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Ross, Stephen, Westerfield, Randolph, Jaffe, Jeffrey, and Jordan, Bradford, Corporate

Core Principles and Applications (5th edition), McGraw-Hill/Irwin,

ISBN: 9781259289903


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Hello I have tried and tried but all in vain ,I have attached 3rd edition. I know it might not help but just understand me .All the best and thank you for understanding me.for the sake of my account not to be banned I can honestly say I did not get the book.Thank you once again

C O R P O R AT E F I N A N C E
C O R E P R I N C I P L E S & A P P L I C AT I O N S

ros30689_fm_i-xxxiv.indd i

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The McGraw-Hill/Irwin Series in Finance, Insurance, and Real Estate
Stephen A. Ross
Franco Modigliani Professor of Finance
and Economics
Sloan School of Management
Massachusetts Institute of Technology
Consulting Editor
FINANCIAL MANAGEMENT
Adair
Excel Applications for Corporate Finance
First Edition
Block, Hirt, and Danielsen
Foundations of Financial Management
Fourteenth Edition
Brealey, Myers, and Allen
Principles of Corporate Finance
Tenth Edition
Brealey, Myers, and Allen
Principles of Corporate Finance, Concise
Second Edition
Brealey, Myers, and Marcus
Fundamentals of Corporate Finance
Sixth Edition
Brooks
FinGame Online 5.0
Bruner
Case Studies in Finance: Managing for
Corporate Value Creation
Sixth Edition
Chew
The New Corporate Finance: Where Theory
Meets Practice
Third Edition
Cornett, Adair, and Nofsinger
Finance: Applications and Theory
First Edition
DeMello
Cases in Finance
Second Edition
Grinblatt (editor)
Stephen A. Ross, Mentor: Influence through
Generations
Grinblatt and Titman
Financial Markets and Corporate Strategy
Second Edition
Higgins
Analysis for Financial Management
Ninth Edition
Kellison
Theory of Interest
Third Edition

ros30689_fm_i-xxxiv.indd ii

Kester, Ruback, and Tufano
Case Problems in Finance
Twelfth Edition

Rose and Marquis
Financial Institutions and Markets
Eleventh Edition

Ross, Westerfield, and Jaffe
Corporate Finance
Ninth Edition

Saunders and Cornett
Financial Institutions Management: A Risk
Management Approach
Seventh Edition

Ross, Westerfield, Jaffe, and Jordan
Corporate Finance: Core Principles and
Applications
Third Edition
Ross, Westerfield, and Jordan
Essentials of Corporate Finance
Seventh Edition
Ross, Westerfield, and Jordan
Fundamentals of Corporate Finance
Ninth Edition
Shefrin
Behavioral Corporate Finance: Decisions
that Create Value
First Edition
White
Financial Analysis with an Electronic
Calculator
Sixth Edition
INVESTMENTS
Bodie, Kane, and Marcus
Essentials of Investments
Eighth Edition
Bodie, Kane, and Marcus
Investments
Ninth Edition
Hirt and Block
Fundamentals of Investment Management
Ninth Edition
Hirschey and Nofsinger
Investments: Analysis and Behavior
Second Edition
Jordan and Miller
Fundamentals of Investments: Valuation
and Management
Fifth Edition
Stewart, Piros, and Heisler
Running Money: Professional Portfolio
Management
First Edition
Sundaram and Das
Derivatives: Principles and Practice
First Edition
FINANCIAL INSTITUTIONS AND MARKETS

Saunders and Cornett
Financial Markets and Institutions
Fourth Edition
INTERNATIONAL FINANCE
Eun and Resnick
International Financial Management
Fifth Edition
Kuemmerle
Case Studies in International
Entrepreneurship: Managing and Financing
Ventures in the Global Economy
First Edition
Robin
International Corporate Finance
First Edition
REAL ESTATE
Brueggeman and Fisher
Real Estate Finance and Investments
Fourteenth Edition
Ling and Archer
Real Estate Principles: A Value Approach
Third Edition
FINANCIAL PLANNING AND INSURANCE
Allen, Melone, Rosenbloom, and Mahoney
Retirement Plans: 401(k)s, IRAs, and Other
Deferred Compensation Approaches
Tenth Edition
Altfest
Personal Financial Planning
First Edition
Harrington and Niehaus
Risk Management and Insurance
Second Edition
Kapoor, Dlabay, and Hughes
Focus on Personal Finance: An Active
Approach to Help You Develop Successful
Financial Skills
Third Edition
Kapoor, Dlabay, and Hughes
Personal Finance
Ninth Edition

Rose and Hudgins
Bank Management and Financial Services
Eighth Edition

18/08/10 7:44 PM

THIRD EDITION

C O R P O R AT E F I N A N C E
C O R E P R I N C I P L E S & A P P L I C AT I O N S
Stephen A. Ross
Sloan School of Management
Massachusetts Institute of Technology

Randolph W. Westerfield
Marshall School of Business
University of Southern California

Jeffrey F. Jaffe
Wharton School of Business
University of Pennsylvania

Bradford D. Jordan
Gatton College of Business and Economics
University of Kentucky

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CORPORATE FINANCE: CORE PRINCIPLES & APPLICATIONS
Published by McGraw-Hill/Irwin, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of
the Americas, New York, NY, 10020. Copyright © 2011, 2009, 2007 by The McGraw-Hill Companies, Inc.
All rights reserved. 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 the prior written consent of The McGraw-Hill Companies,
Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for
distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the
United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 0 RJE/RJE 1 0 9 8 7 6 5 4 3 2 1 0
ISBN 978-0-07-353068-0
MHID 0-07-353068-9
Vice president and editor-in-chief: Brent Gordon
Publisher: Douglas Reiner
Executive editor: Michele Janicek
Director of development: Ann Torbert
Development editor II: Elizabeth Hughes
Vice president and director of marketing: Robin J. Zwettler
Senior marketing manager: Melissa S. Caughlin
Vice president of editing, design, and production: Sesha Bolisetty
Lead project manager: Christine A. Vaughan
Senior buyer: Carol A. Bielski
Senior designer: Mary Kazak Sander
Media project manager: Ron Nelms
Cover and interior design: Pam Verros
Cover image: Toyohiro Yamada, Tohoku Color Agency
Typeface: 10/12 Times New Roman
Compositor: MPS Limited, A Macmillan Company
Printer: R. R. Donnelley
Library of Congress Cataloging-in-Publication Data
Corporate finance : core principles & applications / Stephen A. Ross . . . [et al.]. — 3rd ed.
p. cm. — (The McGraw-Hill/Irwin series in finance, insurance, and real estate)
Includes index.
ISBN-13: 978-0-07-353068-0 (alk. paper)
ISBN-10: 0-07-353068-9 (alk. paper)
1. Corporations–Finance. I. Ross, Stephen A.
HG4026.C643 2011
658.15 —dc22
2010026731

www.mhhe.com

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To our family and friends with love
and gratitude.
—S.A.R.

ros30689_fm_i-xxxiv.indd v

R.W.W.

J.F.J.

B.D.J.

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ABOUT THE AUTHORS

Stephen A. Ross
SLOAN SCHOOL OF MANAGEMENT, MASSACHUSETTS INSTITUTE
OF TECHNOLOGY

Stephen A. Ross is the Franco Modigliani Professor of Financial Economics at
the Sloan School of Management, Massachusetts Institute of Technology. One
of the most widely published authors in finance and economics, Professor Ross
is recognized for his work in developing the Arbitrage Pricing Theory, as well as
for having made substantial contributions to the discipline through his research
in signaling, agency theory, option pricing, and the theory of the term structure
of interest rates, among other topics. A past president of the American Finance
Association, he currently serves as an associate editor of several academic and
practitioner journals. He is a trustee of CalTech.

Randolph W. Westerfield
MARSHALL SCHOOL OF BUSINESS, UNIVERSITY OF SOUTHERN CALIFORNIA

Randolph W. Westerfield is Dean Emeritus of the University of Southern
California’s Marshall School of Business and is the Charles B. Thornton Professor in Finance. Professor Westerfield came to USC from the Wharton School,
University of Pennsylvania, where he was the chairman of the finance department
and member of the finance faculty for 20 years. He is a member of several public company boards of directors including Health Management Associates, Inc.,
William Lyon Homes, and the Nicholas Applegate Growth Fund. His areas of
expertise include corporate financial policy, investment management, and stock
market price behavior.

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Jeffrey F. Jaffe
WHARTON SCHOOL OF BUSINESS, UNIVERSITY OF PENNSYLVANIA

Jeffrey F. Jaffe has been a frequent contributor to finance and economic literature in such journals as the Quarterly Economic Journal, The Journal of Finance,
The Journal of Financial and Quantitative Analysis, The Journal of Financial
Economics, and The Financial Analysts Journal. His best known work concerns
insider trading, where he showed both that corporate insiders earn abnormal profits from their trades and that regulation has little effect on these profits. He has
also made contributions concerning initial public offerings, the regulation of utilities, the behavior of market makers, the fluctuation of gold prices, the theoretical
effect of inflation on the interest rate, the empirical effect of inflation on capital
asset prices, the relationship between small capitalization stocks and the January
effect, and the capital structure decision.

Bradford D. Jordan
GATTON COLLEGE OF BUSINESS AND ECONOMICS, UNIVERSITY OF KENTUCKY

Bradford D. Jordan is Professor of Finance and holder of the Richard W. and
Janis H. Furst Endowed Chair in Finance at the University of Kentucky. He has a
long-standing interest in both applied and theoretical issues in corporate finance
and has extensive experience teaching all levels of corporate finance and financial
management policy. Professor Jordan has published numerous articles in leading
journals on issues such as initial public offerings, capital structure, and the behavior of security prices. He is a past president of the Southern Finance Association,
and he is coauthor of Fundamentals of Investments: Valuation and Management,
5e, a leading investments text, also published by McGraw-Hill/Irwin.

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FROM THE AUTHORS
IN THE BEGINNING…
It was probably inevitable that the four of us would collaborate on this project. Over the last 20 or so years, we have been
working as two separate “RWJ” teams. In that time, we managed (much to our own amazement) to coauthor two widely
adopted undergraduate texts and an equally successful graduate text, all in the corporate finance area. These three books
have collectively totaled more than 25 editions (and counting),
plus a variety of country-specific editions and international
editions, and they have been translated into at least a dozen
foreign languages.
Even so, we knew that there was a hole in our lineup at the
graduate (MBA) level. We’ve continued to see a need for a
concise, up-to-date, and to-the-point product, the majority of
which can be realistically covered in a typical single term or
course. As we began to develop this book, we realized (with
wry chuckles all around) that, between the four of us, we have
been teaching and researching finance principles for well
over a century. From our own very extensive experience with
this material, we recognized that corporate finance introductory classes often have students with extremely diverse educational and professional backgrounds. We also recognized
that this course is increasingly being delivered in alternative
formats ranging from traditional semester-long classes to
highly compressed modules, to purely online courses, taught
both synchronously and asynchronously.

OUR APPROACH
To achieve our objective of reaching out to the many different types of students and the varying course environments,
we worked to distill the subject of corporate finance down to
its core, while maintaining a decidedly modern approach. We
have always maintained that corporate finance can be viewed
as the working of a few very powerful intuitions. We also know
that understanding the “why” is just as important, if not more
so, than understanding the “how.” Throughout the development of this book, we continued to take a hard look at what
is truly relevant and useful. In doing so, we have worked to
downplay purely theoretical issues and minimize the use of extensive and elaborate calculations to illustrate points that are
either intuitively obvious or of limited practical use.
Perhaps more than anything, this book gave us the chance
to pool all that we have learned about what really works in
a corporate finance text. We have received an enormous
amount of feedback over the years. Based on that feedback,
the two key ingredients that we worked to blend together here

ros30689_fm_i-xxxiv.indd viii

are the careful attention to pedagogy and readability that we
have developed in our undergraduate books and the strong
emphasis on current thinking and research that we have
always stressed in our graduate book.
From the start, we knew we didn’t want this text to be encyclopedic. Our goal instead was to focus on what students
really need to carry away from a principles course. After much
debate and consultation with colleagues who regularly teach
this material, we settled on a total of 20 chapters. Chapter
length is typically 30 pages, so most of the book (and, thus,
most of the key concepts and applications) can be realistically
covered in a single term or module. Writing a book that strictly
focuses on core concepts and applications necessarily involves some picking and choosing, with regard to both topics
and depth of coverage. Throughout, we strike a balance by
introducing and covering the essentials, while leaving more
specialized topics to follow-up courses.
As in our other books, we treat net present value (NPV) as
the underlying and unifying concept in corporate finance. Many
texts stop well short of consistently integrating this basic principle. The simple, intuitive, and very powerful notion that NPV
represents the excess of market value over cost often is lost in
an overly mechanical approach that emphasizes computation
at the expense of comprehension. In contrast, every subject we
cover is firmly rooted in valuation, and care is taken throughout
to explain how particular decisions have valuation effects.
Also, students shouldn’t lose sight of the fact that financial
management is about management. We emphasize the role
of the financial manager as decision maker, and we stress
the need for managerial input and judgment. We consciously
avoid “black box” approaches to decisions, and where appropriate, the approximate, pragmatic nature of financial analysis
is made explicit, possible pitfalls are described, and limitations
are discussed.

NEW TO THE 3RD EDITION
With our first two editions of Corporate Finance: Core
Principles & Applications, we had the same hopes and fears
as any entrepreneurs. How would we be received in the market? Based on the very gratifying feedback we received, we
learned that many of you agreed with us concerning the need
for a focused, concise treatment of the major principles of corporate finance.
In developing the third edition, one of the things we focused on was extensive updating. We wanted to be as current
as possible throughout the book. As a result, we revamped,

18/08/10 7:44 PM

rewrote, or replaced essentially all of the chapter opening vignettes, in-chapter real-world examples, and The Real World
readings. We updated facts and figures throughout the book,
and we revised and expanded the already extensive end-ofchapter material.
A list of the most important revisions to the third edition
is below:
Overall:

Completely rewritten Chapter on Financial
Statements and Financial Models
Revised and updated data and figures
More Excel examples
All new chapter openers
All new problems at ends of chapters
Many new boxes
New chapter on Raising Capital
Completely rewritten International Corporate
Finance chapter
Updated real examples
Mergers and Acquisitions moved to online

Chapter 1:

New materials on corporate governance and
regulation, including Sarbanes-Oxley

Chapter 3:

Improved discussion of financial ratios
e.g. EBITDA and EV
More examples

Chapter 4:

New spreadsheet applications

Chapter 9:

New material on the full payout model

Chapter 10:

New material on global equity risk premiums
Update to 2009
New material on the global market collapse

Chapter 12:

New material on how to estimate the WACC
Updated examples

Chapter 13:

More material on bubbles
Changed Chapter title to underscore behavioral
challenges

Chapter 15:

Updated data on capital structure

ros30689_fm_i-xxxiv.indd ix

Our attention to updating and improving also extended to
the extensive collection of support and enrichment materials
that accompany the text. Working with many dedicated and
talented colleagues and professionals, we continue to provide
supplements that are unrivaled at the graduate level (a complete description appears in the following pages). Whether
you use just the textbook, or the book in conjunction with other
products, we believe you will be able to find a combination
that meets your current as well as your changing needs.

—Stephen A. Ross
—Randolph W. Westerfield
—Jeffrey F. Jaffe
—Bradford D. Jordan

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PEDAGOGY
Chapter Opening Case

Corporate Finance: Core
Principles & Applications
is rich in valuable learning
tools and support to help
students succeed in learning
the fundamentals of financial
management.

Each chapter begins with a recent real-world event to
introduce students to chapter concepts.
CHAPTER

4

Discounted Cash Flow
Valuation

OPENING CASE
PART TWO Valuation and Capital Budgeting

W

hat do Chris Iannetta, John Lackey, and Matt Holliday have in common? All
three are star athletes who signed big-money contracts during late 2009 or
early 2010. Their contract values were reported as $8.35 million, $82.5 million, and $120 million, respectively. But reported numbers can be misleading.
For example, catcher Chris Ianetta re-signed with the Colorado Rockies. His

deal called for salaries of $1.75 million, $2.55 million, and $3.55 million over the next three years,
respectively, with a contract buyout of $500,000 or a salary of $5,000,000 in four years. Not bad,
especially for someone who makes a living using the “tools of ignorance” (jock jargon for a catcher’s
equipment).
A closer look at the numbers shows that Chris, John, and Matt did pretty well, but nothing like the
quoted figures. Using Matt’s contract as an example, the value was reported to be $120 million, but it
was actually payable over several years. The terms called for a salary of $17 million per year for seven
years, then a club option for $17 million in 2017 or a club buyout of $1 million. However, of the $17 million annual salary, $2 million each year was to be deferred and paid annually from 2020 to 2029. Since
the payments are spread out over time, we must consider the time value of money, which means his
contract was worth less than reported. How much did he really get? This chapter gives you the “tools
of knowledge” to answer this question.

Explanatory Web Links

p

EXAMPLE

4.12

These Web links are provided in the
margins of the text. They are specifically
selected to accompany text material and
provide students and instructors with
a quick way to check for additional
information using the Internet.

If the stated annual rate of interest, 8 percent, is compounded quarterly, what is the effective annual
rate?
Using (4.7), we have
m

4

.08 ⫺ 1 ⫽ .0824 ⫽ 8.24%
⫺ 1 ⫽ 1 ⫹ ___
4

(

)

Referring back to our earlier example where C0 ⫽ $1,000 and r ⫽ 10%, we can generate the following table:

C0

COMPOUNDING
FR E Q U E N C Y ( m )

C1

$1,000
1,000
1,000
1,000

Yearly (m ⫽ 1)
Semiannually (m ⫽ 2)
Quarterly (m ⫽ 4)
Daily (m ⫽ 365)

$1,100.00
1,102.50
1,103.81
1,105.16

ros30689_fm_i-xxxiv.indd x

y

Online bond calculators
are available at
personal.fidelity.com;
interest rate information
is available at money.
cnn.com/markets/
bondcenter and www.
bankrate.com.

This is just the amount of the discount.
What would the Xanth bond sell for if interest rates had dropped by 2 percent instead of
rising by 2 percent? As you might guess, the bond would sell for more than $1,000. Such a
bond is said to sell at a premium and is called a premium bond.
This case is just the opposite of that of a discount bond. The Xanth bond now has a
coupon rate of 8 percent when the market rate is only 6 percent. Investors are willing to
pay a premium to get this extra coupon amount. In this case, the relevant discount rate
is 6 percent, and there are nine years remaining. The present value of the $1,000 face
amount is:

Examples

Compounding Frequencies

( 1 ⫹ __mr )

,

Annuity present value  $20  (1  1兾1.109)兾.10
 $20  5.7590
 $115.18

E FFE C T I V E A N N U A L
R AT E 
r m
1  _
m  1

(

)

.10
.1025
.10381
.10516

Separate numbered and titled examples are extensively
integrated into the chapters. These examples provide
detailed applications and illustrations of the text
material in a step-by-step format. Each example is
completely self-contained, so students don’t have to
search for additional information.

8/19/10 12:59 PM

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.

Figures and Tables

FIGURE 4.11

THE REAL WORLD

4

Interest
earned

3
2

4

Interest
earned

3

Dollars

4
Dollars

This text makes extensive use of real data
presented in various figures and tables.
Explanations in the narrative, examples,
and end-of-chapter problems refer to
many of these exhibits.

Dollars

Annual, Semiannual, and
Continuous Compounding

2

0

1

2
3
Years

4

5

0

Annual compounding

Interest
earned

2
1

1

1

3

1

2
3
Years

4

5

Semiannual compounding

0

1

2
3
Years

4

5

Continuous compounding

JACKPOT!
If you or someone you know is a regular lottery player, you probably already understand that you are 20 times more
likely to get struck by lightning than you are to win a big lottery jackpot. What are your odds of winning? Below you
will find a table with your chances of winning the Mega Millions Lottery compared to other events.
Odds of winning a Mega Millions jackpot
Odds of being killed by a venomous spider
Odds of being killed by a dog bite
Odds of being killed by lightning
Odds of being killed by drowning
Odds of being killed falling from a bed or other furniture
Odds of being killed in a car crash

The Real World

1:135,145,920*
1:57,018,763
1:11,403,753
1:6,479,405
1:690,300
1:388,411
1:6,029

By exploring information found in recent
publications and building upon concepts
learned in each chapter, these boxes work
through real-world issues relevant to the
surrounding text.

*Source: Virginia Lottery Web site. All other odds from the National Safety Council.

Sweepstakes may have different odds than lotteries, but these odds may not be much better. Probably the
largest advertised potential grand prize ever was Pepsi’s “Play for a Billion,” which, you guessed it, had a $1 billion
(billion!) prize. Not bad for a day’s work, but you still have to read the fine print. It turns out that the winner would
be paid $5 million per year for the next 20 years, $10 million per year for years 21 through 39, and a lump sum
$710 million in 40 years. From what you have learned, you know the value of the sweepstakes wasn’t even close to
$1 billion. In fact, at an interest rate of 10 percent, the present value is about $70.7 million.
In January 2010, a 59-year-old man and his 57-year-old wife in New York won the $162 million Mega Millions
jackpot. They were given the option of receiving the jackpot as $6.231 million immediately and $6.231 million per
year for the next 25 years, or $102 million immediately. So, what discount rate does this imply? After some computational effort, we find the interest rate is about 4.15 percent. Unfortunately for the winners, nearly $1 million was
placed in an escrow account over a dispute about the mismanagement of funds at a homeless shelter the couple
had previously operated.
Some lotteries make your decision a little tougher. The Ontario Lottery will pay you either $2,000 a week for the
rest of your life or $1.3 million now. (That’s in Canadian dollars or “loonies,” by the way.) Of course, there is the
chance you might die in the near future, so the lottery guarantees that your heirs will collect the $2,000 weekly
payments until the twentieth anniversary of the first payment, or until you would have turned 91, whichever comes
first. This payout scheme complicates your decision quite a bit. If you live for only the 20-year minimum, the breakeven interest rate between the two options is about 5.13 percent per year, compounded weekly. If you expect to
live longer than the 20-year minimum, you might be better off accepting $2,000 per week for life. Of course, if you
manage to invest the $1.3 million lump sum at a rate of return of about 8 percent per year (compounded weekly),
you can have your cake and eat it too because the investment will return $2,000 at the end of each week forever!
Taxes complicate the decision in this case because the lottery payments are all on an aftertax basis. Thus, the rates
of return in this example would have to be aftertax as well.

How to Calculate Present Values with
Multiple Future Cash Flows Using a
Spreadsheet

SPREADSHEET TECHNIQUES

We can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows.
Notice that we have simply calculated the present values one at a time and added them up:

Spreadsheet Techniques

A

B

C

D

E

1

Using a spreadsheet to value multiple future cash flows

2

This feature helps students to improve their Excel
spreadsheet skills, particularly as they relate to
corporate finance. This feature appears in selfcontained sections and shows students how to set up
spreadsheets to analyze common financial problems—a
vital part of every business student’s education. For
even more help using Excel, students have access to
Excel Master, an in-depth online tutorial.

3
4
5
6
7
8
9

What is the present value of $200 in one year, $400 the next year, $600 the next year, and
$800 the last year if the discount rate is 12 percent?

