate Finance,
Seventh Edition
27. Cash Management
Companies, 2004
769
Ethical and Legal Questions
The cash manager must work with cash balances collected by the bank and not the firm’s
book balance, which reflects checks that have been deposited but not collected. If not, a
cash manager could be drawing on uncollected cash as a source for making short-term investments. Most banks charge a penalty for use of uncollected funds. However, banks may
not have good enough accounting and control procedures to be fully aware of the use of
uncollected funds. This raises some ethical and legal questions for the firm.
In May 1985, Robert Fomon, chairman of E. F. Hutton, a large investment bank at the
time, pleaded guilty to 2,000 charges of mail and wire fraud in connection with a scheme
the firm had operated from 1980 to 1982. E. F. Hutton employees wrote checks totaling
hundreds of millions of dollars in uncollected cash, which were invested in short-term
money-market assets. E. F. Hutton’s systematic overdrafting of accounts is apparently not
a widespread practice among corporations, and since the E. F. Hutton affair, firms have
been much more careful in managing their cash accounts. Generally, firms are scrupulous
in investing only the cash they actually have on hand. E. F. Hutton paid a $2 million fine,
reimbursed the government (the U.S. Department of Justice) $750,000, and reserved
$8 million for restitution to defrauded banks. We should emphasize that the case against
E. F. Hutton was not a case against float management, but rather writing checks with no
economic value other than to exploit float.
The Internet: Will It Eliminate Float?
Internet e-commerce is a general term that refers to the possibilities and practice of direct,
electronic information exchange between all types of business transactions. One important
implication of Internet e-commerce is to electronically transfer financial information and
funds between people and firms, thereby eliminating paper invoices, paper checks, and
paper mail.
For example, it is now possible for a person to arrange to have her checking account directly debited each month to pay many types of bills. More important, Internet e-commerce
allows a seller to send a bill electronically to a buyer—avoiding paper mail. The seller can
authorize acceptance of electronic payment with the bank transferring the funds to the
seller’s account at a different bank. The net effect of all this is that the length of time required
to complete a business transaction is significantly shortened.
As the Internet becomes more and more important, float management will evolve to
focus on issues surrounding computerized information exchange, most notably security,
viruses, hacking, and proprietary systems. We observe an increasing tendency of firms to
link important vendors and customers via extranets—which are business networks that
extend the firms’ intranets.
Concept
Questions
1. Describe collection and disbursement float.
2. What are lockboxes? Concentration banks? Wire transfers?
3. Suppose an overzealous financial manager writes checks on uncollected funds.
Aside from legal issues, who is the financial loser in this situation?
27.4 Investing Idle Cash
If a firm has a temporary cash surplus, it can invest in short-term marketable securities. The
market for short-term financial assets is called the money market. The maturity of shortterm financial assets that trade in the money market is one year or less.
Most large firms manage their own short-term financial assets, transacting through
banks and dealers. Some large firms and many small firms use money-market funds. These
Corporate Finance,
Seventh Edition
770
FIGURE 27.7
Companies, 2004
27. Cash Management
Total financing needs
Seasonal Cash
Demands
Bank
loans
Marketable
securities
Short-term financing
Long-term financing:
Equity plus long-term debt
Time
0
1
2
3
Time 1: A surplus cash flow exists. Seasonal demand for investing is low. The surplus
cash flow is invested in short-term marketable securities. Time 2: A deficit cash flow exists. Seasonal demand for investing is high. The financial deficit is financed by selling
marketable securities and by bank borrowing.
are funds that invest in short-term financial assets for a management fee. The management
fee is compensation for the professional expertise and diversification provided by the fund
manager. Among the many money-market mutual funds, some specialize in corporate customers. Banks also offer sweep accounts, where the bank takes all excess available funds
at the close of each business day and invests them for the firm.
Firms have temporary cash surpluses for these reasons: to help finance seasonal or
cyclical activities of the firm, to help finance planned expenditures of the firm, and to provide for unanticipated contingencies.
Seasonal or Cyclical Activities
Some firms have a predictable cash flow pattern. They have surplus cash flows during part
of the year and deficit cash flows the rest of the year. For example, Toys “R” Us, a retail toy
firm, has a seasonal cash flow pattern influenced by Christmas. Such a firm may buy marketable securities when surplus cash flows occur and sell marketable securities when deficits
occur. Of course, bank loans are another short-term financing device. Figure 27.7 illustrates
the use of bank loans and marketable securities to meet temporary financing needs.
Planned Expenditures
Firms frequently accumulate temporary investments in marketable securities to provide the
cash for a plant-construction program, dividend payment, and other large expenditures.
Thus, firms may issue bonds and stocks before the cash is needed, investing the proceeds in
short-term marketable securities, and then selling the securities to finance the expenditures.
The important characteristics of short-term marketable securities are their maturity,
default risk, marketability, and taxability.
Maturity
Maturity refers to the time period over which interest and principal payments
are made. For a given change in the level of interest rates, the prices of longer-maturity securities will change more than those for shorter-maturity securities. As a consequence,
firms that invest in long-term maturity securities are accepting greater risk than firms that
invest in securities with short-term maturities. This type of risk is usually called interestrate risk. Most firms limit their investments in marketable securities to those maturing in
less than 90 days. Of course, the expected return on securities with short-term maturities is
usually less than the expected return on securities with longer maturities.
209
210
Corporate Finance,
Seventh Edition
27. Cash Management
Companies, 2004
771
Default Risk Default risk refers to the probability that interest or principal will not be
paid on the due date and in the promised amount. In previous chapters we observed that
various financial reporting agencies, such as Moody’s Investors Service and Standard &
Poor’s, compile and publish ratings of various corporate and public securities. These
ratings are connected to default risk. Of course, some securities have negligible default
risk, such as U.S. Treasury bills. Given the purposes of investing idle corporate cash, firms
typically avoid investing in marketable securities with significant default risk.
Marketability Marketability refers to how easy it is to convert an asset to cash. Sometimes marketability is referred to as liquidity. It has two characteristics:
1. No Price-Pressure Effect. If an asset can be sold in large amounts without changing the
market price, it is marketable. Price-pressure effects are those that come about when the
price of an asset must be lowered to facilitate the sale.
2. Time. If an asset can be sold quickly at the existing market price, it is marketable. In contrast, a Renoir painting or antique desk appraised at $1 million will likely sell for much
less if the owner must sell on short notice.
In general, marketability is the ability to sell an asset for its face market value quickly and
in large amounts. Perhaps the most marketable of all securities are U.S. Treasury bills.
Taxability
Several kinds of securities have varying degrees of tax exemption.
1. The interest on the bonds of state and local governments is exempt from federal taxes,
and usually from the state and local taxes where the bonds are issued. Pretax expected
returns on state and local bonds must be lower than on similar taxable investments and
therefore are more attractive to corporations in high marginal tax brackets.
2. Seventy percent of the dividend income on preferred and common stock is exempt from
corporate income taxes.
The market price of securities will reflect the total demand and supply of tax influences.
The position of the firm may be different from that of the market.
Different Types of Money-Market Securities
Money-market securities are generally highly marketable and short term. They usually
have low risk of default. They are issued by the U.S. government (for example, U.S. Treasury bills), domestic and foreign banks (for example, certificates of deposit), and business
corporations (commercial paper, for example).
U.S. Treasury bills are obligations of the U.S. government that mature in 90, 180, 270,
or 360 days. They are pure discount securities. The 90-day and 180-day bills are sold by
auction every week, and 270-day and 360-day bills are sold every month.
U.S. Treasury notes and bonds have original maturities of more than one year. They are
interest-bearing securities. The interest is exempt from state and local taxes.
Federal agency securities are securities issued by corporations and agencies created by
the U.S. government, such as the Federal Home Loan Bank Board and the Government
National Mortgage Association (Ginnie Mae). The interest rates on agency issues are higher
than those on comparable U.S. Treasury issues. This is true because agency issues are not
as marketable as U.S. Treasury issues, and they have more default risk.
Short-term tax exempts are short-term securities issued by states, municipalities, local
housing agencies, and urban renewal agencies. They have more default risk than U.S.
Treasury issues and are less marketable. The interest is exempt from federal income tax.
Corporate Finance,
Seventh Edition
772
Companies, 2004
27. Cash Management
As a consequence, the pretax yield on tax exempts is lower than those on comparable
securities, such as U.S. Treasury bills.
Commercial paper refers to short-term securities issued by finance companies, banks,
and corporations. Commercial paper typically is unsecured notes. Maturities range from
a few weeks to 270 days. There is no active secondary market in commercial paper. As a
consequence, their marketability is low. (However, firms that issue commercial paper will
directly repurchase before maturity.) The default risk of commercial paper depends on the
financial strength of the issuer. Moody’s and Standard & Poor’s publish quality ratings for
commercial paper.
Certificates of deposit (CDs) are short-term loans to commercial banks. There are active
markets in CDs of 3-month, 6-month, 9-month, and 12-month maturities.
Repurchase agreements are sales of government securities (for example, U.S. Treasury
bills) by a bank or securities dealer with an agreement to repurchase. An investor typically
buys some Treasury securities from a bond dealer and simultaneously agrees to sell them
back at a later date at a specified higher price. Repurchase agreements are usually very
short term—overnight to a few days.
Eurodollar CDs are deposits of dollars with foreign banks.
Banker’s acceptances are time drafts (orders to pay) issued by a business firm (usually
an importer) that have been accepted by a bank that guarantees payment.
Concept
Questions
1. Why do firms find themselves with idle cash?
2. What are the types of money-market securities?
The chapter discussed how firms manage cash.
1. A firm holds cash to conduct transactions and to compensate banks for the various services they
render.
2. The optimal amount of cash for a firm to hold depends on the opportunity cost of holding cash
and the uncertainty of future cash inflows and outflows.The Baumol model and the Miller-Orr
model are two transactions models that provide rough guidelines for determining the optimal
cash position.
3. The firm can make use of a variety of procedures to manage the collection and disbursement of
cash in such a way as to speed up the collection of cash and slow down payments. Some methods to speed up collection are lockboxes, concentration banking, and wire transfers.The financial
manager must always work with collected company cash balances and not with the company’s
book balance. To do otherwise is to use the bank’s cash without the bank knowing it, raising
ethical and legal questions.
4. Because of seasonal and cyclical activities, to help finance planned expenditures, or as a reserve
for unanticipated needs, firms temporarily find themselves with cash surpluses.The money market offers a variety of possible vehicles for parking this idle cash.
KEY TERMS
compensating balances, 754
concentration banking, 764
float, 761
lockbox, 764
target cash balance, 754
transactions motive, 754
wire transfer, 765
zero-balance account (ZBA), 768
211
Corporate Finance,
Seventh Edition
Companies, 2004
27. Cash Management
773
SUGGESTED
READING
For a review of the latest academic research on corporate cash holding, see:
Opler T., L. Pinkowitz, R. Stulz, and R. Williamson. “Corporate Cash Holdings.” Journal of Applied
Corporate Finance, Spring 2001.
QUESTIONS
& PROBLEMS
27.1
What are the reasons for holding cash?
27.2
Indicate whether the following actions increase, decrease, or cause no change in a company’s
cash balance.
a. Interest rates paid on money-market securities rise.
b. Commissions charged by brokers increase.
c. The compensating-balance requirement of a bank is lowered.
d. The cost of borrowing decreases.
e. The firm’s credit rating declines.
f. Direct fees for banking services are established.
27.3
A company’s weekly average cash balances are as follows:
REASONS FOR
HOLDING CASH
DETERMINING THE
TARGET CASH
BALANCE
Week 1
Week 2
Week 3
Week 4
$24,000
34,000
10,000
15,000
If the annual interest rate is 12 percent, what return can be earned on the average cash
balances?
MANAGING THE
COLLECTION AND
DISBURSEMENT
OF CASH
27.4
The Casablanca Piano Company is currently holding $800,000 in cash. It projects that over
the next year its cash outflows will exceed its cash inflows by $345,000 per month. Each
time securities are bought or sold through a broker, the company pays a fee of $500. The
annual interest rate on money-market securities is 7 percent.
a. How much of this cash should be retained and how much should be used to increase the
company’s holdings of marketable securities?
b. After the initial investment of excess cash, how many times during the next 12 months
will securities be sold?
27.5
Lisa Tylor, CFO of Purple Rain Co., concluded from the Baumol model that the optimal
cash balance for the firm is $20 million.The annual interest rate on marketable securities is
7.5 percent.The fixed cost of selling securities to replenish cash is $5,000. Purple Rain’s cash
flow pattern is well approximated by the Baumol model. What can you infer about Purple
Rain’s average weekly cash disbursement?
27.6
The variance of the daily net cash flows for the Tseneg Asian Import Company is $1.44 million.The opportunity cost to the firm of holding cash is 8 percent per year.The fixed cost of
buying and selling securities is $600 per transaction.
What should the target cash level and upper limit be, if the tolerable lower limit has been
established at $20,000?
27.7
Gold Star Co. and Silver Star Co. both manage their cash flows according to the Miller-Orr
model. Gold Star’s daily cash flow is controlled between $100,000 and $200,000, whereas
Silver Star’s daily cash flow is controlled between $150,000 and $300,000.The annual interest rates Gold Star and Silver Star can get are 10 percent and 9 percent, respectively, and the
costs per transaction of trading securities are $2,000 and $2,500, respectively.
a. What are their respective target cash balances?
b. Which firm’s daily cash flow is more volatile?
27.8
Garden Groves, Inc., a Florida-based company, has determined that a majority of its customers are located in the New York City area.Therefore, it is considering using a lockbox
system offered by a bank located in New York.The bank has estimated that use of the system
212
Corporate Finance,
Seventh Edition
774
27. Cash Management
Companies, 2004
will reduce collection float by three days. Based on the following information, should the
lockbox system be adopted?
Average number of payments per day: 150
Average value of payment: $15,000
Fixed annual lockbox fee: $80,000
Variable lockbox fee: $0.50/transaction
Annual interest rate on money-market securities: 7.5 percent
27.9
A large New England lumber producer, Salisbury Stakes, Inc., is planning to use a lockbox system to speed collections from its customers located in the midwestern United States. A
Chicago-area bank will provide this service for an annual fee of $15,000 plus $0.25 per transaction.The estimated reduction in collection and processing time is two days.Treasury bills
are currently yielding 6 percent per year.
If the average customer payment in this region is $4,500, how many customers each day,
on average, must use the system to make it profitable?
27.10 Each business day, on average, a company writes checks totaling $12,000 to pay its suppliers.
The usual clearing time for these checks is five days. Each day, the company receives payments from its customers in the form of checks totaling $15,000. The cash from the
payments is available to the firm after three days.
Calculate the company’s disbursement float, collection float, and net float.
How would these values change if the collected funds were available in four days instead
of three?
27.11 It takes the Herman Company about seven days to receive and deposit checks from customers.The top management of the Herman Company is considering a lockbox system. It is
expected that the lockbox system will reduce float time to four days. Average daily collections are $100,000.The marketwide interest rate is 12 percent.
a. What would the reduction in outstanding cash balances be as a result of implementing
the lockbox system?
b. What is the return that could be earned on these savings?
c. What is the maximum monthly charge the Herman Company should pay for this lockbox
system?
27.12 The Walter Company disburses checks every two weeks that average $200,000 in total
and take three days to clear. How much cash can the Walter Company save annually if it
delays the transfer of funds from an interest-bearing account that pays 0.04 percent per day
for these three days?
27.13 The Miller Company has an agreement with the First National Bank by which the bank handles
$4 million in collections each day and requires a $500,000 compensating balance.Miller is contemplating canceling the agreement and dividing its eastern region so that two other banks will
handle its business. Banks 1 and 2 will each handle $2 million of collections each day, requiring
a compensating balance of $300,000. Miller’s financial management expects that collections
will be accelerated by one day if the eastern region is divided.TheT-bill rate is 7 percent.Should
the Miller Company implement the new system?What will the annual net savings be?
27.14 Anthony Marino, CFO of Thousand Years Inc., is evaluating two alternatives of float management: lockbox and concentration banking. The average number of daily payments to lockboxes is 250 with the average size of each payment at $7,500.The lockbox system can reduce the collection float by 1.5 days and concentration banking can reduce the collection
float by 1 day. However, the bank charges an annual fee of $30,000 and $0.30 per check
processed for the lockbox service.Which method is more economical for Thousand Years,
the lockbox system or the concentration-banking system? Assume daily interest on Treasury
bills is 0.03 percent.
INVESTING IDLE
CASH
27.15 What are the important characteristics of short-term marketable securities?
213
214
Corporate Finance,
Seventh Edition
Companies, 2004
29. Mergers and
Acquisitions
Chapter 29
EXECUTIVE SUMMARY
Mergers and Acquisitions
There is no more dramatic or controversial
activity in corporate finance than the acquisition of one firm by another or the merger of
two firms. This chapter addresses two basic
questions:Why does a firm choose to merge
with or acquire another firm and how does it
happen?
The acquisition of one firm by another is,
of course, an investment made under uncertainty.The basic principle of valuation applies:
A firm should be acquired if it generates a
positive net present value to the shareholders
of the acquiring firm. However, because the
NPV of an acquisition candidate is very difficult to determine, mergers and acquisitions
are interesting topics in their own right. Here
are some of the special features of this area of
finance:
1. The benefits from acquisitions are called
synergies. It is hard to estimate synergies
using discounted cash flow techniques.
2. There are complex accounting, tax, and
legal effects when one firm is acquired by
another.
3. Acquisitions are an important control
device of shareholders. It appears that
some acquisitions are a consequence
of an underlying conflict between the
interests of existing managers and of
shareholders. Acquisition by another
firm is one way that shareholders can
remove managers with whom they are
unhappy.
796
4. Acquisition analysis frequently focuses
on the total value of the firms involved.
But usually an acquisition will affect the
relative values of stocks and bonds, as
well as their total value.
5. Mergers and acquisitions sometimes
involve unfriendly transactions.Thus,
when one firm attempts to acquire
another, it does not always involve quiet,
gentlemanly negotiations.The soughtafter firm may use defensive tactics,
including poison pills, greenmail, and
white knights.
This chapter starts by introducing the
basic legal, accounting, and tax aspects of
acquisitions.When one firm acquires another,
it must choose the legal framework, the
accounting method, and tax status. These
choices will be explained throughout the
chapter.
The chapter discusses how to determine
the NPV of an acquisition candidate.The NPV
of an acquisition candidate is the difference
between the synergy from the merger and
the premium to be paid.We consider the following types of synergy: (1) revenue enhancement, (2) cost reduction, (3) lower taxes, and
(4) lower cost of capital. The premium paid
for an acquisition is the price paid minus the
market value of the acquisition prior to the
merger. The premium depends on whether
cash or securities are used to finance the
offer price.
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Chapter 29 Mergers and Acquisitions
Companies, 2004
215
797
29.1 The Basic Forms of Acquisitions
There are three basic legal procedures that one firm can use to acquire another firm:
(1) merger or consolidation, (2) acquisition of stock, and (3) acquisition of assets.
Merger or Consolidation
A merger refers to the absorption of one firm by another. The acquiring firm retains its
name and its identity, and it acquires all of the assets and liabilities of the acquired firm.
After a merger, the acquired firm ceases to exist as a separate business entity.
A consolidation is the same as a merger except that an entirely new firm is created. In a
consolidation, both the acquiring firm and the acquired firm terminate their previous legal
existence and become part of the new firm. In a consolidation, the distinction between the
acquiring and the acquired firm is not important. However, the rules for mergers and consolidations are basically the same. Acquisitions by merger and consolidation result in combinations of the assets and liabilities of acquired and acquiring firms.
EXAMPLE
Suppose firm A acquires firm B in a merger. Further, suppose firm B’s shareholders are given one
share of firm A’s stock in exchange for two shares of firm B’s stock. From a legal standpoint, firm A’s
shareholders are not directly affected by the merger. However, firm B’s shares cease to exist. In a
consolidation, the shareholders of firm A and firm B would exchange their shares for the share of a
new firm (e.g., firm C). Because the differences between mergers and consolidations are not all that
important for our purposes, we shall refer to both types of reorganizations as mergers.
There are some advantages and some disadvantages to using a merger to acquire a firm:
1. A merger is legally straightforward and does not cost as much as other forms of acquisition. It avoids the necessity of transferring title of each individual asset of the acquired
firm to the acquiring firm.
2. A merger must be approved by a vote of the stockholders of each firm.1 Typically, votes
of the owners of two-thirds of the shares are required for approval. In addition, shareholders of the acquired firm have appraisal rights. This means that they can demand that
their shares be purchased at a fair value by the acquiring firm. Often the acquiring firm
and the dissenting shareholders of the acquired firm cannot agree on a fair value, which
results in expensive legal proceedings.
Acquisition of Stock
A second way to acquire another firm is to purchase the firm’s voting stock in exchange for
cash, shares of stock, or other securities. This may start as a private offer from the management of one firm to another. At some point the offer is taken directly to the selling firm’s
stockholders. This can be accomplished by use of a tender offer. A tender offer is a public
offer to buy shares of a target firm. It is made by one firm directly to the shareholders of
another firm. The offer is communicated to the target firm’s shareholders by public announcements such as newspaper advertisements. Sometimes a general mailing is used in a
tender offer. However, a general mailing is very difficult because it requires the names and
addresses of the stockholders of record, which are not usually available.
1
Mergers between corporations require compliance with state laws. In virtually all states the shareholders of each corporation
must give their assent.
216
798
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
Part VIII Special Topics
The following are factors involved in choosing between an acquisition of stock and a
merger:
1. In an acquisition of stock, no shareholder meetings must be held and no vote is required.
If the shareholders of the target firm do not like the offer, they are not required to accept
it and they will not tender their shares.
2. In an acquisition of stock, the bidding firm can deal directly with the shareholders of a
target firm by using a tender offer. The target firm’s management and board of directors
can be bypassed.
3. Acquisition of stock is often unfriendly. It is used in an effort to circumvent the target
firm’s management, which is usually actively resisting acquisition. Resistance by the
target firm’s management often makes the cost of acquisition by stock higher than the
cost by merger.
4. Frequently a minority of shareholders will hold out in a tender offer, and thus the target
firm cannot be completely absorbed.
5. Complete absorption of one firm by another requires a merger. Many acquisitions of
stock end with a formal merger later.
Acquisition of Assets
One firm can acquire another firm by buying all of its assets. A formal vote of the shareholders of the selling firm is required. This approach to acquisition will avoid the potential
problem of having minority shareholders, which can occur in an acquisition of stock.
Acquisition of assets involves transferring title to assets. The legal process of transferring
assets can be costly.
A Classification Scheme
Financial analysts have typically classified acquisitions into three types:
1. Horizontal Acquisition. This is an acquisition of a firm in the same industry as the acquiring firm. The firms compete with each other in their product market.
2. Vertical Acquisition. A vertical acquisition involves firms at different steps of the production process. The acquisition by an airline company of a travel agency would be a
vertical acquisition.
3. Conglomerate Acquisition. The acquiring firm and the acquired firm are not related to
each other. The acquisition of a food-products firm by a computer firm would be considered a conglomerate acquisition.
A Note on Takeovers
Takeover is a general and imprecise term referring to the transfer of control of a firm from
one group of shareholders to another.2 A firm that has decided to take over another firm is
usually referred to as the bidder. The bidder offers to pay cash or securities to obtain the
stock or assets of another company. If the offer is accepted, the target firm will give up control over its stock or assets to the bidder in exchange for consideration (i.e., its stock, its
debt, or cash).
For example, when a bidding firm acquires a target firm, the right to control the operating activities of the target firm is transferred to a newly elected board of directors of the
acquiring firm. This is a takeover by acquisition.
2
Control can usually be defined as having a majority vote on the board of directors.
Corporate Finance,
Seventh Edition
Companies, 2004
29. Mergers and
Acquisitions
217
799
FIGURE 29.1
Merger or consolidation
Varieties of Takeovers
Takeovers
Acquisition
Acquisition of stock
Proxy contest
Acquisition of assets
Going private
Takeovers can occur by acquisition, proxy contests, and going-private transactions.
Thus, takeovers encompass a broader set of activities than acquisitions. Figure 29.1 depicts
this.
If a takeover is achieved by acquisition, it will be by merger, tender offer for shares of
stock, or purchase of assets. In mergers and tender offers, the acquiring firm buys the voting
common stock of the acquired firm.
Takeovers can occur with proxy contests. Proxy contests occur when a group of shareholders attempts to gain controlling seats on the board of directors by voting in new
directors. A proxy authorizes the proxy holder to vote on all matters in a shareholders’
meeting. In a proxy contest, proxies from the rest of the shareholders are solicited by an
insurgent group of shareholders.
In going-private transactions, all the equity shares of a public firm are purchased by a
small group of investors. The group usually includes members of incumbent management
and some outside investors. The shares of the firm are delisted from stock exchanges and
can no longer be purchased in the open market.
Concept
Questions
1. What is a merger? How does a merger differ from other forms of acquisition?
2. What is a takeover?
29.2 The Tax Forms of Acquisitions
If one firm buys another firm, the transaction may be taxable or tax-free. In a taxable acquisition, the shareholders of the acquired firm are considered to have sold their shares, and
they have realized capital gains or losses that will be taxed. In a taxable transaction, the
appraised value of the assets of the selling firm may be revalued, as we explain below.
In a tax-free acquisition, the selling shareholders are considered to have exchanged their
old shares for new ones of equal value, and they have experienced no capital gains or
losses. In a tax-free acquisition, the assets are not revalued.
EXAMPLE
Suppose that 15 years ago Bill Evans started Samurai Machinery (SM) and purchased plant and equipment costing $80,000.These have been the only assets of SM, and the company has no debts. Bill is
the sole proprietor of SM and owns all the shares. For tax purposes the assets of SM have been depreciated using the straight-line method over 10 years, and have no salvage value.The annual depreciation expense has been $8,000 ($80,000兾10).The machinery has no accounting value today (i.e., it
has been written off the books). However, because of inflation, the fair market value of the machinery is $200,000. As a consequence, the S. A. Steel Company has bid $200,000 for all of the outstanding stock of Samurai.
218
Corporate Finance,
Seventh Edition
800
TABLE 29.1
29. Mergers and
Acquisitions
Companies, 2004
The Incremental Tax Consequences of S. A. Steel Company’s Acquisition of Samurai Machinery
Type of Acquisition
Buyer or Seller
Taxable Acquisition
Tax-Free Acquisition
Bill Evans
S. A. Steel
Immediate tax on $120,000 ($200,000 $80,000)
S. A. Steel may elect to write up assets. Here:
1. Assets of Samurai written up to $200,000
(with useful life of 10 years). Annual depreciation
expense is $20,000.
2. Immediate tax on $200,000 write-up of assets.
Alternatively, S. A. Steel may elect not to write up
assets. Here, there is neither additional depreciation
nor immediate tax.Typically, acquirer elects not to
write up assets.
Capital gain tax not paid until
Evans sells shares of S. A. Steel
No additional depreciation
S. A. Steel acquires Samurai Machinery for $200,000, which is the market value of Samurai’s equipment.The book value of the equipment is $0. Bill Evans
started Samurai Steel 15 years ago with a contribution of $80,000.
The tax consequences of a tax-free acquisition are better than the tax consequences of a taxable acquisition, because the seller pays no immediate tax on
a tax-free acquisition.
Tax-Free Transaction
If Bill Evans receives shares of S. A. Steel worth $200,000, the
IRS will treat the sale as a tax-free transaction. Thus, Bill will not have to pay taxes on any
gain received from the stock. In addition, S. A. Steel will be allowed the same depreciation
deduction that Samurai Machinery was allowed. Because the asset has already been fully
depreciated, S. A. Steel will receive no depreciation deduction.
Taxable Transaction If S. A. Steel pays $200,000 in cash for Samurai Machinery, it
will be a taxable transaction. There will be a number of tax consequences:
1. In the year of the merger, Bill Evans must pay taxes on the difference between the merger
price of $200,000 and his initial contribution to the firm of $80,000. Thus, his taxable
income is $120,000 ($200,000 $80,000).
2. S. A. Steel may elect to write up the value of the machinery. In this case, S. A. Steel will be
able to depreciate the machinery from an initial tax basis of $200,000. If S. A. Steel depreciates straight-line over 10 years, depreciation will be $20,000 ($200,000兾10) per year.
If S. A. Steel elects to write up the machinery, S. A. Steel must treat the $200,000
write-up as taxable income immediately.3
3. Should S. A. Steel not elect the write-up, there is no increase in depreciation. Thus,
depreciation remains zero in this example. In addition, because there is no write-up,
S. A. Steel does not need to recognize any additional taxable income.
Because the tax benefits from depreciation occur slowly over time and the taxable
income is recognized immediately, the acquirer generally elects not to write up the value
of the machinery in a taxable transaction.
Because the write-up is not allowed for tax-free transactions and generally not chosen
for taxable ones, the only real tax difference between the two types of transactions concerns
the taxation of the selling shareholders. Because these individuals can defer taxes under a
tax-free situation but must pay taxes immediately under a taxable situation, the tax-free
transaction has better tax consequences. The tax implications for both types of transactions
are displayed in Table 29.1.
3
Technically, Samurai Machinery pays this tax. However, because Samurai is now a subsidiary of S. A. Steel, S. A. Steel is the
effective taxpayer.
Corporate Finance,
Seventh Edition
Companies, 2004
29. Mergers and
Acquisitions
219
801
29.3 Accounting for Acquisitions
Earlier in this text we mentioned that firms keep two distinct sets of books: the stockholders’
books and the tax books. The previous section concerned the effect of acquisitions on the tax
books. We now consider the stockholders’ books. When one firm acquires another firm, the
acquisition is treated using a purchase accounting on the stockholders’ books.
The Purchase Method
The purchase method of reporting acquisitions requires that the assets of the acquired firm
be reported at their fair market value on the books of the acquiring firm. This allows the
acquiring firm to establish a new cost basis for the acquired assets.
In a purchase, an accounting term called goodwill is created. Goodwill is the excess of
the purchase price over the sum of the fair market values of the individual assets acquired.
EXAMPLE
Suppose firm A acquires firm B, creating a new firm, AB. Firm A’s and firm B’s financial positions at the
date of the acquisition are shown in Table 29.2.The book value of firm B on the date of the acquisition is $10 million. This is the sum of $8 million in buildings and $2 million in cash. However, an
appraiser states that the sum of the fair market values of the individual buildings is $14 million.With
$2 million in cash, the sum of the market values of the individual assets in firm B is $16 million.This
represents the value to be received if the firm is liquidated by selling off the individual assets separately. However, the whole is often worth more than the sum of the parts in business. Firm A pays
$19 million in cash for firm B.This difference of $3 million ($19 million $16 million) is goodwill. It
represents the increase in value by keeping the firm intact as an ongoing business. Firm A issued
$19 million in new debt to finance the acquisition.The last balance sheet in Table 29.2 shows what
happens under purchase accounting.
1. The total assets of firm AB increase to $39 million.The buildings of firm B appear in the new balance sheet at their current market value.That is, the market value of the assets of the acquired
firm becomes part of the book value of the new firm. However, the assets of the acquiring firm
(firm A) remain at their old book value. They are not revalued upwards when the new firm is
created.
2. The excess of the purchase price over the sum of the fair market values of the individual assets
acquired is $3 million. This amount is reported as goodwill. Financial analysts generally ignore
goodwill because it has no cash flow consequences.The current accounting practice says that each
year firms must assess the value of goodwill on their balance sheets. If the value goes down (this
is called impairment in accounting speak), the firm must deduct the decrease from earnings otherwise no amortization is required.
TABLE 29.2
Accounting for Acquisitions: Purchase (in $ millions)
Firm A
Cash
Land
Buildings
Total
$ 4
16
___0
$20
___
___
Equity
Firm B
$20
___
$20
___
___
Cash
Land
Buildings
Total
$ 2
0
___8
$10
___
___
Equity
Firm AB
$10
___
$10
___
___
Cash
Land
Buildings
Goodwill
$ 6
16
14
___3
Total
$39
___
___
When the purchase method is used, the assets of the acquired firm (firm B) appear in the combined firm’s books at their fair market value.
Debt
Equity
$19
20
___
$39
___
___
220
802
Corporate Finance,
Seventh Edition
Companies, 2004
29. Mergers and
Acquisitions
29.4 Determining the Synergy from an Acquisition
Suppose firm A is contemplating acquiring firm B. The value of firm A is VA and the value
of firm B is VB. (It is reasonable to assume that, for public companies, VA and VB can be
determined by observing the market price of the outstanding securities.) The difference
between the value of the combined firm (VAB) and the sum of the values of the firms as
separate entities is the synergy from the acquisition:
Synergy VAB (VA VB)
The acquiring firm must generally pay a premium for the acquired firm. For example, if
stock of the target is selling for $50, the acquirer might need to pay $60 a share, implying
a premium of $10 or 20 percent. Firm A will want to determine the synergy before entering
into negotiations with firm B on the premium.
The synergy of an acquisition can be determined from the usual discounted cash flow
model:
T
CFt
Synergy (1
r) t
t1
兺
where CFt is the difference between the cash flows at date t of the combined firm and the
sum of the cash flows of the two separate firms. In other words, CFt is the incremental
cash flow at date t from the merger. The term, r, is the risk-adjusted discount rate appropriate for the incremental cash flows. This is generally considered to be the required rate of
return on the equity of the target.
From the chapters on capital budgeting we know that the incremental cash flows can be
separated into four parts:
CFt Revt Costst Taxest Capital Requirementst
where Revt is the incremental revenue of the acquisition, Costst is the incremental costs
of the acquisition, Taxest is the incremental acquisition taxes, and Capital Requirementst
is the incremental new investment required in working capital and fixed assets.
29.5 Source of Synergy from Acquisitions
It follows from our classification of incremental cash flows that the possible sources of synergy fall into four basic categories: revenue enhancement, cost reduction, lower taxes, and
lower cost of capital.4
Revenue Enhancement
One important reason for acquisitions is that a combined firm may generate greater revenues than two separate firms. Increased revenues may come from marketing gains, strategic benefits, and market power.
4
Many reasons are given by firms to justify mergers and acquisitions. When two firms merge, the boards of directors of the two
firms adopt an agreement of merger. The agreement of merger of U.S. Steel and Marathon Oil is typical. It lists the economic
benefits that shareholders can expect from the merger (key words have been italicized):
U.S. Steel believes that the acquisition of Marathon provides U.S. Steel with an attractive opportunity to diversify into
the energy business. Reasons for the merger include, but are not limited to, the facts that consummation of the merger
will allow U.S. Steel to consolidate Marathon into U.S. Steel’s federal income tax return, will also contribute to greater
efficiency, and will enhance the ability to manage capital by permitting the movement of cash between U.S. Steel and
Marathon. Additionally, the merger will eliminate the possibility of conflicts of interests between the interests of
minority and majority shareholders and will enhance management flexibility. The acquisition will provide Marathon
shareholders with a substantial premium over historical market prices for their shares. However, shareholders will no
longer continue to share in the future prospects of the company.
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
221
803
Marketing Gains
It is frequently claimed that mergers and acquisitions can produce
greater operating revenues from improved marketing. Improvements can be made in the
following:
1. Previously ineffective media programming and advertising efforts.
2. A weak existing distribution network.
3. An unbalanced product mix.
Strategic Benefits
Some acquisitions promise a strategic advantage. This is an opportunity to take advantage of the competitive environment if certain situations materialize.
In this regard, a strategic benefit is more like an option than it is a standard investment
opportunity. For example, imagine that a sewing machine company acquired a computer
company. The firm will be well positioned if technological advances allow computerdriven sewing machines in the future. Michael Porter has used the word beachhead in his
description of the process of entering a new industry to exploit perceived opportunities.5
The beachhead is used to spawn new opportunities based on intangible relationships. He
uses the example of Procter & Gamble’s initial acquisition of the Charmin Paper Company
as a beachhead that allowed Procter & Gamble to develop a highly interrelated cluster
of paper products—disposable diapers, paper towels, feminine hygiene products, and bathroom tissue.
Market or Monopoly Power
One firm may acquire another to reduce competition. If
so, prices can be increased and monopoly profits obtained. Mergers that reduce competition do not benefit society and may be challenged by the U.S. Department of Justice or the
Federal Trade Commission.
Cost Reduction
One of the most basic reasons for merger is that a combined firm may operate more efficiently than two separate firms. Thus, when Bank of America agreed to acquire Security
Pacific, lower costs were cited as the primary reason. A firm can obtain greater operating
efficiency in several different ways through a merger or an acquisition.
Economies of Scale
If the average cost of production falls while the level of production
increases, there is said to be an economy of scale. Figure 29.2 illustrates that economies of
scale result while the firm grows to its optimal size. After this point, diseconomies of scale
occur. In other words, average cost increases with further firm growth.
Though the precise nature of economy of scale is not known, it is one obvious benefit of
horizontal mergers. The phrase spreading overhead is frequently used in connection with
economies of scale. This refers to the sharing of central facilities such as corporate headquarters, top management, and a large mainframe computer.
Economies of Vertical Integration
Operating economies can be gained from vertical
combinations as well as from horizontal combinations. The main purpose of vertical acquisitions is to make coordination of closely related operating activities easier. This is
probably the reason why most forest product firms that cut timber also own sawmills and
hauling equipment. Economies from vertical integration probably explain why most airline
companies own airplanes; it also may explain why some airline companies have purchased
hotels and car-rental companies.
Technology transfers are another reason for vertical integration. Consider the merger of
General Motors and Hughes Aircraft in 1985. An automobile manufacturer might well
5
M. Porter, Competitive Advantage (New York: Free Press, 1985).
222
Corporate Finance,
Seventh Edition
804
Companies, 2004
29. Mergers and
Acquisitions
FIGURE 29.2
Average
cost
Economies of Scale
and the Optimal Size
of the Firm
Minimum
cost
Economies of
scale
Diseconomies
of scale
Size
Optimal
size
acquire an advanced electronics firm if the special technology of the electronics firm can
improve the quality of the automobile.
Complementary Resources Some firms acquire others to make better use of existing
resources or to provide the missing ingredient for success. Think of a ski-equipment store
that could merge with a tennis-equipment store to produce more even sales over both the
winter and summer seasons—and better use of store capacity.
Elimination of Inefficient Management
There are firms whose value could be increased with a change in management. For example, Jensen and Ruback argue that acquisitions can occur because of changing technology or market conditions that require a restructuring of the corporation.6 Incumbent managers in some cases do not understand changing
conditions. They have trouble abandoning strategies and styles they have spent years
formulating.
The oil industry is an example of managerial inefficiency cited by Jensen. In the late
1970s, changes in the oil industry included reduced expectations of the future price of oil,
increased exploration and development costs, and increased real interest rates. As a result
of these changes, substantial reductions in exploration and development were called for.
However, many oil company managers were unable to downsize their firms. For example,
a study by McConnell and Muscarella reports that the stock prices of oil companies tended
to decrease with announcements of increases in exploration and development expenditures
in the period of 1975–1981.7
Acquiring companies sought out oil firms in order to reduce the investment levels of
these oil companies.8 For example, T. Boone Pickens of Mesa Petroleum perceived the
changes taking place in the oil industry and attempted to buy several oil companies: Unocal,
Phillips, and Getty. The results of these attempted acquisitions have been reduced
6
M. C. Jensen and R. S. Ruback, “The Market for Corporate Control: The Scientific Evidence,” Journal of Financial Economics
11 (April 1983); and M. C. Jensen, “Agency Costs of Free Cash Flow, Corporate Finance and Takeovers,” American Economic
Review (May 1986).
7
J. J. McConnell and C. J. Muscarella, “Corporate Capital Expenditure Decisions and the Market Value of the firm,” Journal of
8
More than 26 percent of the total valuation of all takeover transactions involved a selling firm in the oil and gas industry in
1981–1984 [W. T. Grimm, Mergerstat Review (1985), p. 41].
Corporate Finance,
Seventh Edition
223
Companies, 2004
29. Mergers and
Acquisitions
805
TABLE 29.3
Before Merger
Tax Effect of Merger
of Firms A and B
Firm A
Taxable income
Taxes
Net income
After Merger
Firm B
Firm AB
If
State 1
If
State 2
If
State 1
If
State 2
If
State 1
If
State 2
$200
68
____
$132
$100
0
______
$100
$100
0
______
$100
$200
68
____
$132
$100
34
____
$ 66
$100
34
____
$ 66
Neither firm will be able to deduct its losses prior to the merger.The merger allows the losses from A to offset the taxable
profits from B—and vice versa.
expenditures on exploration and development and huge gains to the shareholders of the
affected firms.
Mergers and acquisitions can be viewed as part of the labor market for top management.
Jensen and Ruback have used the phrase market for corporate control, in which alternative
management teams compete for the rights to manage corporate activities.
Tax Gains
Tax gains may be a powerful incentive for some acquisitions. The possible tax gains that
can come from an acquisition are the following:
1. The use of tax losses from net operating losses.
2. The use of unused debt capacity.
3. The use of surplus funds.
Net Operating Losses
Sometimes firms have tax losses they cannot take advantage of.
These tax losses are referred to as NOL (an acronym for net operating losses). Consider the
situation of firm A and firm B.
Table 29.3 shows the pretax income, taxes, and after-tax income for firms A and B.
Firm A will earn $200 under state 1 but will lose money under state 2. The firm will pay
taxes under state 1 but is not entitled to a tax rebate under state 2. Conversely, firm B will
pay taxes of $68 under state 2. Thus, if firms A and B are separate, the IRS will obtain $68
in taxes, regardless of which state occurs. However, if A and B merge, the combined firm
will pay $34 in taxes under both state 1 and state 2.
It is obvious that if firms A and B merge, they will pay lower taxes than if they remain
separate. Without merger, they do not take advantage of potential tax losses.
The message of the preceding example is that firms need taxable profits to take advantage of potential tax losses. Mergers can sometimes accomplish this. However, there are
two qualifications to the previous example:
1. The federal tax laws permit firms that experience alternating periods of profits and
losses to equalize their taxes by carryback and carryforward provisions. A firm that has
been profitable but has a loss in the current year can get refunds of income taxes paid in
three previous years and can carry the loss forward for 15 years. Thus, a merger to exploit unused tax shields must offer tax savings over and above what can be accomplished by firms via carryovers.9
2. The IRS may disallow an acquisition if the principal purpose of the acquisition is to
avoid federal tax. This is one of the Catch 22s of the Internal Revenue Code.