10
11
12
13
14
15
16
17
18
19
20
21
22

Rate:

0.12

Year

Cash flows

1
2
3
4

$200
$400
$600
$800
Total PV:

Present values
$178.57
$318.88
$427.07
$508.41
$1,432.93

Formula used
=PV($B$7,A10,0,⫺B10)
=PV($B$7,A11,0,⫺B11)
=PV($B$7,A12,0,⫺B12)
=PV($B$7,A13,0,⫺B13)
=SUM(C10:C13)

Notice the negative signs inserted in the PV formulas. These just make the present values have
positive signs. Also, the discount rate in cell B7 is entered as $B$7 (an "absolute" reference)
because it is used over and over. We could have just entered ".12" instead, but our approach is more
flexible.

This real rate is the same as we had before. If we take another look at the Fisher effect, we
can rearrange things a little as follows:
1  R  (1  r)  (1  h)
Rrhrh

[5.3]

What this tells us is that the nominal rate has three components. First, there is the real rate
on the investment, r. Next, there is the compensation for the decrease in the value of the
money originally invested because of inflation, h. The third component represents compensation for the fact that the dollars earned on the investment are also worth less because of
the inflation.
This third component is usually small, so it is often dropped. The nominal rate is then
approximately equal to the real rate plus the inflation rate:
R 艐 rh

ros30689_fm_i-xxxiv.indd xi

Numbered Equations
Key equations are numbered within the
text and listed on the back end sheets for
easy reference.

[5.4]

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END-OF-CHAPTER
MATERIAL
The end-of-chapter material
reflects and builds on the
concepts learned from the
chapter and study features.

Summary and Conclusions
Each chapter ends with a numbered and concise, but
thorough, summary of the important ideas presented
in the chapter—helping students review the key points
and providing closure.
SUMMARY AND CONCLUSIONS
This chapter has explored bonds, bond yields, and interest rates. We saw that:
1. Determining bond prices and yields is an application of basic discounted cash flow principles.
2. Bond values move in the direction opposite that of interest rates, leading to potential gains or
losses for bond investors.
3. Bonds have a variety of features spelled out in a document called the indenture.
4. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no risk
of default, whereas so-called junk bonds have substantial default risk.
5. A wide variety of bonds exist, many of which contain exotic or unusual features.
6. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result,
bond price and volume information can be difficult to find for some types of bonds.
7. Bond yields and interest rates reflect the effect of six different things: the real interest rate and
five premiums that investors demand as compensation for inflation, interest rate risk, default
risk, taxability, and lack of liquidity.

CONCEPT QUESTIONS

Concept Questions

1. Treasury Bonds Is it true that a U.S. Treasury security is risk-free?
2. Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year
BB corporate bond?
3. Treasury Pricing With regard to bid and ask prices on a Treasury bond, is it possible for the bid
price to be higher? Why or why not?
4. Yield to Maturity Treasury bid and ask quotes are sometimes given in terms of yields, so there
would be a bid yield and an ask yield. Which do you think would be larger? Explain.
5. Call Provisions A company is contemplating a long-term bond issue. It is debating whether
or not to include a call provision. What are the benefits to the company from including a call
provision? What are the costs? How do these answers change for a put provision?
6. Coupon Rate How does a bond issuer decide on the appropriate coupon rate to set on its
bonds? Explain the difference between the coupon rate and the required return on a bond.

This end-of-chapter section facilitates your
students’ knowledge of key principles, as well
as their intuitive understanding of the chapter
concepts. The questions reinforce students’
critical-thinking skills and provide a review of
chapter material.

7. Real and Nominal Returns Are there any circumstances under which an investor might be
more concerned about the nominal return on an investment than the real return?
8. Bond Ratings Companies pay rating agencies such as Moody’s and S&P to rate their bonds,
and the costs can be substantial. However, companies are not required to have their bonds
rated in the first place; doing so is strictly voluntary. Why do you think they do it?
9. Bond Ratings

U.S. Treasury bonds are not rated. Why? Often, junk bonds are not rated. Why?

Questions and Problems
Because solving problems is so critical to
students’ learning, we provide extensive end-ofchapter questions and problems. The questions
and problems are segregated into three learning
levels: Basic, Intermediate, and Challenge. All
problems are fully annotated so that students
and instructors can readily identify particular
types. Also, most of the problems are available
in McGraw-Hill’s Connect—see the next
section of this preface for more details.

ros30689_fm_i-xxxiv.indd xii

QUESTIONS AND PROBLEMS
1. Stock Values The Starr Co. just paid a dividend of $2.15 per share on its stock. The dividends
are expected to grow at a constant rate of 4 percent per year, indefinitely. If investors require a
12 percent return on the stock, what is the current price? What will the price be in three years?
In 15 years?

Basic
(Questions 1–9)

2. Stock Values The next dividend payment by ZYX, Inc., will be $2.85 per share. The dividends
are anticipated to maintain a 4.5 percent growth rate, forever. If ZYX stock currently sells for
$84 per share, what is the required return?
3. Stock Values For the company in the previous problem, what is the dividend yield? What is the
expected capital gains yield?
4. Stock Values Mickelson Corporation will pay a $2.90 per share dividend next year. The
company pledges to increase its dividend by 4.75 percent per year, indefinitely. If you require
an 11 percent return on your investment, how much will you pay for the company’s stock
today?
5. Stock Valuation Shelter, Inc., is expected to maintain a constant 5.2 percent growth rate in its
dividends, indefinitely. If the company has a dividend yield of 4.4 percent, what is the required
return on the company’s stock?
6. Stock Valuation Suppose you know that a company’s stock currently sells for $73 per share
and the required return on the stock is 12 percent. You also know that the total return on the
stock is evenly divided between a capital gains yield and a dividend yield. If it’s the company’s
policy to always maintain a constant growth rate in its dividends, what is the current dividend
per share?

8/19/10 12:59 PM

What’s On the Web?

W H AT ’ S O N T H E W E B ?
1. Bond Quotes You can find current bond prices at cxa.marketwatch.com/finra/BondCenter.
You want to find the bond prices and yields for bonds issued by Georgia Pacific. You can enter
the ticker symbol “GP” to do a search. What is the shortest maturity bond issued by Georgia
Pacific that is outstanding? What is the longest maturity bond? What is the credit rating for
Georgia Pacific’s bonds? Do all of the bonds have the same credit rating? Why do you think
this is?

Excel Problems

13. Nonconstant Dividends South Side Corporation is expected to pay the following dividends
over the next four years: $10, $8, $5, and $3. Afterward, the company pledges to maintain a constant 5 percent growth rate in dividends forever. If the required return on the stock is 13 percent,
what is the current share price?

Indicated by the Excel icon in the margin,
these problems are integrated in the
Questions and Problems section of almost
all chapters. Located on the book’s Web site,
Excel templates have been created for each
of these problems. Students can use the data
in the problem to work out the solution using
Excel skills.

14. Differential Growth Hughes Co. is growing quickly. Dividends are expected to grow at a
30 percent rate for the next three years, with the growth rate falling off to a constant 7 percent
thereafter. If the required return is 10 percent and the company just paid a $2.40 dividend, what
is the current share price?
15. Differential Growth Janicek Corp. is experiencing rapid growth. Dividends are expected to
grow at 27 percent per year during the next three years, 17 percent over the following year,
and then 7 percent per year indefinitely. The required return on this stock is 12 percent, and the
stock currently sells for $65 per share. What is the projected dividend for the coming year?
16. Negative Growth Antiques R Us is a mature manufacturing firm. The company just paid a
$12 dividend, but management expects to reduce the payout by 4 percent per year, indefinitely. If
you require a 9 percent return on this stock, what will you pay for a share today?

ros30689_fm_i-xxxiv.indd xiii

CLOSING CASE

S T O C K V A L U AT I O N AT R A G A N E N G I N E S
Larissa has been talking with the company’s directors about the future of East Coast Yachts. To this
point, the company has used outside suppliers for various key components of the company’s yachts,
including engines. Larissa has decided that East Coast Yachts should consider the purchase of an
engine manufacturer to allow East Coast Yachts to better integrate its supply chain and get more
control over engine features. After investigating several possible companies, Larissa feels that the
purchase of Ragan Engines, Inc., is a possibility. She has asked Dan Ervin to analyze Ragan’s value.
Ragan Engines, Inc., was founded nine years ago by a brother and sister—Carrington and
Genevieve Ragan—and has remained a privately owned company. The company manufactures
marine engines for a variety of applications. Ragan has experienced rapid growth because of a
proprietary technology that increases the fuel efficiency of its engines with very little sacrifice in
performance. The company is equally owned by Carrington and Genevieve. The original agreement
between the siblings gave each 125,000 shares of stock.

These end-of-chapter activities show
students how to use and learn from the vast
amount of financial resources available on
the Internet.

End-of-Chapter Cases
Located at the end of each chapter,
these mini-cases focus on common
company situations that embody
important corporate finance topics.
Each case presents a new scenario,
data, and a dilemma. Several questions
at the end of each case require students
to analyze and focus on all of the
material they learned in that chapter.

8/19/10 12:59 PM

COMPREHENSIVE TEACHING
DIGITAL SOLUTIONS
Online Learning Center (OLC): Online Support at www.mhhe.com/rwj
The Online Learning Center (OLC) contains FREE access to Web-based study and
teaching aids created for this text, all in one place!

INSTRUCTOR SUPPORT

ros30689_fm_i-xxxiv.indd xiv



Instructor’s Manual
prepared by David Diehl, Aurora University, and Joseph Smolira, Belmont
University
A great place to find new lecture ideas. The IM has three main sections. The first
section contains a chapter outline and other lecture materials. The annotated outline
for each chapter includes lecture tips, real-world tips, ethics notes, suggested
PowerPoint slides, and, when appropriate, a video synopsis. Detailed solutions for
all end-of-chapter problems appear in section three.



Test Bank
prepared by Bruce Costa, University of Montana
Great format for a better testing process. The Test Bank has 75–100 questions per
chapter that closely link with the text material and provide a variety of question
formats (multiple-choice questions problems and essay questions) and levels of difficulty (basic, intermediate, and challenge) to meet every instructor’s testing needs.
Problems are detailed enough to make them intuitive for students and solutions are
provided for the instructor.



Computerized Test Bank
Create your own tests in a snap! These additional questions are found in a computerized test bank utilizing McGraw-Hill’s EZ Test testing software to quickly create
customized exams. This user-friendly program allows instructors to sort questions
by format; edit existing questions or add new ones; and scramble questions for
multiple versions of the same test.



PowerPoint Presentation System
prepared by David Diehl, Aurora University
Customize our content for your course. This presentation has been thoroughly
revised to include more lecture-oriented slides, as well as exhibits and examples
both from the book and from outside sources. Applicable slides have Web links
that take you directly to specific Internet sites, or a spreadsheet link to show an
example in Excel. You can also go to the Notes Page function for more tips in
presenting the slides. This customizable format gives you the ability to edit, print,
or rearrange the complete presentation to meet your specific needs.

18/08/10 7:44 PM

AND LEARNING PACKAGE
Videos
Also available in DVD format. Current set of videos on hot topics! McGraw-Hill/Irwin
has produced a series of finance videos that are 10-minute case studies on topics such as
Financial Markets, Careers, Rightsizing, Capital Budgeting, EVA (Economic Value Added),
Mergers and Acquisitions, and Foreign Exchange. Discussion questions for these videos, as
well as video clips, are available in the Instructor’s Center at www.mhhe.com/rwj.

STUDENT SUPPORT


Narrated PowerPoint Examples
These in-depth slides are designed exclusively for students as part of the premium
content package of this book. Each chapter’s slides follow the chapter topics and provide steps and explanations showing how to solve key problems. Because each student
learns differently, a quick click on each slide will “talk through” its contents with you!



Interactive FinSims
Created by Eric Sandburg, Interactive Media, each module highlights a key concept
of the book and simulates how to solve its problems, asking the student to input
certain variables. This hands-on approach guides students through difficult and
important corporate finance topics.



Excel Master
Created by Brad Jordan and Joe Smolira, this extensive Excel tutorial is fully
integrated with the text. Learn Excel and corporate finance at the same time. For
more details about this exciting new feature see the inside cover of this book!

McGraw-Hill Investments Trader
Students receive free access to this Web-based portfolio simulation with a hypothetical
$100,000 brokerage account to buy and sell stocks and mutual funds. Students can use
the real data found at this site in conjunction with the chapters on investments. They
can also compete against other students around the United States. Please click on the
corresponding link found in the OLC for more details. This site is powered by Stock-Trak,
the leading provider of investment simulation services to the academic community.


And More!
Be sure to check out the other helpful features found on the OLC, including selfgrading quizzes and end-of-chapter problem Excel templates.

PACKAGE OPTIONS AVAILABLE
FOR PURCHASE & PACKAGING
You may also package either version of the text with a variety of additional learning tools
that are available for your students.

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Solutions Manual
(ISBN 10: 0077316363/ISBN 13: 9780077316365)
Prepared by Joseph Smolira, Belmont University, this manual contains detailed, workedout solutions for all of the problems in the end-of-chapter material. It has also been
reviewed for accuracy by multiple sources. The Solutions Manual is also available for
purchase for your students.

FinGame Online 5.0
by LeRoy Brooks, John Carroll University
(ISBN 10: 0077219880/ISBN 13: 9780077219888)
Just $15.00 when packaged with this text. In this comprehensive simulation game,
students control a hypothetical company over numerous periods of operation. The game is
now tied to the text by exercises found on the Online Learning Center. As students make
major financial and operating decisions for their company, they will develop and enhance
their skills in financial management and financial accounting statement analysis.

Financial Analysis with an Electronic Calculator, Sixth Edition
by Mark A. White, University of Virginia, McIntire School of Commerce
(ISBN 10: 0073217093/ISBN 13: 9780073217093)
The information and procedures in this supplementary text enable students to master the
use of financial calculators and develop a working knowledge of financial mathematics
and problem solving. Complete instructions are included for solving all major problem
types on three popular models: HP 10B and 12C, TI BA II Plus, and TI-84. Hands-on
problems with detailed solutions allow students to practice the skills outlined in the text
and obtain instant reinforcement. Financial Analysis with an Electronic Calculator is a
self-contained supplement to the introductory financial management course.

McGRAW-HILL CONNECT FINANCE
Less Managing. More Teaching. Greater Learning.
McGraw-Hill’s Connect Finance is an online assignment and assessment solution that
connects students with the tools and resources they’ll need to achieve success.
Connect helps prepare students for their future by enabling faster learning, more
efficient studying, and higher retention of knowledge.
McGraw-Hill Connect Finance Features Connect Finance offers a number of
powerful tools and features to make managing assignments easier, so faculty can spend
more time teaching. With Connect Finance, students can engage with their coursework
anytime and anywhere, making the learning process more accessible and efficient.
Connect Finance offers you the features described below.

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Simple assignment management With Connect Finance, creating assignments is
easier than ever, so you can spend more time teaching and less time managing. The
assignment management function enables you to:






Create and deliver assignments easily with selectable end-of-chapter questions and
test bank items.
Streamline lesson planning, student progress reporting, and assignment grading to
make classroom management more efficient than ever.
Go paperless with online submission and grading of student assignments.

Smart grading When it comes to studying, time is precious. Connect Finance helps
students learn more efficiently by providing feedback and practice material when they
need it, where they need it. When it comes to teaching, your time is also precious. The
grading function enables you to:






Have assignments scored automatically, giving students immediate feedback on
their work and side-by-side comparisons with correct answers.
Access and review each response; manually change grades or leave comments for
students to review.
Reinforce classroom concepts with practice tests and instant quizzes.

Instructor library The Connect Finance Instructor Library is your repository for
additional resources to improve student engagement in and out of class. You can select
and use any asset that enhances your lecture.
Student study center The Connect Finance Student Study Center is the place for
students to access additional resources. The Student Study Center:



Offers students quick access to lectures, practice materials, and more.
Provides instant practice material and study questions, easily accessible on the go.

Student progress tracking Connect Finance keeps instructors informed about how
each student, section, and class is performing, allowing for more productive use of lecture
and office hours. The progress-tracking function enables you to:




View scored work immediately and track individual or group performance with
assignment and grade reports.
Access an instant view of student or class performance relative to learning
objectives.

Lecture capture through Tegrity Campus For an additional charge Lecture Capture
offers new ways for students to focus on the in-class discussion, knowing they can revisit
important topics later. This can be delivered through Connect or separately. See below for
more details.

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In short, Connect Finance offers you and your students powerful tools and features that
optimize your time and energies, enabling you to focus on course content, teaching, and
student learning. Connect Finance also offers a wealth of content resources for both
instructors and students. This state-of-the-art, thoroughly tested system supports you in
preparing students for the world that awaits.
For more information about Connect, go to www.mcgrawhillconnect.com, or contact
your local McGraw-Hill sales representative.

TEGRITY CAMPUS: LECTURES 24/7
Tegrity Campus is a service that makes class time available 24/7
by automatically capturing every lecture in a searchable format
for students to review when they study and complete assignments. With a simple one-click
start-and-stop process, you capture all computer screens and corresponding audio. Students
can replay any part of any class with easy-to-use browser-based viewing on a PC or Mac.
Educators know that the more students can see, hear, and experience class resources,
the better they learn. In fact, studies prove it. With Tegrity Campus, students quickly
recall key moments by using Tegrity Campus’s unique search feature. This search helps
students efficiently find what they need, when they need it, across an entire semester
of class recordings. Help turn all your students’ study time into learning moments
immediately supported by your lecture.
To learn more about Tegrity watch a 2-minute Flash demo at http://tegritycampus.
mhhe.com.

McGRAW-HILL CUSTOMER CARE CONTACT INFORMATION
At McGraw-Hill, we understand that getting the most from new technology can be
challenging. That’s why our services don’t stop after you purchase our products. You can
e-mail our Product Specialists 24 hours a day to get product-training online. Or you can
search our knowledge bank of Frequently Asked Questions on our support Web site. For
Customer Support, call 800-331-5094, e-mail hmsupport@mcgraw-hill.com, or visit
www.mhhe.com/support. One of our Technical Support Analysts will be able to assist
you in a timely fashion.

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ACKNOWLEDGMENTS

To borrow a phrase, writing a finance textbook
is easy—all you do is sit down at a word processor and open a vein. We never would have completed this book without the incredible amount
of help and support we received from our colleagues, students, editors, family members, and
friends. We would like to thank, without implicating, all of you.
Clearly, our greatest debt is to our many colleagues (and their students). Needless to say,
without this support and feedback we would not
be publishing this text.
To the following reviewers we are grateful for
their many contributions:
Dean Baim, Pepperdine University
Madhulina Bandyopadhyay, University of
Wisconsin, Milwaukee
Peter Basciano, Augusta State University
Elizabeth Booth, Michigan State University
Christa Bouwman, Case Western Reserve
University
Bruce Costa, University of Montana
Isabelle Delalex, Pace University
David Diehl, Aurora University
Robert Duvic, University of Texas at Austin
Yee-Tien Fu, Stanford University
Janet Hamilton, Portland State University
Corrine Hasbany, Rivier College
Rodrigo Hernandez, Radford University
Vanessa Holmes, Penn State Worthington,
Scranton
Gary Kayakachoian, University of Rhode Island
Gregory Kivenzor, Oregon State University
V. Sivarama Krishnan, University of Central
Oklahoma
Sanjay Kudrimoti, Salem State College
Douglas Lamdin, University of Maryland
Baltimore County
Michael Madaris, William Carey University
Robert Nash, Wake Forest University
Ali Ozbeki, Oakland University
Deniz Ozenbas, Montclair State University
Chein-Chih Peng, Morehead State University

Jong Rhim, University of Southern Indiana
Atul Saxena, Georgia Gwinnett College
James Scott, Missouri State University
Michael Sullivan, University of Nevada,
Las Vegas
Alex Tang, Morgan State University
Antoinette Tessmer, Michigan State University
Charles Wellens, North Idaho College
J. Douglas Wellington, Husson University
Jill Wetmore, Saginaw Valley State University
Casey Whilhelm, North Idaho College
We owe a special thanks to Joseph Smolira
of Belmont University for his work on this book.
Joe worked closely with us to develop portions
of the Instructor’s Manual, along with the many
vignettes and real-world examples. In addition,
we would like to thank David Diehl, Aurora
University, for his work on the PowerPoint and
Instructor’s Manual, and Bruce Costa, University of Montana, for his revision of the Test
Bank.
The following doctoral students did outstanding work on this edition: Dane Makhoul and Tim
Riley. To them fell the unenviable task of technical
proofreading, and in particular, careful checking of each calculation throughout the text and
Instructor’s Manual.
Finally, in every phase of this project, we
have been privileged to have had the complete
and unwavering support of a great organization, McGraw-Hill/Irwin. We especially thank
the McGraw-Hill/Irwin sales organization. The
suggestions they provide, their professionalism
in assisting potential adopters, and the service
they provide have been a major factor in our
success.
We are deeply grateful to the select group of
professionals who served as our development
team on this edition: Michele Janicek, Executive
Editor; Elizabeth Hughes, Development Editor;
Melissa Caughlin, Marketing Manager; Christine
Vaughan, Lead Project Manager; Mary Sander,
Designer; Heather Burbridge, Senior Manager,

ACKNOWLEDGMENTS

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EDP; and Brian Nacik, Media Project Manager. Others at
McGraw-Hill/Irwin, too numerous to list here, have improved
the book in countless ways.
Finally, we wish to thank our families, Carol, Kate, Jon, Jan,
Mark, Lynne, and Susan, for their forbearance and help.
Throughout the development of this edition, we have taken
great care to discover and eliminate errors. Our goal is to provide the best textbook available on the subject. To ensure that
future editions are error-free, we gladly offer $10 per arithmetic error to the first individual reporting it as a modest token of
our appreciation. More than this, we would like to hear from

xx

instructors and students alike. Please write and tell us how to
make this a better text. Forward your comments to: Dr. Brad
Jordan, c/o Editorial–Finance, McGraw-Hill/Irwin, 1333 Burr
Ridge Parkway, Burr Ridge, IL 60527, or visit us online at www.
mhhe.com/rwj.
—Stephen A. Ross
—Randolph W. Westerfield
—Jeffrey F. Jaffe
—Bradford D. Jordan

ACKNOWLEDGMENTS

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BRIEF CONTENTS

PART ONE

PART TWO

OVERVIEW
CHAPTER ONE

Introduction to Corporate Finance

CHAPTER TWO

Financial Statements and Cash Flow

1

CHAPTER THREE

Financial Statements Analysis and Financial
Models 44

20

VALUATION AND CAPITAL BUDGETING
CHAPTER FOUR

Discounted Cash Flow Valuation

84

CHAPTER FIVE

Interest Rates and Bond Valuation

CHAPTER SIX

Stock Valuation 168

133

CHAPTER SEVEN

Net Present Value and Other Investment Rules

CHAPTER EIGHT

Making Capital Investment Decisions

CHAPTER NINE

Risk Analysis, Real Options, and Capital
Budgeting 267

199

236

PART THREE RISK AND RETURN

PART FOUR

CHAPTER TEN

Risk and Return Lessons from Market History

CHAPTER ELEVEN

Return and Risk: The Capital Asset Pricing
Model (CAPM) 321

CHAPTER TWELVE

Risk, Cost of Capital, and Capital Budgeting

363

CAPITAL STRUCTURE AND DIVIDEND POLICY
CHAPTER THIRTEEN

PART FIVE

293

Efficient Capital Markets and Behavioral
Challenges 395

CHAPTER FOURTEEN

Capital Structure: Basic Concepts

CHAPTER FIFTEEN

Capital Structure: Limits to the Use of Debt

430

CHAPTER SIXTEEN

Dividends and Other Payouts

459

490

SPECIAL TOPICS
CHAPTER SEVENTEEN

Options and Corporate Finance

CHAPTER EIGHTEEN

Short-Term Finance and Planning

527
568

CHAPTER NINETEEN

Raising Capital 601

CHAPTER TWENTY

International Corporate Finance

CHAPTER TWENTY ONE

Mergers and Acquisitions (Web only)

APPENDIX A

Mathematical Tables

APPENDIX B

Solutions to Selected End-of-Chapter Problems

APPENDIX C

Using the HP 10B and TI BA II Plus
Financial Calculators 677

Indexes

636

663
672

681

BRIEF CONTENTS

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CONTENTS

PART ONE

2.2

OVERVIEW

1.1

What Is Corporate Finance?

1

1

The Balance Sheet Model of the Firm
The Financial Manager
1.2

The Corporate Firm
4

The Corporation

5

4

The Importance of Cash Flows

1.4

The Goal of Financial Management

25
26

Net Working Capital

28

2.5

Financial Cash Flow

28

2.6
7

The Accounting Statement of Cash
Flows 31

10

Cash Flow from Operating
Activities 31

11

Cash Flow from Investing
Activities 32

10

A More General Goal

26

Cash Flow from Financing
Activities 33

12

The Agency Problem and Control
of the Corporation 12

Summary and Conclusions

Agency Relationships

Closing Case: Cash Flows at East Coast
Yachts 42

Management Goals

13
13

Do Managers Act in the Stockholders’
Interests? 14

34

CHAPTER THREE

Stakeholders 15

Financial Statements Analysis
and Financial Models 44

Regulation 15

3.1

Summary and Conclusions

19

3.2

46

Ratio Analysis 48
Short-Term Solvency or Liquidity
Measures 48

Financial Statements and Cash Flow 20
The Balance Sheet

20

Accounting Liquidity
Value versus Cost

45

Common-Size Income Statements

CHAPTER TWO

Debt versus Equity

44

Common-Size Balance Sheets

17

Closing Case: East Coast Yachts

Financial Statements Analysis
Standardizing Statements 45

The Securities Act of 1933 and the
Securities Exchange Act of 1934 16

2.1

Time and Costs
Taxes 25

2.4

7

The Goal of Financial Management

1.6

24

Average versus Marginal Tax Rates

1.3

1.5

Noncash Items

Corporate Tax Rates

4

A Corporation by Another Name . . .

Possible Goals

2.3

3

The Sole Proprietorship
The Partnership

2

23

Generally Accepted Accounting
Principles 24

CHAPTER ONE

Introduction to Corporate Finance

The Income Statement

21
22

22

Long-Term Solvency Measures

50

Asset Management or Turnover
Measures 51
Profitability Measures
Market Value Measures

53
54

CONTENTS

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3.3

The Du Pont Identity

57

CHAPTER FIVE

A Closer Look at ROE

57

Interest Rates and Bond Valuation

Problems with Financial Statement Analysis 59
3.4

3.5

5.1

Financial Models 61

133

Bond Features and Prices

134

A Simple Financial Planning Model

61

Bond Values and Yields

The Percentage of Sales Approach

62

Interest Rate Risk

External Financing and Growth
EFN and Growth

5.2

137

More on Bond Features
The Indenture

74

Closing Case: Ratios and Financial Planning
at East Coast Yachts 81

Security

145

Seniority

145

Repayment

CHAPTER FOUR

Discounted Cash Flow Valuation
4.1

Valuation: The One-Period Case

4.2

The Multiperiod Case

84

145

Present Value and Discounting
The Algebraic Formula
4.3

Simplifications
Perpetuity

101

150
151

Bond Markets 151

5.7

152

152
155

Inflation and Interest Rates

155

Real versus Nominal Rates

155

The Fisher Effect

103

156

Determinants of Bond Yields

157

The Term Structure of Interest Rates
104

Trick 2: Annuity Due

Conclusion

108
110

111
113

113

Stock Valuation

168

The Present Value of Common Stocks
Dividends versus Capital Gains

114

Summary and Conclusions

Closing Case: Financing East Coast Yachts’ Expansion
Plans with a Bond Issue 166

6.1

113

What Is a Firm Worth?

161

CHAPTER SIX

Loan Types and Loan Amortization
Interest-Only Loans

161

Summary and Conclusions

109

Trick 4: Equating Present Value of Two Annuities 110

Pure Discount Loans

157

Bond Yields and the Yield Curve: Putting It All
Together 159

Trick 3: The Infrequent Annuity

Amortized Loans

149

Floating-Rate Bonds

148

A Note on Bond Price Quotes
5.6

101

Trick 1: A Delayed Annuity

4.6

Zero Coupon Bonds

Bond Price Reporting

106

Growing Annuity

148

How Bonds Are Bought and Sold

103

Growing Perpetuity
Annuity

Government Bonds

Other Types of Bonds
5.5

96

Compounding over Many Years

4.5

Some Different Types of Bonds

Compounding Periods 97

Continuous Compounding

146

5.4

91

Distinction between Stated Annual Interest Rate
and Effective Annual Rate 99

4.4

Protective Covenants

88
92

146

Bond Ratings 147

84

The Power of Compounding: A Digression

143

5.3

88

Future Value and Compounding

141

144

The Call Provision

VALUATION AND CAPITAL BUDGETING

139

144

Terms of a Bond

Some Caveats Regarding Financial Planning Models 73

PART TWO

134

Long-Term Debt: The Basics

69

A Note about Sustainable Growth Rate Calculations 72
Summary and Conclusions

133

Finding the Yield to Maturity: More Trial and Error

66

67

Financial Policy and Growth
3.6

Bonds and Bond Valuation

Valuation of Different Types of Stocks
117

Case 1 (Zero Growth)

119

Closing Case: The MBA Decision

170

170

Case 2 (Constant Growth)

131

168

168

Case 3 (Differential Growth)

170
171

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6.2

Estimates of Parameters in the Dividend Discount
Model 173

Summary of Payback

204

7.3

The Discounted Payback Period Method

205

Where Does R Come From?

7.4

The Average Accounting Return Method

205

Total Payout

174
176

Defining the Rule

177

Growth Opportunities 177
Growth in Earnings and Dividends
versus Growth Opportunities 179
The No-Payout Firm

Price-Earnings Ratio 180

6.5

Some Features of Common and Preferred Stocks
Shareholder Rights
Proxy Voting
Other Rights

182

Problems with the IRR Approach

182

183

Problem 1: Investing or Financing?
NPV Rule
185
185

General Rules

185

214

The Scale Problem

186
186

217

Redeeming Qualities of IRR
A Test

187

7.7

187

219

219

The Profitability Index

220

Calculation of Profitability Index
188
7.8

Stock Market Reporting

220

Application of the Profitability Index

189
189

The Practice of Capital Budgeting

Summary and Conclusions

Closing Case: Stock Valuation at Ragan Engines

197

220

222

224

Closing Case: Bullock Gold Mining

192

235

CHAPTER EIGHT

Making Capital Investment Decisions

CHAPTER SEVEN

Net Present Value and Other Investment
Rules 199
7.1

Why Use Net Present Value?

199

7.2

The Payback Period Method

202

8.1

Incremental Cash Flows
Sunk Costs

203

Problem 1: Timing of Cash Flows within the Payback
Period 203

237

238

Allocated Costs
8.2

236

237

Opportunity Costs
Side Effects

236

236

Cash Flows—Not Accounting Income

202

Problems with the Payback Method

215

215

The Timing Problem

186

NASDAQ Operations

214

Problems Specific to Mutually Exclusive Projects

186

Organization of the NYSE

Defining the Rule

213

The Guarantee against Multiple IRRs

Dealers and Brokers

Summary and Conclusions

212

213

Modified IRR

Is Preferred Stock Really Debt?

ECNs

212

Problem 2: Multiple Rates of Return

185

Floor Activity

210

Two General Problems Affecting Both Independent
and Mutually Exclusive Projects 211

Cumulative and Noncumulative Dividends

Operations

207

Definition of Independent and Mutually Exclusive
Projects 210

184

The Stock Markets

207

The Internal Rate of Return

182

Preferred Stock Features

Members

207

7.6

Dividends 184
Stated Value

206

Step 2: Determining Average Investment

7.5

183

Classes of Stock

Step 1: Determining Average Net Income
Step 3: Determining AAR

179

Common Stock Features

205

Analyzing the Average Accounting Return Method 207

6.4

6.6

204

Where Does g Come From? 173
A Healthy Sense of Skepticism
6.3

Managerial Perspective

238

The Baldwin Company: An Example
An Analysis of the Project

Problem 2: Payments after the Payback Period 203

Investments 240

Problem 3: Arbitrary Standard for Payback
Period 204

Income and Taxes
Salvage Value

239

240

241

242

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Cash Flow

PART THREE

243

Net Present Value

243

Which Set of Books?

243

CHAPTER TEN

A Note on Net Working Capital
A Note on Depreciation
Interest Expense
8.3
8.4

8.5

Risk and Return Lessons from Market
History 293

243

244

10.1

245

Returns 293
Dollar Returns

Inflation and Capital Budgeting

245

Discounting: Nominal or Real?

246

The Bottom-Up Approach

249

The Top-Down Approach

249

The Tax Shield Approach

249

248

Holding Period Returns

10.3

Return Statistics

10.4

Average Stock Returns and Risk-Free
Returns 304

10.5

Risk Statistics
Variance

Investments of Unequal Lives: The Equivalent Annual
Cost Method 250
The General Decision to Replace

252

297

303

306

306

Normal Distribution and Its Implications
for Standard Deviation 307
10.6

The U.S. Equity Risk Premium: Historical and
International Perspectives 3 0 8

10.7

2008: A Year of Financial Crisis

10.8

More on Average Returns

254

Closing Cases: Expansion at East Coast Yachts 265
Bethesda Mining Company 265

295

10.2

250

Summary and Conclusions

293

Percentage Returns

Alternative Definitions of Operating Cash Flow

Conclusion

RISK AND RETURN

311

312

Arithmetic versus Geometric Averages

CHAPTER NINE

Risk Analysis, Real Options, and Capital
Budgeting 267
9.1
9.2

Summary and Conclusions

269

CHAPTER ELEVEN

Sensitivity Analysis and Scenario Analysis 270
Costs

Return and Risk: The Capital Asset Pricing
Model (CAPM) 321

270

271

Break-Even Analysis
Accounting Profit
Present Value
9.3

273

11.1

Individual Securities

273

11.2

Expected Return, Variance, and Covariance

Monte Carlo Simulation

Covariance and Correlation

276
11.3

276

Step 3: The Computer Draws One Outcome
Step 4: Repeat the Procedure
Step 5: Calculate NPV

The Return and Risk for Portfolios

The Variance

278

326
326

The Diversification Effect

280

The Efficient Set

329

329

The Two-Asset Case

282

329

The Efficient Set for Many Securities
283

Closing Case: Bunyan Lumber, LLC

11.5

291

327

328

An Extension to Many Assets
11.4

327

327

Standard Deviation of a Portfolio

278

279

The Option to Abandon
Summary and Conclusions

322

Variance and Standard Deviation of a Portfolio

278

Real Options 279
The Option to Expand

322

323

The Expected Return on a Portfolio

Step 2: Specify a Distribution for Each Variable
in the Model 276

Timing Options

321

Expected Return and Variance

275

Step 1: Specify the Basic Model

9.4

315

Closing Case: A Job at East Coast Yachts,
Part 1 319

Sensitivity Analysis, Scenario Analysis, and
Break-Even Analysis 269
Revenues

313

Arithmetic Average Return or Geometric
Average Return? 314

Decision Trees 267
Warning

312

Calculating Geometric Average Returns

Riskless Borrowing and Lending
The Optimal Portfolio

333

334

336

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11.6

12.6

Announcements, Surprises, and Expected
Returns 338
Announcements and News

339

Risk: Systematic and Unsystematic

340

12.7

Cost of Capital for Divisions and Projects 377

Systematic and Unsystematic Risk

340

12.8

Cost of Fixed Income Securities
Cost of Debt

Diversification and Portfolio Risk

12.9

The Principle of Diversification

Diversification and Systematic Risk
Market Equilibrium

Eastman’s Cost of Equity
343

Eastman’s Cost of Debt

343

Eastman’s WACC

344

Definition of the Market Equilibrium Portfolio

A Test

The Basic Approach

Summary and Conclusions

11.10 Relationship between Risk and Expected
Return (CAPM) 349
350

Closing Case: A Job at East Coast Yachts, Part 2

PART FOUR
361

CHAPTER TWELVE

Risk, Cost of Capital, and Capital Budgeting
12.1

The Cost of Equity Capital

12.2

Estimating the Cost of Equity Capital with
the CAPM 364

363

363

13.1

Can Financing Decisions Create
Value? 395

13.2

A Description of Efficient Capital
Markets 397
Foundations of Market Efficiency

Real-World Betas

369

Stability of Beta

Independent Deviations from Rationality

12.4
12.5

Arbitrage
13.3

The Different Types of Efficiency

372

Beta and Covariance

372

The Efficacy of Dart Throwing

Determinants of Beta

373

Price Fluctuations

Operating Leverage

13.4

373
373

The Evidence
The Weak Form

403

403

Stockholder Disinterest

373

Financial Leverage and Beta

401

Some Common Misconceptions about
the Efficient Market Hypothesis 402

Beta and Covariance

Cyclicality of Revenues

400

400

The Semistrong and Strong Forms
370

399

400

The Weak Form

369

Using an Industry Beta

399

Rationality 399

367

Method 2: Using the Dividend Discount Model
(DDM) 367
368

CAPITAL STRUCTURE
AND DIVIDEND POLICY

Efficient Capital Markets and Behavioral
Challenges 395

367

Estimation of Beta

387

387

CHAPTER THIRTEEN

367

Method 1: Using Historical Data

12.3

386

Closing Case: The Cost of Capital for Goff
Computer, Inc. 394

352

Market Risk Premium

385

349

Expected Return on Individual Security

The Risk-Free Rate

384

Internal Equity and Flotation Costs

349

Summary and Conclusions

383

385

Flotation Costs and NPV

347

Expected Return on Market

380

12.11 Flotation Costs and the Weighted Average Cost
of Capital 385

344

Definition of Risk When Investors Hold
the Market Portfolio 345
The Formula for Beta

379

The Weighted Average Cost of Capital

12.10 Estimating Eastman Chemical’s Cost
of Capital 383

341

Diversification and Unsystematic Risk

378

378

Cost of Preferred Stock

341

The Effect of Diversification: Another Lesson
from Market History 341

11.9

375

Can a Low-Dividend or a No-Dividend Stock
Have a High Cost of Capital? 376

Systematic and Unsystematic Components
of Return 340
11.8

375

Comparison of DDM and CAPM

Expected and Unexpected Returns 338
11.7

Dividend Discount Model

403

403
404

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The Semistrong Form
Event Studies

405

The Weighted Average Cost of Capital RWACC
and Corporate Taxes 449

406

The Record of Mutual Funds
The Strong Form
13.5

Stock Price and Leverage under Corporate
Taxes 449

407

408

Summary and Conclusions

The Behavioral Challenge to Market
Efficiency 409
Rationality 409
Independent Deviations from
Rationality 409
Arbitrage

CHAPTER FIFTEEN

Capital Structure: Limits to the Use
of Debt 459

410

13.6

Empirical Challenges to Market Efficiency

13.7

Reviewing the Differences

13.8

410

15.1

416

Representativeness 416

Indirect Bankruptcy Costs

Conservatism 416

Agency Costs

Implications for Corporate Finance

2. The Timing Decision

417

4. Information in Market Prices
Summary and Conclusions

420

420

The Capital Structure Question and the Pie
Theory 430

14.2

Maximizing Firm Value versus Maximizing
Stockholder Interests 431

14.3

Financial Leverage and Firm Value:
An Example 433
The Choice between Debt and Equity
A Key Assumption

Protective Covenants

464

Consolidation of Debt

465

463
464

Pie Again

465

15.4

Signaling

468

15.5

Shirking, Perquisites, and Bad Investments: A Note
on Agency Cost of Equity 469
Effect of Agency Costs of Equity on
Debt-Equity Financing 471

430

14.1

Can Costs of Debt Be Reduced?

Integration of Tax Effects and Financial
Distress Costs 465

CHAPTER FOURTEEN

Leverage and Returns to Shareholders

460

461

15.3

422

Closing Case: Your 401(K) Account at East Coast
Yachts 428

Capital Structure: Basic Concepts

459
460

Summary of Selfish Strategies
15.2

417

3. Speculation and Efficient Markets

Free Cash Flow
15.6

471

The Pecking-Order Theory

472

Rules of the Pecking Order

473

Rule #1 Use Internal Financing

473

Rule #2 Issue Safe Securities First
435

474

Implications 474

433
15.7

Growth and the Debt-Equity Ratio
No Growth

437

Growth

475

475

475

Modigliani and Miller: Proposition II
(No Taxes) 437

15.8

How Firms Establish Capital Structure

Risk to Equityholders Rises with Leverage 437

15.9

A Quick Look at the Bankruptcy Process

Proposition II: Required Return to Equityholders
Rises with Leverage 438
MM: An Interpretation
14.5

Costs of Financial Distress
Direct Bankruptcy Costs

1. Accounting Choices, Financial Choices,
and Market Efficiency 417

14.4

451

Closing Case: Stephenson Real Estate
Recapitalization 458

Taxes

443

481

482

482
483

Financial Management and the Bankruptcy
Process 483

444

Present Value of the Tax Shield
Value of the Levered Firm

Bankruptcy Liquidation

Bankruptcy Reorganization

444

The Basic Insight

Liquidation and Reorganization

477

446

446

Expected Return and Leverage under Corporate
Taxes 448

Agreements to Avoid Bankruptcy
Summary and Conclusions

484

484

Closing Case: McKenzie Corporation’s Capital
Budgeting 489

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CHAPTER SIXTEEN

Value of Stock Splits and Stock Dividends

Dividends and Other Payouts

490

The Benchmark Case

16.1

Different Types of Dividends

490

16.2

Standard Method of Cash Dividend Payment

16.3

The Benchmark Case: An Illustration of the
Irrelevance of Dividend Policy 493

516

Popular Trading Range
491

Reverse Splits

516

517

517

Summary and Conclusions

518

Closing Case: Electronic Timing, Inc.

525

Current Policy: Dividends Set Equal to Cash Flow 493
Alternative Policy: Initial Dividend Is Greater than Cash
Flow 494

PART FIVE

The Indifference Proposition

CHAPTER SEVENTEEN

Homemade Dividends

494

Options and Corporate Finance

494

17.1

Options

17.2

Call Options

Dividend versus Repurchase: Conceptual Example 498

17.3

Put Options

Dividends versus Repurchases: Real-World
Considerations 499

17.4

Selling Options

17.5

Option Quotes

17.6

Combinations of Options

17.7

Valuing Options

A Test

496

Dividends and Investment Policy
16.4

Repurchase of Stock

1. Flexibility

497

499

500

4. Repurchase as Investment
5. Taxes

500

500
500

Firms without Sufficient Cash to Pay a Dividend

501

533

536

Upper Bound

536

536

The Factors Determining Call Option
Values 536

502

Exercise Price

503

Desire for Current Income

Stock Price

503

536
537

537

The Key Factor: The Variability of the
Underlying Asset 538

504

505

The Interest Rate

Information Content of Dividends and Dividend
Signaling 506
The Clientele Effect: a Resolution of Real-World
Factors? 507

539

A Quick Discussion of Factors Determining
Put Option Values 539
17.8

An Option Pricing Formula
A Two-State Option Model

What We Know and Do Not Know about Dividend
Policy 508

Determining the Delta

540
541
541

Dividends and Dividend Payers

508

Determining the Amount of Borrowing

Corporations Smooth Dividends

510

Risk-Neutral Valuation

542

The Black–Scholes Model

543

Payouts Provide Information to the Market
Putting It All Together

511

511

17.9

Some Survey Evidence on Dividends
16.9

532

Real-World Factors Favoring a High-Dividend Policy 503

Agency Costs

529

531

Expiration Date

Behavioral Finance

16.8

529

Lower Bound 536

Personal Taxes, Issuance Costs, and Dividends

Summary on Personal Taxes

16.7

528

Bounding the Value of a Call

Firms with Sufficient Cash to Pay a Dividend
16.6

527

The Value of a Put Option at Expiration

499

3. Offset to Dilution

527

The Value of a Call Option at Expiration 528

497

2. Executive Compensation

16.5

SPECIAL TOPICS

514

Stock Dividends and Stock Splits 515
Some Details on Stock Splits and Stock Dividends 515
Example of a Small Stock Dividend
Example of a Stock Split

515

516

Example of a Large Stock Dividend

516

Stocks and Bonds as Options

547

The Firm Expressed in Terms of Call Options
The Stockholders

548

The Bondholders

549

The Firm Expressed in Terms of Put Options
The Stockholders

550

The Bondholders

550

542

548

550

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A Resolution of the Two Views
A Note on Loan Guarantees

550

18.6

552

Summary and Conclusions

553

Options and Capital Budgeting

591

CHAPTER NINETEEN

554

17.11 Investment in Real Projects and Options
Summary and Conclusions

590

Closing Case: Keafer Manufacturing Working Capital
Management 599

17.10 Options and Corporate Decisions: Some
Applications 552
Mergers and Diversification

A Short-Term Financial Plan

Raising Capital

556

19.1

558

601

The Financing Life Cycle of a Firm: Early-Stage
Financing and Venture Capital 602

Closing Case: Exotic Cuisines Employee Stock
Options 567

Venture Capital

CHAPTER EIGHTEEN

Choosing a Venture Capitalist

Short-Term Finance and Planning

Conclusion

Tracing Cash and Net Working Capital

18.2

The Operating Cycle and the Cash Cycle 570

569

Defining the Operating and Cash Cycles
The Operating Cycle
The Cash Cycle

Some Venture Capital Realities

568

18.1

571

571

19.3

Alternative Issue Methods

19.4

Underwriters

The Operating Cycle and the Firm’s Organization Chart 573
The Operating Cycle

576

The Green Shoe Provision
577

The Aftermarket

Lockup Agreements
The Quiet Period
19.5

Which Financing Policy Is Best?

Cash Outflows

583

18.5

583

584

The Cash Balance

585

Short-Term Borrowing
Unsecured Loans

585

Letters of Credit

586

587

614

19.6

What CFOs Say about the IPO Process

19.7

CEOs and the Value of the Firm

19.8

The Cost of Issuing Securities

19.9

Rights

588

Commercial Paper

588

616

617
618

622
622

623

Effect of Rights Offering on Price of Stock
Effects on Shareholders

587

The Rights Puzzle

625

626

19.10 Dilution 626
Dilution of Proportionate Ownership

588

626

Dilution of Value: Book versus Market Values

Understanding Trade Credit Terms
589

623

623

625

The Underwriting Arrangements

Inventory Loans

Cash Discounts

610

Number of Rights Needed to Purchase a Share
586

587

Accounts Receivable Financing

Trade Credit

609

Why Does Underpricing Exist?