9
Under the 1986 Tax Reform Act a corporation’s ability to carry forward net operating losses (and other tax credits) is limited
when more than 50 percent of the stock changes hands over a three-year period.
224
806
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
Unused Debt Capacity We argued earlier in the text that the optimal debt-equity ratio
is the one where the marginal tax benefit from additional debt is equal to the marginal increase in the financial distress costs from additional debt. Because some diversification occurs when firms merge, the cost of financial distress is likely to be less for the combined
firm than is the sum of these present values for the two separate firms. Thus, the acquiring
firm might be able to increase its debt-equity ratio after a merger, creating additional tax
benefits—and additional value.10
Surplus Funds
Another quirk in the tax laws involves surplus funds. Consider a firm
that has free cash flow. That is, it has cash flow available after payment of all taxes and after
all positive net present value projects have been provided for. In this situation, aside from
purchasing fixed-income securities, the firm has several ways to spend the free cash flow,
including
1. Pay dividends.
2. Buy back its own shares.
3. Acquire shares in another firm.
We have already seen in our previous discussion of dividend policy that an extra dividend will increase the income tax paid by some investors. Investors pay lower taxes in a
share repurchase. However, this is not a legal option if the sole purpose is to avoid taxes
that would otherwise have been paid by shareholders.
The firm can buy the shares of another firm. This accomplishes two objectives. First, the
firm’s shareholders avoid taxes from dividends that would have been paid. Second, the firm
pays little corporate tax on dividends received from the shares of the firm it has purchased,
because 70 percent of the dividend income received from the acquired firm is excluded
from the corporate income tax. However, under Section 532 of the tax code the IRS might
disallow the tax benefits from a continual strategy of this type.
Instead, the firm might make acquisitions with its excess funds. In a merger no taxes at
all are paid on dividends remitted from the acquired firm, and the IRS would not question
mergers of this type.
The Cost of Capital
The cost of capital can often be reduced when two firms merge because the costs of issuing
securities are subject to economies of scale. As we observed in earlier chapters, the costs of
issuing both debt and equity are much lower for larger issues than for smaller issues.
29.6 Calculating the Value of the Firm after an Acquisition
Now that we have listed the possible sources of synergy from a merger, let us see how one
would value these sources. Consider two firms. Gamble, Inc., manufactures and markets
soaps and cosmetics. The firm has a reputation for its ability to attract, develop, and keep
talented people. The firm has successfully introduced several major products in the past
two years. It would like to enter the over-the-counter drug market to round out its product
line. Shapiro, Inc., is a well-known maker of cold remedies. Al Shapiro, the great-grandson
of the founder of Shapiro, Inc., became chairman of the firm last year. Unfortunately, Al
10
Unused debt capacity is cited as a benefit in many mergers. An example was the proposed merger of Hospital Corporation of
America and American Hospital Supply Corporation in 1985. Insiders were quoted as saying that the combined companies
could borrow as much as an additional $1 billion, 10 times the usual borrowing capacity of Hospital Corporation alone (The
Wall Street Journal, April 1, 1985). (The merger never took place.)
Corporate Finance,
Seventh Edition
225
Companies, 2004
29. Mergers and
Acquisitions
807
TABLE 29.4
Acquisition of
Shapiro, Inc.,
by Gamble, Inc.
Gamble, Inc.
Shapiro, Inc.
Benefits from acquisition:
Strategic fit
Tax shelters
Operating efficiencies
Gamble-Shapiro
Net Cash Flow
per Year
(perpetual)
Discount
Rate
Value
$10.0 million
4.5 million
5.5 million
3.0 million
1.0 million
1.5 million
20.0 million
0.10
0.15
0.122
0.20
0.05
0.15
0.114
$100 million
30 million*
45 million
15 million
20 million
10 million
175 million
*The market value of Shapiro’s outstanding common stock is $30 million; 1 million shares are outstanding.
knows nothing about cold remedies, and as a consequence, Shapiro, Inc., has had lackluster
financial performance. For the most recent year, pretax cash flow fell by 15 percent. The
firm’s stock price is at an all-time low.
The financial management of Gamble finds Shapiro an attractive acquisition candidate.
It believes that the cash flows from the combined firms would be far greater than what each
firm would have alone. The cash flows and present values from the acquisition are shown
in Table 29.4. The increased cash flows (CFt ) would come from three benefits:
1. Tax Gains. If Gamble acquires Shapiro, Gamble will be able to use some tax-loss carryforwards to reduce its tax liability. The additional cash flows from tax gains should be
discounted at the cost of debt capital because they can be determined with very little uncertainty. The financial management of Gamble estimates that the acquisition will reduce taxes by $1 million per year in perpetuity. The relevant discount rate is 5 percent,
and the present value of the tax reduction is $20 million.
2. Operating Efficiencies. The financial management of Gamble has determined that
Gamble can take advantage of some of the unused production capacity of Shapiro. At
times Gamble has been operating at full capacity with a large backlog of orders.
Shapiro’s manufacturing facilities, with a little reconfiguration, can be used to produce
Gamble’s soaps. Thus, more soaps and cold remedies can be produced without adding to
the combined firm’s capacity and cost. These operating efficiencies will increase aftertax cash flows by $1.5 million per year. Using Shapiro’s discount rate and assuming perpetual gains, the PV of the unused capacity is determined to be $10 million.
3. Strategic Fit. The financial management of Gamble has determined that the acquisition
of Shapiro will give Gamble a strategic advantage. The management of Gamble believes that the addition of the Shapiro Bac-Rub ointment for sore backs to its existing
product mix will give it a better chance to launch successful new skin care cosmetics if
these markets develop in the future. Management of Gamble estimates that there is a
50-percent probability that $6 million in after-tax cash flow can be generated with the
new skin care products. These opportunities are contingent on factors that cannot be
easily quantified. Because of the lack of precision here, the managers decided to use a
high discount rate. Gamble chooses a 20-percent rate, and it estimates that the present
value of the strategic factors is $15 million (0.50 $6 million兾0.20).
Avoiding Mistakes
The Gamble-Shapiro illustration is very simple and straightforward. It is deceptive because
the incremental cash flows have already been determined. In practice an analyst must estimate these cash flows and determine the proper discount rate. Valuing the benefits of a
226
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
In Their Own Words
Michael C. Jensen on Mergers and Acquisitions
Economic analysis and evidence indicate that takeovers,
LBOs, and corporate restructurings are playing an important role in helping the economy adjust to major competitive changes in the last two decades. The competition
among alternative management teams and organizational
structures for control of corporate assets has enabled vast
economic resources to move more quickly to their highestvalued use. In the process, substantial benefits for the
economy as a whole as well as for shareholders have
been created. Overall gains to selling-firm shareholders
from mergers, acquisitions, leveraged buyouts, and other
corporate restructurings in the 12-year period 1977–1988
total over $500 billion in 1988 dollars. I estimate gains to
buying-firm shareholders to be at least $50 billion for the
same period. These gains equal 53 percent of the total
cash dividends (valued in 1988 dollars) paid to investors
by the entire corporate sector in the same period.
Mergers and acquisitions are a response to new technologies or market conditions which require a strategic
change in a company’s direction or use of resources.
Compared to current management, a new owner is often
better able to accomplish major change in the existing
organizational structure. Alternatively, leveraged buyouts
bring about organizational change by creating entrepreneurial incentives for management and by eliminating the
centralized bureaucratic obstacles to maneuverability that
are inherent in large public corporations.
When managers have a substantial ownership interest
in the organization, the conflicts of interest between
shareholders and managers over the payout of the company’s free cash flow are reduced. Management’s incentives are focused on maximizing the value of the enterprise, rather than building empires—often through poorly
conceived diversification acquisitions—without regard
to shareholder value. Finally, the required repayment of
debt replaces management’s discretion in paying dividends and the tendency to overretain cash. Substantial
increases in efficiency are thereby created.
Michael C. Jensen is Edsel Bryant Ford Professor of Business Administration at Harvard University. An outstanding scholar and researcher, he is famous for
his path-breaking analysis of the modern corporation and its relations with its stockholders.
potential acquisition is harder than valuing benefits for standard capital-budgeting projects.
Many mistakes can be made. The following are some of the general rules:
1. Do Not Ignore Market Values. In many cases it is very difficult to estimate values using
discounted cash flows. Because of this, an expert at valuation should know the market
prices of comparable opportunities. In an efficient market, prices should reflect value.
Because the market value of Shapiro is $30 million, we use this to estimate Shapiro’s
existing value.
2. Estimate Only Incremental Cash Flows. Only incremental cash flows from an acquisition will add value to the acquiring firm. Thus, it is important to estimate the cash flows
that are incremental to the acquisition.
3. Use the Correct Discount Rate. The discount rate should be the required rate of return
for the incremental cash flows associated with the acquisition.11 It should reflect the risk
associated with the use of funds, not their source. It would be a mistake for Gamble to
use its own cost of capital to value the cash flows from Shapiro.
4. If Gamble and Shapiro Combine, There Will Be Transactions Costs. These will include
fees to investment bankers, legal fees, and disclosure requirements.
29.7 A Cost to Stockholders from Reduction in Risk
The previous section discussed gains to the firm from a merger. In a firm with debt, these
gains are likely to be shared by both bondholders and stockholders. We now consider a benefit to the bondholders from a merger, which occurs at the expense of the stockholders.
11
808
Recall that the required rate of return is sometimes referred to as the cost of capital, or the opportunity cost of capital.
Corporate Finance,
Seventh Edition
227
Companies, 2004
29. Mergers and
Acquisitions
809
TABLE 29.5
NPV
Stock-Swap Mergers
Base case: two all-equity firms before merger
Firm A
Firm B
Probability
After merger*
Firm AB
Firm A, equity and risky debt before merger
Firm B, all-equity before merger
Firm A
Debt
Equity
Firm B
After merger†
Firm AB
Debt
Equity
State 1
State 2
State 3
Market Value
$ 80
$ 50
0.5
$50
$40
0.3
$25
$15
0.2
$ 60
$ 40
$130
$90
$40
$100
$
$
$
$
80
40
40
50
$50
$40
$10
$40
$25
$25
$ 0
$15
$
$
$
$
$130
$ 40
$ 90
$90
$40
$50
$40
$40
$ 0
$100
$ 40
$ 60
60
37
23
40
Value of debt rises after merger.Value of original stock in acquiring firm falls correspondingly.
*Stockholders in B receive stock value of $40.Therefore, stockholders of A have a value of $100 $40 $60 and are
indifferent to merger.
†
Because firm B’s stockholders receive stock in firm A worth $40, original stockholders in firm A have stock worth
$20 ($60 $40). Gains and losses from merger are
$20 $23 $3:Therefore, stockholders of A lose $3.
$40 $37 $3:Therefore, bondholders of A gain $3.
When two firms merge, the variability of their combined values is usually less than
would be true if the firms remained separate entities. A reduction of the variability of firm
values can occur if the values of the two firms are less than perfectly correlated. The reduction in variability can reduce the cost of borrowing and make the creditors better off
than before. This will occur if the probability of financial distress is reduced by the merger.
Unfortunately, the shareholders are likely to be worse off. The gains to creditors are at
the expense of the shareholders if the total value of the firm does not change. The relationship among the value of the merged firm, debt capacity, and risk is very complicated. We
now consider two examples.
The Base Case
Consider a base case where two all-equity firms merge. Table 29.5 gives the net present
values of firm A and firm B in three possible states of the economy—prosperity, average,
and depression. The market value of firm A is $60, and the market value of firm B is $40.
The market value of each firm is the weighted average of the values in each of the three
states. For example, the value of firm A is:
$60 $80 0.5 $50 0.3 $25 0.2
The values in each of the three states for firm A are $80, $50, and $25, respectively. The
probabilities of each of the three states occurring are 0.5, 0.3, and 0.2, respectively.
When firm A merges with firm B, the combined firm AB will have a market value of
$100. There is no synergy from this merger, and consequently the value of firm AB is the
sum of the values of firm A and firm B. Stockholders of B receive stock with a value of $40,
and therefore stockholders of A have a value of $100 $40 $60. Thus, stockholders of
A and B are indifferent to the proposed merger.
228
810
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
One Firm Has Debt
Alternatively, imagine firm A has some debt and some equity outstanding before the
merger.12 Firm B is an all-equity firm. Firm A will default on its debt in state 3 because the
net present value of firm A in this state is $25, and the value of the debt claim is $40. As a
consequence, the full value of the debt claim cannot be paid by firm A. The creditors take this
into account, and the value of the debt is $37 ($40 0.5 $40 0.3 $25 0.2).
Though default occurs without a merger, no default occurs with a merger. To see this,
notice that, when the two firms are separate, firm B does not guarantee firm A’s debt. That
is, if firm A defaults on its debt, firm B does not help the bondholders of firm A. However,
after the merger the bondholders can draw on the cash flows from both A and B. When one
of the divisions of the combined firm fails, creditors can be paid from the profits of the other
division. This mutual guarantee, which is called the coinsurance effect, makes the debt less
risky and more valuable than before.
The bonds are worth $40 after the merger. Thus, the bondholders of AB gain $3
($40 $37) from the merger.
The stockholders of firm A lose $3 ($20 $23) from the merger. That is, firm A’s stock is
worth $23 prior to the merger. The stock is worth $60 after the merger. However, stockholders in firm B receive $40 of stock in firm A. Hence, those individuals who were
stockholders in firm A prior to the merger have stock worth only $20 ($60 $40) after the
merger.
There is no net benefit to the firm as a whole. The bondholders gain the coinsurance
effect, and the stockholders lose the coinsurance effect. Some general conclusions emerge
from the preceding analysis.
1. Bondholders in the aggregate will usually be helped by mergers and acquisitions. The
size of the gain to bondholders depends on the reduction of bankruptcy states after the
combination. That is, the less risky the combined firm is, the greater are the gains to
bondholders.
2. Stockholders of the acquiring firm will be hurt by the amount that bondholders gain.
3. The conclusions apply to mergers and acquisitions where no synergy is present. In the
case of synergistic combinations, much depends on the size of the synergy.
How Can Shareholders Reduce Their Losses
from the Coinsurance Effect?
The coinsurance effect allows some mergers to increase bondholder values by reducing
shareholder values. However, there are at least two ways that shareholders can reduce or
eliminate the coinsurance effect. First, the shareholders in firm A could retire its debt before
the merger announcement date and reissue an equal amount of debt after the merger.
Because debt is retired at the low, pre-merger price, this type of refinancing transaction can
neutralize the coinsurance effect to the bondholders.
Also, note that the debt capacity of the combined firm is likely to increase because the
acquisition reduces the probability of financial distress. Thus, the shareholders’ second
alternative is simply to issue more debt after the merger. An increase in debt following the
merger will have two effects, even without the prior action of debt retirement. The interest
deduction from new corporate debt raises firm value. In addition, an increase in debt after
the merger raises the probability of financial distress, thereby reducing or eliminating the
bondholders’ gain from the coinsurance effect.
12
This example was provided by David Babbel.
Corporate Finance,
Seventh Edition
229
Companies, 2004
29. Mergers and
Acquisitions
811
29.8 Two “Bad” Reasons for Mergers
Earnings Growth
An acquisition can create the appearance of earnings growth, which may fool investors into
thinking that the firm is worth more than it really is. Suppose Global Resources, Ltd.,
acquires Regional Enterprises. The financial positions of Global and Regional before the
acquisition are shown in Table 29.6. Regional has had very poor earnings growth and sells
at a price-earnings ratio much lower than that of Global. The merger creates no additional
value. If the market is smart, it will realize that the combined firm is worth the sum of the
values of the separate firms. In this case, the market value of the combined firm will be
$3,500, which is equal to the sum of the values of the separate firms before the merger.
At these values, Global will acquire Regional by exchanging 40 of its shares for 100
Regional shares,13 so that Global will have 140 shares outstanding after the merger. Because
the stock price of Global after the merger is the same as before the merger, the priceearnings ratio must fall. This is true because the market is smart and recognizes that the
total market has not been altered by the merger. This scenario is represented by the third
column of Table 29.6.
Let us now consider the possibility that the market is fooled. One can see from Table 29.6
that the acquisition enables Global to increase its earnings per share from $1 to $1.43. If the
market is fooled, it might mistake the 43-percent increase in earnings per share for true
growth. In this case, the price-earnings ratio of Global may not fall after the merger. Suppose the price-earnings ratio of Global remains equal to 25. The total value of the combined
firm will increase to $5,000 (25 $200), and the stock price per share of Global will increase to $35.71 ($5,000兾140). This is reflected in the last column of Table 29.6.
This is earnings-growth magic. Like all good magic, it is an illusion and the shareholders
of Global and Regional will receive something for nothing. This may work for a while, but
in the long run the efficient market will work its wonders and the value will decline.
Diversification
Diversification often is mentioned as a benefit of one firm acquiring another. Earlier in this
chapter, we noted that U.S. Steel included diversification as a benefit in its acquisition of
Marathon Oil. In 1982 U.S. Steel was a cash-rich company (over 20 percent of its assets
TABLE 29.6
Financial Positions of
Global Resources,
Ltd., and Regional
Enterprises
Global
Resources
before Merger
Earnings per share
Price per share
Price-earnings ratio
Number of shares
Total earnings
Total value
Regional
Enterprises
before Merger
$
$
1.00
25.00
25
100
$ 100
$2,500
$
$
1.00
10.00
10
100
$ 100
$1,000
Global Resources
after Merger
The Market
Is “Smart”
$
$
1.43
25.00
17.5
140
$ 200
$3,500
The Market
Is “Fooled”
$
$
1.43
35.71
25
140
$ 200
$5,000
Exchange ratio: 1 share in Global for 2.5 shares in Regional.
13
This ratio implies a fair exchange because a share of Regional is selling for 40 percent ($10兾$25) of the price of a share of
Global.
230
Corporate Finance,
Seventh Edition
812
29. Mergers and
Acquisitions
Companies, 2004
were in the form of cash and marketable securities). It is not uncommon to see firms with
surplus cash articulating a need for diversification.
However, we argue that diversification, by itself, cannot produce increases in value. To
see this, recall that a business’s variability of return can be separated into two parts:
(1) what is specific to the business and called unsystematic, and (2) what is systematic
because it is common to all businesses.
Systematic variability cannot be eliminated by diversification, so mergers will not eliminate this risk at all. By contrast, unsystematic risk can be diversified away through mergers.
However, the investor does not need widely diversified companies such as General Electric
to eliminate unsystematic risk. Shareholders can diversify more easily than corporations by
simply purchasing common stock in different corporations. For example, the shareholders
of U.S. Steel could have purchased shares in Marathon if they believed there would be diversification gains in doing so. Thus, diversification through conglomerate merger may not
benefit shareholders.14
Diversification can produce gains to the acquiring firm only if two things are true:
1. Diversification decreases the unsystematic variability at lower costs than by investors
via adjustments to personal portfolios. This seems very unlikely.
2. Diversification reduces risk and thereby increases debt capacity. This possibility was
mentioned earlier in the chapter.
Concept
Question
1. Why can a merger create the appearance of earnings growth?
29.9 The NPV of a Merger
Firms typically use NPV analysis when making acquisitions.15 The analysis is relatively
straightforward when the consideration is cash. The analysis becomes more complex when
the consideration is stock.
Cash
Suppose firm A and firm B have values as separate entities of $500 and $100, respectively.
They are both all-equity firms. If firm A acquires firm B, the merged firm AB will have a
combined value of $700 due to synergies of $100. The board of firm B has indicated that it
will sell firm B if it is offered $150 in cash.
14
Evidence suggests that diversification can actually hurt shareholders. Randall Mork, Andrei Shleifer, and Robert W. Vishney
[“Do Managerial Objectives Drive Bad Acquisitions,” Journal of Finance 45 (1990), pp. 31–48] show that shareholders did
poorly in firms that diversified by acquisition in the 1980s. There is also evidence that diversified firms trade at a discount
relative to a portfolio of single-segment firms, most recently from Karl Lins and Henri Servaes, “The International Evidence on
the Value of Corporate Diversification,” Journal of Finance 54 (1999). On the other hand, Matsusaka and Hubbard and Palia
find some benefits to diversification in internal capital allocation. See John Matsusaka, “Takeover Motives During the
Conglomerate Merge Wave,” Rand Journal of Economics 24 (1993).
See also R. Glenn Hubbard and Darius Palia, “A Reexamination of the Conglomerate Merger Wave in the 1960s: An
Internal Capital Markets View,” Journal of Finance (June 1999).
One interesting recent study reports a positive relationship between focus and value for diversified firms. See P. G. Berger
and E. Ofek, “Diversification’s Effect on Firm Value,” Journal of Financial Economics, 37 (1995). Also see P. G. Berger and
E. Ofek, “Causes and Effects of Corporate Refocusing Program,” Review of Financial Studies 12 (1999).
15
The NPV framework for evaluating mergers can be found in S. C. Myers, “A Framework for Evaluating Mergers,” in Modern
Developments in Financial Management, ed. by S. C. Myers (New York: Praeger, 1976).
Corporate Finance,
Seventh Edition
Companies, 2004
29. Mergers and
Acquisitions
813
TABLE 29.7
Before
Acquisition
Cost of Acquisition:
Cash versus Common
Stock
Market value (VA, VB)
Number of shares
Price per share
231
After Acquisition: Firm A
(1)
(2)
(3)
Cash*
(4)
Common Stock†
Exchange Ratio
(0.75:1)
(5)
Common Stock†
Exchange Ratio
(0.6819:1)
Firm A
Firm B
$500
25
$ 20
$100
10
$ 10
$550
25
$ 22
$700
32.5
$ 21.54
$700
31.819
$ 22
*Value of firm A after acquisition: cash
VA VAB Cash
$550 $700 $150
†
Value of firm A after acquisition: common stock
VA VAB
$700 $700
Should firm A acquire firm B? Assuming that firm A finances the acquisition out of its
own retained earnings, its value after the acquisition is:16
Value of firm A after the acquisition Value of combined firm Cash paid
$700
$150
$550
Because firm A was worth $500 prior to the acquisition, the NPV to firm A’s stockholders
is:
$50 $550 $500
(29.1)
Assuming that there are 25 shares in firm A, each share of the firm is worth $20 ($500兾25)
prior to the merger and $22 ($550兾25) after the merger. These calculations are displayed in
the first and third columns of Table 29.7. Looking at the rise in stock price, we conclude
that firm A should make the acquisition.
We spoke earlier of both the synergy and the premium of a merger. We can also value
the NPV of a merger to the acquirer as:
NPV of a merger to acquirer Synergy Premium
Because the value of the combined firm is $700 and the premerger values of A and B
were $500 and $100, respectively, the synergy is $100 [$700 ($500 $100)]. The premium is $50 ($150 $100). Thus, the NPV of the merger to the acquirer is:
NPV of merger to firm A $100 $50 $50
One caveat is in order. This textbook has consistently argued that the market value of a firm
is the best estimate of its true value. However, we must adjust our analysis when discussing
mergers. If the true price of firm A without the merger is $500, the market value of firm A
may actually be above $500 when merger negotiations take place. This occurs because
the market price reflects the possibility that the merger will occur. For example, if the
16
The analysis will be essentially the same if new stock is issued. However, the analysis will differ if new debt is issued to fund
the acquisition because of the tax shield to debt. An adjusted present value (APV) approach would be necessary here.
232
814
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
probability is 60 percent that the merger will take place, the market price of firm A will be:
Market value
Probability
Market value
Probability
of firm A of
of firm A
of no
with merger
merger
without merger
merger
$530 $550
0.60
$500
0.40
The managers would underestimate the NPV from merger in equation (29.1) if the market
price of firm A is used. Thus, managers are faced with the difficult task of valuing their own
firm without the acquisition.
Common Stock
Of course, firm A could purchase firm B with common stock instead of cash. Unfortunately,
the analysis is not as straightforward here. In order to handle this scenario, we need to
know how many shares are outstanding in firm B. We assume that there are 10 shares outstanding, as indicated in column 2 of Table 29.7.
Suppose firm A exchanges 7.5 of its shares for the entire 10 shares of firm B. We call this
an exchange ratio of 0.75:1. The value of each share of firm A’s stock before the acquisition is $20. Because 7.5 $20 $150, this exchange appears to be the equivalent of purchasing firm B in cash for $150.
This is incorrect: The true cost is greater than $150. To see this, note that firm A has
32.5 (25 7.5) shares outstanding after the merger. Firm B shareholders own 23 percent
(7.5兾32.5) of the combined firm. Their holdings are valued at $161 (23% $700). Because
these stockholders receive stock in firm A worth $161, the cost of the merger to firm A’s
stockholders must be $161, not $150.
This result is shown in column 4 of Table 29.7. The value of each share of firm A’s stock
after a stock-for-stock transaction is only $21.54 ($700兾32.5). We found out earlier that the
value of each share is $22 after a cash-for-stock transaction. The difference is that the cost
of the stock-for-stock transaction to firm A is higher.
This nonintuitive result occurs because the exchange ratio of 7.5 shares of firm A for
10 shares of firm B was based on the premerger prices of the two firms. However, since
the stock of firm A rises after the merger, firm B stockholders receive more than $150 in
firm A stock.
What should the exchange ratio be so that firm B stockholders receive only $150 of firm
A’s stock? We begin by defining , the proportion of the shares in the combined firm that
firm B’s stockholders own. Because the combined firm’s value is $700, the value of firm B
stockholders after the merger is:
Value of Firm B Stockholders after Merger:
$700
Setting $700 $150, we find that 21.43%. In other words, firm B’s stockholders
will receive stock worth $150 if they receive 21.43 percent of the firm after merger.
Now we determine the number of shares issued to firm B’s shareholders. The proportion, , that firm B’s shareholders have in the combined firm can be expressed as:
New shares issued
New shares issued
Old shares New shares issued
25 New shares issued
Plugging our value of into the equation yields:
0.2143 New shares issued
25 New shares issued
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
233
815
Solving for the unknown, we have:
New shares 6.819 shares
Total shares outstanding after the merger are 31.819 (25 6.819). Because 6.819 shares of
firm A are exchanged for 10 shares of firm B, the exchange ratio is 0.6819:1.
Results at the exchange ratio of 0.6819:1 are displayed in column 5 of Table 29.7. Each
share of common stock is worth $22, exactly what it is worth in the stock-for-cash transaction. Thus, given that the board of firm B will sell its firm for $150, this is the fair exchange
ratio, not the ratio of 0.75:1 mentioned earlier.
Cash versus Common Stock
Whether to finance an acquisition by cash or by shares of stock is an important decision.
The choice depends on several factors, as follows:
1. Overvaluation. If in the opinion of management the acquiring firm’s stock is overvalued, using shares of stock can be less costly than using cash.
2. Taxes. Acquisition by cash usually results in a taxable transaction. Acquisition by exchanging stock is tax free.
3. Sharing Gains. If cash is used to finance an acquisition, the selling firm’s shareholders
receive a fixed price. In the event of a hugely successful merger, they will not participate
in any additional gains. Of course, if the acquisition is not a success, the losses will not
be shared and shareholders of the acquiring firm will be worse off than if stock were
used.
Concept
Question
1. In an efficient market with no tax effects, should an acquiring firm use cash or
stock?
29.10 Defensive Tactics
Target-firm managers frequently resist takeover attempts. Resistance usually starts with
press releases and mailings to shareholders that present management’s viewpoint. It can
eventually lead to legal action and solicitation of competing bids. Managerial action to defeat a takeover attempt may make target shareholders better off if it elicits a higher offer
premium from the bidding firm or another firm. Of course, management resistance may
simply reflect pursuit of self-interest at the expense of shareholders. That is, the target managers may resist a takeover in order to preserve their jobs. It is also possible that the targetfirm management will take corrective action to increase stock price in order to reduce the
takeover benefits. In this section we describe various defensive tactics that have been used
by target-firm managements to resist unfriendly takeover attempts.
Divestitures
Target-firm managers considering the prospect of a takeover may decide a narrowing of
strategic focus can increase stock price, thereby making a takeover too expensive. If so,
they will consider the pros and cons of three kinds of divestitures: a sale of assets, a spinoff, and the issuance of a tracking stock. The basic idea of all three types of divestitures is
to reduce the potential diversification discount associated with commingled operations
and to increase corporate focus. The sale of a business segment is usually for cash. With a
spin-off, the parent company distributes shares of a subsidiary to its shareholders. As a consequence, the shareholders end up with a stake in the parent as well as the subsidiary.
234
Corporate Finance,
Seventh Edition
816
29. Mergers and
Acquisitions
Companies, 2004
Typically, the stock in the subsidiary is distributed pro rata to the parent-company shareholders. No actual asset sale is involved, and the subsidiary becomes a completely separate
company (with its own board of directors, etc.). A variant of the spin-off is called an equity
curveout, where the stock of the subsidiary is sold to the public in an IPO. Sometimes a
spin-off and an equity curveout are combined. A tracking stock is a class of common stock
whose value is connected to the performance of a particular segment (division or subsidiary) of the parent company’s business. The intent of a tracking stock is quite similar to
an asset sale or spin-off, which is to give shareholders a pure play on a particular part of the
firm. The issue of tracking stock shares can be some form of combination between a pro
rata distribution and an IPO. The first tracker was when General Motors issued stock that
tracked Electronic Data Systems (EDS). Recently General Motors, AT&T, and Sprint PCS
have issued trackers. Tracking stock does not involve a separate, formal entity, as in the
case of a spin-off or equity curveout.17
The Corporate Charter
The corporate charter refers to the articles of incorporation and corporate bylaws that
govern the firm. The corporate charter establishes the conditions that allow a takeover.
Firms frequently amend corporate charters to make acquisitions more difficult. For example, usually two-thirds of the shareholders of record must approve a merger. Firms can make
it more difficult to be acquired by requiring 80-percent approval by the shareholders. This
is called a supermajority amendment. Another device is to stagger the election of the board
members, which increases the difficulty of electing a new board of directors quickly.
Repurchase Standstill Agreements
Managers may arrange a targeted repurchase to forestall a takeover attempt. In a targeted
repurchase, a firm buys back its own stock from a potential bidder, usually at a substantial
premium. These premiums can be thought of as payments to potential bidders to delay or
stop unfriendly takeover attempts. Critics of such payments label them greenmail.
In addition, managers of target firms may simultaneously negotiate standstill agreements. Standstill agreements are contracts where the bidding firm agrees to limit its holdings of another firm. These agreements usually lead to cessation of takeover attempts, and
announcement of such agreements has had a negative effect on stock prices.
EXAMPLE
On April 2, 1986,Ashland Oil, Inc., the nation’s largest independent oil refiner, had 28 million shares
outstanding. The company’s stock price closed the day before at $4934 per share on the New York
Stock Exchange. On April 2, Ashland’s board of directors made two decisions:
1. The board approved management’s agreement with the Belzberg family of Canada to buy, for
$51 a share, the Belzbergs’ 2.6 million shares in Ashland.This was part of a standstill agreement
that ended a takeover skirmish in which the Belzberg family offered $60 per share for all of the
common stock of Ashland.
17
There have been several studies of tracking stocks that seem to suggest returns of about three percent upon the announcement
of a tracking stock issue. For example: M. T. Billet and D. C. Mauer, “Diversification and the Value of Internal Capital Market,
The Case of Tracking Stock,” Journal of Banking and Finance (September 2000); J. D. Sousa J. and J. Jacob, “Why Firms Issue
Tracking Stock,” Journal of Financial Economics 56 (2000); D. E. Logue, J. K. Seward, and J. P. Walsh, “Rearranging Residual
Claim: A Case for Targeted Stock,” Financial Management 25 (1996).
On the other hand, Mathew T. Billet and Anand M. Vijh, “Long-Term Returns from Tracking Stocks,” University of Iowa,
unpublished paper, report negative long-term returns from tracking stocks.
Several recent articles report stock-price gains from asset sales spin-offs and equity curveouts that increase a firm’s focus.
See, for example: J. Desai and P. Jain, “Firm Performance and Focus: Long Run Stock Market Performance Following Spinoffs,” Journal of Financial Economics 54 (1999); K. John and E. Ofek, “Asset Sales and Increase in Focus,” Journal of
Financial Economics 37 (1999); and A. Vijh, “Long Term Returns from Equity Curveouts,” Journal of Financial Economics
51 (1999).
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
235
817
2. The board authorized the company to repurchase 7.5 million shares (27 percent of the outstanding shares) of its stock. The board simultaneously approved a proposal to establish an
employee stock-ownership plan to be funded with 5.3 million shares of Ashland stock.
The result of these two actions was to make Ashland invulnerable to unfriendly takeover attempts. In effect, the company was selling about 20 percent of its stock to the employee stockownership plan. Earlier Ashland had put in place a provision that said 80 percent of the stockholders have to approve a takeover.Ashland’s stock price fell by $0.25 over the next two days. Because
this move can probably be explained by random error, there is no evidence that Ashland’s actions
reduced shareholder value.
Exclusionary Self-Tenders
An exclusionary self-tender is the opposite of a targeted repurchase. Here, the firm makes
a tender offer for a given amount of its own stock while excluding targeted stockholders.
In one of the most celebrated cases in financial history, Unocal, a large integrated oil
firm, made a tender offer for 29 percent of its shares while excluding its largest shareholder,
Mesa Partners II (led by T. Boone Pickens). Unocal’s self-tender was for $72 per share,
which was $16 over the prevailing market price. It was designed to defeat Mesa’s
attempted takeover of Unocal by transferring wealth, in effect, from Mesa to Unocal’s other
stockholders.
Going Private and Leveraged Buyouts
Going private refers to what happens when the publicly owned stock in a firm is purchased
by a private group, usually composed of existing management. As a consequence, the
firm’s stock is taken off the market (if it is an exchange-traded stock, it is delisted) and is
no longer traded. Thus, in going-private transactions, shareholders of publicly held firms
are forced to accept cash for their shares.
Going-private transactions are frequently leveraged buyouts (LBOs). In a leveraged
buyout, the cash-offer price is financed with large amounts of debt. LBOs have recently
become quite popular because the arrangement calls for little equity capital. This equity
capital is generally supplied by a small group of investors, some of whom are likely to be
managers of the firm being purchased.
The selling stockholders are invariably paid a premium above market price in an LBO,
just as they are in a merger.18 As with a merger, the acquirer profits only if the synergy
created is greater than the premium. Synergy is quite plausible in a merger of two firms, and
we delineated a number of types of synergy earlier in the chapter. However, it is much more
difficult to explain synergy in an LBO, because only one firm is involved.
There are generally two reasons given for the ability of an LBO to create value. First,
the extra debt provides a tax deduction, which, as earlier chapters suggested, leads to an
increase in firm value. Most LBOs are on firms with stable earnings and with low to moderate debt. The LBO may simply increase the firm’s debt to its optimum level. In fact, Congress has recently taken a skeptical look at LBOs, partly because the increase in debt
reduces the U.S. Treasury’s tax revenues.
Second, the LBO usually turns the previous managers into owners, thereby increasing
their incentive to work hard. The increase in debt is a further incentive because the managers must earn more than the debt service to obtain any profit for themselves.
18
H. DeAngelo, L. DeAngelo, and E. M. Rice, “Going Private: Minority Freezeouts and Shareholder Wealth,” Journal of Law
and Economics 27 (1984). They show that the premiums paid to existing shareholders in LBOs and other going-private
transactions are about the same as in interfirm acquisitions.
236
Corporate Finance,
Seventh Edition
818
29. Mergers and
Acquisitions
Companies, 2004
Though it is easy to value the additional tax shields from an LBO, it is quite difficult to
value the gains from increased efficiency. Nevertheless, this increased efficiency is considered to be at least as important as the tax shield in explaining the LBO phenomenon.
Of course, one cannot be entirely sure that LBOs create value at all, because the stock
price cannot be observed once the company has been taken private. Though one frequently
hears of LBO investors achieving great wealth, this is only casual empirical evidence.
There may be an equal number of LBO investors who are left with little value after purchasing a company at a premium. The full story on LBOs has certainly not been told at this
point.
Other Devices and Jargon of Corporate Takeovers
As corporate takeovers have become more common, a new lexicon has developed. The
terms are colorful, and some are listed here:
1. Golden parachutes. Some target firms provide compensation to top-level management
if a takeover occurs. For example, when the Scoville board endorsed a $523 million tender offer by First City Properties, it arranged for 13 top executives to receive termination payments of about $5 million. This can be viewed as a payment to management to
make it less concerned for its own welfare and more interested in stockholders when
considering a takeover bid. Alternatively, the payment can be seen as an attempt to
enrich management at the stockholders’ expense.
2. Crown jewels. Firms often sell major assets—crown jewels—when faced with a
takeover threat. This is sometimes referred to as the scorched earth strategy.
3. Poison pill. Poison pill is a term taken from the world of espionage. Agents are supposed to bite a pill of cyanide rather than permit capture. Presumably this prevents
enemy interrogators from learning important secrets. In finance, poison pills are used to
make a stock repellent to others. A poison pill is generally a right to buy shares in the
merged firm at a bargain price. The right is granted to the target firm’s shareholders,
contingent on another firm acquiring control. The right dilutes the stock so much that the
bidding firm loses money on its shares. Thus, wealth is transferred from the bidder to the
target.
4. White knight. A firm facing an unfriendly merger offer might arrange to be acquired by
a different friendly suitor. The firm is thereby rescued by the white knight.
5. Lockup. A lockup is an option granted to a friendly suitor (perhaps a white knight) giving the right but not the obligation to purchase stock or a portion of the assets (perhaps
the crown jewels) of the target firm at a fixed price in the event of an unfriendly
takeover.
6. Shark repellent. A shark repellent is any tactic that makes the firm less attractive to a
potential unfriendly offerer.
7. Bear hug. A bear hug is an unfriendly takeover that is so attractive that the target firm’s
management has little choice but to accept it.
Concept
Question
1. What can a firm do to make a takeover less likely?
29.11 Some Evidence on Acquisitions
One of the most controversial issues surrounding our subject is whether mergers and acquisitions benefit shareholders.
Corporate Finance,
Seventh Edition
Companies, 2004
29. Mergers and
Acquisitions
819
TABLE 29.8
Takeover
Technique
Abnormal Stock-Price
Changes Associated
with Successful Corporate Takeover Bids
Tender offer
Merger
Proxy contest
237
Target
Bidders
30%
20%
8%
4%
0
n.a.
n.a. Not applicable.
Modified from Michael C. Jensen and Richard S. Ruback,“The Market for Corporate Control:The Scientific Evidence,” Journal
of Financial Economics 11 (April 1983), pp. 7, 8. © Elsevier Science Publishers B.V. (North-Holland).
TABLE 29.9
Takeover
Technique
Abnormal Stock-Price
Changes Associated
with Unsuccessful Corporate Takeover Bids
Tender offer
Merger
Proxy contest
Target
Bidders
3%
3%
8%
1%
5%
n.a.
n.a. Not applicable.
Modified from Michael C. Jensen and Richard S. Ruback,“The Market for Corporate Control:The Scientific Evidence,” Journal
of Financial Economics 11 (April 1983), pp. 7, 8. © Elsevier Science Publishers B.V. (North-Holland).
Do Acquisitions Benefit Shareholders?
Much research has attempted to estimate the effect of mergers and takeovers on stock
prices of the bidding and target firms. These studies are called event studies because they
estimate abnormal stock-price changes on and around the offer-announcement date—the
event. Abnormal returns are usually defined as the difference between actual stock returns
and a market index or a control group of stocks, to take account of the influence of marketwide effects on the returns of individual securities.
The Short Run
An overview of the short run evidence is reported in Jensen and Ruback. Tables 29.8 and
29.9 summarize the results of numerous studies that look at the effects of mergers and tender offers on stock prices from the announcement date to the completion date. Table 29.8
shows that the shareholders of target companies in successful takeovers achieve large abnormal returns. When the takeover is done by merger the gains are 20 percent, and when
the takeover is done by tender offer the gains are 30 percent.
The shareholders of bidding firms do not fare nearly as well. According to the studies
summarized in Table 29.8, bidders experience abnormal returns of 4 percent in tender offers, and in mergers the percentage is zero. These numbers are sufficiently small to leave
doubt about the effect on bidders. Table 29.9 shows that the shareholders of firms involved
in unsuccessful takeover attempts experience small negative returns in both mergers and
tender offers. What conclusions can be drawn from Tables 29.8 and 29.9?
1. The results of all event studies suggest that the shareholders of target firms achieve substantial short-term gains as a result of successful takeovers.19 The gains appear to be
larger in tender offers than in mergers. This may reflect the fact that takeovers sometimes start with a friendly merger proposal from the bidder to the management of the
target firm. If management rejects the offer, the bidding firm may take the offer directly
19
This has been a consistent finding in all merger studies. G. Mandelker, “Risk and Return: The Case of the Merging Firm,” Journal
of Financial Economics (1974), was one of the first to document the premiums to acquired firms.
238
820
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
Companies, 2004
to the shareholders with an unfriendly tender offer. The target management may actively
oppose the offer with defensive tactics. This often has the result of raising the tender
offer from the bidding firm, and, thus, on the average, friendly mergers are arranged at
a lower premium than unfriendly tender offers.
2. The shareholders of bidding firms earn comparatively little from takeovers. They earn
an average of only 4 percent from tender offers and do not appear to earn anything from
mergers. In fact, in an early study by Asquith the shareholders of acquiring firms in
successful mergers experienced significantly abnormal losses after the announcement of
the merger.20 These findings are a puzzle.
a. One possible explanation is that anticipated merger gains were not completely
achieved, and thus shareholders experienced losses. Managers of bidding firms may
have hubris and tend to overestimate the gains from acquisition.
b. The bidding firms are usually much larger than the target firms. Thus, the dollar gains
to the bidder may be approximately the same as the dollar gains to the shareholders
of the target firm at the same time that the percentage returns are much lower for the
bidding firms.
c. Management may not be acting in the interests of shareholders when it attempts to
acquire other firms. Perhaps it is attempting to increase the size of its firm, even if
this reduces its value.