Subscription Price

Cost of a Compensating Balance
Secured Loans

IPOs and Underpricing

The Mechanics of a Rights Offering

586

Compensating Balances

609

IPO Underpricing: The 1999–2000 Experience 611

Current Assets and Liabilities in Practice 583
Sales and Cash Collections

608

609

Evidence on Underpricing

582

608

609

Alternative Financing Policies for Current Assets 578
578

607

607

Dutch Auction Underwriting

The Size of the Firm’s Investment in Current Assets 577

The Cash Budget

607

Best Efforts Underwriting

Different Policies for Financing Current Assets 580

18.4

607

Firm Commitment Underwriting

574

Some Aspects of Short-Term Financial Policy

An Ideal Case

606

607

Types of Underwriting

574

575

Interpreting the Cash Cycle
18.3

603

Selling Securities to the Public: The Basic
Procedure 603

Choosing an Underwriter

Calculating the Operating and Cash Cycles

603
603

19.2

571

The Cash Cycle

602

588

A Misconception

626

627

The Correct Arguments

628

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19.11 Issuing Long-Term Debt

628

20.6

Exchange Rate Risk

653

19.12 Shelf Registration 629

Short-Run Exposure

653

Summary and Conclusions

Long-Run Exposure

654

630

Closing Case: East Coast Yachts Goes Public

634

Translation Exposure

CHAPTER TWENTY

International Corporate Finance

20.7

636

Terminology

637

20.2

Foreign Exchange Markets and Exchange Rates
Exchange Rates

Types of Transactions

642

Purchasing Power Parity

643

Relative Purchasing Power Parity

645

Solutions to Selected End-of-Chapter
Problems 672
647

Interest Rate Parity, Unbiased Forward Rates, and the
International Fisher Effect 647
Covered Interest Arbitrage

647

648

Forward Rates and Future Spot Rates

Using the HP 10B and TI BA II Plus Financial
Calculators 677
681

COMPANY INDEX

650

The International Fisher Effect
International Capital Budgeting

APPENDIX C

NAME INDEX

649

650

Uncovered Interest Parity

SUBJECT INDEX

683
685

650
651

Method 1: The Home Currency Approach
Method 2: The Foreign Currency Approach
Unremitted Cash Flows

663

APPENDIX B

645

Putting It All Together

Closing Case: East Coast Yachts Goes
International 662

Mathematical Tables

643

645

Interest Rate Parity

657

Mergers and Acquisitions (Web only)

641

Currency Appreciation and Depreciation

20.5

656

APPENDIX A

Absolute Purchasing Power Parity
The Basic Idea

656

CHAPTER TWENTY ONE

639

Cross-Rates and Triangle Arbitrage

20.4

638

639

Exchange Rate Quotations

The Result

Political Risk

Summary and Conclusions

20.1

20.3

655

Managing Exchange Rate Risk

652
652

653

CONTENTS

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LIST OF BOXES

THE REAL WORLD BOXES
CHAPTER 1

Sarbanes-Oxley 16

CHAPTER 2

Putting a Spin on Cash Flows

CHAPTER 3

What’s in a Ratio?

CHAPTER 4

Jackpot!

CHAPTER 5

Beauty Is in the Eye of the Bondholder

150

CHAPTER 6

How Fast Is Too Fast? 176
The Wild, Wild West of Stock Trading

190

32

60

100

CHAPTER 9

When Things Go Wrong . . .

270

CHAPTER 11

Beta, Beta, Who’s Got the Beta?

348

CHAPTER 12

The Cost of Capital, Texas Style

382

CHAPTER 13

Can Stock Market Investors Add and Subtract?

CHAPTER 16

Stock Buybacks: No End in Sight

CHAPTER 18

A Look at Operating and Cash Cycles

CHAPTER 19

IPO Underpricing around the World
Anatomy of an IPO 620

CHAPTER 20

McPricing

412

504
572
612

644

LIST OF BOXES

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Introduction to Corporate
Finance

CHAPTER

1

I

n 2008 and 2009, the U.S. government set up the $700 billion Troubled Asset Relief Program
(TARP) to help companies avoid bankruptcy due to the severe financial turmoil. The loans to
companies such as Bank of America and General Motors created unique governance problems. One such that received special attention was executive compensation. In June 2009,
Kenneth Feinberg was appointed as a Special Master for Compensation (better known as the

“Pay Czar”) and given broad powers over executive compensation for firms participating in the
TARP program.
In October 2009, Mr. Feinberg capped the salaries at the seven largest TARP companies at

PART ONE Overview

OPENING CASE

$500,000. This group’s annualized total pay would be 50 percent lower than a year before through
reduced bonuses and options. Interestingly, 80 of the 136 employees affected actually had their base
salaries increased, including an average base salary increase of about 87 percent at Citigroup.
Some outside experts argued that the pay cuts were overstated. Many employees continued to
receive seven-figure pay packages, including one who received $9.9 million. Of the 136 employees
whose paychecks were reviewed, 29 were on track to collect total 2009 pay of at least $5 million. The
discrepancy arose because the pay cut calculation depended in part on departures of certain highly
paid employees from the previous year.
The Pay Czar’s role in setting compensation limits is an unusual case in the U.S. of direct government involvement in corporate decisions. Understanding how a corporation sets executive pay, and
the role of shareholders in that process, takes us into issues involving the corporate form of organization, corporate goals, and corporate control, all of which we cover in this chapter.

1.1

W H AT I S C O R P O R AT E F I N A N C E ?

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

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will generate cash. This is the basis of value creation. The purpose of the firm is to create
value for you, the owner. 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 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 and trademarks. 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 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 longlived 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 side
of the balance sheet. Of course the types and proportions of assets the firm needs
tend to be set by the nature of the business. We use the term capital budgeting to
describe the process of making and managing expenditures on long-lived assets.
FIGURE 1.1
The Balance Sheet
Model of the Firm

Net
working
capital

Current assets

Current
liabilities

Long-term
debt

Fixed assets
1. Tangible fixed
assets
2. Intangible fixed
assets
Total Value of Assets

2

Shareholders’
equity

=

Total Value of the Firm to Investors

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2. How can the firm raise cash for required capital expenditures? This question
concerns the right side of the balance sheet. The answer to this question involves
the firm’s capital structure, which represents the proportions of the firm’s
financing from current liabilities, long-term 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. 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, short-term cash flow problems come from the mismatching
of cash inflows and outflows. This is the subject of short-term finance.

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 1.2
FIGURE 1.2
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

Information
Systems
Manager

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For current issues
facing CFOs, see
www.cfo.com.

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 for handling cash flows, managing capital expenditure decisions, and making
financial plans. The controller handles the accounting function, which includes taxes, cost
and financial accounting, and information systems.

1.2

T H E C O R P O R AT E F I R M

The firm is a way of organizing the economic activity of many individuals. 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

For more about small
business organization,
see the “Business and
Human Resources”
section at
www.nolo.com.

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 people can get together and form a partnership. Partnerships fall into
two categories: (1) general partnerships and (2) limited partnerships.
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 all of 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. Business licenses and filing fees may
be necessary.

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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 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) difficulty in raising cash.

The Corporation
Of the 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 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.
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 select top management. Members
of top management serve as corporate officers and manage the operations of the corporation
in the best interest of the shareholders. In closely held corporations with few shareholders,

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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 the corporation’s
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.
Limited liability, ease of ownership transfer, and perpetual succession are the major
advantages of the corporate 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 (the states do as well). 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. Table 1.1
summarizes our discussion of partnerships and corporations.
Today all 50 states have enacted laws allowing for the creation of a relatively new
form of business organization, the limited liability company (LLC). The goal of this
TABLE 1.1
A Comparison of Partnerships and Corporations
CORPORAT I O N

6

PA R T N E R S H I P

Liquidity and
marketability

Shares can be exchanged without termination of
the corporation. Common stock can be listed on a
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
partners have 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 personal taxes on
partnership profits.

Reinvestment and
dividend payout

Corporations have broad latitude on dividend
payout decisions.

Partnerships are generally prohibited from reinvesting
partnership profits. All profits are 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 may have a perpetual life.

Partnerships have limited life.

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TABLE 1.2
International Corporations
T Y P E O F C O M PA N Y
COM PANY

COU N T RY O F O R I G I N

I N O R I G I N A L LA N G U A G E

I N T E R P R ETATION

Bayerische
Motoren Werke (BMW) AG

Germany

Aktiengesellschaft

Corporation

Dornier GmBH

Germany

Gesellschaft mit
Beschränkter Haftung

Limited liability company

Rolls-Royce PLC

United Kingdom

Public limited company

Public Ltd. Company

Shell UK Ltd.

United Kingdom

Limited

Corporation

Unilever NV

Netherlands

Naamloze Vennootschap

Joint stock company

Fiat SpA

Italy

Società per Azioni

Joint stock company

Volvo AB

Sweden

Aktiebolag

Joint stock company

Peugeot SA

France

Société Anonyme

Joint stock company

entity is to operate and be taxed like a partnership but retain limited liability for owners,
so an LLC is essentially a hybrid of partnership and corporation. Although states have
differing definitions for LLCs, the more important scorekeeper is the Internal Revenue
Service (IRS). The IRS will consider an LLC a corporation, thereby subjecting it to
double taxation, unless it meets certain specific criteria. In essence, an LLC cannot be
too corporation-like, or it will be treated as one by the IRS. LLCs have become common.
For example, Goldman, Sachs and Co., one of Wall Street’s last remaining partnerships,
decided to convert from a private partnership to an LLC (it later “went public,” becoming a publicly held corporation). Large accounting firms and law firms by the score have
converted to LLCs.

To find out more about
LLCs, visit
www.incorporate.com.

A Corporation by Another Name . . .
The corporate form of organization has many variations around the world. The exact laws
and regulations differ from country to country, of course, but the essential features of public ownership and limited liability remain. These firms are often called joint stock companies, public limited companies, or limited liability companies, depending on the specific
nature of the firm and the country of origin.
Table 1.2 gives the names of a few well-known international corporations, their countries of origin, and a translation of the abbreviation that follows each company name.

1.3

T H E I M P O R TA N C E O F C A S H F L O W S

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? The answer is that the firm should create more cash flow than it uses.
The cash flows paid to bondholders and stockholders of the firm should be greater
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.

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FIGURE 1.3
Cash Flows between the Firm and the Financial Markets

Cash for securities issued by the firm (A)
Firm invests
in assets
(B)
Current assets
Fixed assets

Total Value of Assets

Financial
markets
Retained cash
flows (E)
Cash flow from
firm (C)

Short-term debt
Long-term debt
Equity shares

Dividends and
debt payments (F )
Ta xes

Total Value of the Firm
to Investors in
the Financial Markets

Government
(D)

The interplay of the firm’s activities with the financial markets is illustrated in Figure 1.3.
The arrows in Figure 1.3 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 (assets) 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).
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.

EXAMPLE

1.1

Identification of Cash Flows Unfortunately, it is sometimes not 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.

Accounting Profit versus Cash Flows
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

(continued)

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whom the gold was sold. The following is a standard accounting of Midland’s financial circumstances
at year-end:
T HE M I D LA N D C O M PA N Y
A c c o u n t i n g Vi e w
Income Statement
Ye a r E n d e d D e c e m b e r 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:
T HE M I D LA N D C O M PA N Y
Fi n a n c i a l Vi e w
Income Statement
Ye a r E n d e d D e c e m b e r 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.

EXAMPLE

1.2

Timing of Cash Flows The value of an investment made by a firm depends on the timing
of cash flows. One of the most important principles 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.

C a s h F l o w Ti m i n g
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:
YE AR
1
2
3
4
Total

NE W P R O D U C T A
$

0
0
0
20,000
$20,000

NEW PRODUCT B
$ 4,000
4,000
4,000
4,000
$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 for 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.

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EXAMPLE

1.3

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.

Risk
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 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.

1.4

THE GOAL OF FINANCIAL MANAGEMENT

Assuming that we restrict our discussion to for-profit businesses, the goal of financial management is to make money or add value for the owners. This goal is a little vague, of course,
so we examine some different ways of formulating it to come up with a more precise definition. Such a definition is important because it leads to an objective basis for making and
evaluating financial decisions.

Possible Goals
If we were to consider possible financial goals, we might come up with some ideas like the
following:








Survive.
Avoid financial distress and bankruptcy.
Beat the competition.
Maximize sales or market share.
Minimize costs.
Maximize profits.
Maintain steady earnings growth.

These are only a few of the goals we could list. Furthermore, each of these possibilities
presents problems as a goal for the financial manager.
For example, it’s easy to increase market share or unit sales: All we have to do is lower
our prices or relax our credit terms. Similarly, we can always cut costs simply by doing
away with things such as research and development. We can avoid bankruptcy by never
borrowing any money or never taking any risks, and so on. It’s not clear that any of these
actions are in the stockholders’ best interests.

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Profit maximization would probably be the most commonly cited goal, but even this is
not a precise objective. Do we mean profits this year? If so, then we should note that actions
such as deferring maintenance, letting inventories run down, and taking other short-run
cost-cutting measures will tend to increase profits now, but these activities aren’t necessarily desirable.
The goal of maximizing profits may refer to some sort of “long-run” or “average”
profits, but it’s still unclear exactly what this means. First, do we mean something like
accounting net income or earnings per share? As we will see in more detail in the next
chapter, these accounting numbers may have little to do with what is good or bad for
the firm. We are actually more interested in cash flows. Second, what do we mean by the
long run? As a famous economist once remarked, in the long run, we’re all dead! More
to the point, this goal doesn’t tell us what the appropriate trade-off is between current
and future profits.
The goals we’ve listed here are all different, but they tend to fall into two classes. The
first of these relates to profitability. The goals involving sales, market share, and cost control all relate, at least potentially, to different ways of earning or increasing profits. The
goals in the second group, involving bankruptcy avoidance, stability, and safety, relate in
some way to controlling risk. Unfortunately, these two types of goals are somewhat contradictory. The pursuit of profit normally involves some element of risk, so it isn’t really
possible to maximize both safety and profit. What we need, therefore, is a goal that encompasses both factors.

The Goal of Financial Management
The financial manager in a corporation makes decisions for the stockholders of the firm.
So, instead of listing possible goals for the financial manager, we really need to answer a
more fundamental question: From the stockholders’ point of view, what is a good financial
management decision?
If we assume that stockholders buy stock because they seek to gain financially, then
the answer is obvious: Good decisions increase the value of the stock, and poor decisions
decrease the value of the stock.
From our observations, it follows that the financial manager acts in the shareholders’
best interests by making decisions that increase the value of the stock. The appropriate goal
for the financial manager can thus be stated quite easily:
The goal of financial management is to maximize the current value per share of the
existing stock.
The goal of maximizing the value of the stock avoids the problems associated with
the different goals we listed earlier. There is no ambiguity in the criterion, and there is
no short-run versus long-run issue. We explicitly mean that our goal is to maximize the
current stock value.
If this goal seems a little strong or one-dimensional to you, keep in mind that the stockholders in a firm are residual owners. By this we mean that they are entitled only to what
is left after employees, suppliers, and creditors (and everyone else with legitimate claims)
are paid their due. If any of these groups go unpaid, the stockholders get nothing. So if the
stockholders are winning in the sense that the leftover, residual portion is growing, it must
be true that everyone else is winning also.
Because the goal of financial management is to maximize the value of the stock, we
need to learn how to identify investments and financing arrangements that favorably impact
the value of the stock. This is precisely what we will be studying. In the previous section we
emphasized the importance of cash flows in value creation. In fact, we could have defined

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corporate finance as the study of the relationship between business decisions, cash flows,
and the value of the stock in the business.

A More General Goal

Business ethics are
considered at
www.business-ethics.
com.

If our goal is as stated in the preceding section (to maximize the value of the stock), an
obvious question comes up: What is the appropriate goal when the firm has no traded
stock? Corporations are certainly not the only type of business; and the stock in many
corporations rarely changes hands, so it’s difficult to say what the value per share is at any
particular time.
As long as we are considering for-profit businesses, only a slight modification is needed.
The total value of the stock in a corporation is simply equal to the value of the owners’
equity. Therefore, a more general way of stating our goal is as follows: Maximize the value
of the existing owners’ equity.
With this in mind, we don’t care whether the business is a proprietorship, a partnership, or a corporation. For each of these, good financial decisions increase the value of
the owners’ equity, and poor financial decisions decrease it. In fact, although we choose to
focus on corporations in the chapters ahead, the principles we develop apply to all forms of
business. Many of them even apply to the not-for-profit sector.
Finally, our goal does not imply that the financial manager should take illegal or unethical actions in the hope of increasing the value of the equity in the firm. What we mean
is that the financial manager best serves the owners of the business by identifying goods
and services that add value to the firm because they are desired and valued in the free
marketplace.

1.5 THE AGENCY PROBLEM AND CONTROL
O F T H E C O R P O R AT I O N
The processes, policies, laws, and institutions that direct a company’s actions are all
included under the broad category of corporate governance. Corporate governance can also
include the relationships among various stakeholders including shareholders, management,
employees, the board of directors, suppliers, and the community at large, among others. As
such, corporate governance is a wide-ranging topic.
We’ve seen that the financial manager acts in the best interests of the stockholders by
taking actions that increase the value of the stock. However, in large corporations, ownership can be spread over a huge number of stockholders. This dispersion of ownership
arguably means that management effectively controls the firm. In this case, will management necessarily act in the best interests of the stockholders? Put another way, might not
management pursue its own goals at the stockholders’ expense?
Corporate governance varies quite a bit around the world. For example, in most countries other than the U.S. and the U.K., publicly traded companies are usually controlled by
one or more large shareholders. Moreover, in countries with limited shareholder protection, when compared to countries with strong shareholder protection like the U.S. and the
U.K., large shareholders may have a greater opportunity to take advantage of minority
shareholders. Research shows that a country’s investor protection framework is important
to understanding a firms’ cash holdings and dividend payouts. For example, studies find
that shareholders do not highly value cash holdings in firms in countries with low investor
protection when compared to firms in the U.S. where investor protection is high.1

1
See, for example, “Investor Protection and Corporate Valuation,” by Rafael La Porta, Florencio Lopez-De-Silanes, Andrei Shleifer,
and Robert Vishny, Journal of Finance 57 (2002), pp. 1147–1170; and “Cash Holdings, Dividend Policy, and Corporate Governance:
A Cross-Country Analysis,” by Lee Pinkowitz, René M. Stulz, and Rohan Williamson, Journal of Applied Corporate Finance, Vol. 19,
No. 1 (2007), pp. 81–87.

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In the basic corporate governance setup, the shareholders elect the board of directors
who in turn appoint the top corporate managers, such as the CEO. The CEO is usually a
member of the board of directors. One aspect of corporate governance that has received
attention recently concerns the chair of a firm’s board of directors. In a large number of
U.S. corporations, the CEO and the board chair are the same person. An argument can be
made that combining the CEO and board chair positions can contribute to poor corporate governance. When comparing the corporate governance of the U.S. and the U.K., an
edge is often given to the U.K. in governance partially because over 90 percent of U.K.
companies are chaired by outside directors rather than the CEO.2 This is a contentious
issue confronting many U.S. corporations. For example, in May 2008, 19 institutional
investors, including some of ExxonMobil’s largest shareholders and members of the
founding Rockefeller family, supported a resolution to split the jobs of CEO and board
chair. About 40 percent of the shareholders voted for the split.

Agency Relationships
The relationship between stockholders and management is called an agency relationship.
Such a relationship exists whenever someone (the principal) hires another (the agent) to
represent his or her interests. For example, you might hire someone (an agent) to sell a car
that you own while you are away at school. In all such relationships there is a possibility
of a conflict of interest between the principal and the agent. Such a conflict is called an
agency problem.
Suppose you hire someone to sell your car and you agree to pay that person a flat fee
when he or she sells the car. The agent’s incentive in this case is to make the sale, not necessarily to get you the best price. If you offer a commission of, say, 10 percent of the sales
price instead of a flat fee, then this problem might not exist. This example illustrates that the
way in which an agent is compensated is one factor that affects agency problems.

Management Goals
To see how management and stockholder interests might differ, imagine that a firm is considering a new investment. The new investment is expected to favorably impact the share
value, but it is also a relatively risky venture. The owners of the firm will wish to take the
investment (because the stock value will rise), but management may not because there is
the possibility that things will turn out badly and management jobs will be lost. If management does not take the investment, then the stockholders may lose a valuable opportunity.
This is one example of an agency cost.
More generally, the term agency costs refers to the costs of the conflict of interest between stockholders and management. These costs can be indirect or direct. An indirect
agency cost is a lost opportunity, such as the one we have just described.
Direct agency costs come in two forms. The first type is a corporate expenditure that
benefits management but costs the stockholders. Perhaps the purchase of a luxurious
and unneeded corporate jet would fall under this heading. The second type of direct
agency cost is an expense that arises from the need to monitor management actions. Paying outside auditors to assess the accuracy of financial statement information could be
one example.
It is sometimes argued that, left to themselves, managers would tend to maximize the
amount of resources over which they have control or, more generally, corporate power or
wealth. This goal could lead to an overemphasis on corporate size or growth. For example,
cases in which management is accused of overpaying to buy up another company just to

2
“U.S. Corporate Governance: Accomplishments and Failings, a Discussion with Michael Jensen and Robert Monks” (moderated
by Ralph Walkling), Journal of Applied Corporate Finance , Vol. 20, No. 1 (Winter 2008), pp. 28–46.

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increase the size of the business or to demonstrate corporate power are not uncommon.
Obviously, if overpayment does take place, such a purchase does not benefit the stockholders of the purchasing company.
Our discussion indicates that management may tend to overemphasize organizational
survival to protect job security. Also, management may dislike outside interference, so
independence and corporate self-sufficiency may be important goals.

Do Managers Act in the Stockholders’ Interests?
Whether managers will, in fact, act in the best interests of stockholders depends on
two factors. First, how closely are management goals aligned with stockholder goals?
This question relates, at least in part, to the way managers are compensated. Second,
can managers be replaced if they do not pursue stockholder goals? This issue relates
to control of the firm. As we will discuss, there are a number of reasons to think that,
even in the largest firms, management has a significant incentive to act in the interests
of stockholders.
Managerial Compensation Management will frequently have a significant economic incentive to increase share value for two reasons. First, managerial compensation, particularly at the top, is usually tied to financial performance in general and often to share value
in particular. For example, managers are frequently given the option to buy stock at a
bargain price. The more the stock is worth, the more valuable is this option. In fact, options
are often used to motivate employees of all types, not just top management. According to
The New York Times, in 2009, Alan Mulally, CEO of Ford Motor, made $1,400,003 in salary
and $16 million in bonuses tied to financial performance. As mentioned, many firms also
give managers an ownership stake in the company by granting stock or stock options. In
2009, the total compensation of Jay L. Johnson, CEO of General Dynamics, was reported
by The New York Times to be $12.8 million. His base salary was $1.1 million with bonuses
of $2.5 million, stock option grants of $5.8 million, and restricted stock grants of
$2.9 million. Although there are many critics of the high level of CEO compensation, from
the stockholders’ point of view, sensitivity of compensation to firm performance is usually
more important.
The second incentive managers have relates to job prospects. Better performers within
the firm will tend to get promoted. More generally, managers who are successful in pursuing stockholder goals will be in greater demand in the labor market and thus command
higher salaries.
In fact, managers who are successful in pursuing stockholder goals can reap enormous
rewards. For example, the best-paid executive in 2008 was Larry Ellison, the CEO of Oracle;
according to The New York Times, he made about $84.5 million. By way of comparison,
J. K. Rowling made $300 million and Rachael Ray made about $18 million. Over the
period of 2004–2008, Ellison made $944 million.3

Control of the firm ultimately rests with stockholders. They elect the
board of directors, who, in turn, hire and fire management.
An important mechanism by which unhappy stockholders can replace existing management is called a proxy fight. A proxy is the authority to vote someone else’s stock. A
proxy fight develops when a group solicits proxies in order to replace the existing board
and thereby replace existing management. In 2002, the proposed merger between HP and
Compaq triggered one of the most widely followed, bitterly contested, and expensive proxy
fights in history, with an estimated price tag of well over $100 million.