3. The return to the shareholders of targets of unsuccessful merger, measured from the
offer date to the cancellation date, is negative. Thus, all the initial gains are lost over the
time period during which the merger failure becomes known. The overall average return
to shareholders of unsuccessful tender offers is about the same as for unsuccessful
merger attempts. However, the story is more complicated. Bradley, Desai, and Kim report that how well shareholders of target firms do in unsuccessful tender offers depends
on whether or not future takeover offers are forthcoming. They find that target-firm
shareholders realize additional positive gains when a new offer is made but lose everything previously gained if no other offer occurs.21
The Long Run
The evidence on long run stock returns following acquisition is provided by Loughran and
Vijh. Table 29.10 summarizes the results of their study of nearly 1,000 acquiring (bidding)
firms from 1970 to 1989. They compute the average abnormal return to shareholders from
the date of the acquisition over a subsequent five-year period. Table 29.10 shows that
shareholders of acquiring firms earn negative average abnormal returns. Previously we reported that shareholders of acquiring firms did not fare particularly well in the short run.
Now we see that five years after the date of the acquisition, shareholders of acquiring firms
continue to do poorly, earning an abnormal average return of 6.5 percent.
Table 29.10 also shows that the method of payment in acquisitions is important in the
distribution of long run returns. When the acquirer pays cash for the target, shareholders
gain an abnormal average return of 18.5 percent. However, when the acquirer pays with its
own stock, shareholders experience a negative abnormal average return of 24.2 percent.
Several conclusions can be drawn from Table 29.10.
1. In the long run, the shareholders of acquiring firms experience below average returns. If
significant, this finding raises questions about the efficient market hypothesis, since any
20
P. Asquith, “Merger Bids, Uncertainty and Stockholder Returns,” Journal of Financial Economics 11 (April 1983).
21
M. Bradley, A. Desai, and E. H. Kim, “The Rationale behind Interfirm Tender Offers: Information or Synergy,” Journal of
Financial Economics 11 (April 1983).
Corporate Finance,
Seventh Edition
29. Mergers and
Acquisitions
821
TABLE 29.10
Acquirers using unfriendly cash tender offers
Acquirers who pay cash (both friendly
and unfriendly)
All acquirers
Acquirers using stock
Abnormal Five-Year
Stock Returns of
Acquiring Firms from
1970 to 1989
239
Companies, 2004
61.7%
18.5%
6.5%
24.2%
SOURCE: T. Loughran and A.Vijh,“Do Long-Term Shareholders Benefit from Corporate Acquisitions,” Journal of Finance
(December, 1997),Table II.The abnormal returns are measured over a five-year period beginning at the date of the
acquisition. For example, the overall sample of 947 acquisitions experienced an average five-year return of 88.2 percent
compared to 94.7 percent for a sample of matching firms.The difference equals 6.5 percent (see above).
negative information implicit in an acquisition should be reflected in stock returns by
the date of the acquisition.
2. Cash-financed mergers are different than stock-financed mergers. When an acquisition
is financed by stock, it is useful to think of the acquisition as a combination of two events:
an issue of stock and an acquisition. It is known from Loughran and Ritter (Chapter 18)
that the long-term abnormal returns following new equity issues are negative. The poor
long run performance of stock-financed mergers could be the result of new stock issues
that take place with these mergers.
3. Acquirers can also be divided into friendly and unfriendly cash acquirers. The shares of
unfriendly cash acquirers have significantly outperformed those of friendly cash acquirers. One possible interpretation of this is that unfriendly cash bidders are more likely to
replace poor management. If so, the removal of poor managers may contribute to the
above average long run performance.
Real Productivity
There are many potential synergies from mergers and acquisitions. Unfortunately, it is very
hard to precisely measure synergy. In the previous section, we focused on stock-market
gains or losses to the shareholders of the acquiring and acquired firms. In very general
terms, we found that target-firm shareholders experience stock-market gains and acquiringfirm shareholders experience stock-market losses. There appear to be net gains to stockholders. This would suggest that mergers can increase real productivity. In fact, several recent studies suggest that mergers can increase real productivity. Healey, Palepu, and
Ruback report that merged companies’ after-tax returns increased substantially after the
mergers. They trace this gain to an increase in selling activity (turnover). They find no
evidence that merged firms cut back on positive NPV capital expenditures.22
Concept
Question
1. What does the evidence say about the benefits of mergers and acquisitions?
29.12 The Japanese Keiretsu
In Japan it has been unusual for firms to grow by large-scale mergers and acquisitions.
However, in the late 1980s several Japanese firms acquired large U.S. firms.23 Most notably,
Sony acquired CBS Records in November 1987 and Columbia Pictures in September 1989.
22
P. Healey, K. Palepu, and R. Ruback, “Does Corporate Performance Improve After Mergers,” Journal of Financial Economics
31 (1997).
23
W. Carl Kester, Japanese Takeovers, the Global Contest for Corporate Control, Cambridge, Mass.: 1991 (Harvard Business
School Press). Chapter 5 describes the acquisition experience of several Japanese firms.
240
Corporate Finance,
Seventh Edition
822
Companies, 2004
29. Mergers and
Acquisitions
Sony’s acquisition of Columbia Pictures for $3.45 billion is the largest Japanese acquisition
of a U.S. firm. The second largest was Bridgestone Corporation’s acquisition of Firestone
Tire and Rubber for $2.6 billion in March 1988.
The most interesting Japanese business combinations involve reciprocal shareholding
and trading agreements. These networks are called keiretsu and involve a group of firms
affiliated around a large bank, industrial firm, or trading firm. The Mitsubishi and the Mitsui
keiretsu groups are shown in Figure 29.3.
FIGURE 29.3
Japanese Keiretsu
Financial Services
Computers, Electronics,
and Electrical Equipment
Cars
Trading and Retailing
Mitsubishi
Mitsui
Mitsubishi Bank
Mitsubishi Trust & Banking
Meiji Mutual Life
Tokio Marine & Fire
Mitsubishi Electric
Mitsui Taiyo Kobe Bank
Mitsui Trust & Banking
Mitsui Mutual Life
Taisho Marine & Fire
Toshiba
Mitsubishi Motors
Mitsubishi
Toyota Motor*
Mitsui
Mitsukoshi
Nippon Flour Mills
Mitsui Construction
Sanki Engineering
Japan Steel Works
Mitsui Mining & Smelting
Food and Beverage
Construction
Kirin Brewery
Mitsubishi Construction
Metals
Mitsubishi Steel Mfg.
Mitsubishi Materials
Mitsubishi Aluminum
Mitsubishi Cable Industries
Mitsubishi Estate
Real Estate
Oil and Coal
Rubber and Glass
Chemicals
Fibers and Textiles
Pulp and Paper
Mining and Forestry
Industrial Equipment
Cameras and Optics
Cement
Shipping and Transportation
Mitsubishi Oil
Asahi Glass
Mitsubishi Kasei
Mitsubishi Petrochemical
Mitsubishi Gas Chemical
Mitsubishi Plastics Industries
Mitsubishi Kasei Polytec
Mitsubishi Rayon
Mitsubishi Paper Mills
Mitsubishi Heavy Industries
Mitsubishi Kakoki
Nikon
Nippon Yusen
Mitsubishi Warehouse &
Transportation
This table describes the network of firms in the Mitsubishi and Mitsui keiretsu.
*Companies affiliated with more than one group.
SOURCE: Fortune (July 15, 1991), p. 81.
Mitsui Real Estate
Development
Mitsui Toatsu Chemicals
Mitsui Petrochemical
Industries
Tory Industries
Oji Paper
Mitsui Mining
Hokkaido Colliery &
Steamship
Mitsui Engineering &
Shipbuilding
Onoda Cement
Mitsui OSK Lines
Mitsui Warehouse
Corporate Finance,
Seventh Edition
Companies, 2004
29. Mergers and
Acquisitions
241
823
Participation in the Mitsubishi or Mitsui keiretsu implies significant reciprocal ownership of common stock. It is widely understood that firms within the keiretsu are not to sell
these cross-held shares.
Nobody knows for sure what the main benefit of the keiretsu is. However, one of the
most important features of the keiretsu is the relationship between the industrial firms and
the financial institutions. For example, Mitsubishi Motors may have an extensive relationship with Mitsubishi Trust and Banking, Meiji Mutual Life, and Tokio Marine and Fire.
This connection between industrial firms and financial institutions within the group may
benefit the group by reducing the costs of financial distress that come from getting creditors to agree to a restructuring if one of the keiretsu members gets into financial trouble.24
Reaching an agreement between Mitsubishi Bank and Mitsubishi Motors will be easier if
Mitsubishi Motors gets into trouble because both are in the Mitsubishi keiretsu.
1. Can you describe a keiretsu?
2. What is a benefit of a keiretsu?
1. One firm can acquire another in several different ways.The three legal forms of acquisition are
merger and consolidation, acquisition of stock, and acquisition of assets. Mergers and consolidations are the least costly to arrange from a legal standpoint, but they require a vote of approval by
the shareholders. Acquisition by stock does not require a shareholder vote and is usually done via
a tender offer. However, it is difficult to obtain 100-percent control with a tender offer. Acquisition
of assets is comparatively costly because it requires more difficult transfer of asset ownership.
2. Mergers and acquisitions require an understanding of complicated tax and accounting rules.
Mergers and acquisitions can be taxable or tax-free transactions. In a taxable transaction, each
selling shareholder must pay taxes on the stock’s capital appreciation. Should the acquiring firm
elect to write up the assets, additional tax implications arise. However, acquiring firms do not
generally elect to write up the assets for tax purposes.The selling stockholders do not pay taxes
at the time of a tax-free acquisition.
Accounting for mergers and acquisitions involves a choice of the purchase method or the
pooling-of-interests method. The choice between these two methods does not affect after-tax
cash flows of the combined firm. However, most financial managers prefer the pooling-ofinterests method, because net income of the combined firm under this method is higher than it
is under the purchase method.
3. The synergy from an acquisition is defined as the value of the combined firm (VAB) less the value
of the two firms as separate entities (VA and VB), or
Synergy VAB (VA VB)
The shareholders of the acquiring firm will gain if the synergy from the merger is greater than
the premium.
4. The possible benefits of an acquisition come from the following:
a. Revenue enhancement
b. Cost reduction
24
This is the argument of Takeo Hoshi, Anil K. Kashyup, and David Scharfstein, “The Role of Banks in Reducing Financial
Distress in Japan.” A paper in the Finance and Economic Discussion Series, No. 134, Federal Reserve Board, Washington, D. C.
(October 1990). See also, W. Carl Kester, “Japanese Corporate Governance and the Conservation of Value in Financial Distress,”
Journal of Applied Corporate Finance (Summer 1991).
Concept
Questions
242
Corporate Finance,
Seventh Edition
824
Companies, 2004
29. Mergers and
Acquisitions
c. Lower taxes
d. Lower cost of capital
In addition, the reduction in risk from a merger may actually help bondholders and hurt
stockholders.
5. Some of the most colorful language of finance stems from defensive tactics in acquisition battles.
Poison pills, golden parachutes, crown jewels, and greenmail are terms that describe various antitakeover tactics.These tactics are discussed in this chapter.
6. The empirical research on mergers and acquisitions is extensive. Its basic conclusions are that, on
average, the shareholders of acquired firms fare very well, while the shareholders of acquiring
firms do not gain much.
7. The keiretsu is a Japanese form of business network. It involves reciprocal shareholding and
agreements among member firms.
lockup, 818
merger, 797
poison pill, 818
purchase, 801
shark repellent, 818
tender offer, 797
white knight, 818
KEY TERMS
bear hug, 818
bidder, 798
consolidation, 797
crown jewels, 818
golden parachutes, 818
goodwill, 801
keiretsu, 822
SUGGESTED
READINGS
Several fun-to-read trade books on mergers and acquisitions have recently been published, including:
Wasserstein, Bruce. Big Deal: 2000 and Beyond.Warner Books, 2000. Pitaro, Regina M. Deals, Deals and
More Deals. Gabelli University Press, 1998.
QUESTIONS
& PROBLEMS
29.1
THE BASIC FORMS
OF ACQUISITIONS
The Lager Brewing Corporation has acquired the Philadelphia Pretzel Company in a vertical
merger. Lager Brewing has issued $300,000 in new long-term debt to pay for its purchase.
($300,000 is the purchase price.) Construct the balance sheet for the new corporation if the
merger is treated as a purchase for accounting purposes. The balance sheets shown here
represent the assets of both firms at their true market values. Assume these market values
are also the book values.
LAGER BREWING CORPORATION
Balance Sheet
(in $ thousands)
Current assets
Other assets
Net fixed assets
Total
$ 400
100
500
______
$1,000
______
______
Current liabilities
Long-term debt
Equity
Total
$ 200
100
700
______
$1,000
______
______
PHILADELPHIA PRETZEL COMPANY
Balance Sheet
(in $ thousands)
Current assets
Other assets
Net fixed assets
Total
29.2
$ 80
40
80
_____
$200
_____
_____
Current liabilities
Equity
Total
$ 80
120
_____
$200
_____
_____
Suppose the balance sheet for Philadelphia Pretzel in problem 29.1 shows the assets at their
book value and not their market value of $240,000. Construct the balance sheet for the new
corporation. Again, treat the transaction as a purchase.
243
Companies, 2004
29. Mergers and
Acquisitions
825
29.3
Keep the assumptions of 29.2. Construct the balance sheet for the new corporation. Use the
pooling-of-interests method to treat the transaction.
SOURCE OF
SYNERGY FROM
ACQUISITIONS
29.4
Indicate whether you think the following claims regarding takeovers are true or false. In each
case provide a brief explanation for your answer.
a. By merging competitors, takeovers have created monopolies that will raise product
prices, reduce production, and harm consumers.
b. Managers act in their own interests at times and, in reality, may not be answerable to
shareholders.Takeovers may reflect runaway management.
c. In an efficient market, takeovers would not occur because market price would reflect the
true value of corporations.Thus, bidding firms would not be justified in paying premiums
above market prices for target firms.
d. Traders and institutional investors, having extremely short time horizons, are influenced
by their perceptions of what other market traders will be thinking of stock prospects and
do not value takeovers based on fundamental factors.Thus, they will sell shares in target
firms despite the true value of the firms.
e. Mergers are a way of avoiding taxes because they allow the acquiring firm to write up the
value of the assets of the acquired firm.
f. Acquisitions analysis frequently focuses on the total value of the firms involved. An acquisition, however, will usually affect relative values of stocks and bonds, as well as their
total value.
CALCULATING
THE VALUE OF
THE FIRM AFTER
AN ACQUISITION
29.5
The following table shows the projected cash flows and their respective discount rates after
the acquisition of Small Fry Co. by Whale Co. Fill in the blanks and calculate the stock price
of the new firm if it has $100 million of debt and 5 million shares of stock outstanding.
Net Cash Flow per
Year (Perpetual)
(in $ millions)
Discount Rate (%)
Value
(in $ millions)
$ 8
20
5
2.5
2
0.5
33
16%
10
?
?
10
5
?
?
?
42.5
12.5
?
?
?
Small Fry Co.
Whale Co.
Benefits from acquisition
Revenue enhancement
Cost reduction
Tax shelters
Whale Co.
A COST TO
STOCKHOLDERS
FROM REDUCTION
IN RISK
29.6
The Chocolate Ice Cream Company and the Vanilla Ice Cream Company have agreed to
merge and form Fudge Swirl Consolidated. Both companies are exactly alike except that they
are located in different towns. The end-of-period value of each firm is determined by the
weather, as shown.
State
Probability
Value
Rainy
Warm
Hot
0.1
0.4
0.5
$100,000
200,000
400,000
The weather conditions in each town are independent of those in the other. Furthermore,
each company has an outstanding debt claim of $200,000. Assume that no premiums are paid
in the merger.
a. What is the distribution of joint values?
b. What is the distribution of end-of-period debt values and stock values after the merger?
c. Show that the value of the combined firm is the sum of the individual values.
Corporate Finance,
Seventh Edition
244
Corporate Finance,
Seventh Edition
826
Companies, 2004
29. Mergers and
Acquisitions
d. Show that the bondholders are better off and the stockholders are worse off in the
combined firm than they would have been if the firms remained separate.
29.7
Cholern Electric Company (CEC) is a public utility that provides electricity to the central
Colorado area. Recent events at its Mile-High Nuclear Station have been discouraging.
Several shareholders have expressed concern over last year’s financial statements.
Income Statement
Last Year
(in $ millions)
Revenue
Fuel
Other expenses
Interest
Net income
Balance Sheet
End of Year
(in $ millions)
$110
50
30
30
____
$ 0
Assets
Debt
Equity
$400
300
100
Recently, a wealthy group of individuals has offered to purchase one-half of CEC’s assets at
fair market price. Management recommends that this offer be accepted because,“We believe
our expertise in the energy industry can be better exploited by CEC if we sell our electricity generating and transmission assets and enter the telecommunications business. Although
telecommunications is a riskier business than providing electricity as a public utility, it is also
potentially very profitable.”
Should the management approve this transaction? Why or why not?
TWO “BAD”
REASONS FOR
MERGERS
29.8
Refer to the Global Resources example in section 29.8 of the text. Suppose that instead of
40 shares, Global exchanges 100 of its shares for the 100 shares of Regional.The new Global
Resources will now have 200 shares outstanding and earnings of $200. Assume the market
is smart.
a. Calculate Global’s value after the merger.
b. Calculate Global’s earnings per share.
c. Calculate Global’s price per share.
d. Redo your answers to (a), (b), and (c) if the market is fooled.
29.9
Coldran Aviation has voted in favor of being bought out by Arcadia Financial Corporation.
Information about each company is presented below.
Number of shares
Earnings
Arcadia Financial
Coldran Aviation
16
100,000
$225,000
10.8
50,000
$100,000
Stockholders in Coldran Aviation will receive six-tenths of a share of Arcadia for each share
they hold.
a. How will the earnings per share (EPS) for these stockholders be changed?
b. What will be the effect on the original Arcadia stockholders of changes in the EPS?
THE NPV OF
A MERGER
29.10 Fly-By-Night Couriers is analyzing the possible acquisition of Flash-in-the-Pan Restaurants.
Neither firm has debt.The forecasts of Fly-By-Night show that the purchase would increase
its annual after-tax cash flow by $600,000 indefinitely.The current market value of Flash-inthe-Pan is $20 million.The current market value of Fly-By-Night is $35 million.The appropriate discount rate for the incremental cash flows is 8 percent.
a. What is the synergy from the merger?
b. What is the value of Flash-in-the-Pan to Fly-By-Night?
Fly-By-Night is trying to decide whether it should offer 25 percent of its stock or $15 million in cash to Flash-in-the-Pan.
245
Companies, 2004
29. Mergers and
Acquisitions
827
c. What is the cost to Fly-By-Night of each alternative?
d. What is the NPV to Fly-By-Night of each alternative?
e. Which alternative should Fly-By-Night use?
29.11 Freeport Manufacturing is considering making an offer to purchase Portland Industries.The
treasurer of Freeport has collected the following information:
Number of shares
Earnings
Freeport
Portland
15
1,000,000
$1,000,000
12
250,000
$750,000
The treasurer also knows that securities analysts expect the earnings and dividends (currently $1.80 per share) of Portland to grow at a constant rate of 5 percent each year. Her
research indicates, however, that the acquisition would provide Portland with some
economies of scale that would improve this growth rate to 7 percent per year.
a. What is the value of Portland to Freeport?
b. If Freeport offers $40 in cash for each outstanding share of Portland, what would the
NPV of the acquisition be?
c. If instead Freeport were to offer 600,000 of its shares in exchange for the outstanding
stock of Portland, what would the NPV of the acquisition be?
d. Should the acquisition be attempted, and if so, should it be a cash or stock offer?
e. Freeport’s management thinks that 7-percent growth is too optimistic and that 6 percent
is more realistic. How does this change your previous answers?
29.12 Harrods PLC has a market value of £600 million and 30 million shares outstanding. Selfridge
Department Store has a market value of £200 million and 20 million shares outstanding.
Harrods is contemplating acquiring Selfridge Department Store. Harrods’ CFO concludes
that the combined firm with synergy will be worth £1 billion and Selfridge can be acquired
at a premium of £100 million.
a. If Harrods offers 15 million shares to exchange for the 20 million shares of Selfridge, what
will the after-acquisition stock price of Harrods be?
b. To make the value of a stock offer equivalent to a cash offer of £300 million, what would
be the proper exchange ratio of the two stocks?
29.13 Company A is contemplating acquiring company B. Company B’s projected revenues, cost,
and required investment appear in the table that follows.The table also shows sources for
financing company B’s investments if B is acquired by A.The table incorporates the following
information:
Company B will immediately increase its leverage with a $110 million loan, which would be followed by a $150 million dividend to company A. (This operation will increase the debt-to-equity
ratio of company B from 1兾3 to 1兾1.)
Company A will use $50 million of tax-loss carryforwards available from the firm’s other
operations.
The terminal, total value of company B is estimated to be $900 million in five years, and the
projected level of debt then is $300 million.
The risk-free rate and the expected rate of return on the market portfolio are 6 percent
and 14 percent, respectively. Company A analysts estimate the weighted average cost of capital for their company to be 10 percent.The borrowing rate for both companies is 8 percent.
The beta coefficient for the stock of company B (at its current capital structure) is estimated
to be 1.25.
The board of directors of company A is presented with an offer for $68.75 per share of
company B, or a total of $550 million for the 8 million shares outstanding.
Evaluate this proposal.The table that follows may help you.
Corporate Finance,
Seventh Edition
246
Corporate Finance,
Seventh Edition
828
Companies, 2004
29. Mergers and
Acquisitions
Projections for Company B
If Acquired by Company A
(in $ millions)
Year 1
Year 2
Year 3
Year 4
Year 5
Sales
Production costs
Depreciation
Other expenses
$800
562
75
80
____
$900
630
80
90
____
$1,000
700
82
100
_____
$1,125
790
83
113
_____
$1,250
875
83
125
_____
EBIT
Interest
83
19
____
64
32
____
100
22
____
78
39
____
118
24
_____
94
47
_____
139
25
_____
114
57
_____
167
27
_____
140
70
_____
32
39
47
57
70
20
15
____
35
25
25
____
50
25
18
_____
43
30
12
_____
42
30
_____7
37
35
____0
16
34
____
16
27
_____
15
27
_____
12
25
_____
$ 35
$ 50
EBT
Taxes
Net income
Investments:
Net working capital
Net fixed assets
Total
Sources of financing:
Net debt financing
Profit retention
Total
$
43
$
42
$
37
Cash Flows—Company A
Acquisition of B
Dividends from B
Tax-loss
carryforwards
Terminal value
Total
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
—
150
—
—
—
—
—
—
—
—
—
25
—
—
25
—
—
—
—
—
—
—
DEFENSIVE
TACTICS
29.14 List the defensive tactics commonly used by target-firm managers to resist unfriendly
takeover attempts.
MINICASE
U.S. Steel’s Acquisition of Marathon Oil
In the summer of 1981, Marathon Oil Company commissioned the First Boston Corporation to prepare an analysis of the underlying asset value of Marathon based solely on publicly available information. Before First Boston could complete the study, Mobil Corporation announced a tender offer for Marathon’s common equity, thus launching one of the
most eventful takeover stories in American corporate history.
On October 30, 1981, Mobil bid $85 per share for up to 40 million shares of Marathon’s
common equity. Before the announcement, Marathon stock traded for about $64 per share
on the New York Stock Exchange. Before trading on the new information commenced,
Marathon management rejected Mobil’s offer as grossly inadequate and began seeking
a white knight merger candidate. When trading began on Monday, November 2, 1981,
29. Mergers and
Acquisitions
Companies, 2004
247
829
Marathon’s shares shot up immediately to the $90-per-share range for a one-day abnormal
excess return of more than 30 percent. The market reacted to Mobil’s offer by bidding
Mobil’s common stock down to $2538 for a one-day abnormal return of 4.26 percent.
(November 2, 1981, was also the ex-dividend date for a $0.50 per share dividend declared
earlier. The share price, however, fell $58 .) These data suggest that the market viewed the
possible acquisition of Marathon by Mobil at $85 per share as a near-zero net-present-value
transaction for Mobil. The dramatic response of Marathon’s share price was very likely
caused by anticipation of more bidding. These traders were not to be disappointed.
On November 9, the management of U.S. Steel Corporation expressed an interest in acquiring Marathon. The possible takeover price was rumored to be $100 per share in cash
and notes. Presumably because the market actually valued this offer as less than Mobil’s
offer, Marathon’s common stock showed an abnormal return for the day of 2.91 percent.
The effect of the rumors on U.S. Steel’s share price was insignificant, so it may be concluded that the market felt that the transaction at this price would be a zero net-presentvalue transaction for U.S. Steel as well.
During subsequent negotiations, U.S. Steel raised its price and actually tendered $125
per share for up to 30 million shares of Marathon stock on November 18. On the next trading day Marathon showed a one-day abnormal excess return on its share price of almost
35 percent; again the market roared its approval for the reevaluation of Marathon. U.S.
Steel’s common, however, showed significantly negative abnormal returns in response to
this news. This indicates that the market believed U.S. Steel overbid for Marathon. Mobil’s
share price showed no significant abnormal return on November 18 and 19.
However, on November 25, Mobil raised its bid to $126 per share, and the market responded by lowering the value of both Mobil and U.S. Steel by significant amounts. Apparently the market believed that at this price the merger was unattractive for both Mobil
and U.S. Steel. Marathon’s stock fell in price by a significant amount in response to Mobil’s
offer, perhaps because Mobil’s offer and U.S. Steel’s offer were valued nearly equally by
the market, and this signaled the end of the bidding and the end of speculating in Marathon.
Suppose that a U.S. Steel tender offer is structured in the following way. U.S. Steel will
pay $125 (in cash) for 30 million shares of Marathon giving it 50.1 percent of the Marathon
shares. After gaining voting control, U.S. Steel intends to merge with Marathon and will
pay the remaining shareholders with seven-year notes worth about $85 per share. Further,
suppose you own 10 shares of Marathon stock. Should you tender your shares?
Corporate Finance,
Seventh Edition
Corporate Finance,
Seventh Edition
31. International Corporate
Finance
Companies, 2004
Chapter 31
International Corporate Finance
EXECUTIVE SUMMARY
248
Corporations that have significant foreign
operations are often referred to as international corporations or multinationals. Table 31.1
lists the largest international corporations
using several different measures. There are
many familiar names on this list. International
corporations must consider many financial
factors that do not directly affect purely domestic firms. These include foreign exchange
rates, different interest rates from country
to country, complex accounting methods for
foreign operations, foreign tax rates, and foreign government intervention.
The basic principles of corporate finance
still apply to international corporations; like
domestic companies, they seek to invest
in projects that create more value for the
shareholders than they cost and to arrange
financing that raises cash at the lowest possible cost. That is, the net present value
principle holds for both foreign and domestic operations. However, it is usually more
complicated to apply the NPV principle to
foreign operations.
Perhaps the most important complication
of international finance is foreign exchange.
The foreign exchange markets provide information and opportunities for an international
corporation when it undertakes capitalbudgeting and financing decisions. The relationship among foreign exchange, interest
rates, and inflation is defined by the basic theories of exchange rates: purchasing-power
parity, interest-rate parity, and the expectations theory.
Typically, international financing decisions
involve a choice of three basic approaches:
1. Export domestic cash to the foreign
operations.
2. Borrow in the country where the
investment is located.
3. Borrow in a third country.
We discuss the merits of each approach.
31.1 Terminology
A common buzzword for the student of finance is globalization. The first step in learning
about the globalization of financial markets is to conquer the new vocabulary. Here are
some of the most common terms used in international finance and in this chapter:
1. An American Depository Receipt (ADR) is a security issued in the United States to
represent shares of a foreign stock, allowing that stock to be traded in the United States.
Foreign companies use ADRs, which are issued in U.S. dollars, to expand the pool of
potential U.S. investors.ADRs are available in two forms for about 690 foreign companies:
company-sponsored, which are listed on an exchange, and unsponsored, which are usually
held by the investment bank that makes a market in the ADR. Both forms are available to
individual investors, but only company-sponsored issues are quoted daily in newspapers.
847
Corporate Finance,
Seventh Edition
848
TABLE 31.1
The Top
International
Corporations
Companies, 2004
Finance
Company
Industry
Royal Dutch/Shell
Ford
General Electric
Exxon
General Motors
Volkswagen
IBM
Toyota
Nestlé
Bayer
ABB
Nissan
Elf Aquitaine
Mobil
Daimler-Benz
Energy
Automotive
Electronics
Energy
Automotive
Automotive
Computers
Automotive
Food
Chemicals
Electrical equipment
Automotive
Energy
Energy
Automotive
Foreign
Assets as
% of Total
Foreign
Sales as
% of Total
Foreign
Employment
as % of Total
67.8
29.0
30.4
73.1
24.9
84.8
51.9
30.5
86.9
89.8
84.7
42.7
54.5
61.8
39.2
73.3
30.6
24.4
79.6
29.2
60.8
62.7
45.1
98.2
63.3
87.2
44.2
65.4
65.9
63.2
77.9
29.8
32.4
53.7
33.9
44.4
50.1
23.0
97.0
54.6
93.9
43.5
47.5
52.2
22.2
SOURCE: The Economist, November 22, 1997, p. 92.
2. The cross rate is the exchange rate between two foreign currencies, generally neither of
which is the U.S. dollar. The dollar, however, is used as an interim step in determining
the cross rate. For example, if an investor wants to sell Japanese yen and buy Swiss
francs, he would sell yen against dollars and then buy francs with those dollars. So, although the transaction is designed to be yen for francs, the dollar’s exchange rate serves
as a benchmark.
3. A European Currency Unit (ECU) is a basket of 10 European currencies devised in
1979 and intended to serve as a monetary unit for the European Monetary System
(EMS). By charter, EMS members reevaluate the composition of the ECU every five
years or when there has been a shift of 25 percent or more in the weight of any currency.
The German deutschemark is the most heavily weighted currency in the basket, with the
French franc, the British pound, and the Dutch guilder each comprising more than 10 percent of the currency. The smallest weights are the Greek drachma, the Luxembourg franc,
and the Irish punt.
4. Eurobonds are bonds denominated in a particular currency and issued simultaneously
in the bond markets of several European countries. For many international companies
and governments, they have become an important way to raise capital. Eurobonds are
issued outside the restrictions that apply to domestic offerings and are typically syndicated in London. Trading can and does take place anywhere a buyer and a seller are.
5. Eurocurrency is money deposited in a financial center outside of the country whose
currency is involved. For instance, Eurodollars—the most widely used Eurocurrency—
are U.S. dollars deposited in banks outside the United States.
6. Foreign bonds, unlike Eurobonds, are issued by foreign borrowers in another nation’s
capital market and traditionally denominated in that nation’s currency. Yankee bonds,
for example, are issued in the United States by a foreign country, bank, or company; in
recent years, however, some Yankee offerings have been denominated in currencies
other than the U.S. dollar. Often the country in which these bonds are issued will draw
distinctions between them and bonds issued by domestic issuers, including different tax
laws, restrictions on the amount of issues, or tougher disclosure rules.
249
250
Corporate Finance,
Seventh Edition
Finance
Companies, 2004
Chapter 31 International Corporate Finance
849
Foreign bonds often are nicknamed for the country of issuance: Yankee bonds (United
States), Samurai bonds (Japan), Rembrandt bonds (the Netherlands), and Bulldog bonds
(Britain). Partly because of tougher regulations and disclosure requirements, the foreignbond market hasn’t grown in the past several years with the vigor of the Eurobond
market. Nearly half of all foreign bonds are issued in Switzerland.
7. Gilts, technically, are British and Irish government securities, although the term also includes issues of local British authorities and some overseas public-sector offerings.
8. The London Interbank Offered Rate (LIBOR) is the rate that most international
banks charge one another for loans of Eurodollars overnight in the London market.
LIBOR is a cornerstone in the pricing of money-market issues and other short-term
debt issues by both governments and corporate borrowers. Less creditworthy issuers
will often borrow at a rate of more than one point over LIBOR.
9. There are two basic kinds of swaps: interest rate and currency. An interest-rate swap
occurs when two parties exchange debt with a floating-rate payment for debt with a fixedrate payment, or vice versa. Currency swaps are agreements to deliver one currency
against another currency. Often both types of swaps are used in the same transaction
when debt denominated in different currencies is swapped.
Concept
Question
1. What is the difference between a Eurobond and a foreign bond?
31.2 Foreign Exchange Markets and Exchange Rates
The foreign exchange market is undoubtedly the world’s largest financial market. It is the
market where one country’s currency is traded for another’s. Most of the trading takes
place in a few currencies: the U.S. dollar ($), German deutschemark (DM), British pound
sterling (£), Japanese yen (¥), Swiss franc (SF), and French franc (FF).
The foreign exchange market is an over-the-counter market. There is no single location
where traders get together. Instead, traders are located in the major commercial and investment banks around the world. They communicate using computer terminals, telephones,
and other telecommunication devices. One element in the communications network for foreign transactions is the Society for Worldwide Interbank Financial Telecommunications
(SWIFT). It is a Belgian not-for-profit cooperative. A bank in New York can send messages
to a bank in London via SWIFT’s regional processing centers. The connections are through
data-transmission lines.
The many different types of participants in the foreign exchange market include the
following:
1. Importers who convert their domestic currency to foreign currency to pay for goods
from foreign countries.
2. Exporters who receive foreign currency and may want to convert to the domestic currency.
3. Portfolio managers who buy and sell foreign stocks and bonds.
4. Foreign exchange brokers who match buy and sell orders.
5. Traders who make the market in foreign exchange.
Exchange Rates
An exchange rate is the price of one country’s currency for another’s. In practice, almost
all trading of currencies takes place in terms of the U.S. dollar. For example, both the
Corporate Finance,
Seventh Edition
850
Finance
Companies, 2004
German deutschemark and the British pound will be traded with their price quoted in
U.S. dollars. If the quoted price is the price in dollars of a unit of foreign exchange, the quotation is said to be in direct (or American) terms. For example, $1.50 £1 and $0.40 DM1
are in direct terms. The financial press frequently quotes the foreign currency price of a
U.S. dollar. If the quoted price is the foreign currency price of a U.S. dollar, the quotation
is indirect (or European). For example, £0.67 $1 and DM2.5 $1.
EXAMPLE
FIGURE 31.1
In 1984, Japan’s economic growth and low inflation began to increase the demand for the yen compared to the dollar. Large U.S. trade deficits in the 1980s and 1990s contributed to this tendency.
Figure 31.1 plots the Japanese yen value of a U.S. dollar from 1980 to 2000. The strong U.S. economy in the mid-1990s caused a dollar rebound.
Japanese Yen Price of a U.S. Dollar from 1980 to 2000
300
250
200
150
100
50
0
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Year
SOURCE: Various issues of the Los Angeles Times and The Wall Street Journal.
There are two reasons for quoting all foreign currencies in terms of the U.S. dollar. First,
it reduces the number of possible cross-currency quotes. For example, with five major
currencies, there would potentially be 10 exchange rates. Second, it makes triangular
arbitrage more difficult. If all currencies were traded against each other, it would make
inconsistencies more likely. That is, the exchange rate of the Malaysian ringgit against the
United Kingdom pound would be compared to the exchange rate between the U.S. dollar and
the United Kingdom pound. This implies a particular rate between the Malaysian ringgit and
the U.S. dollar to prevent triangular arbitrage.
251
252
Corporate Finance,
Seventh Edition
Companies, 2004
Finance
851
EXAMPLE
What if the pound traded for 4 ringgit in Malaysia and $1.60 in London? If the dollar traded for 2 ringgit in Malaysia, the trader would have a triangular opportunity. Starting with $1.60, a trader could
purchase £1 in London.This pound could then be used to buy 4 ringgit in Malaysia.With the dollar trading at 2 ringgit, the 4 ringgit could then be traded for $2 in Malaysia as illustrated in Figure 31.2.The net
gain from going around this“triangle” would be $2.00 $1.60 $0.40.Imagine what the return would
be on an initial $1 billion purchase. (Watch out for currency controls in implementing this trade.)
FIGURE 31.2
$1.60 / £
Triangular Arbitrage
2 ringgit / $
4 ringgit / £
Types of Transactions
Three types of trades take place in the foreign exchange market: spot, forward, and swap.
Spot trades involve an agreement on the exchange rate today for settlement in two days.
The rate is called the spot-exchange rate. Forward trades involve an agreement on
exchange rates today for settlement in the future. The rate is called the forward-exchange
rate. The maturities for forward trades are usually 1 to 52 weeks. A swap is the sale (purchase) of a foreign currency with a simultaneous agreement to repurchase (resell) it sometime in the future. The difference between the sale price and the repurchase price is called
the swap rate.
EXAMPLE
On October 11, bank A pays dollars to bank B’s account at a New York bank and A receives pounds
sterling in its account at a bank in London. On November 11, as agreed to on October 11, the transaction is reversed. A pays the sterling back to B, while B pays back the dollars to A. This is a swap.
In effect, A has borrowed pounds sterling while giving up the use of dollars to B.
31.3 The Law of One Price and Purchasing-Power Parity
What determines the level of the spot-exchange rate? One answer is the law of one price
(LOP). The law of one price says that a commodity will cost the same regardless of the
country in which it is purchased. More formally, let S£(t) be the spot-exchange rate, that is,
the number of dollars needed to purchase a British pound at time t.1 Let PUS(t) and PUK(t)
be the current U.S. and British prices of a particular commodity, say, apples. The law of one
price says that:
PUS(t) S£(t) PUK(t)
for apples.
The rationale behind LOP is similar to that of triangular arbitrage. If LOP did not hold,
arbitrage would be possible by moving apples from one country to another. For example,
suppose that apples in New York are selling for $4 per bushel, while in London the price is
1
Throughout this chapter, we quote foreign exchange in direct or American terms.
Corporate Finance,
Seventh Edition
852
Companies, 2004
Finance
£2.50 per bushel. Then the law of one price implies that:
$4 S£(t) £2.50
and
S£(t) $1.60兾£
That is, the LOP implied spot-exchange rate is $1.60 per pound.
Suppose instead that the actual exchange rate is $2.00 per pound. Starting with $4, a
trader could buy a bushel of apples in New York, ship it to London, and sell it there for
£2.50. The pounds sterling could then be converted into dollars at the exchange rate, $2兾£,
yielding a total of $5 for $1 ($5 $4) gain.
The rationale of the LOP is that if the exchange rate is not $1.60兾£ but is instead, say,
$2兾£, then forces would be set in motion to change the rate and/or the price of apples. In
our example, there would be a whole lot of apples flying from New York to London. Thus,
demand for apples in New York would raise the dollar price for apples there, and the supply in London would lower the pound-sterling price. The apple traders converting pounds
sterling into dollars, that is, supplying pounds sterling and demanding dollars, would also
put pressure on the exchange rate to fall from $2兾£.
As you can see, for the LOP to be strictly true, three assumptions are needed:
1. The transactions cost of trading apples—shipping, insurance, wastage, and so on—must
be zero.
2. No barriers to trading apples, such as tariffs or taxes, can exist.
3. Finally, an apple in New York must be identical to an apple in London. It won’t do for
you to send red apples to London if the English eat only green apples.
Given the fact that the transaction costs are not zero and that the other conditions are
rarely exactly met, the LOP is really applicable only to traded goods, and then only to very
uniform ones. The LOP does not imply that a Mercedes costs the same as a Ford or that a
nuclear power plant in France costs the same as one in New York. In the case of the cars,
they are not identical. In the case of the power plants, even if they were identical, they are
expensive and very difficult to ship.
Because consumers purchase many goods, economists speak of purchasing-power
parity (PPP), the idea that the exchange rate adjusts so that a market basket of goods costs
the same, regardless of the country in which it is purchased. In addition, a relative version
of purchasing-power parity has evolved. Relative purchasing-power parity (RPPP) says
that the rate of change in the price level of commodities in one country relative to the rate
of change in the price level in another determines the rate of change of the exchange rate
between the two countries. Formally,
PUS (t 1)
PUS (t)
S £ (t 1)
S £ (t)
PUK (t 1)
PUK (t)
1 U.S.
1 Change in
1 British
inflation rate foreign exchange rate
inflation rate
This states that the rate of inflation in the United States relative to that in Great Britain
determines the rate of change in the value of the dollar relative to that of the pound during
the interval t to t 1. It is common to write US as the rate of inflation in the United States.
253
254
Corporate Finance,
Seventh Edition
Finance
Companies, 2004
853
1 US is equal to PUS(t 1)兾PUS(t). Similarly, UK is the rate of inflation in Great
Britain. 1 UK is equal to PUK(t 1)兾PUK(t).
Using to represent the rate of inflation, the preceding equation can be rearranged as:
1 US S £ (t 1)
1 UK
S £ (t)
(31.1)
We can rewrite this in an appropriate form as:
•
S£
US 艑 UK S£
•
where S£兾S£ now stands for the rate of change in the dollars-per-pound exchange rate.
As an example, suppose that inflation in France during the year is equal to 4 percent and
inflation in the United States is equal to 10 percent. Then, according to the RPPP, the price
of the French franc in terms of the U.S. dollar should rise; that is, the U.S. dollar declines
in value in terms of the French franc. Using our approximation, the dollars-per-franc exchange rate should rise by:
•
SFF
⬇ US F
SFF
10% 4%
6%
•
where SFF兾SFF stands for the rate of change in the dollars-per-franc exchange rate. That is,
if the French franc is worth $0.20 at the beginning of the period, it should be worth approximately $0.212 ($0.20 1.06) at the end of the period.
The RPPP says that the change in the ratio of domestic commodity prices of two countries must be matched in the exchange rate. This version of the law of one price suggests
that to estimate changes in the spot rate of exchange, it is necessary to estimate the difference in relative inflation rates. In other words, we can express our formula in expectational
terms as:
•
SFF
E
E(US ) E(F )
SFF
冢冣
If we expect the U.S. inflation rate to exceed the French inflation rate, we should expect the
dollar price of French francs to rise, which is the same as saying that the dollar is expected
to fall against the franc.