Control of the Firm

3
This raises the issue of the level of top management pay and its relationship to other employees. According to The New York
Times, the average CEO compensation was greater than 180 times the average employee compensation in 2007 and only 90 times
in 1994. However, there is no precise formula that governs the gap between top management compensation and that of employees.

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Another way that management can be replaced is by takeover. Firms that are poorly
managed are more attractive as acquisitions than well-managed firms because a greater
profit potential exists. Thus, avoiding a takeover by another firm gives management another
incentive to act in the stockholders’ interests. Unhappy prominent shareholders can suggest different business strategies to a firm’s top management. This was the case with Carl
Icahn and Motorola. Carl Icahn specializes in takeovers. His stake in Motorola reached
7.6 percent ownership in 2008, so he was a particularly important and unhappy shareholder.
This large stake made the threat of a shareholder vote for new board membership and a
takeover more credible. His advice was for Motorola to split its poorly performing handset
mobile phone unit from its home and networks business and create two publicly traded
companies—a strategy the company adopted.
Until recently, proxy fights were fairly rare. For example, from January to October 2009, only 75 proxy contests occurred in the U.S. As the HP/Compaq proxy fight
shows, expenses in a proxy fight can become large, and the cost is often the reason given
for so few proxy fights. Also, outsiders waging the proxy fight must cover their own
expenses, while the current directors use company finances to back their bid to retain
board seats. In October 2009, HealthSouth became the first company to adopt a corporate
bylaw that would reimburse proxy contestants for “reasonable” costs, provided that they
had won at least 40 percent of the votes cast. Although not yet approved by the Securities
and Exchange Commission, these “proxy access” rules are likely to result in more proxy
contests.
The available theory and evidence are consistent with the view that stockholders control the firm and that stockholder wealth maximization is the relevant goal of the
corporation. Even so, there will undoubtedly be times when management goals are pursued
at the expense of the stockholders, at least temporarily.

Conclusion

Stakeholders
Our discussion thus far implies that management and stockholders are the only parties with
an interest in the firm’s decisions. This is an oversimplification, of course. Employees, customers, suppliers, and even the government all have a financial interest in the firm.
Taken together, these various groups are called stakeholders in the firm. In general, a
stakeholder is someone other than a stockholder or creditor who potentially has a claim
on the cash flows of the firm. Such groups will also attempt to exert control over the firm,
perhaps to the detriment of the owners.

1.6

R E G U L AT I O N

Until now, we have talked mostly about the actions that shareholders and boards of directors can take to reduce the conflicts of interest between themselves and management. We
have not talked about regulation.4 Until recently the main thrust of federal regulation has
been to require that companies disclose all relevant information to investors and potential
investors. Disclosure of relevant information by corporations is intended to put all investors
on a level information playing field and, thereby to reduce conflicts of interest. Of course,
regulation imposes costs on corporations and any analysis of regulation must include both
benefits and costs. Our nearby The Real World box discusses some of the costs exchangelisted companies face arising from disclosure requirements.

4
At this stage in our book, we focus on the regulation of corporate governance. We do not talk about many other regulators in financial markets such as the Federal Reserve Board. In Chapter 8, we discuss the nationally recognized statistical rating organizations
(NRSROs) in the U.S. They are Fitch Ratings, Moody’s, and Standard & Poor’s. Their ratings are used by market participants to help
value securities such as corporate bonds. Many critics of the rating agencies blame the 2007–2009 subprime credit crisis on weak
regulatory oversight of these agencies.

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THE REAL WORLD

SARBANES-OXLEY
In response to corporate scandals at companies such as Enron, WorldCom, Tyco, and Adelphia, Congress enacted
the Sarbanes-Oxley Act in 2002. The act, better known as “Sarbox,” is intended to protect investors from corporate
abuses. For example, one section of Sarbox prohibits personal loans from a company to its officers, such as the
ones that were received by WorldCom CEO Bernie Ebbers.
One of the key sections of Sarbox took effect on November 15, 2004. Section 404 requires, among other things,
that each company’s annual report must have an assessment of the company’s internal control structure and financial reporting. The auditor must then evaluate and attest to management’s assessment of these issues.
Sarbox contains other key requirements. For example, the officers of the corporation must review and sign the
annual reports. They must explicitly declare that the annual report does not contain any false statements or material omissions; that the financial statements fairly represent the financial results; and that they are responsible for
all internal controls. Finally, the annual report must list any deficiencies in internal controls. In essence, Sarbox
makes company management responsible for the accuracy of the company’s financial statements.
Of course, as with any law, there are costs. Sarbox has increased the expense of corporate audits, sometimes
dramatically. In 2004, the average compliance cost was $ 4.51 million. By 2007, the average compliance cost had
fallen to $1.7 million, so the burden seems to be dropping, but it is still not trivial, particularly for a smaller firm. This
added expense has led to several unintended results. For example, in 2003, 198 firms delisted their shares from exchanges, or “went dark,” and about the same number delisted in 2004. Both numbers were up from 30 delistings in
1999. Many of the companies that delisted stated the reason was to avoid the cost of compliance with Sarbox. And
not only small companies delist because of Sarbox; in September 2009, German insurer Allianz applied to delist its
shares from the New York Stock Exchange. The company estimated that canceling its listings outside of its home
exchange of Frankfurt could save 5 million euros ($ 8.1 million) per year.
A company that goes dark does not have to file quarterly or annual reports. Annual audits by independent auditors are not required, and executives do not have to certify the accuracy of the financial statements, so the savings
can be huge. Of course, there are costs. Stock prices typically fall when a company announces it is going dark.
Further, such companies will typically have limited access to capital markets and usually will have a higher interest
cost on bank loans.
Sarbox has also probably affected the number of companies choosing to go public in the United States. For
example, when Peach Holdings, based in Boynton Beach, Florida, decided to go public in 2006, it shunned the
U.S. stock markets, instead choosing the London Stock Exchange’s Alternative Investment Market (AIM). To go
public in the United States, the firm would have paid a $100,000 fee, plus about $2 million to comply with Sarbox.
Instead, the company spent only $500,000 on its AIM stock offering. Overall, the European exchanges had a record
year in 2006, with 651 companies going public, while the U.S. exchanges had a lackluster year, with 224 companies
going public.

The Securities Act of 1933 and the Securities
Exchange Act of 1934
The Securities Act of 1933 (the 1933 Act) and the Securities Exchange Act of 1934 (the
1934 Act) provide the basic regulatory framework in the United States for the public trading of securities.
The 1933 Act focuses on the issuing of new securities. Basically, the 1933 Act requires
a corporation to file a registration statement with the Securities and Exchange Commission (SEC) that must be made available to every buyer of a new security. The intent
of the registration statement is to provide potential stockholders with all the necessary
information to make a reasonable decision. The 1934 Act extends the disclosure requirements of the 1933 Act to securities trading in markets after they have been issued. The
1934 Act establishes the SEC and covers a large number of issues including corporate

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reporting, tender offers, and insider trading. The 1934 Act requires corporations to file
reports to the SEC on an annual basis (Form 10K), on a quarterly basis (Form 10Q), and
on a monthly basis (Form 8K).
As mentioned, the 1934 Act deals with the important issue of insider trading. Illegal
insider trading occurs when any person who has acquired nonpublic, special information
(i.e., inside information) buys or sells securities based upon that information. One section
of the 1934 Act deals with insiders such as directors, officers, and large shareholders, while
another deals with any person who has acquired inside information. The intent of these sections of the 1934 Act is to prevent insiders or persons with inside information from taking
unfair advantage of this information when trading with outsiders.
To illustrate, suppose you learned that ABC firm was about to publicly announce that
it had agreed to be acquired by another firm at a price significantly greater than its current
price. This is an example of inside information. The 1934 Act prohibits you from buying
ABC stock from shareholders who do not have this information. This prohibition would
be especially strong if you were the CEO of the ABC firm. Other kinds of a firm’s inside
information could be knowledge of an initial dividend about to be paid, the discovery of a
drug to cure cancer, or the default of a debt obligation.
A recent example of insider trading involved Raj Rajaratnam, founder of the Galleon
Group, a hedge fund that managed more than $7 billion. Rajaratnam was arrested in October 2009 on insider trading charges involving several public companies. For example, he
was accused of receiving inside information regarding Intel Capital’s decision to invest in
Clearwire before the investment was made public. Conversations between Rajaratnam and
Rajiv Goel, managing director at Intel Capital, included a discussion of the future price of
Clearwire and whether Intel would provide additional capital to the company.

SUMMARY AND CONCLUSIONS
This chapter introduced you to some of the basic ideas in corporate finance:
1. Corporate finance has three main areas of concern:
a. Capital budgeting: What long-term investments should the firm take?
b. Capital structure: Where will the firm get the short-term and long-term financing to pay for its
investments? Also, what mixture of debt and equity should it use to fund operations?
c. Working capital management: How should the firm manage its everyday financial
activities?
2. The goal of financial management in a for-profit business is to make decisions that increase the
value of the stock, or, more generally, increase the value of the equity.
3. The corporate form of organization is superior to other forms when it comes to raising money
and transferring ownership interests, but it has the significant disadvantage of double taxation.
4. There is the possibility of conflicts between stockholders and management in a large
corporation. We called these conflicts agency problems and discussed how they might be
controlled and reduced.
5. The advantages of the corporate form are enhanced by the existence of financial markets.
Of the topics we’ve discussed thus far, the most important is the goal of financial management: maximizing the value of the stock. Throughout the text we will be analyzing many different financial decisions, but we will always ask the same question: How does the decision under consideration affect
the value of the stock?

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www.mhhe.com/rwj
CONCEPT QUESTIONS
1. Forms of Business What are the three basic legal forms of organizing a business? What are
the advantages and disadvantages of each? What business form do most start-up companies
take? Why?
2. Goal of Financial Management What goal should always motivate the actions of the firm’s
financial manager?
3. Agency Problems Who owns a corporation? Describe the process whereby the owners
control the firm’s management. What is the main reason that an agency relationship
exists in the corporate form of organization? In this context, what kinds of problems can
arise?
4. Not-for-Profit Firm Goals Suppose you were the financial manager of a not-for-profit
business (a not-for-profit hospital, perhaps). What kinds of goals do you think would be
appropriate?
5. Goal of the Firm Evaluate the following statement: Managers should not focus on the current
stock value because doing so will lead to an overemphasis on short-term profits at the expense
of long-term profits.
6. Ethics and Firm Goals Can our goal of maximizing the value of the stock conflict with other
goals, such as avoiding unethical or illegal behavior? In particular, do you think subjects
like customer and employee safety, the environment, and the general good of society fit in this
framework, or are they essentially ignored? Try to think of some specific scenarios to illustrate
your answer.
7. International Firm Goal Would our goal of maximizing the value of the stock be different if we
were thinking about financial management in a foreign country? Why or why not?
8. Agency Problems Suppose you own stock in a company. The current price per share is $25.
Another company has just announced that it wants to buy your company and will pay $35 per
share to acquire all the outstanding stock. Your company’s management immediately begins
fighting off this hostile bid. Is management acting in the shareholders’ best interests? Why or
why not?
9. Agency Problems and Corporate Ownership Corporate ownership varies around the world.
Historically, individuals have owned the majority of shares in public corporations in the United
States. In Germany and Japan, however, banks, other large financial institutions, and other
companies own most of the stock in public corporations. Do you think agency problems are
likely to be more or less severe in Germany and Japan than in the United States? Why? In recent
years, large financial institutions such as mutual funds and pension funds have been becoming
the dominant owners of stock in the United States, and these institutions are becoming more
active in corporate affairs. What are the implications of this trend for agency problems and
corporate control?
10. Executive Compensation Critics have charged that compensation to top management in the
United States is simply too high and should be cut back. For example, focusing on large corporations, Ray Irani of Occidental Petroleum has been one of the best compensated CEOs in the United
States, earning about $223 million in 2008 alone and $744 million over the 2004–2008 period. Are
such amounts excessive? In answering, it might be helpful to recognize that superstar athletes
such as Tiger Woods, top people in entertainment such as Oprah Winfrey and Jerry Bruckheimer,
and many others at the peak of their respective fields can earn at least as much, if not a great
deal more.

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W H AT ’ S O N T H E W E B ?
1. Listing Requirements This chapter discussed some of the listing requirements for the NYSE
and NASDAQ. Find the complete listing requirements for the New York Stock Exchange at
www.nyse.com and NASDAQ at www.nasdaq.com. Which exchange has more stringent listing
requirements? Why don’t the exchanges have the same listing requirements?
2. Business Formation As you may (or may not) know, many companies incorporate in Delaware
for a variety of reasons. Visit Bizfilings at www.bizfilings.com to find out why. Which state
has the highest fee for incorporation? For an LLC? While at the site, look at the FAQ section
regarding corporations and LLCs.

In 1969, Tom Warren founded East Coast Yachts. The company’s operations are located near Hilton
Head Island, South Carolina, and the company is structured as a sole proprietorship. The company
has manufactured custom midsize, high-performance yachts for clients, and its products have received high reviews for safety and reliability. The company’s yachts have also recently received the
highest award for customer satisfaction. The yachts are primarily purchased by wealthy individuals
for pleasure use, Occasionally, a yacht is manufactured for purchase by a company for business
purposes.
The custom yacht industry is fragmented, with a number of manufacturers. As with any industry,
there are market leaders, but the diverse nature of the industry ensures that no manufacturer dominates the market. The competition in the market, as well as the product cost, ensures that attention
to detail is a necessity. For instance, East Coast Yachts will spend 80 to 100 hours on hand-buffing the
stainless steel stem-iron, which is the metal cap on the yacht’s bow that conceivably could collide
with a dock or another boat.
Several years ago, Tom retired from the day-to-day operations of the company and turned the
operations of the company over to his daughter, Larissa. Because of the dramatic changes in the
company, Larissa has approached you to help manage and direct the company’s growth. Specifically,
she has asked you to answer the following questions.

CLOSING CASE

E A S T C O A S T YA C H T S

1. What are the advantages and disadvantages of changing the company organization from a sole
proprietorship to an LLC?
2. What are the advantages and disadvantages of changing the company organization from a sole
proprietorship to a corporation?
3. Ultimately, what action would you recommend the company undertake? Why?

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CHAPTER

2

Financial Statements
and Cash Flow

OPENING CASE

I

n November 2009, mortgage giant Fannie Mae announced that it was reviewing a potential writeoff of $5.2 billion in low-income housing tax credits. A so-called write-off occurs when a company
decides that the reported value of one or more of its assets is too high and needs to be reduced
to more accurately represent the company’s finances. In Fannie Mae’s case, the write-off came
about because Fannie Mae owned potentially valuable tax credits, but the company was unlikely

to be profitable enough to use them, so their value was overstated. Fannie Mae’s case was unique
because the Treasury Department would not allow Fannie Mae to sell the tax credits, an option the
company had explored.
While Fannie Mae’s write-off is large, the record holder is media giant Time Warner, which took a
charge of $45.5 billion in the fourth quarter of 2002. This enormous write-off followed an earlier, even
larger, charge of $54 billion.
So, did the stockholders in these companies lose billions of dollars when these assets were written off? Fortunately for them, the answer is probably not. Understanding why ultimately leads us to
the main subject of this chapter, that all-important substance known as cash flow.

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.

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TABLE 2.1
The Balance Sheet of the U.S. Composite Corporation
U . S . C O M P O S I T E C O R P O R AT I O N
Balance Sheet
2009 a n d 2010
( i n $ m i l l i o n s)
ASSE T S
Current assets:
Cash and equivalents
Accounts receivable
Inventories
Other
Total current assets
Fixed assets:
Property, plant, and equipment
Less accumulated depreciation
Net property, plant, and equipment
Intangible assets and others
Total fixed assets

2009

2010

$ 107
270
280
50
$ 707

$ 140
294
269
58
$ 761

$ 1,274
460
$ 814
221
$ 1,035

$1,423
550
$ 873
245
$1,118

LI A B I LI T I E S ( D E B T ) A N D
S T O C K H O LD E R S ’ E Q U I T Y

2009

2010

Current liabilities:
Accounts payable
Notes payable
Accrued expenses
Total current liabilities

$ 197
53
205
$ 455

$ 213
50
223
$ 486

Long-term liabilities:
Deferred taxes
Long-term debt*
Total long-term liabilities

$ 104
458
$ 562

$ 117
471
$ 588

$

39
32
327
347
20
$ 725

$

$1,742

$1,879

Stockholders’ equity:
Preferred stock
Common stock ($1 par value)
Capital surplus
Accumulated retained earnings
Less treasury stock†
Total equity

Total assets

$1,742

$1,879

Total liabilities and
stockholders’ equity‡

39
55
347
390
26
$ 805

*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.


Treasury stock rose by $6 million. This reflects the repurchase of $6 million of U.S. Composite’s company stock.



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.

Table 2.1 gives the 2009 and 2010 balance sheets 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 would typically be paid over time.
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.
When analyzing a balance sheet, the financial manager should be aware of three concerns: accounting liquidity, debt versus equity, and value versus cost.

Two excellent sources
for company financial
information are
finance.yahoo.com and
money.cnn.com.

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

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Annual and quarterly
financial statements
for most public U.S.
corporations can be
found in the EDGAR
database at
www.sec.gov.

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
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.
The home page for the
Financial Accounting
Standards Board
(FASB) is
www.fasb.org.

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 would 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 value for the firm that exceeds its cost.
Many people use the balance sheet, but 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
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, owners’ equity, book equity, and equity capitalization.
3
Generally, GAAP require 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.

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EXAMPLE

2.1

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 information 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. Henceforth, whenever we speak of the value of an asset or the value of the firm, we
will normally mean its market value. So, for example, when we say the goal of the financial
manager is to increase the value of the stock, we mean the market value of the stock.

Market Value versus Book Value
The Cooney Corporation has fixed assets with a book value of $700 and an appraised market value of
about $1,000. Net working capital is $400 on the books, but approximately $600 would be realized if all
the current accounts were liquidated. Cooney has $500 in long-term debt, both book value and market
value. What is the book value of the equity? What is the market value?
We can construct two simplified balance sheets, one in accounting (book value) terms and one in
economic (market value) terms:
COO N E Y C O R P O R AT I O N
Balance Sheets
M a r k e t Va l u e ve r su s B o o k Va l u e
As s e t s

Net working capital
Net fixed assets

BOOK

M ARK E T

$ 400
700
$1,100

$ 600
1,000
$1,600

Li a b i l i t i e s a n d S h a r e h o l d e r s’ E q u i t y

Long-term debt
Shareholders’ equity

BOOK

MARKET

$ 500
600
$1,100

$ 500
1,100
$1,600

In this example, shareholders’ equity is actually worth almost twice as much as what is shown on the
books. The distinction between book and market values is important precisely because book values
can be so different from true economic value.

2.2

T H E I N C O M E S TAT E M E N T

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 2010.
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
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.

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TABLE 2.2

U . S . C O M P O S I T E C O R P O R AT I O N
Income Statement
2010
( i n $ m i l l i o n s)

The Income Statement
of the U.S. Composite
Corporation

Total operating revenues
Cost of goods sold
Selling, general, and administrative expenses
Depreciation
Operating income
Other income
Earnings before interest and taxes (EBIT)
Interest expense
Pretax income
Taxes
Current: $71
Deferred: $13
Net income
Addition to retained earnings:
Dividends:

$2,262
1,655
327
90
$ 190
29
$ 219
49
$ 170
84

$
$

86
43
43

Note: There are 29 million shares outstanding. Earnings per share and dividends per share can be calculated as follows:
Net income
Earnings per share  ____________________
Total shares outstanding
$86
 ___
29
 $2.97 per share
Dividends
Dividends per share  ____________________
Total shares outstanding
$43
 ___
29
 $1.48 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 from 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

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equipment used up in the production process. For example, suppose an asset with a fiveyear 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-peryear 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.
In practice, the difference between cash flows and accounting income can be quite dramatic, so it is important to understand the difference. For example, Sirius XM Radio reported a net loss of about $413 million for the third quarter of 2009. That sounds bad, but
Sirius XM also reported a positive cash flow of $116 million from operating activities for
the same quarter!

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 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. 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.

2.3

TA X E S

Taxes can be one of the largest cash outflows that a firm experiences. For example,
for the fiscal year 2009, ExxonMobil’s earnings before taxes were about $34.8 billion.
Its tax bill, including all taxes paid worldwide, was a whopping $15.1 billion, or about
43.4 percent of its pretax earnings. The size of the tax bill is determined through the tax

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.

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TABLE 2.3

TAXA B LE I N C O M E

TA X R AT E

Corporate Tax Rates
$

0–50,000
50,001–75,000
75,001–100,000
100,001–335,000
335,001–10,000,000
10,000,001–15,000,000
15,000,001–18,333,333
18,333,334

15%
25
34
39
34
35
38
35

code, an often amended set of rules. In this section, we examine corporate tax rates and
how taxes are calculated.
If the various rules of taxation seem a little bizarre or convoluted to you, keep in mind
that the tax code is the result of political, not economic, forces. As a result, there is no reason why it has to make economic sense.

Corporate Tax Rates
Corporate tax rates in effect for 2010 are shown in Table 2.3. A peculiar feature of
taxation instituted by the Tax Reform Act of 1986 and expanded in the 1993 Omnibus
Budget Reconciliation Act is that corporate tax rates are not strictly increasing. As
shown, corporate tax rates rise from 15 percent to 39 percent, but they drop back to
34 percent on income over $335,000. They then rise to 38 percent and subsequently fall
to 35 percent.
According to the originators of the current tax rules, there are only four corporate rates:
15 percent, 25 percent, 34 percent, and 35 percent. The 38 and 39 percent brackets arise
because of “surcharges” applied on top of the 34 and 35 percent rates. A tax is a tax is a tax,
however, so there are really six corporate tax brackets, as we have shown.