The more exact relationship of equation (31.1) can be expressed in expectational
terms as:
E(1 US ) E关S £ (t 1)兴
E(1 UK )
S £ (t)
Concept
Questions
(31.2)
1. What is the law of one price? What is purchasing-power parity?
2. What is the relationship between inflation and exchange-rate movements?
Corporate Finance,
Seventh Edition
854
Companies, 2004
Finance
31.4 Interest Rates and Exchange Rates: Interest-Rate Parity
The forward-exchange rate and the spot-exchange rate are tied together by the same sort
of arbitrage that underlies the law of one price. First, here is some useful terminology. If
forward-exchange rates are greater than the spot-exchange rate in a particular currency, the
forward foreign currency is said to be at a premium (this implies the domestic currency is
at a discount). If the values of forward-exchange rates are less than the spot-exchange rate,
the forward rate of foreign currency is at a discount.
Suppose we observe that the spot Switzerland franc rate is Switzerland franc 2.50 $1.00 and the one-month forward Switzerland franc is Switzerland franc 2.40 $1.00. Because fewer francs are needed to buy a dollar at the forward rate than are needed to buy a
dollar at the spot rate, the franc is more valuable in the forward market than in the spot market. This means that the one-month forward Switzerland franc is at a premium. Of course,
whatever we say for the franc must be the opposite of what we say for the dollar. In this example, the dollar is at a discount because the forward value is less than the spot value. Forward exchange is quoted in terms of the premium or discount that is to be added onto the
spot rate.
Whether forward rates are at a premium or a discount when compared to a domestic
currency depends on the relative interest rates in the foreign and domestic currency markets. The interest-rate–parity theorem implies that, if interest rates are higher domestically than in a particular foreign country, the foreign country’s currency will be selling at a
premium in the forward market; and if interest rates are lower domestically, the foreign
currency will be selling at a discount in the forward market.
We need some notation to develop the interest-rate–parity theorem. Let S(0) be the
current domestic-currency price of spot foreign exchange (current time is denoted by 0).
If the domestic currency is the dollar and the foreign exchange is the Switzerland franc
(SF), we might observe S(0) $0.40兾SF. S(0) is in direct or U.S. terms. Let F(0,1) be the
current domestic-currency price of forward exchange for a contract that matures in one
month. Thus, the contract is for forward exchange one month hence. Let i and i* be the
yearly rates of interest paid on Eurocurrency deposits denominated in the domestic (i) and
foreign (i*) currencies, respectively. Of course, the maturity of the deposits can be chosen
to coincide with the maturity of the forward contract. Now consider a trader who has access
to the interbank market in foreign exchange and Eurocurrency deposits. Suppose the trader
has some dollars to invest for one month. The trader can make a dollar loan or a franc loan.
The annual interest rate is 10 percent in francs and 6 percent in dollars. Which is better?
The Dollar Investment
Given an annual interest rate of 6 percent, the one-month rate of interest is 0.5 percent,
ignoring compounding. If the trader invests $1 million now, the trader will get $1 million 1.005 $1.005 million at the end of the month. Following is an illustration:
Time 0
Time 1
Lend 1 unit of dollars
$1,000,000
Obtain 1 i (1兾12) units of domestic currency
$1,000,000 (1 0.005) $1,005,000
The Switzerland Franc Investment
The current spot rate is $0.40兾SF. This means the trader can currently obtain $1 million兾
0.40 SF2.5 million. The rate of interest on one-year SF loans is 10 percent. For one
month, the interest rate is 0.10兾12 0.0083. Thus, at the end of one month the trader will
255
256
Corporate Finance,
Seventh Edition
Companies, 2004
Finance
855
obtain SF2.5 million 1.0083 SF2,520,750. Of course, if the trader wants dollars at the
end of the month, the trader must convert the francs back into dollars. The trader can fix the
exchange rate for one-month conversion. Suppose the one-month forward is $0.39869兾SF.
Then the trader can sell francs forward. This will ensure that the trader gets SF2,520,750 0.39869 $1.005 million at the end of the month. The general relationships are set forth
here:
Time 0
Time 1
Purchase 1 unit [1兾S(0)]
of foreign exchange
Deposit matures and pays
[1兾S(0)] [1 i (1兾12)]
units of foreign exchange
SF2,500,000 1.0083 SF2,520,750
SF2,500,000
Sell forward
[1兾S(0)] [1 i* (1兾12)]
units of forward exchange
at the forward rate F(0,1)
Deliver foreign exchange in fulfillment
of forward contract, receiving
[1兾S(0)] [1 i* (1兾12)] [F(0,1)]
SF2,500,000 1.0083 0.39869 $1,005,000
In our example, the investments earned exactly the same rate of return and 1 [i (1兾12)] [1兾S(0)] [1 i* (1兾12)] [F(0,1)]. In competitive financial markets, this
must be true for risk-free investments. When the trader makes the franc loan, he or she
gets a higher interest rate. But the return is the same because the franc must be sold
forward at a lower price than it can be exchanged for initially. If the domestic interest rate
were different from the covered foreign interest rate, the trader would have arbitrage
opportunities.
To summarize, to prevent arbitrage possibilities from existing, we must have equality of
the U.S. interest rate and covered foreign interest rates:
1i
1
(1 i*) F(0,1)
S(0)
or
1i
F(0,1)
1 i*
S(0)
(31.3)
The last equation is the famous interest-rate–parity theorem. It relates the forward-exchange
rate and the spot-exchange rate to interest-rate differentials. Notice that, if i i*, the spot
rate (expressed as dollars per unit of foreign currency) will be less than the forward rate.
EXAMPLE
Let the spot rate S(0) $0.40兾SF and the one-year forward rate F(0,1) $0.42兾SF. Let the oneyear rates on Eurodollar deposits and Euro-SF deposits be, respectively, i 11.3% and i* 6%.Then,
comparing the return on domestic borrowing with the return on covered foreign lending,
$(1 i) $(1 0.113) $1.113
$[1兾S(0)] (1 i*) F(0,1) $(1兾0.40) (1 0.06) $0.42 $1.113
For each dollar borrowed domestically, a trader must repay $1.113.The return from using the $1.00
to buy spot foreign exchange, placing the deposit at the foreign rate of interest, and selling the total
return forward would be $1.113.These two amounts are equal, so it would not be worth anyone’s
time to try to exploit the difference. In this case, interest parity can be said to hold.
Corporate Finance,
Seventh Edition
856
Finance
Companies, 2004
The Forward-Discount and Expected Spot Rates
A close connection exists between forward-exchange rates and expected spot rates. A
trader’s buy and sell decisions in today’s forward market are based on the trader’s market
expectation of the future spot rate. In fact, if traders were completely indifferent to risk, the
forward rate of exchange would depend solely on expectations about the future spot rate.
For example, suppose the one-year forward rate of Switzerland francs is $0.40兾SF [that is,
F(0,1) $0.40兾SF]. This must mean that traders expect the spot rate to be $0.40兾SF in one
year [E(S(1)) $0.40兾SF]. If they thought it would be higher, it would create an arbitrage
opportunity. Traders would buy francs forward at the low price and sell francs one year
later at the expected higher price. This implies that the forward rate of exchange is equal to
the expected spot, or (in general terms):
F(0,1) E[S(1)]
and
F(0,1) E[S(1)]
S(0)
S(0)
(31.4)
An equilibrium is achieved only when the forward discount (or premium) equals the
expected change in the spot-exchange rate.
Exchange-Rate Risk
Exchange-rate risk is the natural consequence of international operations in a world where
foreign currency values move up and down. International firms usually enter into some
contracts that require payments in different currencies. For example, suppose that the treasurer of an international firm knows that one month from today the firm must pay £2 million for goods it will receive in England. The current exchange rate is $1.50兾£, and if that
rate prevails in one month, the dollar cost of the goods to the firm will be $1.50兾£ £2 million $3 million. The treasurer in this case is obligated to pay pounds in one month. (Alternately, we say that he is short in pounds.) A net short or long position of this type can be
very risky. If the pound rises in the month to $2兾£, the treasurer must pay $2兾£ £2 million $4 million, an extra $1 million.
This is the essence of foreign exchange risk. The treasurer may want to hedge his position. When forward markets exist, the most convenient means of hedging is the purchase or
sale of forward contracts. In this example, the treasurer may want to consider buying 2 million pounds sterling one month forward. If the one-month forward rate quoted today is also
$1.50兾£, the treasurer will fulfill the contract by exchanging $3 million for £2 million in
one month. The £2 million he receives from the contract can then be used to pay for the
goods. By hedging today, he fixes the outflow one month from now to exactly $3 million.
Should the treasurer hedge or speculate? There are usually two reasons why the treasurer should hedge:
1. In an efficient foreign exchange-rate market, speculation is a zero NPV activity. Unless
the treasurer has special information, nothing will be gained from foreign exchange
speculation.
2. The costs of hedging are not large. The treasurer can use forward contracts to hedge, and
if the forward rate is equal to the expected spot, the costs of hedging are negligible. Of
course, there are ways to hedge foreign exchange risk other than to use forward contracts.
For example, the treasurer can borrow dollars and buy pounds sterling in the spot market
today and lend them for one month in London. By the interest-rate–parity theorem, this
will be the same as buying the pounds sterling forward.
257
258
Corporate Finance,
Seventh Edition
Finance
Companies, 2004
In Their Own Words
Richard M. Levich on Forward Exchange Rates
What is the relationship between today’s three-month forward exchange rate, which can be observed in the market,
and the spot exchange rate of three months from today,
which cannot be observed until the future? One popular
answer is that there is no relationship. As every bank
trader knows, the possibility of covered interest arbitrage
between domestic and foreign securities establishes a
close link between the forward premium and the interest
rate differential. At any moment, a trader can check his
screen and observe that the forward premium and the
interest rate differentials are nearly identical, especially
when Eurocurrency interest rates are used. Thus the trader
might say, “The forward rate reflects today’s interest differential. It has nothing to do with expectations.”
To check the second popular belief, that the forward rate
reflects exchange rate expectations, takes a bit more work.
Take today’s three-month forward rate as of January 15 and
compare it to the spot exchange rate that actually exists
three months later on April 15. This produces one observation on the forward rate as a forecaster—not enough to accept or reject a theory. The idea that the forward rate might
be an unbiased predictor of the future spot rate suggests
that, on average and looking at many observations, the prediction error is small. So collect more data using the
forward rate of April 15 and match it with the spot rate of
July 15, and then the forward rate of July 15 matched to
the spot rate of October 15, and so on. Look at the data for
8–10 years to have a large sample of observations.
The data suggest that in the early 1980s when the dollar
was very strong, the forward rate significantly underestimated the strength of the dollar, and the forward rate was a
biased predictor. But from 1985–1987 when the dollar
depreciated sharply, the forward rate tended to overestimate the strength of the dollar, and the forward rate was
again a biased predictor, but with the opposite sign as the
earlier period. Looking at all of the 1980s—you guessed
it—the forward rate was on average very close to the
future spot exchange rate.
There are two messages here. First, even if there were
“no relationship” between the forward rate and the future
spot rate, the treasurer of General Motors would want to
know exactly what that “nonrelationship” was. Because
if the forward rate were consistently 3 percent higher
than, or consistently 5 percent lower than, the future spot
rate, the treasurer would be facing a tantalizing profit
opportunity. A watch that is three minutes fast or five
minutes slow is a very useful watch, as long as the bias is
known and consistent.
Richard M. Levich is professor of finance and international business at New York University. He has written extensively on exchange rates and other issues in
international economics and finance.
Which Firms Hedge Exchange-Rate Risk?
Not all firms with exchange-rate risk exposure hedge. Géczy, Minton, and Schrand report
about 41 percent of Fortune 500 firms with foreign currency risk actually attempt to hedge
these risks.2 They find that larger firms with greater growth opportunities are more likely to
use currency derivatives to hedge exchange-rate risk than smaller firms with fewer investment opportunities. This suggests that some firms hedge to make sure that they have enough
cash on hand to finance their growth. In addition, firms with greater growth opportunities
will tend to have higher indirect bankruptcy costs. For these firms, hedging exchange-rate
risk will reduce these costs and increase the probability that they will not default on their
debt obligations.
The fact that larger firms are more likely to use hedging techniques suggests that the costs
of hedging are not insignificant. There may be fixed costs of establishing a hedging operation,
in which case, economies of scale may explain why smaller firms hedge less than larger firms.
Concept
Questions
1. What is the interest-rate–parity theorem?
2. Why is the forward rate related to the expected future spot rate?
3. How can one offset foreign exchange risk through a transaction in the forward
markets?
2
C. Géczy, B. Minton, and C. Schrand, “Why Firms Use Currency Derivatives,” Journal of Finance (September 1997). See also
D. R. Nance, C. Smith, Jr., and C. W. Smithson, “On the Determinants of Corporate Hedging,” Journal of Finance, 1993.
857
Corporate Finance,
Seventh Edition
858
Companies, 2004
Finance
31.5 International Capital Budgeting
Kihlstrom Equipment, a U.S.-based international company, is evaluating an investment in
China. Kihlstrom’s exports of drill bits have increased to such a degree that the company is
considering operating a plant in China. The project will cost 20 million yuan, and it is
expected to produce cash flows of 8 million yuan a year for the next three years. The current spot-exchange rate for Chinese yuan is S(0) $0.20兾yuan. How should Kihlstrom
calculate the net present value of the projects in U.S. dollars?
Nothing about the fact that the investment is made abroad alters Kihlstrom’s NPV criterion. Kihlstrom must identify incremental cash flows and discount them at the appropriate
cost of capital. After making the required discounted cash flow calculations, Kihlstrom
should undertake projects with a positive NPV. However, two major factors that complicate
such international NPV calculations are foreign exchange conversion and repatriation of
funds.
Foreign Exchange Conversion
The simplest way for Kihlstrom to calculate the NPV of the investment is to convert all
Chinese yuan cash flows to U.S. dollars. This involves a three-step process:
Step 1. Estimate future cash flows in Chinese yuan.
Step 2. Convert to U.S. dollars at the predicted exchange rate.
Step 3. Calculate NPV using the cost of capital in U.S. dollars.
In Table 31.2 we show the application of these three steps to Kihlstrom’s China investment.
Notice in Table 31.2 that Kihlstrom’s Chinese yuan cash flows were converted to dollars by
multiplying the foreign cash flows by the predicted foreign exchange rate.
How might Kihlstrom predict future exchange rates? Using the theory of efficient
markets, Kihlstrom could calculate NPV using the foreign exchange market’s implicit predictions. To figure these out, Kihlstrom can use the basic foreign exchange relationships
described in earlier sections of this chapter.
Kihlstrom begins by obtaining publicly available information on exchange rates and
interest rates. It finds:
Exchange rate:
Interest rate in United States:
Interest rate in China:
SFF(0) $0.15兾FF, i.e., 1 Chinese yuan can be
purchased for $0.15.
iUS 8%
iChina 12%
TABLE 31.2
Net Present Value of
Foreign Cash Flows:
Kihlstrom Equipment
End of Year
Incremental cash
flows (CFYuan)
(yuan millions)
Foreign exchange rate
($Ⲑyuan)
Foreign exchange-rate
conversion
Incremental cash
flows ($ millions)
NPV at 15% $0.43 million.
0
1
2
3
20
8
8
8
0.15
0.145
0.14
0.135
20 0.15
8 0.145
8 0.14
8 0.135
3
1.16
1.12
1.08
259
260
Corporate Finance,
Seventh Edition
Companies, 2004
Finance
859
Using equations (31.2), (31.3), and (31.4), Kihlstrom can calculate the following set of
relationships:
E(1 US )
E(1 China )
E(Syuan (1) )
Syuan (0)
— Relative purchasing- —
power parity
(31.2)
Fyuan (0,1)
Syuan (0)
1 iUS
1 iChina
(31.5)
— Forward rate — — Interest-rate —
related to
parity
expected spot rate
(31.4)
(31.3)
From the left, the first equality follows from relative purchasing-power parity. The expected
inflation rates in the two countries determine the expected movement in the spot rate,
expressed earlier in equation (31.2). The equality between the second and third terms is a consequence of our discussion on forward rates and expected spot rates, expressed earlier in
equation (31.4). The last equality is interest-rate parity and appeared earlier in equation (31.3).
We now compare the left-hand term to the right-hand term. We have:
1 iUS
E(1 US )
1 iChina E(1 China )
1.08
E(1 US )
1.12 E(1 China )
If the expected inflation rate in the United States is 8 percent, it follows that the expected
inflation rate in China is 12 percent:
1.08
1.08
1.12 E(1 China )
E(China ) 12%
Using relative purchasing-power parity, Kihlstrom can compute the expected spotexchange rate in one year:
E(1 US )
E[Syuan (1)]
E(1 China )
Syuan (0)
1.08 E[Syuan (1)]
1.12
0.15
which implies E[Syuan(1)] 0.145. The exchange rate expected at the end of year 2 is
obtained from:
1.08 2
0.15 0.14
1.12
冢冣
For year 3, the expected exchange rate is obtained from:
0.15 冢1.12冣 0.135
1.08
3
Finally, the NPV of the project is computed:
CFyuan (t) E[Syuan (t)]
(1 r * )t
t0
3
NPV 兺
Corporate Finance,
Seventh Edition
860
Finance
Companies, 2004
where CFyuan(t) refers to the Chinese yuan forecasted to be received in each of the next
three years. The discount rate we use is Kihlstrom’s U.S. cost of capital. We do not use the
U.S. risk-free rate of 8 percent because Kihlstrom’s project is risky; a risk-adjusted discount rate must be used. Because the NPV at 15 percent is $430,000, Kihlstrom should
not invest in a subsidiary in China.
In this example we used the foreign exchange market’s implicit forecast of future
exchange rates. Why not use management’s own forecast of foreign exchange rates in the
calculations? Suppose that the financial management of Kihlstrom feels optimistic about
the Chinese yuan. If its forecasts are sufficiently optimistic and they are used, Kihlstrom’s
investment in a Chinese subsidiary will generate a positive NPV. But, in general, it is a
good idea to separate the economic prospects of an investment and the foreign exchange
prospects, and it is unwise to use the latter projections in the NPV calculation. If Kihlstrom
wishes to speculate on an increase in the Chinese yuan relative to the U.S. dollar, the best
way to do this is to buy Chinese yuan in the forward foreign exchange market. (However,
some currencies are more difficult to trade this way than others.) By using the forwardexchange rates implicit in the domestic and foreign interest rates, the firm is using the
actual dollar flows that it could, in principle, lock in today by borrowing in the foreign
currency. This makes the foreign cash flows equivalent to domestic cash flows.
Unremitted Cash Flows
The previous example assumed that all after-tax cash flows from the foreign investment were
remitted to the parent firm. The remittance decision is similar to the dividend for a purely
domestic firm. Substantial differences can exist between the cash flows of a project and the
amount that is actually remitted to the parent firm. Of course, the net present value of a
project will not be changed by deferred remittance if the unremitted cash flows are reinvested
at a rate of return equal (as adjusted for exchange rates) to the domestic cost of capital.
A foreign subsidiary can remit funds to a parent in many ways, including the following:
1. Dividends.
2. Management fees for central services.
3. Royalties on the use of trade names and patents.
International firms must pay special attention to remittance for two reasons. First, there
may be present and future exchange controls. Many governments are sensitive to the charge
of being exploited by foreign firms. Therefore, governments are tempted to limit the ability
of international firms to remit cash flows. Another reason is taxes. It is always necessary to
determine what taxes must be paid on profits generated in a foreign country. International
firms must usually pay foreign taxes on their foreign profits. The total taxes paid by an international firm may be a function of the time of remittance. For example, Kihlstrom’s Chinese
subsidiary would need to pay taxes in China on the profits it earns in China. Kihlstrom will
also pay taxes on dividends it remits to the United States. In most cases Kihlstrom can offset
the payment of foreign taxes against the U.S. tax liability. Thus, if the Chinese corporate
income tax is 34 percent, Kihlstrom will not be liable for additional U.S. taxes.
The Cost of Capital for International Firms
An important question for firms with international investments is whether the required return for international projects should be different from that of similar domestic projects.
Lower Cost of Capital from International Firm Diversification
In the previous
chapter, we expressed some skepticism concerning the benefits of diversification. We can
261
262
Corporate Finance,
Seventh Edition
Finance
Companies, 2004
861
make a stronger case for diversification in international firms than for purely domestic
firms. Suppose barriers prevented shareholders in the United States from holding foreign
securities; the financial markets of different countries would be segmented. Further suppose that firms in the United States were not subject to the same barriers. In such a case, a
firm engaging in international investing could provide indirect diversification for U.S.
shareholders that they could not achieve by investing within the United States. This could
lead to the lowering of the risk premium on international projects. In general, if the costs of
investing abroad are lower for a firm than for its shareholders, there is an advantage to international diversification by firms, and this advantage will be reflected in a lower riskadjusted discount rate.
Alternatively, if there were no barriers to international investing for shareholders, shareholders could obtain the benefit of international diversification for themselves by buying foreign securities. In this case the project cost of capital for a firm in the United States would not
depend on whether the project was in the United States or in a foreign country. In practice,
holding foreign securities involves substantial expenses. These expenses include taxes, the
costs of obtaining information, and trading costs. This implies that although U.S. investors
are free to hold foreign securities, they will not be perfectly internationally diversified.
Lower Cost of Capital from International Shareholder Diversification
Recall
our discussion of the CAPM and the market portfolio. Consider the U.S. stock market and
a U.S. investor who is not internationally diversified but, instead, is invested only in U.S.
stocks. From our previous discussion of diversification, we know this investor would be
bearing more risk than if she were able to diversify in the stocks of different countries. Now
imagine she can invest in many foreign stocks by diversifying internationally. She should
be able to reduce the variance (or standard deviation) of her portfolio significantly.
For this investor, the market-risk premium will be lower than for investors who cannot
diversify internationally. In internationally integrated markets, investors with internationally diversified portfolios will measure the risk of an individual stock in terms of a worldmarket portfolio and global betas. Therefore, the cost of capital of a particular firm will be
in terms of a global CAPM, such as:
E(RI) rF BG [E(RG) rF]
where RI is the required return on a stock when markets are global, rF is the risk-free rate,
BG is the global beta, and RG is the return on the world-market portfolio. A firm with internationally diversified investors will have a cost of capital with a lower market-risk
premium [i.e., E(RG rF)] and a global beta when compared to a firm with investors that
cannot diversify internationally.
Solnik has presented evidence that suggests that international diversification significantly reduces risk for shareholders.3 He shows that the variance of an internationally
diversified portfolio of common stocks is about 33 percent of the variance of individual
securities. A diversified portfolio of U.S. stocks will reduce variance by only 50 percent.
Table 31.3 shows that a world portfolio has lower risk than a portfolio of stocks within a
single country. For example, a citizen of Hong Kong can reduce risk from 12.8 percent to
4.2 percent by investing in a world portfolio. This evidence is consistent with a lower
global market-risk premium than is a purely domestic-risk premium. Global betas will be
different than purely domestic betas. Stulz has argued that the preceding claim for why
3
B. H. Solnik, “Why Not Diversify Internationally Rather than Domestically?” Financial Analysts Journal (July–August 1974).
A recent estimate of the benefits of international diversification can be found in Georgio DeSantis and Bruno Gerard, “International
Asset Pricing and Portfolio Diversification with Time-Varying Risk, Journal of Finance 52 (1997). They estimate that an
internationally diversified portfolio will reduce standard deviation by 20 percent when compared to investing in U.S. stocks only.
Corporate Finance,
Seventh Edition
862
Companies, 2004
Finance
TABLE 31.3
Risk Measures for
Foreign Market
Portfolios
Hong Kong
Japan
Sweden
Norway
Belgium
Netherlands
United Kingdom
Denmark
France
Austria
Germany
Switzerland
Australia
Canada
United States
World
Beta
Monthly Standard
Deviation (%)
2.08
1.42
.73
.57
1.06
1.01
1.38
.49
.69
.19
.70
.83
1.39
1.04
.97
1.00
12.8%
6.1
6.2
5.3
6.0
5.6
7.9
5.5
7.4
5.4
6.0
5.7
8.2
5.9
4.7
4.2
SOURCE: Campbell R. Harvey,“The World Price of Covariance Risk,” Journal of Finance (March 1991) from Table I, p. 122 and
Table VI, p. 140.
internationalization reduces the cost of capital doesn’t capture the complete picture. He
agrees that the global market-risk premium is likely to be substantially lower than the risk
premium for an isolated country. In addition, he argues that global investing is likely to
improve corporate governance and reduce agency costs. The argument goes something like
this: Firms in countries with less-developed financial markets will need to improve their
governance so that they can raise capital in well-developed capital markets such as the U.S.
Foreign firms raising capital in the U.S. must appeal to more sophisticated investors and
better market architectures with superior monitoring abilities.4 Table 31.3 also shows that
the systematic risk of foreign stock investment can be very low, as is the case of Austria, or
very high, as is the case of Hong Kong.
Foreign Political Risks
Firms may determine that international investments inherently
involve more political risk than domestic investments. This extra risk may offset the gains
from international diversification. Firms may increase the discount rate to allow for the risk
of expropriation and foreign exchange remittance controls.
Concept
Question
1. What problems do international projects pose for the use of net-present-value
techniques?
31.6 International Financial Decisions
An international firm can finance foreign projects in three basic ways:
1. It can raise cash in the home country and export it to finance the foreign project.
2. It can raise cash by borrowing in the foreign country where the project is located.
3. It can borrow in a third country where the cost of debt is lowest.
4
René M. Stulz, “Globalization, Corporate Finance, and the Cost of Capital,” Journal of Applied Corporate Finance 12 (1999).
See also Ronald M. Schramm and Henry N. Wang, “Measuring the Cost of Capital in an International CAPM Framework,”
Journal of Corporate Finance 12 (1999) and Thomas I. O’Brian, “The Global CAPM and a Firm’s Cost of Capital in Different
Currencies,” Journal of Corporate Finance 12 (1999).
263
264
Corporate Finance,
Seventh Edition
Finance
Companies, 2004
863
If a U.S. firm raises cash for its foreign projects by borrowing in the United States, it has
an exchange-rate risk. If the foreign currency depreciates, the U.S. parent firm may experience an exchange-rate loss when the foreign cash flow is remitted to the United States. Of
course, the U.S. firm may sell foreign exchange forward to hedge this risk. However, it is
difficult to sell forward contracts beyond one year.
Firms in the United States may borrow in the country where the foreign project is located. This is the usual way of hedging long-term foreign exchange risk. Thus, if Kihlstrom
Equipment wishes to invest 20 million yuan in China, it may attempt to raise much of the
cash in France. Kihlstrom should know that long-term hedging of foreign exchange risk by
borrowing in the foreign country is effective only up to the amount borrowed. Any residual
(equity) would not be hedged.
Another alternative is to find a country where interest rates are low. However, foreign
interest rates may be lower because of lower expected foreign inflation. Thus, financial
managers must be careful to look beyond nominal interest rates to real interest rates.
Short-Term and Medium-Term Financing
In raising short-term and medium-term cash, U.S. international firms often have a choice
between borrowing from a U.S. bank at the U.S. interest rate or borrowing Eurodollars in
the Eurocurrency market.
A Eurodollar is a dollar deposited in a bank outside the United States. For example,
dollar deposits in Paris, France, are Eurodollars. The Eurocurrency markets are the banks
(Eurobanks) that make loans and accept deposits in foreign currencies. Most Eurocurrency trading involves the borrowing and lending of time deposits at Eurobanks. For
example, a Eurobank receives a Eurodollar deposit from a domestic U.S. bank. Afterward,
the Eurobank will make a dollar-denominated loan to a borrowing party. This is the
Eurocurrency market. It is not a retail bank market. The customers are corporations and
governments.
One important characteristic of the Eurocurrency market is that loans are made on a
floating-rate basis. The interest rates are set at a fixed margin above the London Interbank
Offered Rate for the given period and currency involved. For example, if the margin is
0.5 percent for dollar loans and the current LIBOR is 8 percent for dollar loans, the dollar
borrower will pay an interest rate of 8.5 percent. This rate is usually changed every six
months. The dollar loans will have maturities ranging from 3 to 10 years.
It is obvious that in a perfectly competitive financial market the interest rate on a
Eurodollar loan in a Eurocurrency market must be the same as the interest rate in the U.S.
loan market. If the interest rate on a Eurodollar loan were higher than that on a domesticdollar loan, arbitrageurs would borrow in the domestic-dollar market and lend in the
Eurodollar market. This type of arbitrage trading would force interest rates to be the same
in both dollar markets. However, from time to time there are differences between the
Eurodollar loan rate and the domestic loan rate. Risk, government regulations, and taxes
explain most of the differences.
International Bond Markets
The worldwide public bond market is made up of $21.5 trillion in bonds issued in many
currencies. Table 31.4 shows that bonds denominated in dollars make up 44.6 percent
of the total. The total worldwide bond market can be divided into domestic bonds and
international bonds. Domestic bonds are those issued by a firm in its home country. International bonds are those issued by firms in another currency than the currency of the home
country.
Corporate Finance,
Seventh Edition
864
Finance
Companies, 2004
TABLE 31.4
Bond Market
The Top 5 Bond
Markets
U.S. dollar
Japanese yen
British pound
Canadian dollar
Danish krone
Rest of the world
Total world bonds
Total Publicly Issued
(in $ billions)
Percentage
of Total
$ 9,683
3,666
662
446
288
6,855
$21,500
44.6%
17.1
3.1
2.1
1.3
31.9
100.00%
Trading in international bonds is over the counter and takes place in loosely connected
individual markets. These individual markets are closely tied to the corresponding domestic
bond markets. International bonds can be divided into two main types: foreign bonds and
Eurobonds.
Foreign Bonds
Foreign bonds are bonds that are issued by foreign borrowers in a particular country’s domestic bond market. They are often nicknamed for the country of
issuance. They are denominated in the country’s domestic currency. For example, suppose
a Swiss watch company issues U.S. dollar-denominated bonds in the United States.
These foreign bonds would be called Yankee bonds. Like all foreign bonds issued in
the United States, Yankee bonds must be registered under the Securities Act of 1933.
Yankee bonds are usually rated by a bond-rating agency such as Standard & Poor’s Corporation. Many Yankee bonds are listed on the New York Stock Exchange.
Many foreign bonds, such as Yankee bonds, are registered. This makes them less attractive to investors having a disdain for tax authorities. For obvious reasons, these traders
like the Eurobond market better than the foreign-bond market. Registered bonds have an
ownership name assigned to the bond’s serial number. The transfer of ownership of a registered bond can take place only via legal transfer of the registered name. Transfer agents (for
example, commercial banks) are required.
Eurobonds
Eurobonds are denominated in a particular currency and are issued simultaneously in the bond markets of several countries. The prefix Euro means that the bonds are
issued outside the countries in whose currencies they are denominated.
Most Eurobonds are bearer bonds. The ownership of the bonds is established by possession of the bond. In contrast, many foreign bonds are registered.
Most issues of Eurobonds are arranged by underwriting. However, some Eurobonds are
privately placed.5 A public issue with underwriting is similar to the public debt sold in
domestic bond markets. The borrower sells its bonds to a group of management banks.
Managing banks, in turn, sell the bonds to other banks. The other banks are divided into two
groups: underwriters and sellers. The underwriters and sellers sell the bonds to dealers and
fund investors. The managing banks also serve as underwriters and sellers. Underwriters
usually sell Eurobonds on a firm commitment basis. That is, they are committed to buy the
bonds at a prenegotiated price and attempt to sell them at a higher price in the market.
5
In general, the issue costs are lower in private placements, as compared to public issues, and the yields are higher.
265
266
Corporate Finance,
Seventh Edition
Finance
Companies, 2004
865
Eurobonds appear as straight bonds, floating-rate notes, convertible bonds, zero-coupon
bonds, mortgage-backed bonds, and dual-currency bonds.6
EXAMPLE
EXAMPLE
A French automobile firm issues 50,000 bonds with a face value of $1,000 each. When the bonds
are issued, they are managed by London merchant bankers and listed on the London Stock
Exchange. These are Eurobonds. Each bond has a fixed coupon rate of 6 percent paid annually on
August 15.
An American firm makes an offering of $500 million of floating-rate notes. The notes are offered
in London. The notes mature in 2020 and have semiannual interest of 0.5 percent above the sixmonth London Interbank Offered Rate.When the bonds are issued, the six-month LIBOR is 10 percent.Thus, in the first six months the American firm will pay interest (at the annual rate) of 10% 0.5% 10.5%.
31.7 Reporting Foreign Operations
When a U.S. company prepares consolidated financial statements, the firm translates the
local-currency accounts of foreign subsidiaries into the currency that is used for reporting
purposes, usually the currency of the home country (that is, dollars). If exchange rates
change during the accounting period, accounting gains or losses can occur.
Suppose a U.S. firm acquired a British company in 1982. At that time the exchange rate
was £1 $2. The British firm performed very well during the next few years (according to
sterling measurements). During the same period, the value of the pound fell to $1.25. Did
the corresponding increase in the value of the dollar make the U.S. company better off?
Should the increase be reflected in the measurement of income?
These questions have been among the most controversial accounting questions in recent
years. Two issues seem to arise:
1. What is the appropriate exchange rate to use for translating each balance-sheet account?
2. How should unrealized accounting gains and losses from foreign-currency translation
be handled?
Currency is currently translated under complicated rules set out in Financial Accounting
Standards Boards (FASB) Statement Number 52, which was issued in December 1981. For
the most part, FASB Number 52 requires that all assets and liabilities be translated from the
subsidiary’s currency into the parent’s, using the exchange rate that currently prevails.
Gains and losses are accumulated in a special account within the shareholders’ equity
section of the balance sheet. Thus, the impact of translation gains and losses will not be
recognized explicitly in net income until the underlying assets and liabilities are sold or
liquidated.
6
There is a small but growing international equity market. International equities are stock issues underwritten and distributed to
a mix of investors without regard to national borders. Our definition of international equity encompasses two basic types: those
issues that have been internationally syndicated and distributed outside all national exchanges (termed Euroequities) and those
that are issued by underwriters in domestic markets other than their own.
Corporate Finance,
Seventh Edition
866
EXAMPLE
Companies, 2004
Finance
To illustrate the accounting problem, suppose we started a small foreign subsidiary in Denmark a
year ago.The local currency is the krone, abbreviated Dkr. At the beginning of the year, the exchange
rate was Dkr 2 $1 and the balance in krones looked like this:
Assets
Dkr 8,000
Liabilities
Equity
Dkr 4,000
Dkr 4,000
At 8 krone to the dollar, the beginning balance sheet in dollar was as follows:
Assets
$1,000
Liabilities
Equity
$500
$500
Denmark is a quiet place and nothing at all actually happened during the year. As a result, net
income was zero before consideration of exchange rate changes. However, the exchange rate did
change to 12 krone $1 because Denmark’s inflation was higher than the U. S. inflation rate. (Note
this is a hypothetical example.)
Because nothing happened, the accounting ending balance sheet in krone is the same as the beginning. However, if we convert it to dollars at the new exchange rate we obtain:
Assets
$667
Liabilities
Net worth
$333.5
$333.5
Notice that the equity has decreased by $167.5 ($500 $333.5) even though net income was
zero.Also notice we have not made any adjustments to the income statement.
The exchange rate gains or losses will not be recognized explicitly in net income until the underlying assets and liabilities are sold or otherwise liquidated.
Concept
Question
1. What issues arise when reporting foreign operations?
The international firm has a more complicated life than the purely domestic firm. Management must
understand the connection between interest rates,foreign-currency exchange rates,and inflation,and
it must become aware of a large number of different financial market regulations and tax systems.
1. This chapter describes some fundamental theories of international finance:
• The purchasing-power–parity theorem (law of one price).
• The expectations theory of exchange rates.
• The interest-rate–parity theorem.
2. The purchasing-power–parity theorem states that $1 should have the same purchasing power in
each country. This means that an apple costs the same whether you buy it in New York or in
Tokyo. One version of the purchasing-power–parity theorem states that the change in exchange
rates between the currencies of two countries is connected to the inflation rates in the countries’ commodity prices.
3. The expectations theory of exchange rates states that the forward rate of exchange is equal to
the expected spot rate.
4. The interest-rate–parity theorem states that the interest-rate differential between two countries
will be equal to the difference between the forward-exchange rate and the spot-exchange rate.
This equality must prevail to prevent arbitrageurs from devising get-rich-quick strategies. The
267
Corporate Finance,
Seventh Edition
Finance
Companies, 2004
867
equality requires the rate of return on risk-free investments in the United States to be the same
as that in other countries.
Of course, in practice the purchasing-power–parity theorem and the interest-rate-parity theorem cannot work perfectly. Government regulations and taxes prevent this. However, there is
much empirical work and intuition that suggests that these theories describe international financial markets in an approximate way.
5. The chapter also describes some of the problems of international capital budgeting. The netpresent-value rule is still the appropriate way to choose projects, but the main problem is to
choose the correct cost of capital.We argue that it should be equal to the rate that shareholders
can expect to earn on a portfolio of domestic and foreign securities.This rate should be about the
same as is true for a portfolio of domestic securities. However, two adjustments may be necessary:
a. The cost of capital of an international firm may be lower than that of a domestic counterpart
because of the benefits of international diversification.
b. The cost of capital of an international firm may be higher because of the extra foreign political risks.
6. We briefly describe international financial markets. International firms may want to consider borrowing cash in the local financial market or in Eurocurrency and Eurobond markets.The interest
rates are likely to appear different in these markets.Thus, international firms must be careful to
consider differences in taxes and government regulations.
KEY TERMS
American Depository Receipt (ADR), 847
cross rate, 848
Eurobanks, 863
Eurobonds, 848
Eurocurrency, 848
Eurodollar, 863
European Currency Unit (ECU), 848
exchange rate, 849
foreign bonds, 848
foreign exchange market, 849
forward-exchange rate, 851
forward trades, 851
gilts, 849
SUGGESTED
READINGS
Some of the latest academic research in international finance appears in the Journal of Applied Corporate Finance: “Global Finance” (Fall 1999); “Emerging Markets and the Asian Crisis” (Fall 1998);
“Global Finance and Risk Management” (Fall 1997).
QUESTIONS
& PROBLEMS
31.1
SOME BASICS
globalization, 847
interest-rate–parity theorem, 854
law of one price (LOP), 851
London Interbank Offered Rate (LIBOR), 849
purchasing-power parity (PPP), 852
relative purchasing-power parity (RPPP), 852
spot-exchange rate, 851
spot trades, 851
swap rate, 851
swaps, 849
triangular arbitrage, 850
Yankee bonds, 864
Use Table 31.5 to answer the following questions:
a. What is the quote in direct terms for the British (i.e., United Kingdom) pound sterling and
the U.S. dollar on spot exchange?
b. Is the Japanese yen at a premium or a discount to the U.S. dollar in the forward markets?
c. To which type of foreign exchange participants would the forward prices of the Japanese
yen be important? Why? What types of transactions might these participants use to cover
their exposed risk in the foreign exchange markets?
d. Suppose you are a Swiss exporter of watches. If you are to be paid in U.S. dollars three
months from now for a shipment made to the United States worth $100,000, how many
Swiss francs would you receive if you locked in the price today with a forward contract?
Would you buy or sell the dollar forward?
e. Calculate the U.K. pound–Indonesian rupiah cross rate for spot exchange in terms of the
U.S. dollar. Do the same for the yen–Swiss franc cross rate.
f. In the text a swap transaction is described.Why might both banks profit from the use of
such a mutual agreement?
268
Corporate Finance,
Seventh Edition
868
Companies, 2004
TABLE 31.5
Foreign Exchange,
Week Ended
Thursday, April 16,
200X
Finance
f-Argent (Austral)
Australia (Dollar)
Brazil (Cruzado)
Britain (Pound)
30-day fut
60-day fut
90-day fut
Canada (Dollar)
30-day fut
60-day fut
90-day fut
y-Chile (Peso)
Colombia (Peso)
Denmark (Krone)
c-Egypt (Pound)
f-Ecuador (Sucre)
Finland (Mark)
Greece (Drachma)
Hong Kong (Dollar)
y-India (Rupee)
Indonesia (Rupiah)
Israel (Shekel)
Japan (Yen)
30-day fut
60-day fut
90-day fut
Jordan (Dinar)
Kuwait (Dinar)
Lebanon (Pound)
z-Mexico (Peso)
New Zealand (Dollar)
Norway (Krone)
Pakistan (Rupee)
y-Peru (Inti)
z-Philippines (Peso)
Portugal (Escudo)
Saudi Arabia (Rijal)
Singapore (Dollar)
S. Korea (Won)
S.Africa (Rand)
Spain (Peseta)
Sweden (Krona)
Switzerland (Franc)
30-day fut
60-day fut
90-day fut
Taiwan (NT $)
Foreign Currency
in Dollars
Dollar in
Foreign Currency
0.6515
0.7160
0.0419
1.6317
1.6277
1.6238
1.6204
0.7593
0.7591
0.7588
0.7584
0.0047
0.0043
0.1466
0.7353
0.006325
0.2270
0.0075
0.1282
0.0779
0.000611
0.6246
0.006993
0.007009
0.007027
0.007042
3.0211
3.6740
0.00813
0.000860
0.5800
0.1477
0.0578
0.0673
0.0494
0.007153
0.2666
0.4690
0.001183
0.4975
0.007890
0.1586
0.6691
0.6710
0.6730
0.6743
0.0294
1.5350
1.3966
23.88
0.6129
0.6144
0.6158
0.6171
1.3170
1.3173
1.3179
1.3185
211.34
230.50
6.8220
1.3600
158.10
4.4050
132.75
7.8015
12.8400
1635.75
1.6010
143.00
142.66
142.30
142.01
0.33100
0.27218
123.00
1163.00
1.7241
6.7700
17.30
14.85
20.2500
139.80
3.7505
2.1320
845.50
2.01010
126.75
6.3070
1.4945
1.4904
1.4858
1.4830
33.97
269
Corporate Finance,
Seventh Edition
Companies, 2004
Finance
869
TABLE 31.5
(concluded)
Turkey (Lira)
U.A.E. (Dirham)
z-Uruguay (Peso)
z-Venezuela (Bolivar)
Yugoslavia (Dinar)
Foreign Currency
in Dollars
Dollar in
Foreign Currency
0.001273
0.2723
0.0050
0.0422
0.001774
785.85
3.6723
201.4
23.7000
563.71
The Federal Reserve Board’s index measuring the value of the dollar against 10 other currencies weighted on the basis
of trade was 96.92 Thursday, up 18 points or 0.18 percent from Wednesday’s 96.74. A year ago the index was 115.10.
Late prices as of 3:30 P.M. Eastern time as gathered by First American Bank of New York. c, commercial rate; f, financial rate;
y, official rate; z, floating rate; r, revised.
Reprinted by permission of The Wall Street Journal. © Dow Jones & Company, Inc. All rights reserved.
31.2
Determine whether arbitrage opportunities exist given the following foreign exchange rates.
a. $1.8/L
SF2/$
SF4/L
b. ¥100/$
SF2/$
¥50/SF
c. HKD7.8/$
¥100/$
¥14/HKD
31.3
Are the following statements true or false? Explain.
a. If the general price index in Japan rises faster than that in the United States (assuming that
there are zero transaction costs, that no barriers to trade exist, and that products are identical in both countries), we would expect the yen to appreciate with respect to the dollar.
b. Suppose you are a Swiss wine exporter who receives all payments in foreign currency.
The French government begins to undertake an expansionary monetary policy. If it is certain that the result will be higher inflation in Switzerland than in other countries, you
would be wise to use forward markets to protect yourself against future losses resulting
from the deterioration of the value of the Swiss franc.
c. If you could accurately estimate differences in relative inflation between two countries
over a long period of time (and other participants in the market were unable to do so),you
could successfully speculate in spot currency markets.
31.4
The inflation rates for Empire White and Empire Black are 5 percent and 10 percent, respectively. At the beginning of the year, the spot rate between the two currencies is 2.5 black
dollars per white dollar.What is the approximate spot rate at year-end?
INTEREST RATES
AND EXCHANGE
RATES: INTERESTRATE PARITY
31.5
A U.S. corporation, Forever Young, Inc., intends to import $1,000,000 worth of cosmetics
from Switzerland and will make payment in SF three months from now.The foreign exchange
spot rate of Swiss franc to the U.S. dollar is SF6/$. Annual interest rates for U.S. dollar and
Swiss franc are 5 percent and 8 percent, respectively.
a. What is the three-month forward rate for French franc if interest-rate parity holds?
b. How can Forever Young, Inc., use currency trading to hedge against the foreign exchange
risk associated with the purchase?
INTERNATIONAL
CAPITAL
BUDGETING
31.6
a. The treasurer of a major U.S. firm has $5 million to invest for three months.The annual
interest rate in the United States is 12 percent.The interest rate in the United Kingdom
is 9 percent. The spot rate of exchange is $2/£ and the three-month forward rate is
$2.015/£. Ignoring transaction costs, in which country would the treasurer want to invest
the company’s capital if he can fix the exchange rate three months hence through a
forward contract?
b. The spot rate of foreign exchange between the United States and the United Kingdom
at time t is $1.50/£. If the interest rate in the United States is 13 percent and it is 8 percent in the United Kingdom, what would you expect the one-year forward rate to be if
no immediate arbitrage opportunities existed?
c. If you are an exporter who must make payments in foreign currency three months after
receiving each shipment and you predict that the domestic currency will appreciate in
value over this period, is there any value in hedging your currency exposure?
THE LAW OF
ONE PRICE AND
PURCHASINGPOWER PARITY
270
Corporate Finance,
Seventh Edition
870
Finance
Companies, 2004
31.7
a. Suppose it is your task to evaluate two different investments in new subsidiaries for your
company, one in your own country and the other in a foreign country.You calculate the
cash flows of both projects to be identical after exchange-rate differences. Under what
circumstances might you choose to invest in the foreign subsidiary? Give an example of
a country where certain factors might influence you to alter this decision and invest at
home.
b. Suppose Strom Equipment comes across another investment in Switzerland.The project
costs SF10 million and is expected to produce cash flows of SF4 million in year 1 and
SF3 million in each of years 2 and 3.The current spot-exchange rate is $0.5/SF1 and the
current risk-free rate in the United States is 11.3 percent, compared to that in
Switzerland of 6 percent.The appropriate discount rate for the project is estimated to be
15 percent, the U.S. cost of capital for the company. In addition, the subsidiary can be sold
at the end of three years for an estimated SF2.1 million.What is the NPV of the project?
c. An investment in a foreign subsidiary is estimated to have a positive NPV, after the discount rate used in the calculations is adjusted for political risk and any advantages from
diversification. Does this mean the project is acceptable? Why or why not?
d. If a U.S. firm raises funds for a foreign subsidiary, what are the disadvantages to borrowing in the United States? How would you overcome them?
INTERNATIONAL
FINANCIAL
DECISIONS
31.8
a. What is a Euroyen?
b. If financial markets are perfectly competitive and the Eurodollar rate is above that offered
in the U.S. loan market, you would immediately want to borrow money in the United
States and invest it in Eurodollars.True or false? Explain.
c. What distinguishes a Eurobond from a foreign bond? Which particular feature makes the
Eurobond more popular than the foreign bond?
d. How would you describe a bond issued by a Canadian firm in the United States with payments denominated in U.S. dollars?
S&P
PROBLEM
31.9
Nokia stock trades as an American Depository Receipt on the New York Stock Exchange.
Assume that one ADR is exchangeable for one share of Nokia stock on the Finnish stock
market. Find the monthly closing price of the Nokia ADR for July 2003. Assuming the
exchange rate was $1.09/C and Nokia shares traded for C14.28, explain how you could
make an arbitrage profit. What was the profit per share? What exchange rate is necessary
to eliminate the arbitrage opportunity?
271
272
Baker−Lembke−King:
Advanced Financial
Accounting, Sixth Edition
Text
Companies, 2004
Chapter Nineteen
Not-for-Profit Entities
Multi-Corporate
Entities
Multinational
Entities
Reporting
Requirements
Partnerships
Governmental
Entities and
Not-for-Profit
Governmental
Entities
Special Funds
Not-for-Profits
Corporations in
Financial Difficulty
This chapter presents the accounting and financial reporting principles used by both governmental (public) and nongovernmental (private) colleges and universities, by health care
providers such as hospitals and nursing homes, voluntary health and welfare organizations
such as the Red Cross and United Way, and other not-for-profit organizations such as professional or fraternal associations.
The accounting and financial reporting for governmental, nonprofit entities is controlled by the GASB. Accounting and financial reporting for nongovernmental, nonprofit
entities is controlled by the FASB. Thus, it is important to determine the role the government has in the organization.
FINANCIAL REPORTING FOR PRIVATE, NOT-FOR-PROFIT
ENTITIES
Private, not-for-profit entities follow the accounting and reporting standards established
by the FASB. Several FASB standards and statements are particularly relevant for private,
not-for-profit entities.
Private, not-for-profit entities must report their net assets in accordance with Financial
Accounting Concepts Statement No. 6, “Elements of Financial Statements” (FAC 6).
FAC 6 specifies three mutually exclusive classes of net assets (assets less liabilities), as
follows:
1. Unrestricted net assets. This class of net assets is not restricted by a donor. They are
used for the entity’s general operations. Unrestricted net assets include all assets and liabilities that do not have externally imposed restrictions on their use.
2. Temporarily restricted net assets. This net asset class reports net assets that have
donor-imposed time or purpose restrictions, typically detailed in the contribution agreement between the donor and the organization. A time restriction means that the assets will
not be available for use until after a specific time has passed. Term endowments that have
limited lives are included in temporarily restricted net assets. A purpose restriction means
that the resources may be used only for specified purposes. For example, the donor may
restrict the contribution to use in a specific program or for specified building and equipment acquisitions.
3. Permanently restricted net assets. This class of net assets includes permanently restricted contributions such as regular endowments for which the principal must be preserved into perpetuity.
It is very important to properly account for, and report, each class of net assets. Some
not-for-profit entities use a fund structure to account for each type of net asset class to
apply the account discipline that fund accounting provides. These entities would have
funds such as the general fund, specific-purpose fund, building fund, endowment fund,
995
Advanced Financial
Text
Companies, 2004
996 Chapter 19 Not-for-Profit Entities
and so on. Other not-for-profit entities maintain only an accounting record to show the
amounts in each net asset class. The specific identification of any restricted asset must be
made when the asset comes into the entity, generally by donation or bequest. The gifting
agreement must be examined fully to determine whether the gift has any donor-imposed
restrictions on its principal and/or on the income generated from the principal. Revenue is
recorded in only one net asset class when the contribution is made. Then, as restrictions
are eliminated or met, the resources are released and transferred from a restricted net asset
class to the unrestricted net asset class.
For example, if C. Alt donates $40,000 to a not-for-profit organization to be used
specifically for a research program, the following entry is made in the temporarily restricted class of net assets because of the donor-imposed use restriction:
(1)
Cash
Contribution Revenue
Receipt of $40,000 donor-restricted contribution
for a specified research program.
40,000
40,000
Note that the contribution revenue is recorded in the temporarily restricted net assets
when the restricted contribution is received.
Then, when the research program costs are approved in the unrestricted net asset class,
a reclassification entry is made in the temporarily restricted net asset class to record the
transfer of the resources from the temporarily restricted class to the unrestricted net assets.
Note that the reclassification entry is not an expense of the restricted class.
(2)
Reclassification from Temporarily Restricted Net
Assets—Satisfaction of Program Restriction
Cash
Reclassification of temporarily restricted resources to
the unrestricted fund upon satisfaction of the use restriction.
40,000
40,000
Entries are then made in the unrestricted net asset class to show the receipt of the cash and
the reclassification for satisfaction of the program restriction. The reclassification is not
a revenue in the unrestricted net asset class because the revenue from the contribution has
already been recognized once in the temporarily restricted net asset class. A key concept
is that revenue should be recognized only once and only by the appropriate receiving net
asset class. The entries in the unrestricted net asset class follow:
(3)
(4)
Cash
Reclassification into Unrestricted Net Assets—
Satisfaction of Program Restriction
Receipt of resources from the temporarily restricted net
asset class due to satisfaction of use restriction.
Expenses
Cash
Expenses for research program.
40,000
40,000
40,000
40,000
Some not-for-profit entities use the terms “net assets released from restriction” instead of
“reclassification.” The purpose is the same; the resources are released from a restricted
net asset class and assigned or transferred to another asset class.
It is very important to note that the restricted asset classes, either temporarily or permanently, do not report expenses on the organization’s statement of activities. The restricted asset classes (temporarily or permanently) report restricted contribution revenue
273
274
Advanced Financial
Text
Companies, 2004
Chapter 19 Not-for-Profit Entities 997
and any restricted investment income/losses but cannot report any expenses. Expenses are
reported only in the unrestricted asset class. Thus, the reclassification entry records the
transfer of the resources from a restricted asset class to the unrestricted asset class. The reclassification and transfer is made when appropriate evidence is provided to the restricted
asset class that the cash can be released due to the satisfaction of the temporary restriction
or that the permanent restriction is no longer valid. The reclassification entry ensures that
the resources are being spent by the unrestricted asset class in accordance with the donor’s
wishes.
Important FASB Standards for Not-for-Profit Entities
The FASB has issued five standards that have direct applicability to private, not-for-profit
entities: FASB 93, which guides depreciation; FASB 116, which guides accounting for
contributions; FASB 117, which establishes financial display requirements; FASB 124,
which establishes the accounting for investments; and FASB 136, which guides the accounting for transfers of assets to a not-for-profit organization that raises or holds contributions for others.
FASB Statement No. 93, “Recognition of Depreciation by Not-for-Profit Organizations” (FASB 93), requires that private not-for-profit entities must show depreciation. Depreciation must be recognized on long-lived tangible assets, other than works of art or
historical treasures that have cultural, aesthetic, or historical value that is worth preserving perpetually and whose holders have the ability to preserve that value and are so doing.
The depreciation is reported as an expenditure of the fund that uses the tangible long-lived
assets during the period. FASB 93 requires disclosure of the following items: (1) depreciation for the period, (2) the balance of the major classes of depreciable assets, (3) the accumulated depreciation at the balance sheet due, and (4) the method used to compute
depreciation for the major classes of depreciable assets.
FASB Statement No. 116, “Accounting for Contributions Received and Contributions
Made” (FASB 116), establishes the guidelines for private not-for-profit entities to account
for contributions. Contributions can be of cash, other assets, or a promise to give (a
pledge). The general rule is that contributions received are measured at their fair value and
are recognized as revenues or gains in the period received. The contributions are reported
as unrestricted support or, if there are donor-imposed restrictions, as restricted support. A
private not-for-profit entity does not need to recognize contributions of works of art, historical treasures, and similar assets if the donated items are added to collections that (1)
are held for public exhibition, education, or research, (2) are protected, cared for, and preserved, and (3) has an organizational policy in existence that proceeds from the sales of
collection items are to be used to acquire other items for collections.
Contributions of services are recognized as a revenue, with an equivalent amount
recorded as an expenditure, if the services received (1) create or enhance nonfinancial assets or (2) require specialized skills, are provided by individuals possessing those skills,
and typically need to be purchased if not provided by donation. Examples of contributed
services are specialized skills provided by accountants, architects, doctors, teachers, and
other professionals. Some religious-based colleges record revenue, with an offsetting
amount to an expenditure, for the fair value of contributed lay teaching services. This
recognition is made to report the full cost of the teaching mission of these private colleges.
FASB Statement No. 124, “Accounting for Certain Investments Held by Not-forProfit Organizations” (FASB 124), is discussed before FASB 117, which is presented in
the next paragraph. FASB 124 extended to not-for-profit organizations the basic standard
of fair value for investments that was presented in FASB 115 on investments. FASB 124
specifies that fair value should be the measurement basis for investments in all debt
securities and in equity securities that have readily determinable fair values (other than
Advanced Financial
Text
Companies, 2004
those equity securities that are accounted for under the equity method in accordance with
APB 18). Note that FASB 124 requires that debt securities be valued at fair value. Investment income for the period includes interest or dividends and the changes in fair
value. Changes in fair value of investments in temporarily restricted or permanently restricted net assets are recognized in accordance with donor restrictions as to the income.
Otherwise, investment income is reported as a change in unrestricted net assets.
FASB Statement No. 117, “Financial Statements of Not-for-Profit Organizations”
(FASB 117), specifies the financial display standards for private not-for-profit entities.
The three major financial statements are (1) a statement of financial position, (2) a statement of activities, and (3) a statement of cash flows. The unique features of the statement
of financial position and statement of activities for not-for-profit organizations are presented in greater detail in the following discussions. While some flexibility exists in the
presentation of financial statements under FASB 117, a major feature of the statement of
financial position is the combined presentation of all assets and equities in a single, simplified statement. In addition, the net assets are separated into those that are (1) unrestricted, (2) temporarily restricted, and (3) permanently restricted.
FASB Statement No. 136, “Transfers of Assets to a Not-for-Profit Organization or
Charitable Trust that Raises or Holds Contributions for Others” (FASB 136), issued in
1999, establishes the accounting for contributions made to foundations or other similar organizations that raise resources for not-for-profit entities. FASB 136 defines three parties
to the typical contribution process. The donor is the initial provider of the resources. The
recipient organization received the assets from the donor. The beneficiary is the entity that
eventually receives the assets through the recipient organization, as specified by the
donor.
Many not-for-profit, private colleges and universities have a foundation that is responsible for raising financial support from alumni and other donors. Typically, these foundations are institutionally related to the college or university and use its assets for the benefit
of the college or university. In most cases, at the time the assets contribution from the
donor to the foundation (the recipient organization), the foundation records an increase in
assets and a contribution revenue for the fair value of the donation. Usually these assets
are temporarily restricted until the foundation transfers them to the college or university.
When the foundation does transfer the assets to the university (the beneficiary), the foundation records an expense and a decrease in its assets. For the college or university accounting, it normally has an interest in the net assets of the foundation and, at the time of
the donation to the foundation, the college or university will recognize the change in its
interest in the university foundation, usually as a temporarily restricted net asset, unless
the donor specified a permanent restriction on the donation. Then, when the college or
university actually receives the assets, it increases the specific assets received and decreases its interest in the net assets of the foundation. The institutionally related foundation recognized the contribution revenue when it received the donation.
Some recipient organizations, such as United Way, do fund-raising that will benefit a
number of not-for-profit organizations. Donors may name the specific recipient of their
gifts or the donor may give to United Way without a restriction as to where the gift
should be used. When the donor specifies the beneficiary, United Way recognizes an increase in its assets and records a liability to the specified beneficiary. The organization
specified by the donor records an increase in its net assets, usually as a receivable, and
records contribution revenue at the time of the donation. When United Way transferred
the assets to the specified beneficiaries, United Way decreases its liabilities and its assets. For unrestricted donations for which United Way may determine the best uses of the
resources, it records an increase in its assets and records the unrestricted gifts as contribution revenue. Then, when the assets are distributed, United Way records the expense
275
276
Advanced Financial
Text
Companies, 2004
and the decrease in its assets, and the beneficiary records contribution revenue for the
fair value of the assets transferred.
Therefore, the key issues are the relationship between the recipient organization and
the beneficiary and whether the donor placed any use restrictions on the donation. If the
donor does not specify a beneficiary and the recipient organizations and beneficiary are
not institutionally related, the beneficiary cannot recognize an increase in its net assets
until it actually receives the assets and records contribution revenue at that time. If the
donor does specify a beneficiary or the recipient organizations and the beneficiary are institutionally related, the beneficiary recognizes the fair value of the donation when it is
made to the recipient organization. Finally, in the case of nonfinancial assets such as artwork, the recipient organizations may choose whether to record the fair value of these
nonfinancial assets in its books. However, all financial assets must be recorded at their
fair values.
COLLEGES AND UNIVERSITIES
There are more than 3,000 colleges and universities in the United States. Some offer twoyear programs, some offer four-year programs, and others offer a wide selection of both
undergraduate and graduate programs. Public and private institutions provide a large variety of liberal arts, science, and professional programs for our society. Public colleges
and universities receive a significant portion of their operating resources from state governments. Private not-for-profit colleges and universities receive most of their resources
from tuition and fees.
Special Conventions of Revenue and Expenditure Recognition
Both public and private colleges and universities follow several conventions of recognizing revenue and expenses as follows:
1. Tuition and fee remissions/waivers and uncollectible accounts. Tuition and fees are
important revenue sources for colleges and universities. In college and university accounting, the full amount of the standard rate for tuition and fees is recognized as revenue.
The university first recognizes revenue at the standard rate of tuition and fees. The accounting for university-sponsored scholarships, fellowships, tuition and fee remissions or
waivers depends on the whether the recipient provides any services to the university. For
example, if a student receives a university-sponsored scholarship that does not require any
employment-type of work to be given to the university, the university accounts for this as
a deduction from revenue (i.e., reduces revenue). On the other hand, if the student must
provide employment-type work to the university, the university accounts for the scholarship as an expense. Another example is the tuition remission (reduction) often given to
graduate students who accept teaching assistantships. The university records revenue for
the graduate student’s tuition at the standard rate and then records the tuition remission as
an expense of the year in which the graduate student is a teaching assistant.
2. Tuition and fee reimbursements for withdrawals from coursework. Students withdrawing from classes after the beginning of the class term may be able to collect a reimbursement or return of some of the tuition and fees paid at the beginning of the term.
Colleges and universities account for these reimbursements of tuition and fees as a reduction of revenue. When the check to the student is approved, the university debits revenue from tuition and fee reimbursements and credits cash or accounts payable.
3. Academic terms that span two fiscal periods. Some academic terms may begin
in one fiscal year of the university and be completed in another. This is often true for
Advanced Financial
Text
Companies, 2004
summer school sessions. For example, many universities end their fiscal years on June 30
of each year. Colleges and universities account for the tuition and fees collected for a term
of instruction as revenue in the fiscal year in which the term is predominantly conducted,
along with all expenses incurred to finance that term. For example, if tuition and fees are
collected at the beginning of summer school, which takes place predominantly in the next
fiscal period, the university records the collection as a debit to Cash and a credit to Deferred Revenue. The deferred revenue and any deferred expenses are then recognized as
revenue and expenses of the next fiscal period.
Board-Designated Funds
The governing board, sometimes termed regents or trustees, may designate unrestricted
current fund resources for specific purposes in future periods. These board-designated
funds are internal designations similar to appropriations of retained earnings for a commercial entity. The governing board may make any designations at its own volition. For
example, it might designate $50,000 of future spending in the unrestricted current fund
for the development of a foreign student counseling office. Such designations are usually
reported in the footnotes to the financial statements, but they may also be shown as allocations of part of the fund balance in the unrestricted current fund balance sheet. However, FASB 117 specifies that these board-designated funds are not reported as restricted
net assets because only external, donor-imposed restrictions can result in restricted net
assets.
Public Colleges and Universities
The accounting and reporting for public colleges and universities is specified by the
GASB. GASB Statement No. 35, “Basic Financial Statements—and Management’s Discussion and Analysis—for Public Colleges and Universities” (GASB 35), issued in 1999,
requires that these institutions follow the standards for governmental entities as specified
in GASB 34. Most public institutions will be special-purpose government entities engaged in only business-type activities. This is so because most public colleges and universities do not have their own taxing authority. These special-purpose governmental
entities present only the financial statements required for enterprise funds and then are included as component units of the state government. However, some community colleges
do have their own taxing authority, and these are special-purpose government entities engaged in both governmental- and business-type activities. These community colleges provide both fund financial statements and government-wide financial statements.
Private Colleges and Universities
The FASB specifies the accounting and financial reporting standards for private colleges
and universities. Although many private colleges and universities are not-for-profit entities, some private colleges, such as the University of Phoenix, are profit-seeking. Accounting for profit-seeking educational entities is similar to accounting for any
commercial entity and is not covered in this chapter.
The three financial statements required for private, not-for-profit colleges and universities are the (1) statement of financial position, (2) statement of activities, and (3) statement of cash flows. Private colleges and universities are free to select any account
structure that best serves its management and financial reporting needs, but some choose
to use fund accounting similar to that of governmental entities. Fund accounting creates
an accounting discipline and provides an accounting vehicle to track revenues and expenses related to specific programs.
277
278
Advanced Financial
Text
Companies, 2004
FIGURE 19–1
SOL CITY COLLEGE
Statement of Financial Position
June 30, 20X2 and 20X1
Statement of
Financial Position for
a Private College
20X2
579,000
10,763,000
125,000
161,000
(13,000)
275,000
45,000
14,000
20,330,000
20X1
Cash
Investments, at Fair Value
Deposits with Trustees
Accounts Receivable
Less: Allowance for Uncollectibles
Loans to Students, Faculty, and Staff
Inventories
Prepaid Expenses
Property, Plant, and Equipment (net)
$
Total Assets
$32,279,000
$30,550,000
Accounts Payable
Accrued Liabilities
Students’ Deposits
Deferred Credits
Annuities Payable
Notes Payable
Bonds Payable
Mortgage Payable
Deposits Held in Custody
$
$
Total Liabilities
$ 2,795,000
$ 2,589,000
Net Assets:
Unrestricted
Temporarily Restricted by Donors
Permanently Restricted by Donors
$20,221,000
5,363,000
3,900,000
$20,294,000
4,307,000
3,360,000
Total Net Assets
$29,484,000
$27,961,000
Total Liabilities and Net Assets
$32,279,000
$30,550,000
70,000
10,000
15,000
15,000
1,080,000
50,000
1,300,000
200,000
55,000
$
514,000
9,536,000
122,000
182,000
(14,000)
190,000
40,000
10,000
19,970,000
53,000
8,000
18,000
10,000
1,155,000
—
1,200,000
100,000
45,000
The statement of financial position for Sol City University, a private, not-for-profit
college, is presented in Figure 19–1. This statement presents all assets and equities in a
single statement. Note that the net assets are separated into three categories: (1) unrestricted, (2) temporarily restricted, and (3) permanently restricted. The unrestricted category includes all assets, including property, plant, and equipment, whose use is not
restricted by the provider or donor. Temporarily restricted assets include those that the
donor has designated for specific use or for use in subsequent periods. Term endowments,
funds donated for support of special activities, and those donated for unrestricted (or
other) use in future periods are included as temporarily restricted net assets. Permanently
restricted assets typically include only the principal balance of permanent endowments.
The statement of activities presented in Figure 19–2 presents separately the revenues
and expenses of the unrestricted, temporarily restricted, and permanently restricted net
asset categories. It also shows the transfer of assets between the three categories of net assets during the period. For example, contributions received in 20X1 and available for use
in 20X2 are shown as a transfer from temporarily restricted to unrestricted net assets in
the statement of activities for 20X2. Auxiliary enterprises include activities such as a student union bookstore, cafeterias, and residence halls.
The statement of cash flows presented in Figure 19–3 is similar to that used for commercial entities. Either the direct or indirect method may be used to compute cash flows
Advanced Financial
Text
Companies, 2004
FIGURE 19–2 Statement of Activities for a Private College
SOL CITY COLLEGE
Statement of Activities
For the Year Ended June 30, 20X2
Unrestricted
Revenues, Gains, and Other Support:
Tuition and Fees
Government Appropriations
Government Grants and Contracts
Contributions
Auxiliary Enterprises
Investment Income
Gain on Investments
Net Assets Transferred Or Released From Restriction:
Program Use Restriction
Transferred to Restricted Funds
Expired Term Endowment
Transferred to Endowment
$ 1,290,000
650,000
20,000
425,000
1,100,000
265,000
Temporarily
Restricted
$
601,000
(101,000)
50,000
Total Revenue, Gains, and Other Support
$ 4,300,000
Expenditures and Other Deductions:
Instruction
Research
Public Service
Academic Support
Student Services
Scholarships and Fellowships
Institutional Support
Operation and Maintenance
Depreciation Expense
Interest Expense
Auxiliary Enterprises
Other Operating Costs
$ 1,725,000
250,000
77,000
125,000
100,000
95,000
275,000
110,000
500,000
106,000
915,000
95,000
Permanently
Restricted
40,000
300,000
1,063,000
$ 495,000
139,000
69,000
15,000
25,000
(601,000)
101,000
(50,000)
(5,000)
5,000
$1,056,000
$ 540,000
Total
$ 1,290,000
690,000
320,000
1,983,000
1,100,000
419,000
94,000
$ 5,896,000
$ 1,725,000
250,000
77,000
125,000
100,000
95,000
275,000
110,000
500,000
106,000
915,000
95,000
Total expenses
$ 4,373,000
$
-0-
$ 4,373,000
Change in net assets
Net assets at beginning of year
$
$1,056,000
4,307,000
$ 540,000
3,360,000
$ 1,523,000
27,961,000
Net assets at end of year
$20,221,000
$5,363,000
$3,900,000
$29,484,000
(73,000)
20,294,000
-0-
$
from operating activities. Activities in the restricted funds are noted separately from those
in the unrestricted funds. Note that the statement begins with the change in net assets for
all funds but reconciles to the cash at the end of the year.
HEALTH CARE PROVIDERS
The health care environment is currently undergoing a revolution. Rapidly increasing
costs of providing medical care are forcing hospitals to merge at an increasing rate in
order to consolidate the types of services offered. The cost of new technology is also requiring health care providers to reevaluate their missions to the communities they serve.
Although the major focus of this chapter section is on hospitals, the accounting and financial reporting guidelines for hospitals are the same as those used by all health care
279
280
Advanced Financial
Text
Companies, 2004
FIGURE 19–3
SOL CITY COLLEGE
Statement of Cash
Flows for a Private
College
Cash flows from Operating Activities:
Change in Net Assets
Adjustments to Reconcile Changes in Net Assets
to Net Cash Provided by Operating Activities:
Depreciation
Increase in Deposits with Trustees
Decrease in Accounts Receivable
Increase in Loans to Students, Faculty, and Staff
Increase in Inventories
Increase in Prepaid Expenses
Increase in Accounts Payable
Increase in Accrued Liabilities
Decrease in Students’ Deposits
Increase in Deferred Credits
Restricted Contributions and Investment Income:
Contributions, Grants, and Investment Income
in Permanently Restricted Funds
$(1,611,000)
in Temporarily Restricted Funds
(535,000)
Total Restricted Contributions and Investment
Income
$(2,146,000)
Total Adjustments
Net Cash Provided by Operating Activities
Cash Flows from Investing Activities:
Acquisition of Property, Plant, and Equipment
Sale of Used Equipment
Net Acquisition of Investments
Flows Related to Restricted Items:
Net Acquisition of Temporarily Restricted
Investments
Net Acquisition of Permanently Restricted
Investments
Net Cash Flow Related to Restricted Items
Net Cash Provided by Investing Activities
Cash Flows from Financing Activities:
Decrease in Annuities Payable
Increase in Notes Payable
Increase in Bonds Payable
Increase in Mortgage Payable
Increase in Deposits Held in Custody
in Temporarily Restricted Funds
in Permanently Restricted Funds
Cash Flows Related to Restricted Items
$1,523,000
$
500,000
(3,000)
20,000
(85,000)
(5,000)
(4,000)
17,000
2,000
(3,000)
5,000
(2,146,000)
$(1,702,000)
(1,702,000)
$ (179,000)
(920,000)
60,000
(65,000)
$ (112,000)
(1,050,000)
$(1,162,000)
(1,162,000)
(2,087,000)
$
(75,000)
50,000
100,000
100,000
10,000
$
185,000
$ 1,611,000
535,000
$ 2,146,000
Net Cash Provided by Financing Activities
2,331,000
Net Change in Cash
Cash at the Beginning of the Year
$
65,000
514,000
Cash at the End of the Year
$ 579,000
Advanced Financial
Text
Companies, 2004
providers included within the scope of the AICPA’s audit and accounting guide for Health
Care Organizations.1 The audit and accounting guide applies to the following health care
entities:
1. Clinics, medical group practices, individual practice associations, individual practitioners, emergency care facilities, laboratories, surgery centers, and other ambulatory
care organizations.
2. Continuing-care retirement communities (CCRCs).
3. Health maintenance organizations (HMOs) and similar prepaid health care plans.
4. Home health agencies.
5. Hospitals.
6. Nursing homes that provide skilled, intermediate, and less intensive levels of health
care.
7. Drug and alcohol rehabilitation centers and other rehabilitation facilities.2
The AICPA audit guide serves as an important authoritative source in selecting accounting and financial reporting procedures for health care providers. The hospital financial statements illustrated in this chapter incorporate the disclosure standards of FASB
117, as presented and amplified in the AICPA’s 1996 Audit and Accounting Guide for
Health Care Organizations.
Hospital Accounting
Hospitals may be classified as (1) investor-owned businesses, (2) not-for-profit entities
that cover their costs by generating fees from their activities, or (3) governmental entities.
Private-sector hospitals use the FASB’s accounting guidelines and requirements; publicsector (governmental) hospitals follow the GASB’s accounting guidance. Investor-owned
hospitals seek additional financial resources through the sale of stocks and the issuance of
large amounts of debt. These profit-seeking hospitals provide the same types of financial
reports as commercial entities. Not-for-profit hospitals present their financial results using
a specific format required by the FASB. Not-for-profit hospitals are often affiliated with a
religious group or a civic association. Governmental hospitals are managed by or affiliated
with a government unit. Governmental hospitals follow the GASB’s accounting and reporting requirements and are considered special-purpose entities engaged in business-type
activities.3 As such, they present financial statements that are required for enterprise funds
as presented in Chapter 18 of this textbook. Governmental hospitals then are included in
the government unit’s government-wide financial statements.
Two professional associations, the American Hospital Association (AHA) and the Hospital Financial Management Association (HFMA), are active in developing and improving hospital management, accounting, and financial reporting. Publications of both
organizations can be useful to individuals seeking additional information on hospital accounting and reporting practices.
In this chapter, it is assumed that the hospital is a separate, not-for-profit reporting
entity and is not a component unit of any government. The focus of this chapter is on
1
The AICPA periodically revises its audit and accounting guides for specialized industries. The 2001 Audit
and Accounting Guide for Health Care Organizations, which includes hospitals, revises and supersedes earlier
audit guides for hospitals.
2
AICPA Audit and Accounting Guide for Health Care Organizations, 2001, p. vii.
3
Governmental Accounting Standards Board Codification of Governmental Accounting and Financial
Reporting Standards, updates issued frequently, Section H.50.101.
281
282
Advanced Financial
Text
Companies, 2004
FIGURE 19–4
Fund Gr oups
Overview of Hospital
Accounting and
Reporting
Restricted
General
Accounting
basis
Distinguishing
features
Financial
statements
Accrual
Specific
Purpose
Time Restricted
Plant
Replacement
and Expansion
Endowment
Contributions, transfers, and other changes are recorded directly in the
fund. Resources are held until transferred to general fund for
expenditures.
Resources
restricted
for specific
operating
purposes.
Resources not
available until
date specified by
donor.
Resources
restricted for
additions to plant
assets.
Principal
must be
preserved.
Balance Sheet
Statement of Operations
Statement of Changes in Net Assets
not-for-profit hospitals because of the large number of such hospitals and because of their
special accounting and financial reporting issues.
Hospital Fund Structure
Although not required to do so, many hospitals have used a fund accounting structure for
accounting purposes. In general, operating activities have been carried on in the general
fund, and a series of restricted funds has been used to account for assets whose use has
been restricted by the donor. The presentation of financial statement information under
FASB 117 requires a distinction between those net assets that are unrestricted, temporarily restricted, and permanently restricted. The discussion of accounting and financial reporting for hospitals that follows assumes that unrestricted assets are accounted for in the
general fund and that one or more separate funds are used to account for temporarily restricted and permanently restricted assets.
All transactions involving the use of unrestricted assets are recorded in the general
fund. As such, the general fund is the hospital’s primary operating fund. Assets that were
restricted as to the period of use or that must be used for particular purposes are accounted
for in restricted funds until the restriction is satisfied. When the restriction is satisfied, the
assets are transferred (reclassified) from the restricted fund to the general (unrestricted)
fund. Any expenses that are incurred in satisfying the restrictions are reported as expenses
in the general fund.
Restricted funds account for assets received from donors or other third parties who
have imposed certain restrictions on their use. The restricted funds are often termed
“holding” funds because they must hold the restricted assets and transfer expendable resources to the general funds for expenditure. Figure 19–4 presents an overview of the fund
structure and the typical financial reporting for hospitals.
General Fund The general fund accounts for the resources received and expended
in the hospital’s primary health care mission. The basis of accounting is the accrual
method in order to measure fully all expenses of providing services during the period.
Advanced Financial
Text
Companies, 2004
Depreciation is included in the operating expenses. Fixed assets are included in the fund
based on the theory that the governing board may use these assets in any manner desired.
The governing board may establish board-designated resources within the general
fund. For example, the board may designate resources for the expansion of the hospital,
for retirement of debt, or for other purposes. Funds designated in this manner are considered to be part of the unrestricted funds, but this designation provides information on the
intended use of the resources.
Donor Restricted Funds All restricted funds account for resources whose use is restricted by the donor. For financial reporting purposes, a distinction is made between temporarily and permanently restricted funds. The major temporarily restricted funds are (1)
specific-purpose funds, (2) time-restricted funds, and (3) plant replacement and expansion funds. Permanently restricted funds are assets that must be held into perpetuity and
generally are included in an endowment fund. Hospitals may also have restricted loan
funds and annuity and life income funds; however, few hospitals use these funds, and they
are not discussed in this chapter.
Specific-purpose funds are restricted for specific operating purposes. For example,
a donor may specify that a donation of $25,000 may be used only for maternity care.
The donation is held in the specific-purpose fund until the maternity expenditure is approved in the general fund when the specific-purpose fund transfers the resources to the
general fund.
Time-restricted funds account for assets received or that have been pledged by donors
for use in future periods. The donor’s restriction is satisfied by the passage of time. A
pledge received in 20X1 to contribute a stated amount in 20X2 to be used for unrestricted
purposes is included in the time-restricted fund in the balance sheet prepared at December 31, 20X1.
Plant replacement and expansion restricted funds account for contributions to be used
only for additions to fixed assets. When the general fund approves or makes the appropriate expenditures for the fixed assets, the plant replacement and expansion fund transfers
the resources to the general fund.
Endowment funds account for resources when the principal must be preserved. The income from these resources is usually available for either a restricted or a general purpose.
Endowments may be either permanent or term. Term endowments are for limited time periods, for example, 5 or 10 years, or until a specific event occurs, such as the death of the
donor. After the term expires, governing board uses the principal of the fund in accordance with the gift agreement.
Financial Statements for a Not-for-Profit Hospital
Separate, not-for-profit hospitals issue four basic financial statements: (1) the balance
sheet, (2) the statement of operations, (3) the statement of changes in net assets, and (4)
the statement of cash flows. Comparative data for prior fiscal periods are normally presented within each statement. Each of the four statements is demonstrated in the comprehensive illustration presented later in this chapter.
Balance Sheet
The balance sheet presents the total assets, liabilities, and net assets of the organization as
a whole.
Receivables Receivables may include amounts due from patients, third-party payors,
other insurers of health care, pledges or grants, and interfund transactions. Receivables
should be reported at the anticipated realizable amount. Thus, the realizable amounts
may include reductions due to contractual agreements with third-party payors or provider
practices, such as allowing courtesy discounts to medical staff members and employees.
283
284
Advanced Financial
Text
Companies, 2004
An allowance for uncollectibles is recognized for estimated bad debts. Note that not-forprofit hospitals recognize estimated uncollectibles from providing services as bad debts
expense. Charity care occurs when health care services are provided to a patient who has
demonstrated, in accordance with the hospital’s established criteria, an inability to pay. In
these cases, charity care does not qualify for recognition as either receivables or revenue
in the hospital’s financial statements. The determination of a charity care case may not be
able to be made when the patient is admitted, but at some point the hospital must be able
to determine that the person does meet the necessary qualifications for charity care before
reducing the amount owed. Receivables from pledges of future contributions are reported
in the period the pledge is made, net of an allowance for uncollectible amounts.
Investments Investments are initially recorded at cost if purchased or at fair value at the
date of receipt if received as a gift. Subsequently, for investor-owned, profit-seeking hospitals, equity and debt securities are reported in accordance with FASB Statement No.
115, “Accounting for Certain Investments in Debt and Equity Securities,” (FASB 115).
FASB 115 establishes three portfolios of investments: trading securities, available-for-sale
securities, and hold-to-maturity debt securities. The accounting and reporting of the investment differs according to the category. For nonprofit hospitals, equity securities with
readily determinable fair values and all investments in debt securities are measured at fair
value, in accordance with FASB Statement No. 124, “Accounting for Certain Investments Held by Not-for Profit Organizations,” (FASB 124). The Audit and Accounting
Guide for Health Care Organizations states that the investment return (including realized
and unrealized gains and losses) not restricted by donors should be classified as changes
in unrestricted net assets in the hospital’s statement of operations. The investment return
designated for current operations is included above the operation performance indicator
line (Excess of Revenues, Gains, and Other Support Over Expenses) reflecting operations; the investment return in excess of amounts designated for current operations is reported in the statement of operations below the operating performance indicator line.
Investment returns restricted by donors or by law are reported as changes in net assets
in the appropriate restricted funds. For governmental health care entities, GASB Statement No. 31, “Accounting and Financial Reporting for Certain Investments and for External Investment Pools” (GASB 31), specifies the general rule of fair value accounting
for investments.
For these three types of hospitals, investments in stock accounted for under the equity
method are reported in accordance with APB Statement No. 18, “The Equity Method of
Accounting for Investments in Common Stock” (APB 18). Some hospitals receive income from trusts that donors have established with fiduciaries, such as banks. If the hospital does not own the trust or its investments, the independent trusts are not an asset of
the hospital and are not reported on the hospital’s balance sheet. Footnote disclosure may
be made of major independent endowment or trust agreements that benefit the hospital.
Plant Assets Property, plant, and equipment is reported with any accumulated depreciation. Depreciation is recorded in the general fund because the use of assets is part of the
cost of providing medical services. The assets are reported in the general fund because
they are available for use in any manner deemed necessary by the governing board.
Assets Whose Use Is Limited Separate disclosure should be made for assets that have
restrictions placed on their use by the donor or that have been designated by the board of
directors for special use. Such funds may come from a variety of sources. For example,
grant monies received for cancer research are reported as funds restricted for specific
purposes and classified as temporarily restricted until used in support of research. Funds
contributed to assist in constructing a new children’s wing of the hospital are reported as
restricted for plant replacement and expansion and classified as temporarily restricted
Advanced Financial
Text
Companies, 2004
until used in construction. Funds received for permanent investment in the principal of an
endowment fund are reported as permanently restricted. Only those funds whose use is restricted by the donor are classified as restricted; thus, assets set aside for identified purposes by the governing board and over which the board retains control are not classified
as restricted but are regarded as assets whose use is limited.
Long-Term Debt The hospital must also account for its long-term debt and pay the
principal and interest as it becomes due. The debt is shown in the balance sheet. This practice differs from that used by most governmental entities that establish a separate debt service fund to service debt.
Net Assets The hospital segregates its net assets (1) unrestricted net assets available for
use at the discretion of hospital staff and board of directors, (2) temporarily restricted net
assets available for use when specific events established by the donor are satisfied, and (3)
permanently restricted net assets by the donor as to their use.
The results of not-for-profit hospitals’ operations are reported in a statement of operations, also often termed “the statement of activities.” This statement includes the revenues,
expenses, gains and losses, and other transactions affecting the unrestricted net assets during the period. Gains and losses from transactions that are peripheral or ancillary to the
provision of health services are reported separately from net patient service revenue. The
statement of operations should report an operating performance indicator, which reports
the results of the hospital’s operating activities for the period. This performance indicator
should include both operating income (loss) for the period and other income available for
current operations. FASB 117 requires that net assets released from restrictions for use in
operations be included before the performance indicator line on the statement of activities, generally termed “above the line.” This is so because the transfer of net assets from
the restricted group of assets for use in the entity’s operations in the unrestricted group of
net assets can then be matched with the expenses incurred to fulfill the operating restriction. The title of the performance indicator should be descriptive, such as the “Excess of
Operating Revenues, Gains, and Other Support Over Operating Expenses.”
Other changes in the unrestricted net assets during the period should be reported after
the performance indicator, generally termed “below the line.” These changes include investment return in excess of amounts designated for current operations as defined by
FASB 124. For example, a hospital’s board of directors could reserve a portion of the investment return from the revaluation of investments for use in future periods, thus making
them unavailable for current operations. The AICPA’s audit guide for hospitals indicates
that the investment return from other than trading securities should be presented below the
operating performance line, and investment return from trading securities should be presented above the operating line. However, an audit guide is lower than an FASB standard
in the hierarchy of generally accepted accounting principles. Other changes reported
below the operating performance measure line would include transfers from restricted net
assets of resources used for the purchase of property and equipment. Note that the statement of operations must separately report those items related to the acquisitions of property or equipment from those related to operating activities.