Average versus Marginal Tax Rates
In making financial decisions, it is frequently important to distinguish between average and marginal tax rates. Your average tax rate is your tax bill divided by your
taxable income, in other words, the percentage of your income that goes to pay taxes.
Your marginal tax rate is the tax you would pay (in percent) if you earned one
more dollar. The percentage tax rates shown in Table 2.3 are all marginal rates. Put
another way, the tax rates apply to the part of income in the indicated range only, not
all income.
The difference between average and marginal tax rates can best be illustrated with a
simple example. Suppose our corporation has a taxable income of $200,000. What is the
tax bill? Using Table 2.3, we can figure our tax bill as:
.15($ 50,000)
 $ 7,500
.25($ 75,000  50,000) 
6,250
.34($100,000  75,000) 
8,500
.39($200,000  100,000)  39,000
$61,250
The IRS has a great
Web site!
(www.irs.gov)

26

Our total tax is thus $61,250.
In our example, what is the average tax rate? We had a taxable income of $200,000 and
a tax bill of $61,250, so the average tax rate is $61,250/200,000  30.625%. What is the

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EXAMPLE

2.2

marginal tax rate? If we made one more dollar, the tax on that dollar would be 39 cents, so
our marginal rate is 39 percent.
D e e p i n t h e H e a r t o f Ta x e s
Algernon, Inc., has a taxable income of $85,000. What is its tax bill? What is its average tax rate? Its
marginal tax rate?
From Table 2.3, we see that the tax rate applied to the first $50,000 is 15 percent; the rate applied to
the next $25,000 is 25 percent, and the rate applied after that up to $100,000 is 34 percent. So Algernon
must pay .15  $50,000  .25  25,000  .34  (85,000  75,000)  $17,150. The average tax rate is
thus $17,150/85,000  20.18%. The marginal rate is 34 percent because Algernon’s taxes would rise by
34 cents if it had another dollar in taxable income.

Table 2.4 summarizes some different taxable incomes, marginal tax rates, and average
tax rates for corporations. Notice how the average and marginal tax rates come together at
35 percent.
With a flat-rate tax, there is only one tax rate, so the rate is the same for all income
levels. With such a tax, the marginal tax rate is always the same as the average tax rate. As
it stands now, corporate taxation in the United States is based on a modified flat-rate tax,
which becomes a true flat rate for the highest incomes.
In looking at Table 2.4, notice that the more a corporation makes, the greater is the
percentage of taxable income paid in taxes. Put another way, under current tax law, the average tax rate never goes down, even though the marginal tax rate does. As illustrated, for
corporations, average tax rates begin at 15 percent and rise to a maximum of 35 percent.
It will normally be the marginal tax rate that is relevant for financial decision making.
The reason is that any new cash flows will be taxed at that marginal rate. Because financial
decisions usually involve new cash flows or changes in existing ones, this rate will tell us
the marginal effect of a decision on our tax bill.
There is one last thing to notice about the tax code as it affects corporations. It’s easy
to verify that the corporate tax bill is just a flat 35 percent of taxable income if our taxable
income is more than $18.33 million. Also, for the many midsize corporations with taxable
incomes in the range of $335,000 to $10,000,000, the tax rate is a flat 34 percent. Because
we will normally be talking about large corporations, you can assume that the average and
marginal tax rates are 35 percent unless we explicitly say otherwise.
Before moving on, we should note that the tax rates we have discussed in this section
relate to federal taxes only. Overall tax rates can be higher once state, local, and any other
taxes are considered.
(1)
TAX ABL E I NCOM E
$

45,000
70,000
95,000
250,000
1,000,000
17,500,000
50,000,000
100,000,000

(2)
M ARGI NAL TA X R AT E
15%
25
34
39
34
38
35
35

( 3)
T O TA L TA X
$

6,750
12,500
20,550
80,750
340,000
6,100,000
17,500,000
35,000,000

( 3) / ( 1)
AV E R A G E TA X R AT E

TABLE 2.4
Corporate Taxes
and Tax Rates

15.00%
17.86
21.63
32.30
34.00
34.86
35.00
35.00

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2.4

N E T W O R K I N G C A P I TA L

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 2010
and $252 million in 2009:
Current assets
($ millions)



Current liabilities
($ millions)



Net working capital
($ millions)

2010

$761



$486



$275

2009

707



455



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 2010 is the difference between the net working capital in 2010 and 2009; that is,
$275 million  252 million  $23 million. The change in net working capital is usually
positive in a growing firm.

2.5

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,
which for U.S. Composite is $33 million in 2010. (See Section 2.6.) Notice in Table 2.1 that
cash and equivalents increase from $107 million in 2009 to $140 million in 2010. 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 8.)
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 2.5, 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.
I N $ M I LLI O N S
Earnings before interest and taxes
Depreciation
Current taxes
Operating cash flow

$219
90
71
$238

Another important component of cash flow involves changes in fixed assets. For example,
when U.S. Composite sold its power systems subsidiary in 2010, it generated $25 in

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TABLE 2.5

U.S. COM P O S I T E C O R P O R AT I O N
F i na n c i a l C a sh Fl o w
2010
( i n $ m i l l i o n s)

Financial Cash Flow
of the U.S. Composite
Corporation

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
Total

$238
173
 23
$ 42

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

cash flow. The net change in fixed assets equals the acquisition of fixed assets minus sales
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)

We can also calculate capital spending simply as:
Capital spending  Ending net fixed assets  Beginning net fixed assets
 Depreciation
 $1,118  1,035  90
 $173

Cash flows are also used for making investments in net working capital. In U.S. Composite Corporation in 2010, additions to net working capital are:
Additions to net working capital

$23

Note that this $23 is the change in net working capital we previously calculated.
Total cash flows generated by the firm’s assets are the sum of:
Operating cash flow
Capital spending
Additions to net working capital
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 2.5 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 the sale of new debt. U.S. Composite’s longterm debt increased by $13 million (the difference between $86 million in new debt and

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$73 million in retirement of old debt).5 Thus, an increase in long-term debt is the net effect
of new borrowing and repayment of maturing obligations plus interest expense.
C A S H FLO W PA I D T O C R E D I T O R S
( i n $ m i l l i o n s)
Interest
Retirement of debt
Debt service
Proceeds from long-term debt sales
Total

$ 49
73
122
 86
$ 36

Cash flow paid to creditors can also be calculated as:
Cash flow paid to creditors  Interest paid  Net new borrowing
 Interest paid  (Ending long-term debt
 Beginning long-term debt)
 $49  (471  458)
 $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.
C A S H FLO W T O S T O C K H O LD E R S
( i n $ m i l l i o n s)
Dividends
Repurchase of stock
Cash to stockholders
Proceeds from new stock issue
Total

$43
6
49
43
$ 6

In general, cash flow to stockholders can be determined as:
Cash flow to stockholders  Dividends paid  Net new equity raised
 Dividends paid  (Stock sold
 Stock repurchased)

To determine stock sold, notice that the common stock and capital surplus accounts went
up by a combined $23  20  $43, which implies that the company sold $43 million worth
of stock. Second, Treasury stock went up by $6, indicating that the company bought back
$6 million worth of stock. Net new equity is thus $43  6  $37. Dividends paid were $43,
so the cash flow to stockholders was:
Cash flow to stockholders  $43  (43  6)  $6,

which is what we previously calculated.
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 is usually positive; a firm is
in trouble if operating cash flow is negative for a long time because the firm is
5

30

New debt and the retirement of old debt are usually found in the “notes” to the balance sheet.

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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.
2. Net income is not cash flow. The net income of the U.S. Composite Corporation
in 2010 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.
A firm’s total cash flow sometimes goes by a different name, free cash flow. Of course,
there is no such thing as “free” cash (we wish!). Instead, the name refers to cash that the
firm is free to distribute to creditors and stockholders because it is not needed for working capital or fixed asset investments. We will stick with “total cash flow of the firm” as
our label for this important concept because, in practice, there is some variation in exactly
how free cash flow is computed; different users calculate it in different ways. Nonetheless,
whenever you hear the phrase “free cash flow,” you should understand that what is being
discussed is cash flow from assets or something quite similar.

2 . 6 T H E A C C O U N T I N G S TAT E M E N T
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 2010. 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
and notes payable). The result is cash flow from operating activities.
U.S. COM P O S I T E C O R P O R AT I O N
Ca s h F l o w f r o m O p e r a t i n g A c t i vi t i e s
2010
( i n $ m i l l i o n s)
Net income
Depreciation
Deferred taxes
Change in assets and liabilities
Accounts receivable
Inventories
Accounts payable
Accrued expense
Other
Cash flow from operating activities

$ 86
90
13
 24
11
16
18
 8
$202

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THE REAL WORLD

PUTTING A SPIN ON CASH FLOWS
One of the reasons why cash flow analysis is popular is the difficulty in manipulating, or spinning, cash flows. GAAP
accounting principles allow for significant subjective decisions to be made regarding many key areas. The use of cash
flow as a metric to evaluate a company comes from the idea that there is less subjectivity involved, and, therefore, it
is harder to spin the numbers. But several recent examples have shown that companies can still find ways to do it.
In November 2009, the SEC settled charges against SafeNet, Inc. and some of its former officers, employees,
and accountants, in connection with earnings management and options backdating schemes. This case represented the SEC’s first enforcement action brought under Regulation G of Sarbox. Of course other companies have
spun financial results without legal action. For example, in March 2007, rental car company Avis Budget Group was
forced to revise its first quarter 2007 operating cash flow by more than $45 million. The company had improperly
classified the cash flow as an operating cash flow rather than an investing cash flow. This maneuver had the effect
of increasing operating cash flows and decreasing investing cash flows by the same amount.
Tyco used several ploys to alter cash flows. For example, the company purchased more than $800 million of
customer security alarm accounts from dealers. The cash flows from these transactions were reported in the
financing activity section of the accounting statement of cash flows. When Tyco received payments from customers, the cash inflows were reported as operating cash flows. Another method used by Tyco was to have acquired
companies prepay operating expenses. In other words, the company acquired by Tyco would pay vendors for
items not yet received. In one case, the payments totaled more than $50 million. When the acquired company was
consolidated with Tyco, the prepayments reduced Tyco’s cash outflows, thus increasing the operating cash flows.
Dynegy, the energy giant, was accused of engaging in a number of complex “round trip trades.” The round trip
trades essentially involved the sale of natural resources to a counterparty, with the repurchase of the resources
from the same party at the same price. In essence, Dynegy would sell an asset for $100, and immediately repurchase it from the buyer for $100. The problem arose with the treatment of the cash flows from the sale. Dynegy
treated the cash from the sale of the asset as an operating cash flow, but classified the repurchase as an investing
cash outflow. The total cash flows of the contracts traded by Dynegy in these round trip trades totaled $300 million.
Adelphia Communications was another company that apparently manipulated cash flows. In Adelphia’s case,
the company capitalized the labor required to install cable. In other words, the company classified this labor expense as a fixed asset. While this practice is fairly common in the telecommunications industry, Adelphia capitalized a higher percentage of labor than is common. The effect of this classification was that the labor was treated
as an investment cash flow, which increased the operating cash flow.
In each of these examples, the companies were trying to boost operating cash flows by shifting cash flows to a
different heading. The important thing to notice is that these movements don’t affect the total cash flow of the firm,
which is why we recommend focusing on this number, not just operating cash flow.
We should also note that, for 2008, the total number of financial restatements fell nearly 30 percent from 2007,
which had itself experienced a 31 percent decline in restatements from 2006. While this is a positive trend, restatements due to cash flow misclassification increased in prevalence over the same period.

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.
U . S . C O M P O S I T E C O R P O R AT I O N
C a sh Fl o w f r o m I n ve st i n g A c t i vi t i e s
2010
( i n $ m i l l i o n s)
Acquisition of fixed assets
Sales of fixed assets
Cash flow from investing activities

32

$198
25
$173

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Cash Flow from Financing Activities
Cash flows to and from creditors and owners include changes in equity and debt.

U.S. COM P O S I T E C O R P O R AT I O N
Ca s h F l o w f r o m Fi n a n c i n g A c t i vi t i e s
2010
( i n $ m i l l i o n s)
Retirement of long-term debt
Proceeds from long-term debt sales
Change in notes payable
Dividends
Repurchase of stock
Proceeds from new stock issue
Cash flow from financing activities

$73
86
 3
 43
 6
43
$ 4

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 2.6. When we add all the cash flows together, we get the change in cash on the balance sheet of $33 million.
TABLE 2.6

U.S. COM P O S I T E C O R P O R AT I O N
St a t em e n t o f C a sh Fl o w s
2010
( i n $ m i l l i o n s)

Statement of
Consolidated Cash Flows
of the U.S. Composite
Corporation

Operations
Net income
Depreciation
Deferred taxes
Changes in assets and liabilities
Accounts receivable
Inventories
Accounts payable
Accrued expenses
Other
Total cash flow from operations

 24
11
16
18
 8
$202

Investing activities
Acquisition of fixed assets
Sales of fixed assets
Total cash flow from investing activities

$198
25
$173

Financing activities
Retirement of long-term debt
Proceeds from long-term debt sales
Change in notes payable
Dividends
Repurchase of stock
Proceeds from new stock issue
Total cash flow from financing activities
Change in cash (on the balance sheet)

$ 73
86
 3
 43
 6
43
$ 4
$ 33

$ 86
90
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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 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, a primary difference between the accounting cash flow and the financial cash
flow of the firm (see Table 2.5) is interest expense. The Real World box on page 32 discusses
some ways in which companies have attempted to “spin the numbers” in the accounting
statement of cash flows.

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.

CONCEPT QUESTIONS
1. Liquidity What does liquidity measure? Explain the trade-off a firm faces between high liquidity and low liquidity levels.
2. Accounting and Cash Flows Why is it that the revenue and cost figures shown on a standard
income statement may not be representative of the actual cash inflows and outflows that occurred during the period?
3. Accounting Statement of Cash Flows Looking at the accounting statement of cash flows, what
does the bottom line number mean? How useful is this number for analyzing a company?
4. Cash Flows How do financial cash flows and the accounting statement of cash flows differ?
Which is more useful when analyzing a company?
5. Book Values versus Market Values Under standard accounting rules, it is possible for a company’s liabilities to exceed its assets. When this occurs, the owners’ equity is negative. Can this
happen with market values? Why or why not?
6. Cash Flow from Assets Suppose a company’s cash flow from assets was negative for a
particular period. Is this necessarily a good sign or a bad sign?
7. Operating Cash Flow Suppose a company’s operating cash flow was negative for several
years running. Is this necessarily a good sign or a bad sign?
8. Net Working Capital and Capital Spending Could a company’s change in net working capital
be negative in a given year? (Hint: Yes.) Explain how this might come about. What about net
capital spending?

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9. Cash Flow to Stockholders and Creditors Could a company’s cash flow to stockholders be
negative in a given year? (Hint: Yes.) Explain how this might come about. What about cash flow
to creditors?
10. Firm Values Referring back to the Fannie Mae example used at the beginning of the chapter,
note that we suggested that Fannie Mae’s stockholders probably didn’t suffer as a result of the
reported loss. What do you think was the basis for our conclusion?

QUESTIONS AND PROBLEMS
1. Building a Balance Sheet Brees, Inc., has current assets of $7,500, net fixed assets of $28,900,
current liabilities of $5,900, and long-term debt of $18,700. What is the value
of the shareholders’ equity account for this firm? How much is net working capital?

Basic
(Questions 1–10)

2. Building an Income Statement Tyler, Inc., has sales of $753,000, costs of $308,000, depreciation expense of $46,000, interest expense of $21,500, and a tax rate of 35 percent. What is the net
income for the firm? Suppose the company paid out $67,000 in cash dividends. What is the addition to retained earnings?
3. Market Values and Book Values Klingon Cruisers, Inc., purchased new cloaking machinery
three years ago for $7 million. The machinery can be sold to the Romulans today for $5.2 million. Klingon’s current balance sheet shows net fixed assets of $4.5 million, current liabilities of
$1.8 million, and net working capital of $750,000. If all the current assets were liquidated today,
the company would receive $2.7 million cash. What is the book value of Klingon’s assets today?
What is the market value?
4. Calculating Taxes The Conard Co. had $285,000 in taxable income. Using the rates from Table
2.3 in the chapter, calculate the company’s income taxes. What is the average tax rate? What is
the marginal tax rate?
5. Calculating OCF Williams, Inc., has sales of $25,300, costs of $9,100, depreciation expense
of $1,700, and interest expense of $950. If the tax rate is 40 percent, what is the operating cash
flow, or OCF?
6. Calculating Net Capital Spending Martin Driving School’s 2009 balance sheet showed net
fixed assets of $4.7 million, and the 2010 balance sheet showed net fixed assets of $5.3 million.
The company’s 2010 income statement showed a depreciation expense of $760,000. What was
the company’s net capital spending for 2010?
7. Building a Balance Sheet The following table presents the long-term liabilities and stockholders’ equity of Information Control Corp. one year ago:

Long-term debt
Preferred stock
Common stock ($1 par value)
Capital surplus
Accumulated retained earnings

$35,000,000
4,000,000
11,000,000
26,000,000
75,000,000

During the past year, Information Control issued 8 million shares of new stock at a total price of
$29 million, and issued $6 million in new long-term debt. The company generated $7 million in
net income and paid $2.5 million in dividends. Construct the current balance sheet reflecting the
changes that occurred at Information Control Corp. during the year.

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8. Cash Flow to Creditors The 2009 balance sheet of Maria’s Tennis Shop, Inc., showed longterm debt of $2.4 million, and the 2010 balance sheet showed long-term debt of $2.5 million. The
2010 income statement showed an interest expense of $195,000. What was the firm’s cash flow
to creditors during 2010?
9. Cash Flow to Stockholders The 2009 balance sheet of Maria’s Tennis Shop, Inc., showed
$730,000 in the common stock account and $6.2 million in the additional paid-in surplus account.
The 2010 balance sheet showed $775,000 and $6.9 million in the same two accounts, respectively. If the company paid out $400,000 in cash dividends during 2010, what was the cash flow to
stockholders for the year?
10. Calculating Total Cash Flows Given the information for Maria’s Tennis Shop, Inc., in the previous two problems, suppose you also know that the firm’s net capital spending for 2010 was
$810,000, and that the firm reduced its net working capital investment by $85,000. What was the
firm’s 2010 operating cash flow, or OCF?
Intermediate
(Questions 11–25)

11. Cash Flows Ritter Corporation’s accountants prepared the following financial statements for
year-end 2010.

R I T T E R C O R P O R AT I O N
Income Statement
2010
Revenue
Expenses
Depreciation
EBT
Tax
Net income
Dividends

$780
620
50
$110
39
$ 71
$ 22

R I T T E R C O R P O R AT I O N
Balance Sheets
D e c e m b e r 31

Assets
Cash
Other current assets
Net fixed assets
Total assets
Liabilities and Equity
Accounts payable
Long-term debt
Stockholders’ equity
Total liabilities and equity

2009

2010

$ 38
143
320
$501

$ 45
140
408
$593

$140
0
361
$501

$143
40
410
$593

a. Explain the change in cash during the year 2010.
b. Determine the change in net working capital in 2010.
c. Determine the cash flow generated by the firm’s assets during the year 2010.

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12. Cash Flow Identity Freeman, Inc., reported the following financial statements for the last two
years. Construct the cash flow identity for the company. Explain what each number means.
2010 INCOME STATEMENT
Sales
Cost of goods sold
Selling & administrative
Depreciation
EBIT
Interest
EBT
Taxes

$565,200
274,025
124,733
54.576
$111,866
19,296
$ 92,570
48,137
$ 44,433
$ 9,600
$ 34,833

Net income
Dividends
Addition to retained earnings

Fr e e m a n , I n c .
Ba l a n c e Sh ee t a s o f D e c e m b e r 31, 2009
Cash
Accounts receivable
Inventory
Current assets
Net fixed assets
Total assets

$ 13,320
18,994
13,794
$ 46,108
$344,426
$390,534

Accounts payable
Notes payable
Current liabilities
Long-term debt
Owners’ equity
Total liabilities and
owners’ equity

$ 9,504
14,508
$ 24,012
$136,800
$229,722
$390,534

Fr e e m a n , I n c .
Ba l a n c e Sh ee t a s o f D e c e m b e r 31, 2010
Cash
Accounts receivable
Inventory
Current assets
Net fixed assets
Total assets

$ 14,306
21,099
22,754
$ 58,159
$406,311
$464,470

Accounts payable
Notes payable
Current liabilities
Long-term debt
Owners’ equity
Total liabilities and
owners’ equity

$ 10,512
16,466
$ 26,978
$152,000
$285,492
$464,470

13. Financial Cash Flows The Stancil Corporation provided the following current information:
Proceeds from long-term borrowing
Proceeds from the sale of common stock
Purchases of fixed assets
Purchases of inventories
Payment of dividends

$12,000
3,000
15,000
2,100
6,000

Determine the cash flows from the firm and the cash flows to investors of the firm.

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14. Building an Income Statement During the year, the Senbet Discount Tire Company had gross
sales of $870,000. The firm’s cost of goods sold and selling expenses were $280,000 and $155,000,
respectively. Senbet also had notes payable of $650,000. These notes carried an interest rate of
6 percent. Depreciation was $86,000. Senbet’s tax rate was 35 percent.
a. What was Senbet’s net income?
b. What was Senbet’s operating cash flow?
15. Calculating Total Cash Flows Schwert Corp. shows the following information on its 2010
income statement: sales  $193,000; costs  $96,500; other expenses  $5,100; depreciation
expense  $13,800; interest expense  $10,400; taxes  $23,520; dividends  $12,500. In addition, you’re told that the firm issued $6,000 in new equity during 2010, and redeemed $7,500 in
outstanding long-term debt.
a. What was the 2010 operating cash flow?
b. What was the 2010 cash flow to creditors?
c. What was the 2010 cash flow to stockholders?
d. If net fixed assets increased by $28,000 during the year, what was the addition to NWC?
16. Using Income Statements Given the following information for O’Hara Marine Co., calculate the
depreciation expense: sales  $43,000; costs  $26,000; addition to retained earnings  $5,600;
dividends paid  $1,300; interest expense  $1,900; tax rate  35 percent.
17. Preparing a Balance Sheet Prepare a 2010 balance sheet for Jarrow Corp. based on the following information: cash  $175,000; patents and copyrights  $730,000; accounts payable 
$435,000; accounts receivable  $240,000; tangible net fixed assets  $3,650,000; inventory 
$405,000; notes payable  $160,000; accumulated retained earnings  $1,980,000; long-term
debt  $2,140,000.
18. Residual Claims Huang, Inc., is obligated to pay its creditors $12,500 very soon.
a. What is the market value of the shareholders’ equity if assets have a market value of $15,100?
b. What if assets equal $10,200?
19. Marginal versus Average Tax Rates (Refer to Table 2.3.) Corporation Growth has $86,000 in
taxable income, and Corporation Income has $8,600,000 in taxable income.
a. What is the tax bill for each firm?
b. Suppose both firms have identified a new project that will increase taxable income by
$10,000. How much in additional taxes will each firm pay? Why is this amount the same?
20. Net Income and OCF During 2010, Raines Umbrella Corp. had sales of $835,000. Cost of goods
sold, administrative and selling expenses, and depreciation expenses were $620,000, $120,000,
and $85,000, respectively. In addition, the company had an interest expense of $68,000 and a tax
rate of 35 percent. (Ignore any tax loss carryback or carryforward provisions.)
a. What was Raines’s net income for 2010?
b. What was its operating cash flow?
c. Explain your results in (a) and (b).
21. Accounting Values versus Cash Flows In the previous problem, suppose Raines Umbrella
Corp. paid out $45,000 in cash dividends. Is this possible? If spending on net fixed assets and net
working capital was zero, and if no new stock was issued during the year, what was the change
in the firm’s long-term debt account?
22. Calculating Cash Flows Cusic Industries had the following operating results for 2010; sales 
$25,700; cost of goods sold  $18,400; depreciation expense  $3,450; interest expense  $790;
dividends paid  $1,100. At the beginning of the year, net fixed assets were $19,280, current

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assets were $5,100, and current liabilities were $3,400. At the end of the year, net fixed assets
were $23,650, current assets were $5,830, and current liabilities were $3,580. The tax rate for
2010 was 40 percent.
a. What was net income for 2010?
b. What was the operating cash flow for 2010?
c. What was the cash flow from assets for 2010? Is this possible? Explain.
d. If no new debt was issued during the year, what was the cash flow to creditors? What was
the cash flow to stockholders? Explain and interpret the positive and negative signs of your
answers in (a) through (d).
23. Calculating Cash Flows Consider the following abbreviated financial statements for Weston
Enterprises:

W E ST ON E NT E RPR I S E S
2 0 0 9 a n d 2 0 1 0 Pa r t i a l Ba l a n c e S h e e t s

WE S T O N E N T E R P R I S E S
2010 I n c o m e S t a t e m e n t

Assets

Sales
Costs
Depreciation
Interest paid

Current assets
Net fixed assets

Liabilities and Owners’ Equity

2009
$ 740
3,600

2010
$ 795
3,800

Current liabilities
Long-term debt

2009
$ 330
2,000

2010
$ 360
2,150

$10,900
4,680
930
390

a. What was owners’ equity for 2009 and 2010?
b. What was the change in net working capital for 2010?
c. In 2010, Weston Enterprises purchased $1,900 in new fixed assets. How much in fixed assets
did Weston Enterprises sell? What was the cash flow from assets for the year? (The tax rate
is 35 percent.)
d. During 2010, Weston Enterprises raised $440 in new long-term debt. How much long-term
debt must Weston Enterprises have paid off during the year? What was the cash flow to
creditors?
Use the following information for Ingersoll, Inc., for Problems 24 and 25 (assume the tax rate
is 35 percent):

Sales
Depreciation
Cost of goods sold
Other expenses
Interest
Cash
Accounts receivable
Short-term notes payable
Long-term debt
Net fixed assets
Accounts payable
Inventory
Dividends

2009

2010

$ 26,115
3,750
8,985
2,130
1,345
13,695
18,130
2,645
45,865
114,850
14,885
32,235
3,184

$ 28,030
3,755
10,200
1,780
2,010
14,010
20,425
2,485
53,510
117,590
13,950
33,125
3,505

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24. Financial Statements Draw up an income statement and balance sheet for this company for
2009 and 2010.
25. Calculating Cash Flow For 2010, calculate the cash flow from assets, cash flow to creditors,
and cash flow to stockholders.
Challenge
(Questions 26–28)

26. Cash Flows You are researching Time Manufacturing and have found the following accounting statement of cash flows for the most recent year. You also know that the company paid
$231 million in current taxes and had an interest expense of $120 million. Use the accounting
statement of cash flows to construct the financial statement of cash flows.

T I M E M A N U FA C T U R I N G
S t a t e m e n t o f C a sh Fl o w s
( i n $ m i l l i o n s)
Operations
Net income
Depreciation
Deferred taxes
Changes in assets and liabilities
Accounts receivable
Inventories
Accounts payable
Accrued expenses
Other
Total cash flow from operations
Investing activities
Acquisition of fixed assets
Sale of fixed assets
Total cash flow from investing activities
Financing activities
Retirement of long-term debt
Proceeds from long-term debt sales
Change in notes payable
Dividends
Repurchase of stock
Proceeds from new stock issue
Total cash flow from financing activities
Change in cash (on balance sheet)

$401
221
43
 65
51
41
 21
5
$676
$415
53
$362
$240
131
12
 198
 32
62
$265
$ 49

27. Net Fixed Assets and Depreciation On the balance sheet, the net fixed assets (NFA) account
is equal to the gross fixed assets (FA) account, which records the acquisition cost of fixed
assets, minus the accumulated depreciation (AD) account, which records the total depreciation
taken by the firm against its fixed assets. Using the fact that NFA  FA  AD, show that the
expression given in the chapter for net capital spending, NFAend  NFAbeg  D (where D is
the depreciation expense during the year), is equivalent to FAend  FAbeg.
28. Tax Rates Refer to the corporate marginal tax rate information in Table 2.3.
a. Why do you think the marginal tax rate jumps up from 34 percent to 39 percent at a taxable
income of $100,001, and then falls back to a 34 percent marginal rate at a taxable income
of $335,001?

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b. Compute the average tax rate for a corporation with exactly $335,001 in taxable income. Does
this confirm your explanation in part (a)? What is the average tax rate for a corporation with
exactly $18,333,334? Is the same thing happening here?
c. The 39 percent and 38 percent tax rates both represent what is called a tax “bubble.”
Suppose the government wanted to lower the upper threshold of the 39 percent marginal
tax bracket from $335,000 to $200,000. What would the new 39 percent bubble rate have
to be?

W H AT ’ S O N T H E W E B ?
1. Change in Net Working Capital Find the most recent abbreviated balance sheets for General
Dynamics at finance.yahoo.com. Enter the ticker symbol “GD” and follow the “Balance Sheet”
link. Using the two most recent balance sheets, calculate the change in net working capital.
What does this number mean?
2. Book Values versus Market Values The home page for Coca-Cola Company can be found at
www.coca-cola.com. Locate the most recent annual report, which contains a balance sheet for
the company. What is the book value of equity for Coca-Cola? The market value of a company
is the number of shares of stock outstanding times the price per share. This information can
be found at finance.yahoo.com using the ticker symbol for Coca-Cola (KO). What is the market
value of equity? Which number is more relevant for shareholders?
3. Cash Flows to Stockholders and Creditors Cooper Tire and Rubber Company provides financial information for investors on its Web site at www.coopertires.com. Follow the “Investors”
link and find the most recent annual report. Using the consolidated statements of cash flows,
calculate the cash flow to stockholders and the cash flow to creditors.

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CLOSING CASE

C A S H F L O W S AT E A S T C O A S T YA C H T S
Because of the dramatic growth at East Coast Yachts, Larissa decided that the company should be
reorganized as a corporation (see our Chapter 1 Closing Case for more detail). Time has passed and,
today, the company is publicly traded under the ticker symbol “ECY”.
Dan Ervin was recently hired by East Coast
E A S T C O A S T YA C H T S
Yachts to assist the company with its short2008 I n c o m e S t a t e m e n t
term financial planning and also to evaluate the
company’s financial performance. Dan graduSales
$617,760,000
ated from college five years ago with a finance
Cost of goods sold
435,360,000
degree, and he has been employed in the treaSelling, general, and administrative
73,824,000
sury department of a Fortune 500 company
Depreciation
20,160,000
since then.
EBIT
$ 88,416,000
The company’s past growth has been someInterest expense
11,112,000
what hectic, in part due to poor planning. In anEBT
$ 77,304,000
ticipation of future growth, Larissa has asked
Taxes
30,921,600
Dan to analyze the company’s cash flows. The
Net
income
$
46,382,400
company’s financial statements are prepared
by an outside auditor. Below you will find the
Dividends
$ 17,550,960
most recent income statement and the balance
Retained earnings
$ 28,831,440
sheets for the past two years.

E A S T C O A S T YA C H T S
Balance Sheet
2009

2010

$ 10,752,000
19,116,000
17,263,200
1,108,800
$ 48,240,000

$ 11,232,000
20,208,000
22,656,000
1,184,000
$ 55,280,000

$408,816,000
(94,836,000)
$313,980,000
6,840,000
$320,820,000

$ 462,030,000
(114,996,000)
$ 347,034,000
6,840,000
$ 353,874,000

Current assets
Cash and equivalents
Accounts receivable
Inventories
Other
Total current assets

Less accumulated depreciation
Net property, plant, and equipment
Intangible assets and others
Total fixed assets

Accounts payable
Notes payable
Accrued expenses
Total current liabilities

Long-term debt
Total long-term liabilities

Preferred stock
Capital surplus
Accumulated retained earnings
Less treasury stock
Total equity

42

$ 23,701,440
20,220,000
5,472,000
$ 49,393,440

$ 24,546,000
18,725,000
6,185,000
$ 49,456,000

$ 129,360,000
$ 129,360,000

$146,560,000
$146,560,000

$

3,000,000
30,000,000
12,000,000
157,306,560
(12,000,000)
$ 190,306,560

$ 3,000,000
40,800,000
31,200,000
186,138,000
(48,000,000)
$213,138,000

$ 369,060,000

$409,154,000

Stockholders’ equity
Common stock

Total assets

2010

Current liabilities

Fixed assets
Property, plant, and equipment

2009

$369,060,000

$ 409,154,000

Total liabilities and shareholders’
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Larissa has also provided the following information. During the year, the company raised
$40 million in new long-term debt and retired $22.8 million in long-term debt. The company also
sold $30 million in new stock and repurchased $36 million. The company purchased $60 million in
fixed assets, and sold $6,786,000 in fixed assets.
Larissa has asked Dan to prepare the financial statement of cash flows and the accounting statement of cash flows. She has also asked you to answer the following questions:
1. How would you describe East Coast Yachts’ cash flows?
2. Which cash flows statement more accurately describes the cash flows at the company?
3. In light of your previous answers, comment on Larissa’s expansion plans.

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CHAPTER

3

Financial Statements
Analysis and Financial
Models
OPENING CASE

T

he price of a share of common stock in electronics retailer Best Buy closed at about $40
on January 4, 2010. At that price, Best Buy had a price-earnings (PE) ratio of 15.4. That is,
investors were willing to pay $15.4 for every dollar in income earned by Best Buy. At the
same time, investors were willing to pay $6.0, $24.9, and $40.4 for each dollar earned by
Jackson Hewitt Tax Service, American Eagle Outfitters, and Google, respectively. At the

other extreme was the greeting card company, American Greetings, which had negative earnings for
the previous year, yet the stock was priced at about $22 per share. Because it had negative earnings,
the PE ratio would have been negative, so it was not reported. At the same time, the typical stock
in the S&P 500 Index of large company stocks was trading at a PE of about 15.8, or about 15.8 times
earnings, as they say on Wall Street.
Price-to-earnings comparisons are examples of the use of financial ratios. As we will see in this
chapter, there are a wide variety of financial ratios, all designed to summarize specific aspects of a
firm’s financial position. In addition to discussing how to analyze financial statements and compute
financial ratios, we will have quite a bit to say about who uses this information and why.

3.1

F I N A N C I A L S TAT E M E N T S A N A LY S I S

In Chapter 2, we discussed some of the essential concepts of financial statements and cash
flows. This chapter continues where our earlier discussion left off. Our goal here is to
expand your understanding of the uses (and abuses) of financial statement information.
A good working knowledge of financial statements is desirable simply because such
statements, and numbers derived from those statements, are the primary means of communicating financial information both within the firm and outside the firm. In short, much of
the language of business finance is rooted in the ideas we discuss in this chapter.
Clearly, one important goal of the accountant is to report financial information to the
user in a form useful for decision making. Ironically, the information frequently does not
come to the user in such a form. In other words, financial statements don’t come with a
user’s guide. This chapter is a first step in filling this gap.

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Standardizing Statements
One obvious thing we might want to do with a company’s financial statements is to compare them to those of other, similar companies. We would immediately have a problem,
however. It’s almost impossible to directly compare the financial statements for two
companies because of differences in size.
For example, Ford and GM are obviously serious rivals in the auto market, but GM
is larger, so it is difficult to compare them directly. For that matter, it’s difficult even to
compare financial statements from different points in time for the same company if the
company’s size has changed. The size problem is compounded if we try to compare GM
and, say, Toyota. If Toyota’s financial statements are denominated in yen, then we have size
and currency differences.
To start making comparisons, one obvious thing we might try to do is to somehow standardize the financial statements. One common and useful way of doing this is to work with
percentages instead of total dollars. The resulting financial statements are called commonsize statements. We consider these next.

Common-Size Balance Sheets
For easy reference, Prufrock Corporation’s 2009 and 2010 balance sheets are provided in
Table 3.1. Using these, we construct common-size balance sheets by expressing each item
as a percentage of total assets. Prufrock’s 2009 and 2010 common-size balance sheets are
shown in Table 3.2.
Notice that some of the totals don’t check exactly because of rounding errors. Also
notice that the total change has to be zero because the beginning and ending numbers must
add up to 100 percent.

TABLE 3.1

PRUF R O C K C O R P O R AT I O N
Ba l a n c e Sh e e t s as o f D e c e m b e r 31, 2009 a n d 2010
( $ i n m i l l i o n s)
Assets
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
Liabilities and Owners’ Equity
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Retained earnings
Total
Total liabilities and owners’ equity

2009

2010

$

84
165
393
$ 642

$

98
188
422
$ 708

$ 2,731
$ 3,373

$ 2,880
$ 3,588

$ 312
231
$ 543
$ 531

$ 344
196
$ 540
$ 457

$ 500
1,799
$ 2,299
$ 3,373

$ 550
2,041
$ 2,591
$ 3,588

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TABLE 3.2

P R U FR O C K C O R P O R AT I O N
C o m m o n - S i ze B a l a n c e S h e e t s
D e c e m b e r 31, 2009 a n d 2010
As s e t s
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
Liabilities and Owners’ Equity
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Retained earnings
Total
Total liabilities and owners’ equity

2009

2010

C h a nge

2.5%
4.9
11.7
19.0

2.7%
5.2
11.8
19.7

 .2%
 .3
 .1
 .7

81.0
100.0%

80.3
100.0%

 .7
.0%

9.2%
6.8
16.1
15.7

9.6%
5.5
15.1
12.7

 .4%
1.3
1.0
3.0

14.8
53.3
68.2
100.0%

15.3
56.9
72.2
100.0%

 .5
3.5
4.1
.0%

In this form, financial statements are relatively easy to read and compare. For example, just looking at the two balance sheets for Prufrock, we see that current assets
were 19.7 percent of total assets in 2010, up from 19.0 percent in 2009. Current liabilities declined from 16.1 percent to 15.1 percent of total liabilities and equity over that
same time. Similarly, total equity rose from 68.2 percent of total liabilities and equity to
72.2 percent.
Overall, Prufrock’s liquidity, as measured by current assets compared to current liabilities, increased over the year. Simultaneously, Prufrock’s indebtedness diminished as a percentage of total assets. We might be tempted to conclude that the balance sheet has grown
“stronger.”

Common-Size Income Statements
Table 3.3 describes some commonly used measures of earnings. A useful way of standardizing the income statement shown in Table 3.4 is to express each item as a percentage of
total sales, as illustrated for Prufrock in Table 3.5.
This income statement tells us what happens to each dollar in sales. For Prufrock,
interest expense eats up $.061 out of every sales dollar, and taxes take another $.081.
When all is said and done, $.157 of each dollar flows through to the bottom line (net
income), and that amount is split into $.105 retained in the business and $.052 paid out
in dividends.
These percentages are useful in comparisons. For example, a relevant figure is the cost
percentage. For Prufrock, $.582 of each $1.00 in sales goes to pay for goods sold. It would
be interesting to compute the same percentage for Prufrock’s main competitors to see how
Prufrock stacks up in terms of cost control.

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Investors and analysts look closely at the income statement for clues on how well a company has performed
during a particular year. Here are some commonly used measures of earnings (numbers in millions).
Net Income

The so-called bottom line, defined as total revenue minus total expenses. Net income
for Prufrock in the latest period is $363 million. Net income reflects differences in a
firm’s capital structure and taxes as well as operating income. Interest expense and
taxes are subtracted from operating income in computing net income. Shareholders
look closely at net income because dividend payout and retained earnings are closely
linked to net income.

EPS

Net income divided by the number of shares outstanding. It expresses net income
on a per-share basis. For Prufrock, the EPS  (Net income)/(Shares outstanding) 
$363/33  $11.

EBIT

Earnings before interest expense and taxes. EBIT is usually called “income from
operations” on the income statement and is income before unusual items, discontinued
operating or extraordinary items. To calculate EBIT, operating expenses are subtracted
from total operations revenues. Analysts like EBIT because it abstracts from
differences in earnings from a firm’s capital structure (interest expense) and taxes.
For Prufrock, EBIT is $691 million.

EBITDA

Earnings before interest expense, taxes, depreciation, and amortization. EBITDA 
EBIT  depreciation and amortization. Here amortization refers to a noncash expense
similar to depreciation except it applies to an intangible asset (such as a patent), rather
than a tangible asset (such as a machine). The word amortization here does not refer
to the payment of debt. There is no amortization in Prufrock’s income statement. For
Prufrock, EBITDA  $691  $276  $967 million. Analysts like to use EBITDA because
it adds back two noncash items (depreciation and amortization) to EBIT and thus is a
better measure of before-tax operating cash flow.

TABLE 3.3
Measures of Earnings

Sometimes these measures of earnings are preceded by the letters LTM, meaning the last twelve months. For
example, LTM EPS is the last twelve months of EPS and LTM EBITDA is the last twelve months of EBITDA. At
other times, the letters TTM are used, meaning trailing twelve months. Needless to say, LTM is the same as TTM.

TABLE 3.4

PRUF R O C K C O R P O R AT I O N
2010 Income Statement
( $ i n m i l l i o n s)
Sales
Cost of goods sold
Depreciation
Earnings before interest and taxes
Interest paid
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings

$2,311
1,344
276
$ 691
141
$ 550
187
$ 363
$121
242

TABLE 3.5

PRUF R O C K C O R P O R AT I O N
Co mmo n - S i ze I n c o m e S t a t e m e n t 2010
Sales
Cost of goods sold
Depreciation
Earnings before interest and taxes
Interest paid
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings

100.0%
58.2
11.9
29.9
6.1
23.8
8.1
15.7%
5.2%
10.5

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3.2

R AT I O A N A LY S I S

Another way of avoiding the problems involved in comparing companies of different sizes
is to calculate and compare financial ratios. Such ratios are ways of comparing and investigating the relationships between different pieces of financial information. We cover some
of the more common ratios next (there are many others we don’t discuss here).
One problem with ratios is that different people and different sources frequently don’t
compute them in exactly the same way, and this leads to much confusion. The specific
definitions we use here may or may not be the same as ones you have seen or will see elsewhere. If you are using ratios as tools for analysis, you should be careful to document how
you calculate each one; and, if you are comparing your numbers to those of another source,
be sure you know how their numbers are computed.
We will defer much of our discussion of how ratios are used and some problems that
come up with using them until later in the chapter. For now, for each ratio we discuss,
several questions come to mind:
Go to
www.reuters.com/
finance/stocks
and find the ratios link
to examine comparative
ratios for a huge number
of companies.

1.
2.
3.
4.

How is it computed?
What is it intended to measure, and why might we be interested?
What is the unit of measurement?
What might a high or low value be telling us? How might such values be
misleading?
5. How could this measure be improved?
Financial ratios are traditionally grouped into the following categories:
1.
2.
3.
4.
5.

Short-term solvency, or liquidity, ratios.
Long-term solvency, or financial leverage, ratios.
Asset management, or turnover, ratios.
Profitability ratios.
Market value ratios.

We will consider each of these in turn. In calculating these numbers for Prufrock, we will
use the ending balance sheet (2010) figures unless we explicitly say otherwise.

Short-Term Solvency or Liquidity Measures
As the name suggests, short-term solvency ratios as a group are intended to provide information about a firm’s liquidity, and these ratios are sometimes called liquidity measures.
The primary concern is the firm’s ability to pay its bills over the short run without undue
stress. Consequently, these ratios focus on current assets and current liabilities.
For obvious reasons, liquidity ratios are particularly interesting to short-term creditors. Because financial managers are constantly working with banks and other short-term
lenders, an understanding of these ratios is essential.
One advantage of looking at current assets and liabilities is that their book values and
market values are likely to be similar. Often (though not always), these assets and liabilities
just don’t live long enough for the two to get seriously out of step. On the other hand, like
any type of near-cash, current assets and liabilities can and do change fairly rapidly, so
today’s amounts may not be a reliable guide to the future.
One of the best-known and most widely used ratios is the current ratio. As
you might guess, the current ratio is defined as:

Current Ratio

Current assets
Current ratio  ___________________
Current liabilities

48

[3.1]

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For Prufrock, the 2010 current ratio is:
$708
Current ratio  ______  1.31 times
$540

EXAMPLE

3.1

Because current assets and liabilities are, in principle, converted to cash over the following
12 months, the current ratio is a measure of short-term liquidity. The unit of measurement is
either dollars or times. So, we could say Prufrock has $1.31 in current assets for every $1 in
current liabilities, or we could say Prufrock has its current liabilities covered 1.31 times over.
To a creditor, particularly a short-term creditor such as a supplier, the higher the current
ratio, the better. To the firm, a high current ratio indicates liquidity, but it also may indicate
an inefficient use of cash and other short-term assets. Absent some extraordinary circumstances, we would expect to see a current ratio of at least 1; a current ratio of less than 1
would mean that net working capital (current assets less current liabilities) is negative. This
would be unusual in a healthy firm, at least for most types of businesses.
The current ratio, like any ratio, is affected by various types of transactions. For example, suppose the firm borrows over the long term to raise money. The short-run effect
would be an increase in cash from the issue proceeds and an increase in long-term debt.
Current liabilities would not be affected, so the current ratio would rise.
Current Events
Suppose a firm were to pay off some of its suppliers and short-term creditors. What would happen to
the current ratio? Suppose a firm buys some inventory. What happens in this case? What happens if
a firm sells some merchandise?
The first case is a trick question. What happens is that the current ratio moves away from 1. If it is
greater than 1 (the usual case), it will get bigger, but if it is less than 1, it will get smaller. To see this,
suppose the firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. If we use
$1 in cash to reduce current liabilities, the new current ratio is ($4  1)/($2  1)  3. If we reverse the
original situation to $2 in current assets and $4 in current liabilities, the change will cause the current
ratio to fall to 1/3 from 1/2.
The second case is not quite as tricky. Nothing happens to the current ratio because cash goes
down while inventory goes up—total current assets are unaffected.
In the third case, the current ratio would usually rise because inventory is normally shown at
cost and the sale would normally be at something greater than cost (the difference is the markup).
The increase in either cash or receivables is therefore greater than the decrease in inventory. This
increases current assets, and the current ratio rises.

Finally, note that an apparently low current ratio may not be a bad sign for a company
with a large reserve of untapped borrowing power.
Quick (or Acid-Test) Ratio Inventory is often the least liquid current asset. It’s also the one
for which the book values are least reliable as measures of market value because the quality
of the inventory isn’t considered. Some of the inventory may later turn out to be damaged,
obsolete, or lost.
More to the point, relatively large inventories are often a sign of short-term trouble. The
firm may have overestimated sales and overbought or overproduced as a result. In this case,
the firm may have a substantial portion of its liquidity tied up in slow-moving inventory.
To further evaluate liquidity, the quick, or acid-test, ratio is computed just like the current ratio, except inventory is omitted:
Current assets  Inventory
Quick ratio  _____________________________
Current liabilities

[3.2]

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Notice that using cash to buy inventory does not affect the current ratio, but it reduces the
quick ratio. Again, the idea is that inventory is relatively illiquid compared to cash.
For Prufrock, this ratio in 2010 was:
$708  422
Quick ratio  _____________  .53 times
$540

The quick ratio here tells a somewhat different story than the current ratio because inventory accounts for more than half of Prufrock’s current assets. To exaggerate the point, if
this inventory consisted of, say, unsold nuclear power plants, then this would be a cause
for concern.
To give an example of current versus quick ratios, based on recent financial statements,
Walmart and Manpower, Inc., had current ratios of .88 and 1.61, respectively. However,
Manpower carries no inventory to speak of, whereas Walmart’s current assets are virtually
all inventory. As a result, Walmart’s quick ratio was only .22, and Manpower’s was 1.61, the
same as its current ratio.
Cash Ratio

A very short-term creditor might be interested in the cash ratio:

Cash
Cash ratio  ___________________
Current liabilities

[3.3]

You can verify that this works out to be .18 times for Prufrock.