A separate, third statement, entitled the statement of changes in net assets, is used to report items affecting the temporarily restricted and permanently restricted net assets. This
third statement is covered in this chapter following discussion of the statement of operations.
Net Patient Service Revenue Net patient service revenue represents the hospital’s revenue from inpatient and outpatient care excluding charity care and contractual adjustments. Net patient service revenue represents the billings for services provided and the
285
286
Advanced Financial
Text
Companies, 2004
earning capacity of the hospital. Many hospitals are required to perform a certain amount
of charity care for which it recognizes no revenue. The charity cases are imposed by terms
of certain federal medical care grant programs. Charity care helps ensure that indigent
persons living in the region served by the hospital may obtain adequate medical services.
When charity care is provided, no revenue is recognized, but disclosure of the estimated
amount of charity care is presented in the footnotes to the financial statements.
Contractual Adjustments Contractual adjustments constitute a major deduction from
gross patient service revenue. Contractual adjustments result from the involvement of
third-party payors in the medical reimbursement process. Insurance companies or government units (especially the federal government) reimburse less than the full standard
rate for medical services provided to patients covered by insurance- or by governmentprovided services such as medicare. These third-party payors may stipulate limits on the
amount of costs they will pay. A hospital may have a standard rate for a specific service
but may contract with the third-party payor to accept a lower amount for that service. For
example, medicare establishes specific reimbursement rates for various services, termed
a “diagnosis-related group” (DRG). The hospital makes a contractual adjustment from
its normal service charge, and this adjustment is a deduction from gross Patient Service
Revenue.
Income from Ancillary Programs Income from ancillary programs represents the income earned from nonpatient sources such as television rentals, cafeteria sales, sales in
hospital-operated gift shops, parking fees, and tuition on hospital-provided educational
programs. The income reported typically represents the net earnings from such operations
rather than the gross receipts.
Interfund Transfers It is not appropriate to hold assets in a restricted fund when the
donor-specified requirements have been satisfied. For example, when contributions received to purchase plant and equipment are used to purchase new assets or when contributions received for use in educational programs are used for that purpose, the funds
should be transferred from the restricted fund to the unrestricted fund. For financial reporting purposes, this transfer between funds is reported as “net assets released” in the
statement of operations and is shown as an addition to unrestricted funds. If the interfund
transfer to the unrestricted fund is to be used for operations, the unrestricted fund reports
it above the operating performance indicator line in the statement of operations. If the
interfund transfer to the unrestricted fund is to be used for acquiring long-term assets, the
unrestricted fund reports it below the performance indicator line in the statement of
operations.
General Fund Expenses The major expenses in the general fund are for nursing services, other professional services, depreciation, bad debts, and the general and administrative costs of the hospital. These costs are recognized on the accrual basis of accounting,
similar to commercial entities. Hospitals that self-insure for malpractice costs should recognize an expense and a liability for malpractice costs in the period during which the incidents that give rise to the claims occur if it is probable that liabilities have been incurred
and the amounts of the losses can be reasonably estimated. Any expenses related to fundraising should be classified separately. Patients pay physicians directly for their medical
services.
Donations
Hospitals often receive a wide variety of services from volunteers. For example, retired
physicians or pharmacists may voluntarily work part-time in their professional roles. In
addition, the hospital may receive donations of supplies or equipment. The rules on accounting for donations and contributions to hospitals are as follows:
Advanced Financial
Text
Companies, 2004
1. Donated services. Because it is often difficult to place a value on donated services,
their values are usually not recorded. However, if the following conditions exist, the estimated value of the donated services is reported as an expense and a corresponding
amount is reported as contributions. FASB 116 specifies that a contribution of services
should be recognized if the services received (a) create or enhance nonfinancial assets
or (b) require specialized skills, are provided by individuals possessing those skills, and
would typically need to be purchased if not provided by donations.4
2. Donated assets. Donated assets are reported at fair market value at the date of the
contribution:
a. Donated assets are reported as contributions in the statement of operations, if unrestricted. For example, a donation of medical supplies is recorded as a contribution
in the unrestricted fund in the period received.
b. Donated assets that are restricted in use by the donor are reported as contributions
to the temporarily restricted or permanently restricted fund at the time of receipt.
When the restriction no longer applies, the net assets released from restriction are
reported in the unrestricted fund. For example, when donated property is placed in
service or new assets are purchased with funds that have been contributed for that
purpose, the transfer is made from the restricted to the general (unrestricted) fund
and reported as assets released from restriction in the statement of operations.
Appropriate expense accounts are charged as the donated assets are consumed. For example, donated supplies such as medicines, linen, and disposable medical items are
charged to an expense as used from inventory. For donated physical plant or equipment
having an estimated economic life of more than one year, depreciation is charged to each
period in which the plant or equipment is used.
Statement of Changes in Net Assets The third of the four financial statements for a notfor-profit hospital is termed the statement of changes in net assets. It presents the changes
in all three categories of net assets: unrestricted, temporarily restricted, and permanently
restricted. Donor-restricted contributions are reported in the appropriate category of restricted net assets. Net assets released from restrictions are shown as deductions from restricted net assets and as transfers to the unrestricted net assets. This release could be due
to the completion of a time restriction, the fulfillment of a use restriction, or the satisfaction of any other donor-specified restriction.
Statement of Cash Flows The fourth, and final, financial statement for a not-for-profit
hospital is the statement of cash flows. Its format is similar to that for commercial entities
and is presented as part of the comprehensive illustration in the next section of this chapter.
Comprehensive Illustration of Hospital Accounting and
Financial Reporting
Sol City Community Hospital, a not-for-profit hospital operated by a community group,
provides medical care for the region surrounding Sol City. The hospital has established the
following funds: (1) general, (2) specific purpose, (3) time restricted, (4) plant replacement and expansion, and (5) endowment.
Entries to record transactions in each of the funds during the 20X2 fiscal year,
ending December 31, 20X2, are presented in the next section of the chapter. First the
financial statements for the period are presented, and then the transactions from which
these statements resulted are discussed. The balance sheet for both the general and the restricted funds is presented in Figure 19–5. Note that the balance sheet is presented in what
is generally termed an aggregated style rather than a columnar or layered style that would
4
Ibid., para. 9.
287
288
Advanced Financial
Text
Companies, 2004
FIGURE 19–5
SOL CITY COMMUNITY HOSPITAL
Balance Sheet
December 31, 20X2 and 20X1
Balance Sheet for a
Not-for-Profit
Hospital
20X2
20X1
Assets
Current:
Cash
Receivables
Less: Estimated Uncollectibles
Contributions and Pledges Receivable
Inventories
Prepaid Expenses
$ 295,000
460,000
(40,000)
-050,000
15,000
$
Total Current Assets
$ 780,000
$ 476,000
$
75,000
$ 210,000
15,000
120,000
Assets Limited as to Use:
Cash Restricted as to Use for Plant Expansion
and Endowment
Pledges Receivable Restricted for Plant
Expansion and Replacement
Investments Restricted as to Use for Plant
Expansion and Endowment
14,000
400,000
(30,000)
12,000
60,000
20,000
1,330,000
808,000
Total Limited Assets
$1,420,000
$1,138,000
Investments (at fair value)
$ 681,000
$ 716,000
Property, Plant, and Equipment
Less: Accumulated Depreciation
$3,375,000
(1,150,000)
$3,200,000
(1,000,000)
Net Property, Plant, and Equipment
$2,225,000
$2,200,000
Total Assets
$5,106,000
$4,530,000
$
$
Liabilities and Net Assets
Current:
Notes Payable to Bank
Current Portion of Long-Term Debt
Accounts Payable
Accrued Expenses
Estimated Malpractice Costs Payable
Advances from Third Parties
Deferred Revenue
65,000
50,000
50,000
30,000
30,000
160,000
5,000
70,000
60,000
90,000
25,000
-0125,000
5,000
Total Current Liabilities
Long-Term Debt:
Mortgage Payable
$ 390,000
$ 375,000
1,050,000
1,100,000
Total Liabilities
$1,440,000
$1,475,000
Net Assets:
Unrestricted
$2,025,000
426,000
1,215,000
$1,685,000
570,000
800,000
Total Net Assets
$3,666,000
$3,055,000
$5,106,000
$4,530,000
separately show the financial position of each fund. The selection of display formats is the
choice of the hospital’s governing board, but the aggregated format for the entity as a
whole is more in keeping with the recommendations of FASB 117. An analysis of the
composition of the net assets held as temporarily and permanently restricted at December
31, 20X2 and 20X1, provides the following amounts:
Advanced Financial
Text
Companies, 2004
FIGURE 19–6
For the Year Ended December 31, 20X2
Statement of
Operations for a Notfor-Profit Hospital
Unrestricted Revenue, Gains, and Other Support:
Net Patient Service Revenue
Ancillary Programs
Unrestricted Gifts Used in Operations
Disposal of Hospital Assets
Donated Services
Investment Income Designated for Current Operations
Net Assets Released from Restrictions for Use in Operations
$2,360,000
30,000
93,000
5,000
10,000
10,000
192,000
Total Revenue, Gains, and Other Support
$2,700,000
Expenses:
Nursing Services
Other Professional Services
General Services
Fiscal Services
Administrative Services
Medical Malpractice Costs
Bad Debts
Depreciation
$ 800,000
630,000
700,000
100,000
80,000
30,000
60,000
200,000
Total Expenses
$2,600,000
Excess of Operating Revenues over Operating Expenses
Other Items:
Investment Return in Excess of Amounts Designated for Current Operations
Net Assets Released from Restrictions Used for Acquisition of Equipment
$ 100,000
Increase in Unrestricted Net Assets
$ 340,000
Dec. 31, 20X2
15,000
225,000
Net Change
Dec. 31, 20X1
50,000
15,000
140,000
$(150,000)
(105,000)
122,000
$200,000
120,000
18,000
Net assets
$ 205,000
$(133,000)
$338,000
Specific-Purpose Fund
Cash
Investments
$
3,000
20,000
$
1,000
-0-
$
Net assets
$
23,000
$
1,000
$ 22,000
$
2,000
-0196,000
$
-0(12,000)
-0-
Temporarily restricted:
Plant Replacement and Expansion Fund
Cash
Pledges receivable
Investments
$
Time-Restricted Fund
Cash
Contributions receivable
Investments
Net assets
Permanently restricted:
Endowment Fund
Cash
Investments
Net assets
2,000
20,000
$
2,000
12,000
196,000
$ 198,000
$ (12,000)
$210,000
$
25,000
1,190,000
$ 15,000
400,000
$ 10,000
790,000
$1,215,000
$ 415,000
$800,000
289
290
Advanced Financial
Text
Companies, 2004
FIGURE 19–7
Statement of Changes
in Net Assets for a
Not-for-Profit
Hospital
Statement of Changes in Net Assets
Unrestricted Net Assets:
Excess of Operating Revenues over Operating Expenses
Investment Return in Excess of Amounts Designated for Current Operations
Net Assets Released from Equipment Acquisition Restrictions
Increase in Unrestricted Net Assets
Temporarily Restricted Net Assets:
Contributions
Investment Gains
Net Assets Released from:
Program Use Restrictions
Equipment Acquisition Restrictions
Passage of Time
100,000
15,000
225,000
$ 340,000
$ 200,000
73,000
(180,000)
(225,000)
(12,000)
Decrease in Temporarily Restricted Net Assets
$ (144,000)
Permanently Restricted Net Assets:
Contributions
$ 415,000
Increase in Permanently Restricted Net Assets
$ 415,000
Increase in Net Assets
Net Assets at Beginning of Year
$ 611,000
3,055,000
Net Assets at End of Year
$3,666,000
The specific-purpose fund and the time-restricted fund contain resources that will be
available for operations as the restrictions are met.
The statement of operations is presented in Figure 19–6, the statement of changes in
net assets, in Figure 19–7, and the statement of cash flows in Figure 19–8. Each of these
statements is discussed after presentation of the journal entries for 20X2 for Sol City
Community Hospital.
General Fund
The transactions in the general fund for 20X2 are presented in accordance with their relative degree of importance in the hospital’s operations. The first series of entries presented
are for the revenues generated from patient care and the associated operating expenses for
the period.
Net Patient Care Revenue The hospital provides patient services of $2,600,000 measured by standard rates. From this amount, $240,000 is deducted for contractual adjustments with third-party payors, which results in a net patient revenue of $2,360,000:
(5)
(6)
Accounts Receivable
Patient Services Revenue
Gross charges at standard rates.
Contractual Adjustments
Accounts Receivable
Deduction from gross revenue for contractual adjustments.
2,600,000
2,600,000
240,000
240,000
Revenue from Ancillary Programs The hospital receives income in 20X2 from providing nonpatient services that include operating a cafeteria and gift shop and from vending
machine commissions.
Advanced Financial
Text
Companies, 2004
FIGURE 19–8 Statement of Cash Flows for a Not-for-Profit Hospital (Indirect Method)
Cash Flows from Operating Activities:
Change in Total Net Assets
Adjustments to Reconcile Changes in Net Assets
To Net Cash Provided by Operating Activities:
Depreciation
Investment Unrealized Holding Gain (not
available for current operations)
Contribution of Property, Plant, and Equipment
Gain on Disposal of Equipment
Increase in Advances from Third Parties
Increase in Malpractice Costs
Increase in Accrued Expenses
Decrease in Accounts Payable
Increase in Receivables, Net
Decrease in Pledges Receivable—Current
Decrease in Prepaid Expenses
Decrease in Inventories
Restricted Contributions and Investment Income:
Contribution for Permanent Endowment
Contributions Restricted for Plant Acquisition
Investment Income Restricted for Plant Acquisition
$611,000
$ 200,000
(15,000)
(25,000)
(5,000)
35,000
30,000
5,000
(40,000)
(50,000)
12,000
5,000
10,000
$(415,000)
(60,000)
(7,000)
Total Restricted Contributions and Investment Income
(482,000)
Total Adjustments
(320,000)
Sale of Used Hospital Assets
Sale of Investments
Acquisition of Plant, Property, and Equipment
Purchase of Investments in Endowment and Plant Replacement Funds
Remainder of Contributions to Endowment Fund Restricted to Investing
Remainder of Contributions to Plant Fund Restricted to Plant Purchases
Cash Transferred from Plant Fund for Plant Expansion
$ 291,000
$55,000
50,000
(250,000)
$(522,000)
(15,000)
(50,000)
200,000
Total Investing Flows Related to Restricted Items
(387,000)
Net Cash Used by Investing Activities
Paid Notes Payable
Paid Current Portion of Long-Term Debt
Proceeds from Restricted Contributions:
Contributions Restricted for Permanent Endowment
Contributions Restricted for Acquiring Fixed Assets
Total Restricted Proceeds
$(532,000)
$
(5,000)
(60,000)
$ 415,000
172,000
587,000
$ 522,000
Net Increase in Cash
Cash at the Beginning of Year
$ 281,000
14,000
Cash at the End of Year (unrestricted)
$ 295,000
291
292
Advanced Financial
Text
Companies, 2004
(7)
Cash
Revenue from Cafeteria Sales
Revenue from Gift Shop Sales
Revenue from Vending Machine Commissions
Income from ancillary services.
30,000
20,000
4,000
6,000
Operating Expenses The hospital incurs $2,600,000 in operating expenses for nursing
and other professional care, for general and administrative expenses, for bad debts expense, and for depreciation. Not-for-profit hospitals account for estimated uncollectibles
from provided services as an operating expense. Fiscal Services Expense includes interest expense on the hospital’s debt. The hospital recognized $30,000 in estimated malpractice costs that are probable and reasonably estimated. Cash payments are made for
$2,125,000 of the total operating expenses, and the remainder is consumption of Prepaid
Assets, Allowance for Uncollectibles, Depreciation, and increases in liabilities. The hospital receives donated services valued at $10,000, which are recognized in entry (9):
(8)
(9)
Nursing Services Expense
Other Professional Services Expense
General Services Expense
Fiscal Services Expense
Administrative Services Expense
Medical Malpractice Costs
Bad Debts Expense
Depreciation Expense
Cash
Allowance for Uncollectibles
Inventories
Prepaid Expenses
Accumulated Depreciation
Accounts Payable
Accrued Expenses
Estimated Medical Malpractice Costs Payable
Record operating expenses.
Other Professional Services Expense
Donated Services-Revenue
Receive donated services.
800,000
620,000
700,000
100,000
80,000
30,000
60,000
200,000
2,125,000
60,000
90,000
5,000
200,000
50,000
30,000
30,000
10,000
10,000
Entry (9) records the fair value of donated services both as a debit for the operating expense and as a credit for operating revenue. Therefore, donated services do not affect the
bottom line of the hospital’s statement of revenue and expenses, but they do affect the
amounts shown for the expenses and revenue sections of the statement.
Contribution Revenue During 20X2, Sol City Community Hospital received unrestricted cash gifts in the amount of $63,000 and donated medicines and medical supplies
with a market value of $30,000:
(10)
(11)
Cash
Contributions—Unrestricted
Unrestricted contributions received.
Inventory
Donated supplies received.
63,000
63,000
30,000
30,000
Advanced Financial
Text
Companies, 2004
Other Revenues and Gains Also during 20X2, income of $10,000 was earned in the unrestricted fund and is available for current operations. In addition, a gain of $5,000 was realized on the sale of equipment:
(12)
(13)
Cash
Investment Income—Designated for Current Operations
Investment earnings available for current operations.
Cash
Gain on Disposal of Equipment
Sale of hospital equipment. The cash will be
used in the operations of the hospital.
10,000
10,000
55,000
50,000
100,000
5,000
Net Assets Released from Restriction Assets were released for unrestricted use from a
variety of sources in 20X2, as follows:
Amount
From Restricted Fund
Description
$120,000
60,000
200,000
25,000
12,000
Plant Expansion and Replacement
Plant Expansion and Replacement
Resources for education and research
Income from endowment investment
Resources to acquire equipment
Donated assets placed into use
Collection of pledges receivable
Entries to record these transactions are presented here:
(14)
(15)
(16)
(17)
(18)
Cash
Net Assets Released from Program Use Restrictions
Record payment for reimbursement of operating
expenses incurred in accordance with restricted gift.
Cash
Net Assets Released from Program Use Restrictions
Receipt of endowment earnings from specific-purpose fund
upon approval and completion of specified purpose.
Cash
Net Assets Released from Equipment Acquisition Restriction
Transfer from temporarily restricted plant
replacement and expansion fund for use in
acquiring plant assets.
Net Assets Released from Equipment Acquisition Restriction
Transfer from temporarily restricted plant
replacement and expansion fund of donated
assets placed in service.
Cash
Net Assets Released from Passage of Time
Transfer from temporarily restricted funds
restricted for use in 20X2.
120,000
120,000
60,000
60,000
200,000
200,000
25,000
25,000
12,000
12,000
Each of the transfers from temporarily restricted funds involves one or more journal entries in those funds. These amounts are not included among 20X2 contributions or income
in the unrestricted fund because they were recorded as contributions or income at the time
of receipt in the temporarily restricted or permanently restricted funds. The transfer of
donated equipment initially is recorded in the temporarily restricted plant fund until the
293
294
Advanced Financial
Text
Companies, 2004
hospital begins using the asset. At the time the assets are placed in service, the value of
the donated equipment is transferred to the unrestricted fund.
Other Transactions in the General Fund The remaining transactions during the 20X2
fiscal year affect only the balance sheet accounts. Transactions affecting only the asset accounts include collecting receivables, acquiring inventory, selling an investment, and purchasing additional physical plant assets, as follows:
(19)
(20)
(21)
(22)
Cash
Accounts Receivable
Collect some receivables and write off
$50,000 as uncollectible.
Inventories
Cash
Acquire inventories.
Cash
Investments
Sell investment at cost.
Cash
Purchase new plant with cash of $50,000
from sale of investments and $200,000 from
transfer in from temporarily restricted plant
replacement and expansion fund.
2,250,000
50,000
2,300,000
50,000
50,000
50,000
50,000
250,000
250,000
Transactions affecting the current liability accounts include paying current liabilities
and recording the receipt of cash in advance of billings from third parties. The hospital reclassified the portion of the long-term mortgage that is currently due. The hospital also
revalues, to fair value, the general fund’s investment securities.
FASB 124 requires that not-for-profit organizations value their investment securities,
other than those equity investments accounted for under APB 18, at fair market value at
each balance sheet date. The total investment income during a period is from dividends,
interest, and realized and unrealized holding gains. For a not-for-profit hospital, after the
total investment income is determined, the portion of investment income designated for
current operations is reported above the operating performance indicator line on the hospital’s statement of activities. The investment return in excess of the amount designated
for current operations is separately reported below the operating performance indicator
line on the hospital’s statement of activities. The not-for-profit entity’s management is permitted to establish a policy as to the separation of total investment return for current operations or for other purposes. This policy should be described in the footnotes of the
hospital’s financial statements. For our example, assume that Sol City Community Hospital’s board of directors has a policy to set aside the recognition of unrealized holding
gains of unrestricted investments for possible future operations. Therefore, the entire
$15,000 of unrealized holding gain recognized on the hospital’s year-end revaluation of its
investment securities is separated and reported below the operating performance indicator line on the hospital’s statement of activities.
(23)
Notes Payable to Bank
Accounts Payable
Accrued Expenses
Cash
Pay liabilities outstanding at beginning of period.
5,000
60,000
90,000
25,000
180,000
Advanced Financial
Text
Companies, 2004
(24)
(25)
(26)
Cash
Advances from Third Parties
Increase in cash received from third parties for
deposits in advance of service billings.
Mortgage Payable
Reclassify current portion of long-term debt.
Investments
Unrealized Holding Gain on Investment Securities
Revalue securities to fair value and report
as not designated for current operations.
35,000
35,000
50,000
50,000
15,000
15,000
Closing entries, required for all nominal accounts, are not presented because the focus
is on other aspects of hospital accounting and because the closing process for hospitals is
the same as for any other accounting entity. As presented in Figure 19–7, the statement of
changes in net assets includes a reconciliation of net assets between the beginning of the
year and the year-end.
The statement of cash flows (Figure 19–8) is a required statement. Either the direct or
the indirect method may be used to display net cash flows from operations. Under the direct method, the specific inflows and outflows from operations are presented. Under the
indirect method, the statement begins with the change in net assets as presented on the
statement of changes in net assets. It then presents the adjustments necessary to reconcile
the net amount shown on the statement of changes in net assets with the cash flow that is
provided by operating activities. Figure 19–8 presents the indirect method because of its
popularity and wide use by hospitals. The statement of cash flows is similar to that required of commercial, profit-seeking entities. The three categories of operating activities,
investing activities, and financing activities are the same as for commercial entities.
There is an important feature, however, for the statement of cash flows for a nonprofit
hospital. A nonprofit hospital’s cash flow statement reconciles to the change in cash and
cash equivalents that is reported as a current asset on the hospital’s balance sheet. This
cash amount does not include the cash balances in the restricted accounts not available
for operations (the plant fund and the endowment fund in the Sol City Community Hospital example). The Audit and Accounting Guide for Health Care Organizations states,
“Cash and claims to cash that (a) are restricted as to withdrawal or use for other than current operations, (b) are designated for expenditure in the acquisition or construction of
noncurrent assets, (c) are required to be segregated for the liquidation of long-term debts,
or (d) are required by a donor-imposed restriction that limits their use to long-term purposes are reported separately and are excluded from current assets.”5 For example, Sol
City Community Hospital received a cash contribution to the endowment fund in the
amount of $415,000 in transaction (40) (presented later in this chapter). The $415,000
must first be subtracted from the change in net assets in the operating section of the statement of cash flows because the endowment fund does not constitute operating activities.
The $415,000 is reported as an increase in financing activities on the statement of cash
flows. Of the $415,000 received, $400,000 was used to acquire investments [transaction
(41) presented later in this chapter] and this amount is included as an investing activity
on the statement of cash flows. The $15,000 of contributions not used to acquire investments in 20X2 is reported on the statement of cash flows as an investing activity, “Remainder of contributions to endowment fund restricted to investing.” This is so because
the amount of financing resources from the restricted endowment fund must equal the
5
AICPA Audit and Accounting Guides for Health Care Organizations, 2001, Section 3.01.
295
296
Advanced Financial
Text
Companies, 2004
amount of investing resources from that restricted fund. Thus, the statement of cash
flows reconciles only to the change in cash shown as a current asset on the hospital’s balance sheet.
In addition to the primary financial statements for the present fiscal period, with comparatives for the prior period, hospitals are required to present extensive footnotes similar
to those of a commercial entity. A specific footnote disclosure is required to report the estimated value of charity care services provided by the hospital during the period.
Temporarily Restricted Funds
Sol City Community Hospital uses three funds to account for temporarily restricted funds.
The specific-purpose fund is for contributions designated for a particular use by the donor
other than plant replacement and expansion. The time-restricted fund is for contributions
pledged or received in advance that will be available for unrestricted use in the future. The
plant replacement and expansion fund is for contributions to be used in acquiring additional land, buildings, and equipment.
The specific-purpose fund is used to account for contributions received for which a
donor-specific use has been designated. For the most part, such contributions support particular operating activities of the hospital, such as educational or research programs, or
provide a particular type of service to patients. The specific-purpose fund does not directly spend the resources; it holds the restricted resources until the general fund satisfies
the terms of the restriction, usually by making the appropriate operating cost or by having
the restricted cost approved by the governing board, upon which the resources are transferred from the specific-purpose fund to the general fund to pay for the operating cost.
The specific-purpose restricted fund typically invests its cash and receives interest or
dividends from its investments. A variety of investment transactions can affect the fund
balance. Nevertheless, the specific fund is only a holding fund for temporarily restricted
resources until they are released for use by the hospital.
The following entries record the transactions in Sol City Community Hospital’s specificpurpose fund during the 20X2 fiscal year and are reflected in the statement of financial
position in Figure 19–5 and the statement of changes in net assets in Figure 19–7.
Additions to Specific-Purpose Fund The specific-purpose fund receives $6,000 of interest income from its investment of funds from a restricted gift to support the hospital’s
research activity. Restricted gifts of $115,000 are received in response to a community
fund-raising effort. The restricted gifts are allocated based on the donors’ specifications.
In addition, endowment fund earnings in the amount of $60,000 were deposited directly
in the temporarily restricted fund:
(27)
(28)
(29)
Cash
Investment Income—Research
Interest on investment of research gift resources.
Cash
Contributions—Education
Contributions—Research
Receive restricted gifts.
Cash
Investment Income—Endowment Earnings
Earnings of endowment fund deposited in
temporarily restricted funds until released
for specified purposes.
6,000
6,000
115,000
60,000
55,000
60,000
60,000
Advanced Financial
Text
Companies, 2004
Entry (29) shows the earnings generated by the permanently restricted endowment fund’s
investments as reported by the temporarily restricted fund. FASB 124 specifies that dividend, interest, and other investment income should be reported in the period earned as
increases in unrestricted net assets unless there are donor-imposed restrictions on the use
of the assets. However, in the case of Sol City Community Hospital, the earnings are reported as investment income of the temporarily restricted fund because of a donorimposed restriction on those earnings. After clearance is given, the resources are then
transferred to the general fund to be expended for the donor-specified purposes. If the
donor-restricted investment income is permanently restricted, the income is reported in
the permanently restricted net assets.
Gains or losses from valuation adjustments to fair value or from sales of securities
must also be applied in accordance with any donor restrictions. For example, if the donor
specifies that a specific investment be held for perpetuity, any valuation or sales transaction gain or loss on that investment is reported in the permanently restricted net asset
class. The important point is to follow any restrictions imposed by the donor or applicable laws. If no restrictions are applicable, the investment income and gains or losses are
reported in the unrestricted net asset class.
Deductions from Specific-Purpose Fund The specific-purpose fund is notified that the
general fund fulfilled the terms of agreements for specific restricted grants totaling
$120,000. In addition to the $120,000, the specific-purpose fund also transferred $60,000
from endowment income to the general fund.
(30)
Net Assets Released from Program Use
Restriction—Education
Restriction—Research
Restriction—Endowment Income
Cash
Funds released from temporary restriction.
61,000
59,000
60,000
180,000
This interfund transaction was also recorded in the general fund [see entries (14) and (15)
earlier in the chapter].
Under FASB 116, procedures for recording contributions were changed. Earlier recognition of contribution revenue generally is now required for most not-for-profit organizations, including hospitals. Because of the critical nature of contributions to the operations
of voluntary health and welfare organizations, a thorough treatment of this topic is included later in the chapter as part of the discussion of voluntary health and welfare organizations. For purposes of illustration in the hospital setting, it is assumed that in 20X1 the
hospital received pledges for $12,000 to be collected in 20X2. During 20X2, the $12,000
in pledges was collected and immediately transferred to the general fund for unrestricted
use [see entry (18) earlier in the chapter].
(31)
(32)
Cash
Pledges Receivable
Collection of prior period pledge.
Net Assets Released from Time Restrictions
Cash
Funds released from time restrictions.
12,000
12,000
12,000
12,000
297
298
Advanced Financial
Text
Companies, 2004
Plant Replacement and Expansion Fund
The plant replacement and expansion fund, sometimes called the “plant fund,” is used to
account for restricted resources given to the hospital to be used only for additions or major
modifications to the physical plant. This fund is used as a holding fund until the expenditures for plant assets are approved in the general fund by the governing board. The resources are then transferred to the general fund.
A primary source of resources for the plant replacement and expansion fund is from
fund-raising efforts in the communities served by the hospital. Hospitals often ask potential donors to sign pledges specifying a giving level for a period of time, for example,
$100 per month for the next 12 months. The pledges become receivables of the fund, and
typically require a substantial allowance for uncollectibles. The fund records contribution
revenue at the time the pledge is received.
The entries recorded in Sol City Community Hospital’s plant replacement and expansion fund during 20X2 are presented next and are reflected in the statement of financial
position in Figure 19–5.
Additions to Plant Fund Increases in the plant replacement and expansion fund during
the period are a donation of equipment with a fair value of $25,000 that is recorded in the
restricted plant fund until the equipment is placed into service; a donation of $60,000 for
use to acquire additional equipment; and the receipt of $7,000 of interest on the plant
fund’s investments restricted to the purchase of plant. Entries to record these events follow:
(33)
(34)
(35)
Contributions—Plant
Receive donated equipment with fair value of $25,000.
Cash
Contributions—Plant
Receive restricted gifts for use to acquire equipment.
Cash
Investment Income—Plant
Receive interest on fund’s investments.
25,000
25,000
60,000
60,000
7,000
7,000
Deductions from Plant Fund Deductions from the plant fund during the year are two
interfund transfers to the general fund. The first is the transfer of $25,000 of donated
equipment that is placed into service, and the second is the transfer of $200,000 to the
general fund for expenditures for fixed assets. These two interfund transfers are also
recorded in the general fund [see entries (16) and (17) earlier in the chapter]:
(36)
(37)
Net Assets Released—Plant Acquisition
Transfer donated equipment to general
fund at time of placement into service.
Net Assets Released—Plant Acquisition
Cash
Transfer cash to general fund for use in
acquiring plant assets.
25,000
25,000
200,000
200,000
Other Transactions in Plant Funds Other transactions affecting only the asset or liability accounts of the plant funds represent a collection of pledges made by individual
donors during the last capital fund-raising drive as well as the acquisition of additional investments in the fund. Entries for these transactions are presented here:
Advanced Financial
Text
Companies, 2004
(38)
(39)
Cash
Pledges Receivable
Collect pledges receivable.
Investments
Cash
Increase investments.
105,000
105,000
122,000
122,000
Endowment Fund
An endowment fund is a collection of cash, securities, or other assets. The use of its assets may be permanently restricted, temporarily restricted, or unrestricted based on the
donor’s wishes. Generally, endowment funds are established by donors to permanently restrict the capital of the donation and specify the use(s) of any income from those investments. The classification of an endowment fund is based, however, on the terms of the
donor’s contribution. If the endowment fund is temporarily restricted for a stated period
of time after which the principal becomes available for the specified uses, it is normally
described as a term endowment. If an endowment fund is permanently restricted into perpetuity, it is normally described as a regular or permanent endowment.
Sol City Hospital has a permanently restricted endowment fund to account for resources for which the donors have specified that the principal must be maintained in perpetuity. The income from the investments in the endowment fund is recorded in the
appropriate fund based on the donor’s specifications. If the investment income is restricted, it is recorded in the appropriate restricted fund. If no donor-imposed restriction is
present, the investment income should be recorded and reported in the unrestricted net
asset fund.
The statement of financial position in Figure 19–5 and the statement of changes in net
assets in Figure 19–7 include the entries in Sol City Community Hospital’s endowment
fund for 20X2.
Additions to Endowment Fund The endowment fund earns $60,000 interest and dividends from its permanent investments that are deposited directly in the temporarily
restricted fund (see entry 29). In addition, a total of $415,000 in new permanent endowments is received and $400,000 is used to acquire additional investments:
(40)
(41)
Cash
Contributions—Permanent Endowment
Receive additional endowments.
Investments
Cash
Acquire additional investments.
415,000
415,000
400,000
400,000
Summary of Hospital Accounting and Financial Reporting
The major operating activities of a hospital take place in the general fund. The restricted
funds are holding funds that transfer resources to the general fund for expenditures upon
satisfaction of their respective restrictions. The accrual basis of accounting is used in the
general fund to fully measure the revenue and costs of providing health care. Patient services revenue is reported at gross amounts measured at standard billing rates. A deduction
for contractual adjustments is then made to arrive at net patient services revenue. Other
revenue is recognized for ongoing nonpatient services, such as cafeteria sales and television rentals, and donated supplies and medicines. Charity care services are presented only
in the footnotes; no revenue is recognized for them. Operating expenses in the general
fund include depreciation, bad debts, and the value of recognized donated services that
299
300
Advanced Financial
Text
Companies, 2004
are in support of the basic services of the hospital. Not all donated services are recognized. Donated property and equipment are typically recorded in a restricted fund, such as
the plant fund, until placed into service, at which time they are transferred to the general
fund. Donated assets are recorded at their fair market values at the date of gift.
The financial statements of a hospital are (1) the balance sheet, (2) the statement of operations, (3) the statement of changes in net assets, and (4) the statement of cash flows.
VOLUNTARY HEALTH AND WELFARE ORGANIZATIONS
Voluntary health and welfare organizations (VHWOs) provide a variety of social services.
Examples of such organizations are United Way, the American Heart Association, the
March of Dimes, the American Cancer Society, the Red Cross, and the Salvation Army.
These organizations solicit funds from the community at large and typically provide their
services for no fee, or they may charge a nominal fee to those with the ability to pay.
As in the case of hospitals, accounting and financial reporting principles for VHWOs
have undergone major change with the publication of FASB 116 and FASB 117. Additional information on VHWOs may be obtained from a variety of sources. The AICPA
Audit Guide for Not-for-Profit Organizations requires the use of generally accepted accounting principles for VHWOs.6 VHWOs are typically audited, and the audited reports
are made available to contributors and to others interested in knowing about the financial
condition of the organization and how the resources are being used. The federal government normally provides tax-exempt status to these organizations. Another source for accounting and reporting guidelines for VHWOs is the Standards of Accounting and
Financial Reporting for Voluntary Health and Welfare Organizations, published by the
combined group of the National Health Council, the National Assembly of National Voluntary Health and Social Welfare Organizations, and the United Way of America.7 The
standards book, known as “The Black Book,” for the color of its cover, represents an effort to incorporate accounting and financial reporting standards as well as the actual experiences of the largest VHWOs in the United States.
Accounting for a VHWO
The accrual basis of accounting is required for VHWOs in order to measure fully the resources available to the organization. Depreciation is reported as an operating expense
each period because the omission of depreciation would result in an understatement of the
costs of providing the organization’s services. Therefore, accounting for VHWOs is similar to other not-for-profit organizations except for special financial statements that report
on the important aspects of VHWOs. An overview of the accounting and financial reporting principles for a VHWO is presented in this section.
Even though not required to do so, VHWOs have been free to use fund accounting in
their accounting and reporting processes. In the past, the typical VHWO has been portrayed as using a fund structure with a (1) current unrestricted fund, (2) current restricted
fund, (3) land, building, and equipment fund, and (4) an endowment fund. Many VHWOs
are considerably smaller in size and scope of activity than hospitals and may find it convenient to convert from the traditional fund structure to a single accounting entity or a
fund structure that distinguishes between unrestricted, temporarily restricted, and permanently restricted assets. The journal entries for Voluntary Health and Welfare Service
6
The AICPA periodically issues updates of its audit guides. The updates supersede earlier audit guides for
VHWOs.
7
Standards of Accounting and Financial Reporting for Voluntary Health and Welfare Organizations
(Washington D.C.) National Health Council, Inc., updated periodically.
Advanced Financial
Text
Companies, 2004
presented in this section assume the use of a single fund or accounting entity. When appropriate, designations have been added to the journal entry captions to show which of the
three classes of assets (unrestricted, temporarily restricted, or permanently restricted) is
affected. Thus, the entries could be used equally well if separate funds were established
for each of the three asset classifications. Journal entries are presented in the following
discussion for only a portion of the transactions of Voluntary Health and Welfare Service
in 20X2.
Financial Statements for a VHWO
A VHWO must provide the following financial statements: (1) statement of financial position, (2) statement of activities, (3) statement of cash flows, and (4) statement of functional expenses.
The financial statements are designed primarily for those who are interested in the organizations as “outsiders,” not members of management. These include contributors, beneficiaries of services, creditors and potential creditors, and related organizations. A clear
distinction should be maintained between restricted resources and those resources available for expenditure for the organization’s major missions. As outlined in FASB Concepts
Statement No. 6, “Elements of Financial Statements” (FAC 6), net assets of not-for-profit
organizations are divided into three mutually exclusive classes: permanently restricted net
assets, temporarily restricted net assets, and unrestricted net assets. Restricted resources
are subject to externally imposed constraints, not internal or board-designated decisions
that may be changed by the governing board of the VHWO. In addition, readers of the
general-purpose financial statements should be able to clearly evaluate management’s performance in accomplishing the objectives of the VHWO.
Statement of Financial Position for a VHWO
Figure 19–9 presents a statement of financial position for a VHWO. The format used is
similar to that used in the hospital illustration. Although it is not required by existing standards, the assets and liabilities are segregated into current and noncurrent classifications.
The net asset section of the statement of financial position for VHWOs must be segregated into unrestricted, temporarily restricted, and permanently restricted, as illustrated.
Major balance sheet accounts are as follows.
Pledges from Donors Pledges may be unconditional or conditional promises to give.
Conditional promises to give, which depend on the occurrence of a specified future and
uncertain event, are recognized only after the conditions on which they depend are substantially met (i.e., when the conditional promise becomes unconditional). The pledges
may be unrestricted, temporarily restricted, or permanently restricted based on the circumstances of the pledge and the donor’s specifications.
For the VHWO example, the current unrestricted fund includes net pledges receivable
of $78,400 in 20X2. The accrual basis of accounting recognizes the receivable and associated revenue when the unconditional pledge is received. If the contribution is available
to support current-period activities, there is no restriction. Of course, an adequate allowance for uncollectibles must be recognized as a direct reduction from the contribution
revenue. Pledges or other contributions applicable to future periods should be reported in
temporarily restricted net assets as “Contributions—Temporarily Restricted” to show that
these resources are not currently available for the entity’s operations. Further accuracy
could be attained by identifying the temporary restriction as “Contributions—Temporarily Restricted—Time Restrictions.” Conditional pledges are not recognized until the conditions on which they depend have been substantially met.
The following illustrates the entries used in accounting for a portion of the pledges received by Voluntary Health and Welfare Organization in 20X2. Note that this discussion
301
302
Advanced Financial
Text
Companies, 2004
FIGURE 19–9
VOLUNTARY HEALTH AND WELFARE SERVICE
December 31, 20X2 and 20X1
Statement of
a Voluntary Health
and Welfare
Organization
20X2
20X1
Assets
Current:
Cash
Short-Term Investments
Accounts Receivable
Inventories
Net Pledges Receivable
Prepaid Expenses
$ 68,000
39,000
1,200
6,400
78,400
8,000
$ 47,600
48,000
1,000
8,300
61,600
7,200
Total Current Assets
Cash Restricted for Long-Term Use
Long-Term Investments
$201,000
1,000
383,000
125,500
$173,700
-0351,900
121,600
Total Assets
$710,500
$647,200
Liabilities and Net Assets
Current:
Accounts Payable
Accrued Expenses
$ 16,100
4,800
$ 12,400
4,300
Total Current Liabilities
$ 20,900
$ 16,700
Noncurrent:
Mortgage Payable
Capital Leases
$ 21,000
8,000
$ 23,000
7,000
Total Liabilities
$ 49,900
$ 46,700
Net Assets:
Unrestricted
$498,200
22,900
139,500
$437,800
24,100
138,600
Total Net Assets
$660,600
$600,500
$710,500
$647,200
is for only a part of the pledges, not all pledges received in the year, nor does the following discussion attempt to reconcile to the $78,400 balance in net pledges receivable at the
end of the year. It shows the accounting for the pledges from only one of the organization’s several pledge campaigns during the year.
A special pledge campaign resulted in $100,000 of new pledges received. Of this total,
$5,000 is to be received in the current period but is to be held for use for unrestricted purposes in the following period. Experience shows that 20 percent of pledges are uncollectible for this organization. An allowance for uncollectibles is recognized in the amount
of $20,000. Note that both the current and deferred pledges are reported as contribution
revenue in the period the unconditional pledges are received and that provisions for estimated uncollectibles are then recorded as reductions of contribution revenue.
(42)
Pledges Receivable—Unrestricted
Pledges Receivable—Temporarily Restricted
Contributions—Temporarily Restricted
Receive pledges and recognize receivables.
95,000
5,000
95,000
5,000
Advanced Financial
Text
Companies, 2004
(43)
19,000
1,000
Allowance for Uncollectible Pledges—Unrestricted
Allowance for Uncollectible Pledges—Restricted
Provide for estimated uncollectible pledges as a reduction of contributions.
19,000
1,000
Note that the contributions accounts are reduced for the estimated amount of uncollectible
pledges. FASB 116 states that unconditional promises to give that are expected to be collected in less than one year may be measured at net realizable value (net settlement
value).8 Pledged contributions expected to be collected in the future beyond one year
should be valued at their present value of the estimated future cash flows. Subsequent increases in the present value of the future cash flows due to the reduction of the present
value discount are accounted for as contribution income in the appropriate fund for which
the pledge was received.
All $5,000 of the funds pledged for use the following year and $85,000 of unrestricted
pledges are collected in the current period, requiring an adjustment to both unrestricted
and temporarily restricted contribution revenue. Temporarily restricted contribution revenue is increased by $1,000 to the full $5,000 received, and $9,000 is added to unrestricted contribution revenue due to collections of $85,000 in pledges versus the initial
estimate of $76,000 ($95,000 .80). Of the remaining balance, $3,000 is written off as
uncollectible, and the remainder is carried over to the following period:
(44)
(45)
Cash—Unrestricted
Cash—Temporarily Restricted
Allowance for Uncollectible Pledges—Restricted
Contribution Revenue—Unrestricted
Contribution Revenue—Temporarily Restricted
Collect pledges including $10,000 above initial
estimate of collectibility.
Write off uncollectible pledges in unrestricted net asset class.
85,000
5,000
9,000
1,000
85,000
5,000
9,000
1,000
3,000
3,000
In the following period when the $5,000 is available for unrestricted use, the balance is reclassified as unrestricted. Some organizations would use the terms “net assets released”
instead of “reclassification,” but the terms are synonymous, and both terms are used in
this chapter to show their equality.
(46)
(47)
Cash—Unrestricted
Reclassification of Contributions to Unrestricted
Reclassify time restricted funds to unrestricted.
Reclassification of Contributions from Temporarily Restricted
Cash—Temporarily Restricted
Reclassify time restricted funds from temporarily restricted.
5,000
5,000
5,000
5,000
FASB 116 also prescribes appropriate treatment for unconditional pledges to be received over a longer period of time. In general, contribution revenue is recognized at the
8
FASB 116, para. 21.
303
304
Advanced Financial
Companies, 2004
Text
present value of future cash receipts. As is the normal practice in utilizing present value
procedures in the corporate sector, the present value is used to record contributions to be
received in the following accounting periods. For example, if a donor agrees to contribute
$10,000 per year at the end of each of the next five years, the stream of the payments is
discounted at an appropriate rate (e.g., 8 percent), and the present value is recognized at
the time the pledge is received:
(48)
Receipt of pledge.
39,927
39,927
At the end of the first year when the first payment of $10,000 is received, that amount is
reclassified from temporarily restricted to unrestricted, and the increase in present value
of the contributions receivable is recognized as an increase in temporarily restricted contributions and contributions receivable:
(49)
(50)
(51)
Cash—Unrestricted
Reclassification of Contributions to Unrestricted
Reclassify time restricted funds to unrestricted.
Reclassification of Contributions from Temporarily Restricted
Reclassify time restricted funds from temporarily restricted.
Increase in the present value of contributions receivable.
10,000
10,000
10,000
10,000
3,194
3,194
Investments Investments may be purchased or donated to the organization. Purchased
investments should be recorded at cost. Securities donated to the organization should be
recorded at their fair market values at the dates of the gifts. Subsequently, equity investments (other than APB 18 equity investments) and all investments in bonds are reported
at market value. Appreciation gains (or reductions in value) are separately identified as
unrealized gains (losses) in the organization’s statement of activity in accordance with
FASB 124. Transfers of investments from one portfolio to another should be made at market value, with any gains or losses in valuation recorded.
Investment earnings or losses should be reported as unrestricted, temporarily restricted,
or permanently restricted, depending on how they are to be used. For example, the donor
of a donor-restricted endowment fund may not specify any limitations on the uses of the
income or losses from the fund. In that case, the gains or losses on the investments are reported on the statement of activities as changes in unrestricted net assets. However, if the
donor stipulates the treatment of the earnings or losses from the donor-restricted endowment fund, that treatment must be followed. In some cases, the donor may impose some
time or dollar requirement on the earnings such as requiring that the income for the first
five years be added to the permanent endowment or that only income above some dollar
amount can be transferred to an unrestricted fund while the income below that amount
must be added to the principal of the permanent endowment. The key point is that the notfor-profit association must follow the donor’s specifications as presented in the contribution agreement between the donor and the not-for-profit association and any applicable
law regarding a not-for-profit association’s management of restricted resources.
Land, Buildings, and Equipment Land, buildings, and equipment, depreciation expense, and the accumulated depreciation on the fixed assets generally are reported as unrestricted unless restricted by the donor. The basis of fixed assets is cost, and donated
Advanced Financial
Text
Companies, 2004
assets are recorded at their fair market values at the dates of the gifts. Donations of fixed
assets that will be sold by the organization in the near future are equivalent to other contributions and should be separately reported as unrestricted assets until sold. For example,
assume that the VHWO receives land as a donation. The VHWO plans to sell the land and
use the proceeds from the sale in supporting the entity’s program services. The land
should be recorded at fair value as an unrestricted asset and reported as land held for resale until sold.
A VHWO may use any one of the methods of depreciation available to commercial entities. Not-for-profit entities are not required to depreciate assets such as works of art or
other historically valuable assets in instances in which the not-for-profit entity has made
a commitment to preserve the value of the art or historically valuable assets, and has
shown the capacity to do so.
Liabilities Liabilities are recorded in the normal manner under the accrual model. In
most situations, liabilities will be reported as part of the unrestricted net assets. For example, in Figure 19–9, the mortgage payment made by Voluntary Health and Welfare Service in 20X2 was recorded as a $2,000 debit to Mortgage Payable and a $2,000 credit to
Cash. In this illustration, property, plant, and equipment is classified as an unrestricted
asset. In some cases, mortgage payments on assets classified as restricted are made from
unrestricted funds. The following entries are needed in the latter case:
(52)
(53)
Reclassification to Restricted Assets
Cash (Unrestricted)
Mortgage payment made from unrestricted assets.
Mortgage Payable—Restricted Assets
Reclassification from Unrestricted Assets
Reduction of carrying value of mortgage.
2,000
2,000
2,000
2,000
Net Assets Separate disclosure should be provided for the amounts of net assets designated as unrestricted, temporarily restricted, and permanently restricted. The VHWO’s
governing board also may show its intent to use unrestricted resources for specific needs
in the future by creating one or more board-designated captions. For example, the
$498,200 of unrestricted net assets at December 31, 20X2, shown in Figure 19–9 could be
separated into board designated and undesignated. Board-designated purposes might be
for purchases of new equipment, research, construction of new facilities, or other asset acquisitions. While the statement of financial position could reflect the designation of resources, the governing board may change these at any time.
Figure 19–10 presents the major operating statement for VHWOs, the statement of activities. The overall structure of the statement of activities for voluntary health and welfare
organizations and other not-for-profit entities should be very similar as a result of FASB
117. As for other types of nonprofit entities, a number of organizations have issued standards relating to VHWOs. Both the National Health Council’s “black book” of standards
for VHWOs and the AICPA Audit Guide for Not-for-Profit Organizations contain recommendations for accounting for VHWOs. Several of the unique aspects of VHWOs are discussed next.
Public Support Historically, a distinction has been made in the sources of funding received by VHWOs. Nonprofit organizations generally provide services to those who cannot afford to pay for the benefits received or support programs for which little
compensation is received. For VHWOs, the primary source of funds is likely to be contributions from individuals or organizations who do not derive any direct benefit from the
305
306
Advanced Financial
Companies, 2004
Text
FIGURE 19–10 Statement of Activities for a Voluntary Health and Welfare Organization
Unrestricted
Contributions
Legacies and Bequests
Collections through Affiliates
Allocated from Federated Fund-Raising Effort
Memberships
Program Fees
Sale of Materials
Investment Income
Gain on Investments
Donated Services
Net Assets Released from Restriction:
Passage of Time
Equipment Acquisition
Endowment Transfers
$627,000
15,000
2,800
45,300
6,100
700
200
36,400
12,000
3,000
Temporarily
Restricted
$42,300
Permanently
Restricted
$ 9,900
500
1,000
Total
$679,200
15,000
2,800
45,300
6,100
700
200
36,900
13,000
3,000
25,000
8,100
10,900
10,000
(25,000)
(8,100)
(10,900)
Total Revenues, Gains and Other Support
$802,500
$ (1,200)
Program Services and Operating Costs:
Research
Public Health Education
Professional Training
Community Services
Management and General
Fund Raising
Payments to National Offices
$274,300
92,000
106,000
98,600
91,700
64,500
15,000
Total Expenses
$742,100
$
-0-
$742,100
$ 60,400
437,800
$ (1,200)
24,100
$
900
138,600
$ 60,100
600,500
$498,200
$22,900
$139,500
$660,600
(10,000)
$
900
$802,200
$274,300
92,000
106,000
98,600
91,700
64,500
15,000
-0-
$
VHWO for their gifts. The magnitude of funds received and the diversity of contributors
are important in evaluating the effectiveness of VHWOs. Four sources of resources included in the 20X2 statement of activities for Voluntary Health and Welfare Service in
Figure 19–10 are considered to fall in the category of support. They include contributions,
legacies and bequests, collections through affiliates (other organizations in the same community or with similar goals), and contributions received from the federated (national or
regional) organization’s fund-raising efforts.
A recent change has occurred in accounting for support received from special events.
In the past, the costs of providing the event were deducted from the total proceeds generated and the net amount was reported as support. Under the guidelines of FASB 117, total
proceeds from a sponsored event such as a dance gala or marathon are reported as support
from special events, and the costs of sponsoring the event are reported as fund-raising
costs. Even though many of the necessary items are contributed for such activities, the
costs of sponsoring an event can be rather substantial. The frequency of such events undoubtedly was a factor in the change in the tax laws that now require nonprofit organiza-
Advanced Financial
Text
Companies, 2004
tions sponsoring a special event to provide participants with a statement detailing the portion of the cost of a ticket or other contribution that may be treated as a charitable contribution for tax purposes.
Revenues Funds received in exchange for services provided or other activities are classified as revenues. Although the majority of a VHWO’s resources are obtained from public support, funds also are received from memberships, fees charged to program
participants, sales of supplies and services, and investment income.
Gains Investments and other assets may be sold from time to time, and the difference
between the sale price and the carrying value is included in the statement of activities as
a gain or loss. Much of the time, gains received from sales of investments are reinvested
in anticipation of future earnings; nevertheless, all gains and losses should be included in
the statement of activities for the period.
Donated Materials and Services A VHWO often relies heavily on donated materials
and services. Donated materials should be recorded at fair value when received. If the donated materials are used in one of the VHWO’s program services, their recorded value
should be reported as an expense in the period used. If the donated materials simply pass
through the VHWO to its charitable beneficiaries, the VHWO is acting as an agent, and
the materials are not recorded as a contribution or an expense.
Donated services are an essential part of a VHWO. Because of the difficulty of valuing
these services, they often are not recorded as contributions. However, if donated services
are significant, the VHWO should recognize them if the services (1) create or enhance
nonfinancial assets or (2) require specialized skills, are provided by individuals possessing those skills, and typically need to be purchased if not provided by donation.9 If these
conditions are satisfied, the value of donated services should be reported as part of the
public support and as an expense in the period in which the services are provided. As an
example of donated services, assume that a CPA donates audit services with an estimated
value of $3,000. The VHWO makes the following entry in the current unrestricted fund to
recognize the donated services:
(54)
Expenses—Supporting Services
Support—Donated Services
CPA donates audit.
3,000
3,000
Expenses The statement of activities should contain information about the major costs
of providing services to the public, fund-raising, and general and administrative costs in
order to provide contributors and others information that is useful in assessing the
VHWO’s effectiveness. Those costs of providing goods and services to beneficiaries, customers, or members in fulfilling the primary VHWO mission are referred to as program
service costs. A VHWO’s statement of activities normally should include the total costs of
providing each of the major classes of program services. As shown in Figure 19–10, the
primary activities for Voluntary Health and Welfare Service are research, public health education, professional training, and community services. A detailed breakdown of these
costs is presented in the statement of functional expenses required of all VHWO organizations; presented later in this chapter, it provides information on the amount of salary expense, telephone, travel, supplies, and other costs incurred in providing each of the major
programs.
Information also is presented in the statement of activities on the costs of other activities needed to operate effectively but that may not be directly assignable to a particular program. These costs generally are reported either as management and general administrative
9
FASB 116, para. 9.
307
308
Advanced Financial
Text
Companies, 2004
costs or as fund-raising costs. Management and general activities include the costs of maintaining the general headquarters, record-keeping, business management, and other management and administrative activities not directly assignable to program services or
fund-raising activities. Fund-raising activities include the costs of special mailings, compiling potential donor lists, conducting campaigns through contacts with foundations and
governmental agencies, and other similar costs. In those organizations whose membership
contributions are an important source of funds, separate disclosure of the costs of soliciting members and providing special benefits to those who are members should be made.
Depreciation costs for 20X2 included in the statement of activities in Figure 19–10 totaled $9,500. An allocation is made to each of the program services and supporting services based on square footage used or some other reasonable basis. For example, an
allocation of the $9,500 of depreciation, based on square footage occupied, to each of the
program and supporting services is recorded with the following entry:
(55)
Research—Depreciation
Public Health—Depreciation
Professional Training—Depreciation
Community Services—Depreciation
Management and General—Depreciation
Fund-Raising—Depreciation
Record depreciation for 20X2.
4,300
1,000
2,000
1,200
500
500
9,500
Costs of Informational Materials That Include a Fund-Raising Appeal Not-for-profit
entities often prepare informational materials that include a direct or indirect message soliciting funds. The issue is how to record the cost of these materials. Should these costs be
a program expense or a fund-raising expense? Many VHWOs prefer to classify such costs
as program rather than fund-raising to highlight the fulfillment of its basic service mission. Users of the general-purpose financial statements are concerned with the amounts
that VHWO organizations spend to solicit contributions, as opposed to the amounts spent
for program services. If a not-for-profit entity cannot show that a program or management
function has been conducted in conjunction with the appeal for funds, the entire cost of
the informational materials or activities should be reported as a fund-raising expense.
However, if it can demonstrate that a bona fide program or management function has been
conducted in conjunction with the appeal for funds, then the costs of informational materials are allocated between programs and fund-raising. Evidence of a bona fide program
intent in a brochure would be an appeal designed to motivate its audience to action other
than providing financial support to the organization. An informational content of a
brochure might include a description of the symptoms of a disease and the actions an individual should take if one or more of the symptoms occur. Thus, the content of the message and the intended audience are significant factors.
The third required financial statement for VHWOs is the statement of cash flows, as presented in Figure 19–11. The format of this statement is similar to that for hospitals as discussed earlier in the chapter. Note that under the indirect approach, the statement begins
with the change in net assets and reconciles to the net change in cash during the period.
Statement of Functional Expenses
The fourth statement required of all VHWOs is the statement of functional expenses. This
statement details the items reported in the expenses section of the statement of activities in
Advanced Financial
Text
Companies, 2004
FIGURE 19–11
Statement of Cash
Flows for a Voluntary
Health and
Welfare Organization
Adjustments to Reconcile Changes in Net Assets to Net Cash
Provided by Operating Activities:
Depreciation
Gain on Sale of Investments
Decrease in Short-Term Investments
Increase in Accounts Receivable
Increase in Contributions Receivable (net)
Decrease in Inventories
Increase in Prepaid Expenses
Increase in Accounts Payable
Increase in Accrued Expenses
Contributions Restricted for Equipment Acquisition
Endowment Contributions Restricted for Acquisition
of Investments
Purchase of Property, Plant, and Equipment
Proceeds from Sale of Investments
Purchase of Investments
Investment Gain Restricted to Purchase of Investments
Mortgage Payments
Capital Lease Agreements
Contributions Restricted to Acquiring Fixed Assets
Endowment Gain Restricted to Acquiring Investments
Net Cash Used in Financing Activities
$60,100
$
9,500
(13,000)
9,000
(200)
(16,800)
1,900
(800)
3,700
500
(10,900)
(9,900)
(27,000)
$33,100
$(13,400)
40,000
(59,100)
(1,000)
(33,500)
$ (2,000)
1,000
10,900
1,000
9,900
20,800
Cash at the Beginning of Year
$20,400
47,600
Cash at the End of Year
$68,000
Figure 19–10. Figure 19–12 is a standard format for the statement of functional expenses.
The expense categories are presented across the columns. The rows are the specific nature
of the items composing these expense categories from the various funds.
Bad Debts Expense is from estimated uncollectibles directly related to program services and operations, including membership fees. Note that any estimated uncollectible
pledges are deducted directly from contribution revenue.
The statement of functional expenses includes depreciation of $9,500 for the year, allocated among the various programs and supporting services. Total expenses of $742,100
in Figure 19–10 are analyzed and reconciled on the statement of functional expenses in
Figure 19–12.
Summary of Accounting and Financial Reporting for VHWOs
The accounting and financial reporting requirements for VHWOs are specified in
FASB 116, FASB 117, and the AICPA Audit Guide for Not-for-Profit Organizations. The
accrual basis of accounting is used. Primary activities of the VHWO are reported in the
unrestricted asset class. Resources restricted by the donor for specific operating purposes
309
$92,000
Total Functional Expenses
Total Expenses
Payments to National Office
$91,000
1,000
Total Expenses Before Depreciation
$270,000
Depreciation of Buildings and Equipment
4,300
$106,000
$104,000
2,000
$ 56,600
5,200
1,000
1,200
900
6,000
3,400
6,500
10,800
10,500
600
1,300
$ 51,100
2,900
2,600
$98,600
$97,400
1,200
$59,600
1,600
1,000
4,300
2,800
9,000
400
1,400
4,200
1,600
10,300
1,200
$53,800
2,900
2,900
$570,900
$562,400
8,500
$234,600
8,000
3,000
7,300
7,300
19,400
4,800
19,700
18,600
14,700
221,400
3,600
$212,100
11,500
11,000
$91,700
$91,200
500
200
$73,800
3,000
2,100
2,500
2,600
3,000
600
900
1,100
1,400
$66,100
4,100
3,600
20X2
20X1
12,000
$742,100 $696,600
15,000
$64,500 $156,200 $727,100 $684,600
$64,000 $155,200 $717,600 $678,100
500
1,000
9,500
6,500
$36,900 $100,700 $345,300 $379,300
1,500
4,500
12,500
12,000
3,000
5,100
8,100
7,900
7,200
9,700
17,000
16,800
6,000
8,600
15,900
14,300
1,000
4,000
23,400
20,500
100
700
5,500
4,800
7,400
8,300
28,000
23,000
200
1,300
19,900
21,500
600
2,000
16,700
16,300
221,400 157,500
100
300
3,900
4,200
$34,100 $100,200 $312,300 $347,000
1,000
5,100
16,600
16,800
1,800
5,400
16,400
15,500
Total
Text
$274,300
$64,200
1,000
600
1,400
3,200
3,400
800
11,200
2,000
1,800
1,200
200
$ 54,200
200
400
400
400
1,000
200
600
1,600
800
209,300
900
Total Salaries and Related Expenses
Professional Fees
Supplies
Telephone
Bad Debts and Other
Occupancy
Rental of Equipment
Printing and Publications
Travel
Conferences and Meetings
Awards and Grants
Postage and Shipping
$58,200
2,900
3,100
$ 49,000
2,800
2,400
Total
Management
and
FundGeneral
Raising
Total Program
and Supporting
Services Expenses
Salaries
Employee Benefits
Payroll Taxes, etc.
Public
Health
Professional Community
Research Education
Training
Services
Supporting Services
Advanced Financial
Program Services
Statement of Functional Expenses
Year Ended December 31, 20X2
(with comparative totals for 20X1)
FIGURE 19–12 Statement of Functional Expenses for a Voluntary Health and Welfare Organization
310
Companies, 2004
1033
Advanced Financial
Text
Companies, 2004
or future periods are reported as temporarily restricted assets. Assets contributed by the
donor with permanent restrictions are reported as permanently restricted assets.
A VHWO provides four financial statements: (1) statement of financial position,
(2) statement of activities, (3) cash flow statement, and (4) statement of functional expenses. The statement of functional expenses is required of all VHWOs to provide an
analysis of all of the organization’s expenses, including depreciation. Expenses are broken
down into types, such as salaries, supplies, and travel, and are summarized by individual
program services and individual supporting services.
OTHER NOT-FOR-PROFIT ENTITIES
There are many types of not-for-profit entities in addition to hospitals and voluntary
health and welfare organizations. Our society depends heavily on such organizations for
religious, educational, social, and recreational needs. Examples of other not-for-profit organizations (ONPOs) include the following:
Cemetery organizations
Civic organizations
Fraternal organizations
Labor unions
Libraries
Museums
Other cultural institutions
Performing arts organizations
Political parties
Private and community foundations
Private elementary and secondary schools
Professional associations
Public broadcasting stations
Religious organizations
Research and scientific organizations
Social and country clubs
Trade associations
Zoological and botanical societies
Accounting for ONPOs
The issuance of FASB 116 and FASB 117 has done much to bring the financial reporting
standards of hospitals, voluntary health and welfare organizations, and other not-forprofit organizations into agreement. In addition to the two FASB statements, the AICPA
Audit Guide for Not-for-Profit Organizations provides guidance for accounting and financial reporting standards for ONPOs.
ONPOs vary significantly in size and scope of operations. While accrual accounting is
required for all ONPOs, some small organizations operate on a cash basis during the year
and convert to an accrual basis at year-end. Other ONPOs have thousands or even millions of members and hold assets worth substantial sums of money. From the viewpoint
of asset management and control procedures, such organizations may be virtually identical to a large business entity. The fact that they are not in business to earn profits from
selling goods and services continues to distinguish some aspects of financial reporting for
ONPOs from that of business entities, however.
In the past, it has been assumed that fund accounting would be used by ONPOs in a
manner similar to accounting for VHWOs. With the adoption of FASB 116 and FASB 117,
it is likely the procedures used by ONPOs and VHWOs will move away from the traditional
funds used and account for all transactions in a single entity or by establishing separate accounts for unrestricted, temporarily restricted, and permanently restricted assets.
Financial Statements of ONPOs
The principal purpose of the financial statements of an ONPO is to explain how the available resources have been used to carry out the organization’s activities. Therefore, the
statements should disclose the nature and source of the resources acquired, any restrictions
311
312
Advanced Financial
Text
Companies, 2004
FIGURE 19–13
ELLWOOD HISTORICAL SOCIETY
June 30, 20X2 and 20X1
Statement of
an Other Not-forProfit Organization
20X2
20X1
Cash
Accounts Receivable
Contributions Receivable
Inventories
Prepaid Expenses
Cash Restricted for Long-Term Investments
Long-Term Investments (at fair value)
Property, Plant, and Equipment (net)
$ 32,000
17,500
48,000
3,000
6,500
2,000
184,000
242,000
$ 16,800
1,500
30,000
1,000
6,500
-087,000
246,000
Total Assets
$535,000
$388,800
Accounts Payable
Mortgage Payable
Net Assets:
Unrestricted
$ 28,000
178,000
$ 28,000
187,000
179,000
48,000
102,000
130,800
43,000
-0-
$535,000
$388,800
on the resources, and the principal programs and their costs; they should also provide information on the organization’s ability to continue to carry out its objectives. An ONPO
must provide the following financial statements: (1) a statement of financial position, (2)
a statement of activities, and (3) a statement of cash flows. Although the statement of functional expenses is not required of ONPOs, it may be appropriate to prepare a statement
providing information on expenses by function for each major program when an ONPO is
involved in a broad range of activities or conducts activities that are very distinct from one
another.
Statement of Financial Position for an ONPO
Figure 19–13 presents a statement of financial position for Ellwood Historical Society, a
nonprofit organization that renovates and preserves historical buildings in Sol City. The
society has its own governing board and is not associated with a government. The illustrated statement of financial position is a very simple one in light of the well-defined mission of the organization.
Land, Buildings, and Equipment Land, buildings, and equipment owned by the ONPO
and used in its activities generally are recorded at historical cost and depreciated in the
normal manner. Operating assets that are donated should be recorded at fair market value
at the date of contribution. Unless the donor restricts the use of the asset, land, buildings,
and equipment should be included in unrestricted net assets reported on the statement of
financial position.
Inexhaustible Collections Libraries, museums, art galleries, and similar entities often
have collections of works of art or other historical treasures that are held for public viewing or for research. Some organizations recognize such works of art or other historical
treasures as assets, but most do not. Moreover, when individual works of art or historical
treasures are recorded, the Financial Accounting Standards Board in FASB 93 concluded
not-for-profit organizations are not required to record depreciation.10 Specific rules for
10
Financial Accounting Standards Board Statement No. 93, “Recognition of Depreciation by Not-forProfit Organizations,” August 1987, para. 6.
Advanced Financial
Text
Companies, 2004
FIGURE 19–14 Statement of Activities for an Other Not-for-Profit Organization (ONPO)
Unrestricted
Contributions
Donated Services
Membership Dues
Admissions
Investment Income
Gain on Investments
Net Assets Released from Restriction:
Equipment Acquisition
Endowment Transfers
$130,000
3,000
16,000
12,000
12,200
5,000
62,600
13,000
10,000
Total Revenues, Gains, and Other Support
$263,800
Program Services and Support:
Community Education
Research
Auxiliary Activities
General and Administrative
Fund-Raising
$139,400
24,200
19,000
20,000
13,000
Total Expenses
$215,600
Temporarily
Restricted
Permanently
Restricted
$78,000
$100,000
2,600
12,000
Total
$308,000
3,000
16,000
12,000
26,800
5,000
(62,600)
(13,000)
(10,000)
$ 5,000
$102,000
$370,800
$139,400
24,200
19,000
20,000
13,000
$
-0-
$
-0-
$215,600
$48,200
130,800
$ 5,000
43,000
$102,000
-0-
$155,200
173,800
$179,000
$48,000
$102,000
$329,000
disclosure of the costs of items purchased and funds generated from the sale of such items
are presented in FASB 116.11
A statement of activities for Ellwood Historical Society, presented in Figure 19–14, reports the support, revenue, expenses, transfers, and changes in fund balance during the
fiscal period.
The format for the statement of activities is comparable to the statement of activities
for a VHWO. For the Ellwood Historical Society, contributions are the primary source of
support. However, both membership dues and admissions provide a greater source of revenue than they do in the voluntary health and welfare setting. Memberships often provide
free admission or admission at reduced rates in the case of a museum, art gallery, or library. Thus, memberships and admissions may be interrelated in these organizations.
Other types of organizations may have very different sources of funds and major expense
categories. The financial statement captions and presentation should be adjusted to focus
on these attributes in such cases.
As with VHWOs, depreciation charges for the period have been apportioned to the
ONPO’s primary programmatic activities and reported as expenses in the unrestricted assets section of the statement of activities. Disclosure should be made of the depreciation
11
Ibid., para. 26.
313
314
Advanced Financial
Text
Companies, 2004
FIGURE 19–15
Statement of Cash
Flows for an Other
Not-for-Profit
Organization
Adjustments to Reconcile Changes in Net Assets to Net Cash
Provided by Operating Activities:
Depreciation
Gain on Sale of Equipment
Increase in Accounts Receivable
Increase in Contributions Receivable
Increase in Inventories
Contribution for Permanent Endowment
Contribution Restricted for Plant
Permanently Restricted Endowment Income
Purchase of Property, Plant, and Equipment
Proceeds from Sale of Investments
Purchase of Additional Investments
Investment Income Restricted for Investments
Proceeds from Sale of Equipment
Investment Income Restricted for Permanent Endowment
Contributions Restricted for Acquiring Fixed Assets
Mortgage Payments
$155,200
$ 17,000
(5,000)
(16,000)
(18,000)
(2,000)
(100,000)
(13,000)
(2,000)
(139,000)
$ 16,200
$ (16,000)
3,000
(100,000)
(2,000)
8,000
(107,000)
$100,000
2,000
13,000
(9,000)
106,000
Cash at Beginning of Year
$ 15,200
16,800
Cash at End of Year
$ 32,000
charges for the period and the balance of accumulated depreciation in the financial statements or footnotes to the ONPO’s financial statements to assist financial statement readers in assessing the ONPO’s operating effectiveness and financial position.
Assets released from restriction during the period are shown as reclassifications in the
statement of activities. Thus, a contribution of $21,000 for research on Civil War activities would be included in the $78,000 reported as temporarily restricted contributions in
Figure 19–14. If $19,500 of the contribution is spent during 20X2, that amount is part of
the $62,600 reclassified from temporarily restricted to unrestricted assets (net assets released from program use restrictions) in 20X2. The $19,500 expense incurred in conducting the research is included in the $24,200 total reported as research expense in
20X2.
Figure 19–15 presents the statement of cash flows for Elmwood Historical Society. It begins with the net change in assets for the combined entity taken from the statement of activities. Adjustments are made for noncash revenues and expenses and changes in
account balances to arrive at cash provided by operating activities. Net cash flows from
investing activities and financing activities are added (deducted) in arriving at the net increase (decrease) in cash for the period. The net cash flow for the period is added to the
Advanced Financial
Text
Companies, 2004
beginning cash balance in unrestricted assets to arrive at the balance at the end of the
period.
Summary of Accounting and Financial Reporting for ONPOs
Accounting for ONPOs is similar to that for VHWOs. The accrual basis of accounting is
used for financial reporting purposes. A statement of financial position, a statement of activities, and a statement of cash flows are required for financial reporting purposes. When
a large number of programs or a number of very different types of programs are part of
the operations of an ONPO, it may be desirable to prepare a statement of expenses by
functional area or major program as well. As a result of FASB 116 and FASB 117, the reporting requirements of ONPOs are substantially the same as VHWOs.
Summary of
Key Concepts
Colleges and universities may be public or private. The accounting and financial standards for public
(governmental) colleges and universities are specified by the GASB, as provided in GASB 34 and
GASB 35. Accounting and reporting for private colleges and universities are specified by the FASB.
Four FASB standards are important for not-for-profit entities. FASB 93 specified that depreciation must
be charged to operations and that the balance of net assets be reported. FASB 116 presented the standards for accounting for contributions. FASB 117 presented the display standards for not-for-profit entities. FASB 124 specified the accounting for investments held by not-for-profit entities. Private colleges
and universities must provide three financial statements: (1) a statement of financial position, (2) a statement of activities, and (3) a statement of cash flows. The net assets must be separated into three categories: (1) unrestricted, (2) temporarily restricted, and (3) permanently restricted based on restrictions
imposed by donors, law, or contract.
Health care providers, voluntary health and welfare organizations, and other not-for-profit entities use
the accrual basis of accounting and account for a majority of transactions in the unrestricted asset class.
The restricted funds of a health care provider and other not-for-profit entities are reported as temporarily or permanently restricted, depending on the terms established by the donor. Such funds are classified
as restricted until the conditions of the restrictions are met and the resources are reclassified to the unrestricted net asset category. Hospitals deduct contractual adjustments from gross billings in arriving at net
patient services revenue in the statement of operations. Donated medical supplies and medicines are included as revenue in the period of receipt. Nonprofit hospitals provide a statement of financial position,
a statement of operations, a statement of changes in net assets, and a statement of cash flows. The statement of operations for a hospital must present a performance indicator, called something such as “Excess of revenues over expenses,” that includes both operating income and other income such as
investment income from trading securities in the general fund’s investment portfolio. Below this operating indicator, hospitals present unrealized gains or losses on the general fund’s other-than-trading securities, amounts for net assets released from restrictions used for purchase of property and equipment, and
other nonoperating items.
VHWOs and ONPOs recognize contribution revenue, investment income, and gains and losses on investments for unrestricted, temporarily restricted, and permanently restricted asset classes. Contributions
are reported in the unrestricted asset class unless they are intended for future periods or for specificpurpose use, in which case they are included as contributions in the temporarily or permanently restricted
asset classes. When restrictions on temporarily restricted contributions are satisfied, a reclassification to
unrestricted assets is shown in the statement of activities, and any expenses associated with the release
from restricted funds are included in expenses for unrestricted assets for the period. Earnings of permanently restricted funds that are available for temporarily restricted or unrestricted purposes are shown as
income in those net asset classes in the statement of activities for the period as well.
VHWOs and ONPOs prepare a statement of financial position, a statement of activities, and a statement of cash flows. VHWOs also must prepare a statement of functional expenses. Because of differences in the types and scope of activities of the various organizations, the statements may have
differences in account titles and items included; however, many of the prior differences in financial presentation between not-for-profit organizations were eliminated by the requirements of FASB 116 and
FASB 117.
315
316
Advanced Financial
Text
Companies, 2004
general fund, 1005
performance indicator, 1008
permanently restricted net
assets, 1008
pledges receivable, 1024
restricted funds, 1006
specific operating
purposes, 1006
statement of functional
expenses, 1031
temporarily restricted net
assets, 1008
unrestricted net assets, 1008
Key Terms
assets whose use is
limited, 1008
board-designated
resources, 1006
costs of informational
materials, 1031
donated materials and
services, 1030
Questions
Q19-1
How are tuition scholarships reported by a private college or university?
Q19-2
What are the classifications of net assets reported in the statement of financial position by private colleges? Identify the types of assets assigned to each classification.
Q19-3
What are the major differences in financial reporting for a public university and a private university?
Q19-4
What is the basis of accounting in a hospital’s general fund? Its restricted funds?
Q19-5
How are donated services accounted for by a hospital? How does it account for donated equipment and
donated medical supplies?
Q19-6
A donor contributes $15,000 to a hospital to be used for operating costs in the intensive care unit. How
does it account for this contribution? How does it account for the expenditure of the $15,000?
Q19-7
What are the components of a hospital’s net patient service revenue?
Q19-8
Where is a gain on the sale of hospital properties recorded by a hospital? How is the gain reported in the
hospital’s financial statements?
Q19-9
Is depreciation accounted for by a hospital? Why or why not?
Q19-10
What is the basis of accounting for the unrestricted assets of a VHWO? What is the basis for the restricted assets?
Q19-11
Where are fixed assets recorded for a VHWO? Is depreciation recorded for a VHWO?
Q19-12
An individual contributes $10,000 to a VHWO for restricted use in a public health education service.
How does the VHWO account for this contribution? How does it account for the expenditure of the
$10,000?
Q19-13
Explain the accounting for pledges from donors to a VHWO.
Q19-14
Why do VHWOs not report all pledges received in the period in the unrestricted assets section of the
statement of activities? Identify what is not included.
Q19-15
How do VHWOs account for donated services?
Q19-16
Describe the statement of functional expenses. What organizations must prepare this statement?
Q19-17
An alumna of a sorority donates $12,000 to it for restricted use in its community service activity. How is
the contribution accounted for by this ONPO? How is the expenditure of the $12,000 accounted for?
Q19-18
Are donated services received by an ONPO accounted for in the same manner as those received by hospitals? Why or why not?
Q19-19
What is the market value unit method of accounting for investments?
Q19-20
Should a rotary club, an ONPO, report depreciation expense? Why or why not?
Q19-21
Describe the statement of activities for an ONPO. Compare it with the statement of activities for a
VHWO.
Q19-22
Give two examples of contributions to an ONPO that should be reported as temporarily restricted and
two that should be reported as permanently restricted.
Advanced Financial
Text
Companies, 2004
Cases
C19-1
Judgment
Accounting for Donations
Hospitals, voluntary health and welfare organizations, and other not-for-profit organizations often rely
heavily on donations of volunteers’ time as well as equipment, supplies, or other assets.
Required
a. Specify the criteria to be used to determine the accounting for donated services to (1) hospitals, (2)
voluntary health and welfare organizations, and (3) other not-for-profit organizations. Discuss the
reasons for any differences in the accounting criteria used.
b. How are donations of capital assets, such as equipment, accounted for by hospitals? Is depreciation
recorded on these donations? Why or why not?
c. How are cash contributions accounted for by (1) hospitals, (2) voluntary health and welfare organizations, and (3) other not-for-profit organizations?
C19-2
Understanding
Public Support to an Other Not-for-Profit Organization
Leslie Dawnes has just been elected treasurer of the local professional association of registered nurses.
The association provides public health messages for the community as well as services for members.
Leslie is now preparing financial statements for the year and comes to you for advice on accounting for
the proceeds from a major fund drive that occurred during the year. The nursing association received
$25,000 in unrestricted donations and $15,000 in restricted donations that are restricted to public health
advertisements. A total of $6,000 has been incurred for public health advertising since the restricted donations were received.
The former treasurer accounted for the $40,000 of donations as revenue in the unrestricted fund.
Leslie believes that this may not be correct because it does not disclose the restricted nature of the donations for the public health messages.
Required
a. Discuss the accounting and financial statement disclosure to be used to account for the $25,000 of
unrestricted donations to the professional association.
b. How should the $15,000 of restricted contributions have been accounted for at the time of the donation? How should they have been reported on this year’s financial statements?
C19-3
Research
Discovery
The purpose of these cases is to provide learning opportunities using available databases and/or the Internet to obtain contemporary information about the topics in advanced financial accounting. Note that
the Internet is dynamic and that addresses of specific Websites may change. In that case, use a good
search engine to locate the Website’s current address.
Required
Access the Website for the American Red Cross (www.redcross.org) and scroll through until you locate
the most recent annual report. It may be under the Publications button of the header bar. Review the report and then prepare a one- to two-page memo summarizing the major information items included in it.
Be sure to examine each of the financial statements to determine the following:
a. The components and amounts of each of the three net asset classes shown on the statement of financial position.
b. The major sources of operating revenues and the categories and amounts of operating expenses, including the amount of the fund-raising costs for the organization, shown on the statement of activities.
c. The costs of the principal program services as shown on the statement of functional expenses.
d. The sources and uses of net cash flows as shown on the statement of cash flows.
C19-4
Research
FARS
Conditional Gift to a Not-for-Profit Organization
Betty Gardner is the treasurer for the Central Illinois chapter of a national not-for-profit organization, the
Alzheimer’s Association. Some of the money raised by the chapter is sent to the national organization to
support research into Alzheimer’s disease. The chapter also provides information about the disease and
sponsors support programs for families of patients within the community. The chapter has just received
a significant pledge from Victor Wyatt, who has offered to contribute $20,000 a year for the next five
317
318
Advanced Financial
Text
Companies, 2004
years on the condition that the Central Illinois chapter sponsor a series of annual educational programs
about Alzheimer’s disease. If it does not do so, he will direct future contributions elsewhere.
The donor has already contributed the first $20,000, and the chapter has made the arrangements
for the first educational workshop, which will take place in six weeks, shortly after the chapter’s fiscal
year-end.
Betty Gardner is aware that the chapter intends to continue the educational workshops and has asked
you, as a public accountant who volunteers to audit the chapter’s financial statements each year, to research the appropriate accounting for Mr. Wyatt’s $20,000 contribution and $80,000 pledge in the chapter’s financial statements for the current fiscal year.
Required
Obtain the most current accounting standards for accounting for conditional gifts to not-for-profit organizations. You can obtain access to accounting standards through the Financial Accounting Research System (FARS), from your library, or from some other source. Write a memo to Betty reporting on your
research findings. Support your recommendations with citations and quotations from the authoritative
financial reporting standards.
C19-5
Research
FARS
Accounting for Contributions to and Activities of a Not-for-Profit Organization
Gerry Finley, a manager in a public accounting firm, has volunteered to audit the financial statements of
the Community Chest, a not-for-profit organization that raises funds to assist people in central Illinois
who are homeless and individuals who have low incomes. In reviewing the statement of activities, he notices the revenue item Auction Extravaganza. The Community Chest treasurer indicates that this amount
is the net proceeds for this event, which is the organization’s largest fund-raising event for the year.
The Auction Extravaganza combines a black-tie dinner, entertainment, and an auction of numerous
donated items. Supporters buy tickets to the event and bid on the auction items. The treasurer informs
Gerry that the dollar amount reported in the statement of activities is the total raised from ticket sales and
from the auction, net of the expenses incurred for the event. These expenses include advertising and part
of the cost of the dinner. The expenses, however, are comparatively low because a local hotel donates the
ballroom and part of the cost of the dinner. A local auctioneer volunteers her time for the auction, the
state university’s music department provides the entertainment, and local businesses donate all auction
items.
Required
Obtain the most current accounting standards for accounting for conditional gifts to not-for-profit organizations. You can obtain access to accounting standards through the Financial Accounting Research System (FARS), from your library, or from some other source. Gerry has asked you, as a staff accountant in
his firm, to research the appropriate accounting for the Auction Extravaganza. Write him a memo reporting on your research findings. Support your recommendations with citations and quotations from the
authoritative financial reporting standards.
Exercises
E19-1
Multiple-Choice Questions on Colleges and Universities [AICPA Adapted]
Select the correct answer for each of the following questions.
1. For the summer session of 20X2, Pacific University assessed its students $1,700,000 (net of refunds)
covering tuition and fees for educational and general purposes. However, only $1,500,000 was expected to be realized because scholarships totaling $150,000 were granted to students, and tuition remissions of $50,000 were allowed to faculty members’ children attending Pacific. What amount
should Pacific include as revenues from student tuition and fees?
a. $1,500,000.
b. $1,550,000.
c. $1,650,000.
d. $1,700,000.
2. Tuition remissions for graduate student teaching assistantships should be classified by a university as:
Advanced Financial
Text
Companies, 2004
a.
b.
c.
d.
Revenue
Expenditures
No
No
Yes
Yes
No
Yes
Yes
No
3. For the fall semester of 20X1, Dover University assessed its students $2,300,000 for tuition and fees.
The net amount realized was only $2,100,000 because of the following revenue reductions:
Refunds occasioned by class cancellations and student withdrawals
Tuition remissions granted to faculty members’ families
Scholarships and fellowships
$ 50,000
10,000
140,000
How much should Dover report for the period for revenue from tuition and fees?
a. $2,100,000.
b. $2,150,000.
c. $2,250,000.
d. $2,300,000.
Items 4 through 6 are based on the following information pertaining to Global University, a private institution, as of June 30, 20X1, and for the year then ended:
Unrestricted net assets comprised $7,500,000 of assets and $4,500,000 of liabilities (including deferred revenues of $150,000). Among the receipts recorded during the year were unrestricted gifts of
$550,000 and restricted grants totaling $330,000, of which $220,000 was expended during the year for
current operations and $110,000 remained unexpended at the close of the year.
Volunteers from the surrounding communities regularly contribute their services to Global and are
paid nominal amounts to cover their travel costs. During the year, the amount for travel paid to these volunteers aggregated $18,000. The gross value of services performed by them, determined by reference to
equivalent wages available in that area for similar services, amounted to $200,000. Global University
normally purchases the types of contributed services, and the university believes the contributed services
enhance its assets.
4. At June 30, 20X1, Global’s unrestricted net asset balance was:
a. $7,500,000.
b. $3,150,000.
c. $3,000,000.
d. $2,850,000.
5. For the year ended June 30, 20X1, what amount should be included in Global’s revenue for the unrestricted gifts and restricted grants?
a. $550,000.
b. $660,000.
c. $770,000.
d. $880,000.
6. For the year ended June 30, 20X1, what amount should Global record as contribution revenue for the
volunteers’ services?
a. $218,000.
b. $200,000.
c. $18,000.
d. $0.
319
320
Advanced Financial
Text
Companies, 2004
E19-2
Multiple-Choice Questions on Hospital Accounting [AICPA Adapted]
Data for Questions 1 through 3
Under Dodge Hospital’s established rate structure, the hospital would have earned patient service revenue of $5,000,000 for the year ended December 31, 20X3. However, Dodge did not expect to collect
this amount because of contractual adjustments of $500,000 to third-party payors. In May 20X3, Dodge
purchased bandages from Hunt Supply Company at a cost of $1,000. However, Hunt notified Dodge that
the invoice was being canceled and that the bandages were being donated. On December 31, 20X3,
Dodge had board-designated assets consisting of $40,000 in cash and investments of $700,000.
1. For the year ended December 31, 20X3, how much should Dodge report as net patient service
revenue?
a. $4,500,000.
b. $5,000,000.
c. $5,500,000.
d. $5,740,000.
2. For the year ended December 31, 20X3, Dodge should record the donation of bandages as:
a. A $1,000 reduction in operating expenses.
b. A decrease in net assets released from restrictions.
c. An increase in unrestricted revenue, gains, and other support.
d. A memorandum entry only.
3. How much of Dodge’s board-designated assets should be included in unrestricted net assets?
a. $0.
b. $40,000.
c. $700,000.
d. $740,000.
4. Donated medicines that normally would be purchased by a hospital should be recorded at fair value
and should be credited directly to:
a. Unrestricted revenue.
b. Expense of medicines.
c. Fund balance.
d. Deferred revenue.
5. Which of the following would normally be included as revenue of a not-for-profit hospital?
a. Unrestricted interest income from an endowment fund.
b. An unrestricted gift.
c. Tuition received from an educational program.
d. All of the above.
6. An unrestricted gift pledge from an annual contributor to a not-for-profit hospital made in December 20X1 and paid in March 20X2 would generally be credited to:
a. Contribution revenue in 20X1.
b. Contribution revenue in 20X2.
c. Other income in 20X1.
d. Other income in 20X2.
7. An organization of high school seniors assists patients at Lake Hospital. These students are volunteers who perform services that the hospital would not otherwise provide, such as wheeling patients
in the park and reading to patients. Lake has no employer-employee relationship with these volunteers, who donated 5,000 hours of service to Lake in 20X2. At the minimum wage, these services
would amount to $18,750, while it is estimated that the fair value of these services was $25,000. In
Lake’s 20X2 statement of operations, what amount should be reported as donated services?
a. $25,000.
Advanced Financial
Text
Companies, 2004
b. $18,750.
c. $6,250.
d. $0.
8. Which of the following would be included in the unrestricted funds of a not-for-profit hospital?
a. Permanent endowments.
b. Term endowments.
c. Board-designated funds originating from previously accumulated income.
d. Funds designated by the donor for plant expansion and replacement funds.
9. During the year ended December 31, 20X1, Greenacre Hospital received the following donations
stated at their respective fair values:
Essential specialized employee-type services from members of a religious group
Medical supplies from an association of physicians. These supplies
were restricted for indigent care and were used for such purpose in 20X1.
$100,000
30,000
How much total revenue from donations should Greenacre report its 20X1?
a. $0.
b. $30,000.
c. $100,000.
d. $130,000.
10. Johnson Hospital’s property, plant, and equipment (net of depreciation) consists of the following:
Land
Buildings
Movable equipment
$
500,000
10,000,000
2,000,000
What amount should be reported as restricted assets?
a. $0.
b. $2,000,000.
c. $10,500,000.
d. $12,500,000.
11. Depreciation should be recognized in the financial statements of:
a. Proprietary (for-profit) hospitals only.
b. Both proprietary and not-for-profit hospitals.
c. Both proprietary and not-for-profit hospitals only when they are affiliated with a college or
university.
d. All hospitals, as a memorandum entry not affecting the statement of revenue and expenses.
12. On March 1, 20X1, J. Rowe established a $100,000 endowment fund, the income from which is to
be paid to Central Hospital for general operating purposes. Central does not control the fund’s principal. The donor appointed Sycamore National Bank as trustee of this fund. What journal entry is
required by Central to record the establishment of the endowment?
Debit
a. Cash
Nonexpendable Endowment Fund
b. Cash
Endowment Fund Balance
c. Nonexpendable Endowment Fund
Endowment Fund Balance
d. Memorandum entry only
Credit
100,000
100,000
100,000
100,000
100,000
—
100,000
—
321
322
Advanced Financial
Text
Companies, 2004
E19-3
Entries for a Hospital’s Unrestricted (General) Fund
The following are transactions and events of the general fund of Sycamore Hospital, a not-for-profit entity, for the 20X6 fiscal year ending December 31, 20X6.
1. A total of $6,200,000 in patient services was provided.
2. Operating expenses total $5,940,000, as follows:
Nursing services
Other professional expenses
Fiscal services
General services
Bad debts
Administration
Depreciation
$2,070,000
1,250,000
225,000
1,510,000
125,000
260,000
500,000
Accounts credited for operating expenses other than depreciation:
Cash
Accounts Payable
Inventories
Donated Services
$4,785,000
125,000
210,000
240,000
80,000
3. Contractual adjustments of $220,000 are allowed as deductions from gross patient revenue.
4. A transfer of $180,000 is received from specific-purpose funds. This transfer is for payment of approved operating costs in accordance with the terms of the restricted gift.
5. A transfer of $200,000 is received from the temporarily restricted plant fund to fund the purchase of
new equipment for the hospital.
6. Sycamore Hospital receives $155,000 of unrestricted gifts.
7. Accounts receivable are collected except for $75,000 written off.
8. A valuation of the investment securities portfolio of the general fund reports a $70,000 increase in the
market value from the beginning of the period. The board designated this entire income for other than
current operations.
Required
a. Prepare journal entries in the general fund for each of the transactions and events.
b. Prepare the statement of operations for the general, unrestricted fund of Sycamore Hospital.
E19-4
Entries for Other Hospital Funds
The following are selected transactions of the specific-purpose fund, the plant fund, and the endowment
fund of Toddville Hospital, a not-for-profit entity:
1. The endowment fund received new permanent endowments totaling $150,000 and new term endowments totaling $120,000.
2. The plant replacement and expansion fund received pledges of $1,500,000 for the new wing. Uncollectibles were estimated at 10 percent.
3. The specific-purpose fund received gifts of $50,000 for research and $30,000 for education.
4. Interest and dividends received on investments follow:
Endowment fund (permanent)
Plant fund
Specific-purpose fund (research)
$100,000
45,000
31,000
This year’s interest and dividends in the endowment fund are permanently restricted by a donorimposed requirement.
Advanced Financial
Text
Companies, 2004
5. The specific-purpose fund was notified that the general fund fulfilled the agreements related to restricted gifts as follows:
Research
Education
$55,000
32,000
Cash of $70,000 was transferred to the general fund, with the balance to be sent later.
6. Investments made:
Endowment fund
Plant fund
Specific-purpose fund
$270,000
160,000
75,000
Required
Prepare journal entries for the transactions in the specific-purpose fund, plant fund, and endowment fund,
as appropriate.
E19-5
Multiple-Choice Questions on Voluntary Health and Welfare Organization
Accounting [AICPA Adapted]
1. Which basis of accounting should a voluntary health and welfare organization use?
a. Cash basis for all funds.
b. Modified accrual basis for all funds.
c. Accrual basis for all funds.
d. Accrual basis for some funds and modified accrual basis for other funds.
Data for Questions 2 and 3
Town Service Center is a voluntary welfare organization funded by contributions from the general public. During 20X6, unrestricted pledges of $800,000 were received, half of which were payable in 20X6,
with the other half payable in 20X7 for use in 20X7. It was estimated that 10 percent of these pledges
would be uncollectible. In addition, Helen Ladd, a social worker on Town’s permanent staff, earning
$30,000 annually for a normal workload of 1,500 hours, contributed an additional 600 hours of her time
to Town at no charge.
2. How much should Town report as unrestricted contribution revenue for 20X6 with respect to the
pledges?
a. $0.
b. $360,000.
c. $720,000.
d. $800,000.
3. How much should Town record in 20X6 for contributed service expenses?
a. $0.
b. $1,200.
c. $10,000.
d. $12,000.
4. A voluntary health and welfare organization received a pledge in 20X1 from a donor specifying that
the amount pledged be used in 20X3. The donor paid the pledge in cash in 20X2. The pledge should
be accounted for as:
a. Contribution revenue in 20X3.
b. Contribution revenue in 20X2.
c. Contribution revenue in 20X1.
d. Contribution revenue in the period in which the funds are spent.
323
324
Advanced Financial
Text
Companies, 2004
5. Turner Fund, a voluntary welfare organization funded by contributions from the general public, received unrestricted pledges of $300,000 during 20X4. It was estimated that 10 percent of these
pledges would be uncollectible. By the end of 20X4, $240,000 of the pledges had been collected. It
was expected that $35,000 more would be collected in 20X5 and that the balance of $25,000 would
be written off as uncollectible. What amount should Turner include as contribution revenue in 20X4?
a. $300,000.
b. $275,000.
c. $270,000.
d. $240,000.
Data for Questions 6 through 9
On January 1, 20X2, State Center Health Agency, a voluntary health and welfare organization, received
a bequest of a $200,000 certificate of deposit maturing on December 31, 20X6. The contributor’s only
stipulations were that the certificate be held to maturity and the interest revenue received annually be
used to purchase books for the children to read in the preschool program run by the agency. Interest revenue each of the years was $9,000, and the full $9,000 was spent for books each year. When the certificate was redeemed, the board of trustees adopted a formal resolution designating $150,000 of the
proceeds for future purchase of playground equipment for the preschool program.
6. What should be reported by the temporarily restricted fund in the 20X2 statement of activities?
a. Legacies and bequests of $200,000.
b. Investment income of $9,000.
c. Transfers to unrestricted fund of $9,000.
d. All of the above.
7. What amounts should be reported in the 20X2 statement of activities for the unrestricted fund?
a. Legacies and bequests of $200,000.
b. Investment income of $9,000.
c. Transfers from the restricted fund of $9,000.
d. Contributions of $209,000.
8. What should be reported in the 20X6 statement of activities for the unrestricted fund?
a. Transfers from restricted fund of $209,000.
b. Board-designated funds of $150,000.
c. Playground equipment of $150,000.
d. Transfers to plant and equipment fund of $150,000.
9. What should be reported in the December 31, 20X6, statement of financial position for the unrestricted fund?
a. Liability for purchase of playground equipment $150,000.
b. Due to plant and equipment fund $150,000.
c. Board-designated funds $150,000.
d. Temporarily restricted funds $200,000.
E19-6
Entries for Voluntary Health and Welfare Organizations
The following are the 20X2 transactions of the Midwest Heart Association, which has the following
funds and fund balances on January 1, 20X2:
Unrestricted net assets
Temporarily restricted net assets
Permanently restricted (endowment) net assets
$281,000
87,000
219,000
1. Unrestricted pledges total $700,000, of which $150,000 is for 20X3. Uncollectible pledges are estimated at 8 percent.
2. Restricted use grants total $150,000.
Advanced Financial
Text
Companies, 2004
3. A total of $520,000 of current pledges are collected, and $30,000 of remaining uncollected current
pledges are written off.
4. Office equipment is purchased for $15,000.
5. Unrestricted funds are used to pay the $3,000 mortgage payment due on the buildings.
6. Interest and dividends received are $27,200 on unrestricted investments and $5,400 on temporarily
restricted investments. An endowment investment with a recorded value of $5,000 is sold for $6,000,
resulting in a realized transaction gain of $1,000. A donor-imposed restriction specified that gains on
sales of endowment investments must be maintained in the permanently restricted endowment fund.
7. Depreciation is recorded and allocated as follows:
Community services
Public health education
Research
Fund-raising
General and administrative
$12,000
7,000
10,000
15,000
9,000
8. Other operating costs of the unrestricted current fund are:
Community services
Public health education
Research
Fund-raising
$250,600
100,000
81,000
39,000
61,000
9. Clerical services donated during the fund drive total $2,400. These are not part of the expenses reported in item 8. It has been determined that these donated services should be recorded.
Required
a. Prepare journal entries for the transactions in 20X2.
b. Prepare a statement of activities for 20X2.
E19-7
Determination of Contribution Revenue
Atwater Health Services, a voluntary health and welfare organization, has provided support for families
with low income in the town of Atwater for approximately 20 years. In 20X6, Atwater Health Services
conducted a major funding campaign to help replace facilities that are no longer adequate and to generate operating and endowment funds.
The community of Atwater ran a number of special events, and the chamber of commerce made the
fund-raising campaign a major activity for 20X6. In 20X6, the following gifts and pledges were received:
1. The family of I. B. Plentiful donated a lot adjacent to the current building for future use as a playground and parking lot. The family had purchased the lot for $22,000 several years ago. It had a current value of $42,000 at the date contributed.
2. A number of new pledges were received and many were partially or fully paid in 20X6. The following information was compiled:
Unrestricted pledges for use in 20X6
Unrestricted pledges for use in 20X7
Pledges to support screening tests for children’s hearing abilities
Pledge to assist in construction of addition to building; donor
agrees to make eight annual payments of $50,000 each
$120,000
70,000
90,000
400,000
$680,000
325
326
Advanced Financial
Text
Companies, 2004
3. Also during 20X6, $45,000 was spent in providing vision tests for grade school children. A total of
$38,000 of funds collected in 20X4 and 20X5 for this purpose were used to help pay for the costs of
providing the tests free of charge to all children in the community.
Required
a. Prepare the journal entries for 20X6 for these activities, including receipt of the first installment
on the pledge for building construction, which was received at the end of 20X6. Atwater currently
earns an 8 percent return on its investments. The present value of the seven future payments of
$50,000 is $260,318.
b. Prepare the journal entry or entries recorded at the end of 20X7 upon receipt of the second payment
on the pledge for building construction.
E19-8
Multiple-Choice Questions on Other Nonprofit Organizations [AICPA Adapted]
1. On January 2, 20X2, a nonprofit botanical society received a gift of an exhaustible fixed asset with
an estimated useful life of 10 years and no salvage value. The donor’s cost of this asset was $20,000,
and its fair market value at the date of the gift was $30,000. What amount of depreciation of this
asset should the society recognize in its 20X2 financial statements?
a. $3,000.
b. $2,500.
c. $2,000.
d. $0.
2. In 20X1, a nonprofit trade association enrolled five new member companies, each of which was obligated to pay nonrefundable initiation fees of $1,000. These fees were receivable by the association
in 20X1. Three of the new members paid the initiation fees in 20X1, and the other two new members paid their initiation fees in 20X2. Annual dues (excluding initiation fees) received by the association from all members have always covered the organization’s costs of services provided to its
members. It can be reasonably expected that future dues will cover all costs of the organization’s future services to members. Average membership duration is 10 years because of mergers, attrition,
and economic factors. What amount of initiation fees from these five new members should the association recognize as revenue in 20X1?
a. $5,000.
b. $3,000.
c. $500.
d. $0.
3. Roberts Foundation received a nonexpendable endowment of $500,000 in 20X3 from Multi Enterprises. The endowment assets were invested in publicly traded securities. Multi did not specify how
gains and losses from dispositions of endowment assets were to be treated. No restrictions were
placed on the use of dividends received and interest earned on fund resources. In 20X4, Roberts realized gains of $50,000 on sales of fund investments, and received total interest and dividends of
$40,000 on fund securities. The amount of these capital gains, interest, and dividends available for
expenditure by Roberts’s unrestricted current fund is:
a. $0.
b. $40,000.
c. $50,000.
d. $90,000.
4. In July 20X2, Ross donated $200,000 cash to a church with the stipulation that the revenue generated from this gift be paid to him during his lifetime. The conditions of this donation are that after
Ross dies, the principal may be used by the church for any purpose voted on by the church elders.
The church received interest of $16,000 on the $200,000 for the year ended June 30, 20X3, and the
interest was remitted to Ross. In the church’s June 30, 20X3, annual financial statements:
a. $200,000 should be reported as temporarily restricted net assets in the balance sheet.
Advanced Financial
Text
Companies, 2004
b. $184,000 should be reported as revenue in the activity statement.
c. $216,000 should be reported as revenue in the activity statement.
d. Both a and c.
5. The following expenditures were among those incurred by a nonprofit botanical society during
20X4:
Printing of annual report
Unsolicited merchandise sent to encourage contributions
$15,000
35,000
What amount should be classified as fund-raising costs in the society’s activity statement?
a. $0.
b. $5,000.
c. $35,000.
d. $40,000.
6. Trees Forever, a community foundation, incurred $5,000 in expenses during 20X3 putting on its annual talent fund-raising show. In the statement of activities of Trees Forever, the $5,000 should be
reported as:
a. A contra asset account.
b. A contra revenue account.
c. A reduction of fund-raising costs.
d. As part of fund-raising costs.
7. In 20X3, the board of trustees of Burr Foundation designated $100,000 from its current funds for
college scholarships. Also in 20X3, the foundation received a bequest of $200,000 from an estate of
a benefactor who specified that the bequest was to be used for hiring teachers to tutor handicapped
students. What amount should be accounted for as temporarily restricted funds?
a. $0.
b. $100,000.
c. $200,000.
d. $300,000.
Information for 8 through 10
United Together, a labor union, had the following receipts and expenses for the year ended December 31,
20X2:
Receipts:
Per capita dues
Initiation fees
Sales of organizational supplies
Nonexpendable gift restricted by donor for loan purposes for 10 years
Nonexpendable gift restricted by donor for loan purposes in perpetuity
Expenses:
Labor negotiations
Fund-raising
Membership development
Administrative and general
$680,000
90,000
60,000
30,000
25,000
500,000
100,000
50,000
200,000
327
328
Advanced Financial
Text
Companies, 2004
Additional Information
The union’s constitution provides that 10 percent of the per capita dues be designated for the strike insurance fund to be distributed for strike relief at the discretion of the union’s executive board.
8. In United Together’s statement of activities for the year ended December 31, 20X2, what amount
should be reported under the classification of revenue from unrestricted funds?
a. $740,000.
b. $762,000.
c. $770,000.
d. $830,000.
9. In United Together’s statement of activities for the year ended December 31, 20X2, what amount
should be reported under the classification of program services?
a. $500,000.
b. $550,000.
c. $600,000.
d. $850,000.
10. In United Together’s statement of activities for the year ended December 31, 20X2, what amounts
should be reported under the classifications of temporarily and permanently restricted net assets?
a. $0 and $55,000, respectively.
b. $55,000 and $0, respectively.
c. $30,000 and $25,000, respectively.
d. $25,000 and $30,000, respectively.
E19-9
Statement of Activities for an Other Nonprofit Organization
The following is a list of selected account balances in the unrestricted operating fund for the Pleasant
School:
Debit
Unrestricted Net Assets, July 1, 20X1
Tuition and Fees
Contributions
Auxiliary Activities Revenue
Investment Income (for current operations)
Other Revenue
Instruction
Auxiliary Activities Expenses
Administration
Fund-Raising
Transfer from Temporarily Restricted Assets
Transfer from Permanently Restricted Assets
Credit
$ 420,000
1,200,000
165,000
40,000
32,000
38,000
$1,050,000
37,000
250,000
28,000
130,000
12,000
Required
Prepare a statement of activities for the unrestricted operating fund of the Pleasant School for the year
ended June 30, 20X2.
Advanced Financial
Text
Companies, 2004
Problems
P19-10
Financial Statements for a Private, Not-for-Profit College
Friendly College is a small, privately supported liberal arts college. The college uses a fund structure;
however, it prepares its financial statements in conformance with FASB 117.
Partial balance sheet information as of June 30, 20X2, is given as follows:
Unrestricted Items:
Cash
Accounts Receivable (student tuition and fees,
less allowance for doubtful accounts of $9,000)
State Appropriation Receivable
Accounts Payable
Deferred Revenue
Unrestricted Net Assets
Restricted Items:
Cash
Investments
Temporarily Restricted Net Assets
$210,000
341,000
75,000
$ 45,000
66,000
515,000
$ 7,000
60,000
$ 67,000
The following transactions occurred during the fiscal year ended June 30, 20X3:
1. On July 7, 20X2, a gift of $100,000 was received from an alumnus. The alumnus requested that half
the gift be restricted to the purchase of books for the university library and the remainder be used
for the establishment of an endowed scholarship fund. The alumnus further requested that the income generated by the scholarship fund be used annually to award a scholarship to a qualified disadvantaged student. On July 20, 20X2, the board of trustees resolved that the funds of the newly
established scholarship endowment fund would be invested in savings certificates. On July 21,
20X2, the savings certificates were purchased.
2. Revenue from student tuition and fees applicable to the year ended June 30, 20X3, amounted to
$1,900,000. Of this amount, $66,000 was collected in the prior year, and $1,686,000 was collected
during the year ended June 30, 20X3. In addition, on June 30, 20X3, the university had received
cash of $158,000 representing deferred revenue fees for the session beginning July 1, 20X3.
3. During the year ended June 30, 20X3, the university had collected $349,000 of the outstanding accounts receivable at the beginning of the year. The balance was determined to be uncollectible and
was written off against the allowance account. On June 30, 20X3, the allowance account was increased by $3,000 to $11,000.
4. During the year, interest charges of $6,000 were earned and collected on late student fee payments.
5. During the year the state appropriation was received. An additional unrestricted appropriation of
$50,000 was made by the state but had not been paid to the university as of June 30, 20X3.
6. An unrestricted gift of $25,000 cash was received from alumni of the university.
7. During the year, restricted investments of $21,000 were sold for $26,000. Temporarily restricted investment interest income amounting to $1,900 was received.
8. During the year, unrestricted operating expenses of $1,777,000 were recorded, not including yearend accruals or transfers from other categories of net assets. On June 30, 20X3, $59,000 of these
expenses remained unpaid.
9. Restricted current funds of $13,000 were released and spent for authorized operating purposes during the year.
10. The accounts payable on June 30, 20X2, were paid during the year.
11. During the year, $7,000 interest was earned and received on the savings certificates purchased in
accordance with the board of trustees’ resolutions, as discussed in transaction 1.
329
330
Advanced Financial
Text
Companies, 2004
Required
a. Prepare a comparative balance sheet for Friendly College as of June 30, 20X2, and June 30, 20X3.
b. Prepare a statement of activities for Friendly College for the year ended June 30, 20X3.
P19-11
Balance Sheet for a Hospital
Brookdale Hospital hired an inexperienced controller early in 20X4. Near the end of 20X4, the board of
directors decided to conduct a major fund-raising campaign. They wished to have the December 31,
20X4, statement of financial position for Brookdale fully conform with current generally accepted principles for hospitals. The trial balance prepared by the controller at December 31, 20X4, is as follows:
Debit
Credit
Cash
Investment in Short-Term Marketable Securities
Investment in Long-Term Marketable Securities
Interest Receivable
Accounts Receivable
Inventory
Land
Buildings and Equipment
Allowance for Depreciation
Accounts Payable
Mortgage Payable
Fund Balance
$ 100,000
200,000
300,000
15,000
55,000
35,000
120,000
935,000
Total
$1,760,000
$ 260,000
40,000
320,000
1,140,000
$1,760,000
1. Your analysis of the contributions receivable as of December 31, 20X4, determined that there were
unrecognized contributions for the following:
For unrestricted use
For use in cancer research
For purchase of equipment
For permanently restricted endowment principal
$ 40,000
10,000
20,000
30,000
Total
$100,000
2. Short-term investments at year-end consist of $150,000 of unrestricted funds and $50,000 of funds
restricted for future cancer research. All of the long-term investments are held in the permanently
restricted endowment fund.
3. Land is carried at its current market value of $120,000. The original owner purchased the land for
$70,000, and at the time of donation to the hospital, the land had an appraised value of $95,000.
4. Buildings were purchased 11 years ago for $600,000 and had an estimated useful life of 30 years.
Equipment costing $150,000 was purchased 7 years ago and had an expected life of 10 years. The
controller had improperly increased the reported values of the buildings and equipment to their current fair value of $935,000 and had incorrectly computed the accumulated depreciation.
5. The board of directors voted on December 29, 20X4, to designate $100,000 of unrestricted funds invested in short-term investments for use in developing a drug rehabilitation center.
Required
Prepare in good form a balance sheet for Brookdale Hospital at December 31, 20X4.
Advanced Financial
Text
Companies, 2004
P19-12
Entries and Statement of Activities for an Other Nonprofit Organization
[AICPA Adapted]
A group of civic-minded merchants in Eldora organized the “Committee of 100” for the purpose of establishing the Community Sports Club, a nonprofit sports organization for local youth. Each of the
committee’s 100 members contributed $1,000 toward the club’s capital and, in turn, received a participation certificate. In addition, each participant agreed to pay dues of $200 a year for the club’s operations.
All dues have been collected in full by the end of each fiscal year ending March 31. Members who have
discontinued their participation have been replaced by an equal number of new members through transfer of the participation certificates from the former members to the new ones. Following is the club’s trial
balance for April 1, 20X2:
Debit
Cash
Investments (at market, equal to cost)
Inventories
Land
Building
Accumulated Depreciation—Building
Furniture and Equipment
Accumulated Depreciation—Furniture and Equipment
Accounts Payable
Participation Certificates (100 at $1,000 each)
Cumulative Excess of Revenue over Expenses
$
Total
$300,000
Credit
9,000
58,000
5,000
10,000
164,000
$130,000
54,000
46,000
12,000
100,000
12,000
$300,000
Transactions for the year ended March 31, 20X3, were as follows:
Collections from participants for dues
Snack bar and soda fountain sales
Interest and dividends received
Additions to voucher register:
House expenses
Snack bar and soda fountain
Vouchers paid
Assessments for capital improvements not yet incurred (assessed on
March 20, 20X3; none collected by March 31, 20X3; deemed 100%
collectible during year ending March 31, 20X4)
Unrestricted bequest received
$20,000
28,000
6,000
17,000
26,000
11,000
55,000
10,000
5,000
Adjustment Data
1. Investments are valued at market, which amounted to $65,000 on March 31, 20X3. There were no investment transactions during the year.
2. Depreciation for year:
Building
Furniture and equipment
$4,000
8,000
331
332
Advanced Financial
Text
Companies, 2004
3. Allocation of depreciation:
House expenses
Snack bar and soda fountain
$9,000
2,000
1,000
4. Actual physical inventory on March 31, 20X3, was $1,000 and pertains to the snack bar and soda
fountain.
Required
a. Record the transactions and adjustments in journal entry form for the year ended March 31, 20X3.
Omit explanations.
b. Prepare the appropriate all-inclusive statement of activities for the year ended March 31, 20X3.
P19-13
Balance Sheet and Entries for a Hospital [AICPA Adapted]
You have been hired to provide accounting assistance to Grace Hospital. The December 31, 20X1, balance sheet was prepared by a bookkeeper who thought hospitals reported funds as follows:
GRACE HOSPITAL
Balance Sheet
As of December 31, 20X1
General Fund
Assets
Cash
Accounts Receivable
Less: Allowance for Uncollectible Accounts
$
$
20,000
Liabilities and Fund Balances
Accounts Payable
Accrued Expenses
$
16,000
6,000
30,000
Total Liabilities
$
22,000
64,000
37,000
(7,000)
Inventory of Supplies
Total
$
14,000
Fund Balance
64,000
Total
$
42,000
Mortgage Bonds Payable
$ 150,000
Plant Fund
Assets
Cash
$
53,800
Investments
Land
Buildings
$1,750,000
(430,000)
1,320,000
Equipment
$ 680,000
(134,000)
546,000
Total
71,200
400,000
Fund Balance:
Investment in Plant
Reserved for Plant Improvement
and Replacement
$2,021,000
220,000
$2,241,000
$2,391,000
Total
$2,391,000
Fund Balance
$ 266,000
Total
$ 266,000
Endowment Fund
Assets
Cash
Investments
$
Total
$ 266,000
6,000
260,000
Advanced Financial
Text
Companies, 2004
During 20X2, the following transactions occurred:
1. Gross charges for patient services, all charged to Accounts Receivable, were as follows:
Room and board charges
Charges for other professional services
$780,000
321,000
2. Deductions from gross earnings were as follows:
Contractual adjustments
$15,000
3. The general fund paid $18,000 to retire mortgage bonds payable with an equivalent fair value.
4. During the year, the general fund received general contributions of $50,000 and income from endowment fund investments of $6,500. The general fund has been designated to receive income
earned on endowment fund investments.
5. New equipment costing $26,000 was acquired from general fund resources. The plant replacement
and expansion fund reimbursed the general fund for the $26,000. An X-ray machine, which originally cost $24,000 and had an undepreciated cost of $2,400, was sold for $500.
6. Vouchers totaling $1,191,000 were issued for the following items:
Administrative service expense
Fiscal service expense
General service expense
Nursing service expense
Other professional service expense
Supplies
Expenses accrued as of December 31, 20X1
$120,000
95,000
225,000
520,000
165,000
60,000
6,000
7. The provision for uncollectible accounts was increased by $30,000. Collections on accounts receivable totaled $985,000. Accounts written off as uncollectible amounted to $11,000.
8. Cash payments on vouchers payable during the year were $825,000.
9. Supplies of $37,000 were issued to nursing services.
10. On December 31, 20X2, accrued interest income on plant fund investments was $800.
11. Depreciation of buildings and equipment was as follows:
Buildings
Equipment
$44,000
73,000
12. On December 31, 20X2, an accrual of $6,100 was made for fiscal service expense on mortgage
bonds.
Required
a. Restate the balance sheet of Grace Hospital as of December 31, 20X1, to reflect the fact that hospitals do not have an investment in plant funds. (Hint: The $53,800 cash and $71,200 investments belong to temporarily restricted funds for plant replacement, and the other assets reported in the plant
fund are properly included as part of unrestricted net assets.)
b. Prepare journal entries to record the transactions for 20X2 in the general fund, the plant replacement
and expansion fund, and the endowment fund. Assume that the plant fund balances have been transferred to the appropriate funds as indicated in part a of this problem. Omit explanations.
P19-14
Entries and Statements for General Fund of a Hospital
The postclosing trial balance of the general fund of Serene Hospital, a not-for-profit entity, on December 31, 20X1, was as follows:
333
334
Advanced Financial
Text
Companies, 2004
Debit
Cash
Accounts Receivable
Due from Specific-Purpose Fund
Inventories
Prepaid Expenses
Investments
Accounts Payable
Accrued Expenses
Deferred Revenue—Reimbursement
Bonds Payable
Fund Balance—Unrestricted
Total
$
Credit
125,000
400,000
$
50,000
40,000
95,000
20,000
900,000
6,100,000
1,500,000
150,000
55,000
75,000
3,000,000
2,850,000
$7,680,000
$7,680,000
During 20X2 the following transactions occurred:
1. The value of patient services provided was $6,160,000.
2. Contractual adjustments of $330,000 from patients’ bills were approved.
3. Operating expenses totaled $5,600,000, as follows:
Nursing services
Other professional services
Fiscal services
General services
Bad debts
Administration
Depreciation
$1,800,000
1,200,000
250,000
1,550,000
120,000
280,000
400,000
Accounts credited for operating expenses other than depreciation:
Cash
Accounts Payable
Accrued Expenses
Inventories
Prepaid Expenses
Donated Services
$4,580,000
120,000
170,000
35,000
195,000
30,000
70,000
4. Received $75,000 cash from specific-purpose fund for partial reimbursement of $100,000 for operating expenditures made in accordance with a restricted gift. The receivable increased by the remaining $25,000 to an ending balance of $65,000.
5. Payments for inventories were $176,000 and for prepaid expenses were $24,000.
6. Received $85,000 income from endowment fund investments.
7. Sold an X-ray machine that had cost $30,000 and had accumulated depreciation of $20,000 for
$17,000.
8. Collected $5,800,000 receivables and wrote off $132,000.
9. Acquired investments amounting to $60,000.
10. Income from board-designated investments was $72,000.
11. Paid the beginning balance in Accounts Payable and Accrued Expenses.
Advanced Financial
Text
335
Companies, 2004
12. Deferred Revenue—Reimbursement increased $20,000.
13. Received $140,000 from the plant replacement and expansion fund for use in acquiring fixed assets.
14. Net receipts from the cafeteria and gift shop were $63,000.
Required
a.
b.
c.
d.
P19-15
Prepare journal entries to record the transactions for the general fund. Omit explanations.
Prepare comparative balance sheets for only the general fund for 20X2 and 20X1.
Prepare a statement of operations for the unrestricted, general fund for 20X2.
Prepare a statement of cash flows for 20X2.
Statements for Current Funds of a Voluntary Health and Welfare Organization
[AICPA Adapted]
Following are the adjusted current funds trial balances of Community Association for Handicapped Children, a voluntary health and welfare organization, on June 30, 20X4:
COMMUNITY ASSOCIATION FOR HANDICAPPED CHILDREN
Adjusted Current Funds Trial Balances
June 30, 20X4
Unrestricted
Debit
Cash
Bequest Receivable
Pledges Receivable
Accrued Interest Receivable
Investments (at market)
Accounts Payable and Accrued Expenses
Deferred Revenue
Allowance for Uncollectible Pledges
Fund Balances, July 1, 20X3:
Designated
Undesignated
Restricted
Transfers of Expired Endowment Fund Principal
Contributions
Membership Dues
Program Service Fees
Investment Income
Deaf Children’s Program Expenses
Blind Children’s Program Expenses
Management and General Services
Fund-Raising Services
Provision for Uncollectible Pledges
$ 40,000
Total
$478,000
Credit
Restricted
Debit
Credit
$ 9,000
5,000
12,000
1,000
100,000
$ 50,000
2,000
3,000
$ 1,000
12,000
26,000
3,000
20,000
300,000
25,000
30,000
10,000
120,000
150,000
45,000
8,000
2,000
15,000
4,000
1,000
$478,000
$19,000
$19,000
Required
a. Prepare a statement of activities for the year ended June 30, 20X4.
b. Prepare a statement of financial position as of June 30, 20X4.
P19-16
Workpaper for Transactions of a Voluntary Health and Welfare Organization
Helping Hand, a voluntary health and welfare organization, provides a variety of services in the local
community. The following transactions occurred in the fiscal year ending June 30, 20X7:
1. The following pledges were received:
336
Advanced Financial
Text
Companies, 2004
Unrestricted
To provide free medical services
Future building project
Endowment fund principal
$400,000
150,000
180,000
250,000
2. The following amounts were collected:
Unrestricted pledges
Building project pledges
Contributions for unrestricted use in 20X8
$280,000
90,000
35,000
3. The following unrestricted revenues were received:
Memberships and dues
Interest and dividends
Bequests
Madrigal dinner
$30,000
18,000
47,000
85,000
4. Expenses incurred during the year were:
Cost of madrigal dinner
Direct payments for medical services
Information packets distributed
General administration
Training volunteer help
$52,000
141,000
44,000
69,000
12,000
5. Equipment costing $40,000 was purchased. Depreciation on buildings and equipment for the year
was allocated as follows:
Medical services program
Community information services
General administration
Fund-raising
$6,000
4,000
3,000
2,000
6. Vouchers totaling $275,000 were paid during the year.
Required
Prepare a workpaper with the following column headings. Record the journal entries (without explanation) for the preceding transactions in the proper asset groups.
Helping Hand
Journal Entry Workpaper
Unrestricted
Account Name
P19-17
Debit
Credit
Temporarily
Restricted
Debit
Credit
Permanently
Restricted
Debit
Credit
Comparative Journal Entries for a Government Entity and a Voluntary Health
and Welfare Organization [AICPA Adapted]
Following are four independent transactions or events that relate to a local government and to a voluntary health and welfare organization:
1. A disbursement of $25,000 was made from the general fund unrestricted assets for the cash purchase
of new equipment.
Advanced Financial
Companies, 2004
Text
2. An unrestricted cash gift of $100,000 was received from a donor.
3. Investments in common stocks with a total carrying value of $50,000 were sold by a permanently restricted endowment fund for $55,000 before any dividends were earned on these stocks. The gain is
donor-restricted to remain in the permanently restricted fund.
4. General obligation bonds payable with a face amount of $1,000,000 were sold at par, with the proceeds required to be used solely for construction of a new building. This building was completed at a
total cost of $1,000,000, and the total amount of bond issue proceeds was disbursed toward this cost.
Disregard interest capitalization.
Required
a. For each of these transactions or events, prepare journal entries without explanations, specifying the
affected funds and showing how these transactions or events should be recorded by a local government whose debt is serviced by general tax revenue.
b. For each of these transactions or events, prepare journal entries without explanations, specifying the
affected funds and showing how these transactions or events should be recorded by a voluntary health
and welfare organization.
P19-18
Matching Effects of Transactions on a Hospital’s Financial Statements [AICPA
Adapted]
DeKalb Hospital, a large not-for-profit organization, has adopted an accounting policy that does not
imply a time restriction on gifts of long-lived assets.
For each of the six items presented, select the best answer from the Answer List
P19-19
Transactions
Answer List
1. DeKalb’s board designates $1,000,000 to
purchase investments whose income will
be used for capital improvements.
2. Income from investments in item 1, which
was not previously accrued, is received.
3. A benefactor provided funds for building
expansion.
4. The funds in item 3 are used to purchase a
building in the fiscal period following the
period in which the funds were received.
5. An accounting firm prepared DeKalb’s
annual financial statements without
charge.
6. DeKalb received investments subject to
the donor’s requirement that investment
income be used to pay for outpatient
services.
A. Increase in unrestricted revenues, gains, and
other support.
B. Decrease in an expense.
C. Increase in temporarily restricted net assets.
D. Increase in permanently restricted net assets.
E. No required reportable event.
Balance Sheet for a Hospital
The following information is contained in the funds that are used to account for the transactions of the
Hospital of Havencrest, which is operated by a religious organization. The balances in the accounts are
as of June 30, 20X8, the end of the hospital’s fiscal year.
337
338
Advanced Financial
Text
Companies, 2004
General
Fund
Cash
Accounts Receivable
Inventories
Prepaid Expenses
Long-Term Investments
Accounts Payable
Accrued Expenses
Deferred Revenue
Current Portion—Long-Term Debt
Mortgage Payable
Specific
Purpose
Fund
Plant
Replacement and
Expansion Fund
Endowment
Fund
$140,000
$ 20,000
60,000
500,000
$ 30,000 $32,000
25,000
(5,000)
50,000
10,000
100,000
300,000
(140,000)
45,000
17,000
11,000
24,000
125,000
The $32,000 in the specific-purpose fund is restricted for research activities to be conducted by the
hospital.
Required
Prepare a balance sheet for Havencrest at June 30, 20X8.
P19-20
Matching of Transactions to Effects on Statement of Changes in Net Assets for
a Hospital
Match the transactions on the left with the effects of the transactions on the statement of changes in net
assets of a private, not-for-profit hospital.
Transactions
1. Patients billed for services rendered.
2. Realized a gain from the sale of securities that are
permanently invested.
3. Recorded depreciation expense for the year.
4. Designated assets for plant expansion.
5. Contributions restricted for research activities received.
6. Contributions restricted for equipment acquisition.
7. Acquired equipment with all of the contributions received
in item 6.
8. Earned endowment income. The donor placed no
restrictions on the investment earnings.
9. Expended 50 percent of the contributions restricted for
research in item 5.
10. Received cash contribution from donor who stipulated the
contribution be permanently invested.
11. Acquired investments with cash received in item 10.
12. Received tuition revenue from hospital nursing program
and cash from sales of goods in the hospital gift shop.
Effects of Transactions
on Statement of
Changes in Net Assets
A. Increases unrestricted
net assets
B. Decreases unrestricted
net assets
C. Increases temporarily
restricted net assets
D. Decreases temporarily
E. Increases permanently
F. Decreases permanently
G. Does not affect the
statement of changes
in net assets
Advanced Financial
Text
Companies, 2004
P19-21
Matching of Transactions to Effects on Statement of Activities for a Voluntary
Health and Welfare Organization
Match the transactions on the left with the effects of the transactions on the statement of activities for a
voluntary health and welfare organization. A transaction may have more than one effect.
Transactions
1. Received cash contributions restricted by donors
for research.
2. Incurred fund-raising costs.
3. Recorded depreciation expense for the year.
4. Designated assets for plant expansion.
5. Realized a gain from the sale of securities that
were permanently restricted. The donor specified
that any gains from sales of these securities must
be preserved and invested in other permanently
restricted investments.
6. Earned endowment income. The donor specified
that the income be used for community service.
7. Received a multiyear pledge, with cash being
received this year and for the next four years.
Donors did not place any use restrictions on how
the pledges were to be spent.
8. Earned income from investments of assets that
the board designated in item 4.
9. Received pledges from donors who placed no
time or use restrictions on how the pledges were
to be spent.
10. Received cash contributions restricted by donors
for equipment.
11. Acquired equipment with all of the contributions
received in item 10.
12. Expended 75 percent of the contributions
received in item 1 for research.
P19-22
Effects of Transactions on
A. Increases unres

Finance - Canis Learning Systems

Transcription

Similar documents

My Brother, My Sister: Shannon Boodram Rob Hill, Sr.

fantastic fabric prices! quilting cottons

Braedale Hill - North Lanarkshire Council

Wychitella Nature Conservation Reserve

View Brochure - Property Pilot

4 WEEk - Bear Grylls Survival Race

`News from the Hill` Rooty Hill Public School

Eating well as you age

IT`S NOT TO LATE TO JOIN!

Printable Details