Long-Term Solvency Measures
Long-term solvency ratios are intended to address the firm’s long-run ability to meet its
obligations or, more generally, its financial leverage. These ratios are sometimes called
financial leverage ratios or just leverage ratios. We consider three commonly used measures and some variations.
The total debt ratio takes into account all debts of all maturities to all
creditors. It can be defined in several ways, the easiest of which is this:

Total Debt Ratio

Total assets  Total equity
Total debt ratio  ____________________________
Total assets
$3,588  2,591
 _________________  .28 times
$3,588

[3.4]

In this case, an analyst might say that Prufrock uses 28 percent debt.1 Whether this is high
or low or whether it even makes any difference depends on whether capital structure matters, a subject we discuss in a later chapter.
Prufrock has $.28 in debt for every $1 in assets. Therefore, there is $.72 in equity
($1 – .28) for every $.28 in debt. With this in mind, we can define two useful variations
on the total debt ratio, the debt-equity ratio and the equity multiplier:
The online Women’s
Business Center has
more information about
financial statements,
ratios, and small
business topics at
www.sba.gov.

Debt- equity ratio  Total debt / Total equity
 $.28/$.72  .39 times

[3.5]

Equity multiplier  Total assets/ Total equity
 $1/$.72  1.39 times

[3.6]

The fact that the equity multiplier is 1 plus the debt-equity ratio is not a coincidence:
Equity multiplier  Total assets / Total equity  $1/$.72  1.39 times
 (Total equity  Total debt)/ Total equity
 1  Debt- equity ratio  1.39 times
1
Total equity here includes preferred stock, if there is any. An equivalent numerator in this ratio would be (Current liabilities 
Long-term debt).

50

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The thing to notice here is that given any one of these three ratios, you can immediately
calculate the other two, so they all say exactly the same thing.
Times Interest Earned Another common measure of long-term solvency is the times interest earned (TIE) ratio. Once again, there are several possible (and common) definitions,
but we’ll stick with the most traditional:
EBIT
Times interest earned ratio  _________
Interest

[3.7]

$691
 ______  4.9 times
$141

As the name suggests, this ratio measures how well a company has its interest obligations
covered, and it is often called the interest coverage ratio. For Prufrock, the interest bill is
covered 4.9 times over.
A problem with the TIE ratio is that it is based on EBIT, which is not really
a measure of cash available to pay interest. The reason is that depreciation and amortization, noncash expenses, have been deducted out. Because interest is most definitely a cash
outflow (to creditors), one way to define the cash coverage ratio is:

Cash Coverage

EBIT  (Depreciation and amortization)
Cash coverage ratio  __________________________________________
Interest

[3.8]

$691  276
$967
 _____________  ______  6.9 times
$141
$141

The numerator here, EBIT plus depreciation and amortization, is often abbreviated
EBITDA (earnings before interest, taxes, depreciation, and amortization). It is a basic measure of the firm’s ability to generate cash from operations, and it is frequently used as a
measure of cash flow available to meet financial obligations.
More recently another long-term solvency measure is increasingly seen in financial
statement analysis and in debt covenants. It uses EBITDA and interest bearing debt. Specifically, for Prufrock:
Interest bearing debt
$196 million  457 million
_______________________
 _____________________________  .68 times
EBITDA
$967 million

Here we include notes payable (most likely notes payable is bank debt) and long-term debt
in the numerator and EBITDA in the denominator. Values below 1 on this ratio are considered very strong and values below 5 are considered weak. However a careful comparison
with other comparable firms is necessary to properly interpret the ratio.

Asset Management or Turnover Measures
We next turn our attention to the efficiency with which Prufrock uses its assets. The
measures in this section are sometimes called asset management or utilization ratios.
The specific ratios we discuss can all be interpreted as measures of turnover. What
they are intended to describe is how efficiently, or intensively, a firm uses its assets to generate sales. We first look at two important current assets: inventory and
receivables.
During the year, Prufrock had a cost of
goods sold of $1,344. Inventory at the end of the year was $422. With these numbers,
inventory turnover can be calculated as:

Inventory Turnover and Days’ Sales in Inventory

Cost of goods sold
Inventory turnover  _____________________
Inventory

[3.9]

$1,344
 ________  3.2 times
$422

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In a sense, we sold off, or turned over, the entire inventory 3.2 times during the year. As
long as we are not running out of stock and thereby forgoing sales, the higher this ratio is,
the more efficiently we are managing inventory.
If we know that we turned our inventory over 3.2 times during the year, we can immediately figure out how long it took us to turn it over on average. The result is the average
days’ sales in inventory:
365 days
Days’ sales in inventory  ____________________
Inventory turnover
365  114 days
 _____
3.2

[3.10]

This tells us that, roughly speaking, inventory sits 114 days on average before it is sold.
Alternatively, assuming we used the most recent inventory and cost figures, it will take
about 114 days to work off our current inventory.
For example, in September 2007, sales of General Motors (GM) pickup trucks could have
used a pickup. At that time, the company had a 120-day supply of the GMC Sierra and a
114-day supply of the Chevrolet Silverado. These numbers mean that at the then-current
rate of sales, it would take GM 120 days to deplete the available supply of Sierras whereas
a 60-day supply is considered normal in the industry. Of course, the days in inventory are
lower for better-selling models, and, fortunately for GM, its crossover vehicles were a hit. The
company had only a 22-day supply of Buick Enclaves and a 32-day supply of GMC Acadias.
Receivables Turnover and Days’ Sales in Receivables Our inventory measures give some
indication of how fast we can sell products. We now look at how fast we collect on those
sales. The receivables turnover is defined in the same way as inventory turnover:
Sales
Receivables turnover  ______________________
Accounts receivable
$2,311
 ________  12.3 times
$188

[3.11]

Loosely speaking, we collected our outstanding credit accounts and lent the money again
12.3 times during the year.2
This ratio makes more sense if we convert it to days, so the days’ sales in receivables is:
365 days
Days’ sales in receivables  _______________________
Receivables turnover
365  30 days
 _____
12.3

[3.12]

EXAMPLE

3.2

Therefore, on average, we collect on our credit sales in 30 days. For obvious reasons, this ratio
is frequently called the average collection period (ACP). Also note that if we are using the most
recent figures, we can also say that we have 30 days’ worth of sales currently uncollected.
P a y a b l e s Tu r n o v e r
Here is a variation on the receivables collection period. How long, on average, does it take for
Prufrock Corporation to pay its bills? To answer, we need to calculate the accounts payable turnover
rate using cost of goods sold. We will assume that Prufrock purchases everything on credit.
The cost of goods sold is $1,344, and accounts payable are $344. The turnover is therefore
$1,344/$344  3.9 times. So, payables turned over about every 365/3.9  94 days. On average, then,
Prufrock takes 94 days to pay. As a potential creditor, we might take note of this fact.

2
Here we have implicitly assumed that all sales are credit sales. If they were not, we would simply use total credit sales in these
calculations, not total sales.

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Total Asset Turnover Moving away from specific accounts like inventory or receivables, we
can consider an important “big picture” ratio, the total asset turnover ratio. As the name
suggests, total asset turnover is:
Sales
Total asset turnover  _____________
Total assets

[3.13]

$2,311
 ________  .64 times
$3,588

PricewaterhouseCoopers has a useful
utility for extracting
EDGAR data. Try it at
www.edgarscan.
pwcglobal.com.

In other words, for every dollar in assets, we generated $.64 in sales.

3.3

M o r e Tu r n o v e r

EXAMPLE

Suppose you find that a particular company generates $.40 in annual sales for every dollar in total
assets. How often does this company turn over its total assets?
The total asset turnover here is .40 times per year. It takes 1/.40  2.5 years to turn assets over
completely.

Profitability Measures
The three types of measures we discuss in this section are probably the best-known and most
widely used of all financial ratios. In one form or another, they are intended to measure
how efficiently the firm uses its assets and how efficiently the firm manages its operations.
Profit Margin

Companies pay a great deal of attention to their profit margin:

Net income
Profit margin  _____________
Sales
$363
 ________  15.7%
$2,311

[3.14]

This tells us that Prufrock, in an accounting sense, generates a little less than 16 cents in
net income for every dollar in sales.
EBITDA Margin Another commonly used measure of profitability is the EBITDA margin.
As mentioned, EBITDA is a measure of before-tax operating cash flow. It adds back noncash expenses and does not include taxes or interest expense. As a consequence, EBITDA
margin looks more directly at operating cash flows than does net income and does not
include the effect of capital structure or taxes. For Prufrock, EBITDA margin is:
$967 million
EBITDA  ________________
_________
 41.8%
Sales
$2,311 million

All other things being equal, a relatively high margin is obviously desirable. This situation
corresponds to low expense ratios relative to sales. However, we hasten to add that other
things are often not equal.
For example, lowering our sales price will usually increase unit volume but will normally cause margins to shrink. Total profit (or, more importantly, operating cash flow) may
go up or down, so the fact that margins are smaller isn’t necessarily bad. After all, isn’t it
possible that, as the saying goes, “Our prices are so low that we lose money on everything
we sell, but we make it up in volume”?3
3

No, it’s not.

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Margins are very different for different industries. Grocery stores have a notoriously
low profit margin, generally around 2 percent. In contrast, the profit margin for the
pharmaceutical industry is about 18 percent. So, for example, it is not surprising that
recent profit margins for Kroger and Pfizer were about 0.2 percent and 17.7 percent,
respectively.
Return on Assets Return on assets (ROA) is a measure of profit per dollar of assets. It can
be defined several ways,4 but the most common is:
Net income
Return on assets  _____________
Total assets
$363
 ________  10.12%
$3,588

[3.15]

Return on equity (ROE) is a measure of how the stockholders fared during the year. Because benefiting shareholders is our goal, ROE is, in an accounting sense,
the true bottom-line measure of performance. ROE is usually measured as:

Return on Equity

Net income
Return on equity  _____________
Total equity
$363
 ________  14.01%
$2,591

[3.16]

Therefore, for every dollar in equity, Prufrock generated 14 cents in profit; but, again, this
is correct only in accounting terms.
Because ROA and ROE are such commonly cited numbers, we stress that it is important to remember they are accounting rates of return. For this reason, these measures
should properly be called return on book assets and return on book equity. In addition,
ROE is sometimes called return on net worth. Whatever it’s called, it would be inappropriate to compare the result to, for example, an interest rate observed in the financial
markets.
The fact that ROE exceeds ROA reflects Prufrock’s use of financial leverage. We will
examine the relationship between these two measures in the next section.

Market Value Measures
Our final group of measures is based, in part, on information not necessarily contained in
financial statements—the market price per share of the stock. Obviously, these measures
can be calculated directly only for publicly traded companies.
We assume that Prufrock has 33 million shares outstanding and the stock sold for
$88 per share at the end of the year. If we recall that Prufrock’s net income was $363 million, then we can calculate that its earnings per share were:
$363
Net income
 ______  $11
EPS  _____________________
33
Shares outstanding

[3.17]

4
For example, we might want a return on assets measure that is neutral with respect to capital structure (interest expense) and
taxes. Such a measure for Prufrock would be:

$691
EBIT
_____________
 ________  19.3%
Total assets
$3,588

This measure has a very natural interpretation. If 19.3 percent exceeds Prufrock’s borrowing rate, Prufrock will earn more money
on its investments than it will pay out to its creditors. The surplus will be available to Prufrock’s shareholders after adjusting for
taxes.

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Price-Earnings Ratio The first of our market value measures, the price-earnings or
PE ratio (or multiple), is defined as:
Price per share
PE ratio  ____________________
Earnings per share

[3.18]

$88
 _____  8 times
$11

In the vernacular, we would say that Prufrock shares sell for eight times earnings, or we
might say that Prufrock shares have, or “carry,” a PE multiple of 8.
Because the PE ratio measures how much investors are willing to pay per dollar of current earnings, higher PEs are often taken to mean that the firm has significant prospects for
future growth. Of course, if a firm had no or almost no earnings, its PE would probably be
quite large; so, as always, care is needed in interpreting this ratio.
Market-to-Book Ratio

A second commonly quoted measure is the market-to-book ratio:

Market value per share
Market-to-book ratio  _________________________
Book value per share
$88
$88
 ___________  _______  1.12 times
$2,591/33
$78.5

[3.19]

Notice that book value per share is total equity (not just common stock) divided by the
number of shares outstanding.
Book value per share is an accounting number that reflects historical costs. In a loose
sense, the market-to-book ratio therefore compares the market value of the firm’s investments to their cost. A value less than 1 could mean that the firm has not been successful
overall in creating value for its stockholders.
Market Capitalization The market capitalization of a public firm is equal to the firm’s
stock market price per share multiplied by the number of shares outstanding. For Prufrock,
this is:
Price per share  Shares outstanding  $88  33 million  $2,904 million

This is a useful number for potential buyers of Prufrock. A prospective buyer of all of the
outstanding shares of Prufrock (in a merger or acquisition) would need to come up with at
least $2,904 million plus a premium.
Enterprise Value Enterprise value is a measure of firm value that is very closely related to
market capitalization. Instead of focusing on only the market value of outstanding shares of
stock, it measures the market value of outstanding shares of stock plus the market value of
outstanding interest bearing debt less cash on hand. We know the market capitalization
of Prufrock but we do not know the market value of its outstanding interest bearing debt.
In this situation, the common practice is to use the book value of outstanding interest
bearing debt less cash on hand as an approximation. For Prufrock, enterprise value is (in
millions):
EV  Market capitalization  Market value of interest bearing debt  cash
[3.20]
 $2,904  ($196  457)  $98  $3,459 million

The purpose of the EV measure is to better estimate how much it would take to buy all of
the outstanding stock of a firm and also to pay off the debt. The adjustment for cash is to

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recognize that if we were a buyer the cash could be used immediately to buy back debt or
pay a dividend.
Financial analysts use valuation multiples based upon a firm’s
enterprise value when the goal is to estimate the value of the firm’s total business rather
than just focusing on the value of its equity. To form an appropriate multiple, enterprise
value is divided by EBITDA. For Prufrock, the enterprise value multiple is:
Enterprise Value Multiples

$3,459 million
EV
_________
 ________________  3.6 times
EBITDA
$967 million

The multiple is especially useful because it allows comparison of one firm with another
when there are differences in capital structure (interest expense), taxes, or capital spending.
The multiple is not directly affected by these differences.
Similar to PE ratios, we would expect a firm with high growth opportunities to have high
EV multiples.
This completes our definition of some common ratios. We could tell you about more of
them, but these are enough for now. We’ll leave it here and go on to discuss some ways of
using these ratios instead of just how to calculate them. Table 3.6 summarizes some of the
ratios we’ve discussed.

TABLE 3.6
Common Financial Ratios
I.

Short-Term Solvency, or Liquidity, Ratios
Current assets
Current ratio  ______________
Current liabilities

365 days
Days’ sales in receivables  __________________
Receivables turnover

Current assets  Inventory
Quick ratio  ______________________
Current liabilities

Sales
Total asset turnover  __________
Total assets

Cash
Cash ratio  ______________
Current liabilities

Total assets
Capital intensity  __________
Sales

II. Long-Term Solvency, or Financial Leverage, Ratios

IV. Profitability Ratios

Total assets  Total equity
Total debt ratio  ______________________
Total assets

Net income
Profit margin  __________
Sales

Debt-equity ratio  Total debt/Total equity

Net income
Return on assets (ROA)  __________
Total assets

Equity multiplier  Total assets/Total equity

Net income
Return on equity (ROE)  __________
Total equity

EBIT
Times interest earned ratio  _______
Interest

Sales  ______
Net income  ______
Assets
ROE  __________
Assets
Equity
Sales

EBITDA
Cash coverage ratio  _______
Interest
III. Asset Utilization, or Turnover, Ratios

56

V.

Market Value Ratios

Cost of goods sold
Inventory turnover  _______________
Inventory

Price per share
Price -earnings ratio  ________________
Earnings per share

365 days
Days’ sales in inventory  _______________
Inventory turnover

Market value per share
Market-to-book ratio  ___________________
Book value per share

Sales
Receivables turnover  _________________
Accounts receivable

Enterprise value
EV multiple  ______________
EBITDA

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3.4
EXAMPLE

Atlantic and Pacific
Consider the following 2009 data for Atlantic’s Companies and Pacific Depot (billions except for price
per share):
AT L ANT I C ’ S C O M PA N I E S , I N C .

T H E PA C I FI C D E P O T, I N C .

$48.3
$ 4.8
$ 2.8
$ .5
$ 1.5
$ 6.7
$30.9
$24
1.5
$16.1

$77.3
$ 7.3
$ 4.4
$ .5
$ 1.9
$13.4
$44.3
$27
1.7
$17.7

Sales
EBIT
Net income
Cash
Depreciation
Interest bearing debt
Total assets
Price per share
Shares outstanding
Shareholder equity

1. Determine the profit margin, ROE, market capitalization, enterprise value, PE multiple, and EV
multiple for both Atlantic’s and Pacific Depot.

Equity multiplier
Asset turnover
Profit margin
ROE
Market capitalization
Enterprise value
PE multiple
EBITDA
EV multiple

AT L ANT I C’S C O M PA N I E S , I N C .

T H E PA C I FI C D E P O T, I N C .

30.9/16.1  1.9
48.3/30.9  1.6
2.8/48.3  5.8%
2.8/16.1  17.4%
1.5  24  $36 billion
(1.5  24)  6.7  .5  $42.2 billion
24/1.87  12.8
4.8  1.5  $6.3
42.2/6.3  6.7

44.3/17.7  2.5
77.3/44.3  1.7
4.4/77.3  5.7%
4.4/17.7  24.9%
1.7  27  $45.9 billion
(1.7  27)  13.4 .5  $58.8 billion
27/2.6  10.4
7.3  1.9  $9.2
58.8/9.2  6.4

2. How would you describe these two companies from a financial point of view? These are similarly
situated companies. In 2009, Pacific Depot had a higher ROE (partially because of using more debt
and higher turnover), but Atlantic’s had slightly higher PE and EV multiples. Both companies’ multiples were somewhat below the general market, raising questions about future growth prospects.

3.3

THE DU PONT IDENTITY

As we mentioned in discussing ROA and ROE, the difference between these two profitability measures reflects the use of debt financing or financial leverage. We illustrate the
relationship between these measures in this section by investigating a famous way of
decomposing ROE into its component parts.

A Closer Look at ROE
To begin, let’s recall the definition of ROE:
Net income
Return on equity  _____________
Total equity

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If we were so inclined, we could multiply this ratio by Assets/Assets without changing
anything:
Assets
Net income  _____________
Net income  ________
Return on equity  _____________
Total equity
Total equity
Assets
Assets
Net income  _____________
 _____________
Assets
Total equity

Notice that we have expressed the ROE as the product of two other ratios—ROA and the
equity multiplier:
ROE  ROA  Equity multiplier  ROA  (1  Debt-equity ratio)

Looking back at Prufrock, for example, we see that the debt-equity ratio was .39 and ROA
was 10.12 percent. Our work here implies that Prufrock’s ROE, as we previously calculated, is:
ROE  10.12%  1.39  14.01%

The difference between ROE and ROA can be substantial, particularly for certain businesses. For example, based on recent financial statements, Wells Fargo has an ROA of only
0.75 percent, which is actually fairly typical for a bank. However, banks tend to borrow a
lot of money, and, as a result, have relatively large equity multipliers. For Wells Fargo, ROE
is about 6.69 percent, implying an equity multiplier of 8.9.
We can further decompose ROE by multiplying the top and bottom by total sales:
Sales  _____________
Assets
Net income  _____________
ROE  ______
Assets
Total equity
Sales

If we rearrange things a bit, ROE is:
Sales  _____________
Assets
Net income  ________
ROE  _____________
Assets
Total equity
Sales
Return on assets
 Profit margin  Total asset turnover  Equity multiplier

[3.21]

What we have now done is to partition ROA into its two component parts, profit margin
and total asset turnover. The last expression of the preceding equation is called the Du Pont
identity after the Du Pont Corporation, which popularized its use.
We can check this relationship for Prufrock by noting that the profit margin was 15.7 percent and the total asset turnover was .64. ROE should thus be:
ROE  Profit margin  Total asset turnover  Equity multiplier
 15.7%

.64

1.39
 14%

This 14 percent ROE is exactly what we had before.
The Du Pont identity tells us that ROE is affected by three things:
1. Operating efficiency (as measured by profit margin).
2. Asset use efficiency (as measured by total asset turnover).
3. Financial leverage (as measured by the equity multiplier).
Weakness in either operating or asset use efficiency (or both) will show up in a diminished
return on assets, which will translate into a lower ROE.
Considering the Du Pont identity, it appears that the ROE could be leveraged up by increasing the amount of debt in the firm. However, notice that increasing debt also increases
interest expense, which reduces profit margins, which acts to reduce ROE. So, ROE could
go up or down, depending. More important, the use of debt financing has a number of other

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TABLE 3.7
The Du Pont Breakdown for Yahoo! and Google
Yahoo!
TW E LVE M ONT HS E NDI NG

ROE



P R O FI T M A R G I N



T O TA L A S S E T T U R N O V E R



E Q U I T Y M ULTIP LIER

12/09
12/08
12/07

4.8%
3.8%
6.9%





9.3%
5.9%
9.5%





0.433
0.527
0.570





1.20
1.22
1.28

Google
TW ELVE M ONT HS E NDI NG

ROE



P R O FI T M A R G I N



T O TA L A S S E T T U R N O V E R



E Q U I T Y M ULTIP LIER

12/09
12/08
12/07

18.1%
14.9%
18.6%





27.6%
19.4%
25.3%





0.584
0.686
0.655





1.12
1.12
1.12

effects, and, as we discuss at some length in later chapters, the amount of leverage a firm
uses is governed by its capital structure policy.
The decomposition of ROE we’ve discussed in this section is a convenient way of systematically approaching financial statement analysis. If ROE is unsatisfactory by some
measure, then the Du Pont identity tells you where to start looking for the reasons.
Yahoo! and Google are among the most important Internet companies in the world.
Yahoo! and Google may be good examples of how Du Pont analysis can be useful in helping to ask the right questions about a firm’s financial performance. The Du Pont breakdowns for Yahoo! and Google are summarized in Table 3.7.
As can be seen, in 2009, Yahoo! had an ROE of 4.8 percent, up from its ROE in 2008 of
3.8 percent. In contrast, in 2009, Google had an ROE of 18.1 percent, up from its ROE in
2008 of 14.9 percent. Given this information, how is it possible that Google’s ROE could
be so much higher than the ROE of Yahoo! during this period of time, and what accounts
for the decline in Yahoo!’s ROE?
On close inspection of the Du Pont breakdown, we see that Yahoo!’s profit margin in
2009 was only 4.8 percent. Meanwhile Google’s profit margin was 18.1 percent in 2009.
Yet Yahoo! and Google have very comparable asset turnover and financial leverage. What
can account for Google’s advantage over Yahoo! in profit margin? Operating efficiencies can come from higher volumes, higher prices, and/or lower costs. It is clear that the
big difference in ROE between the two firms can be attributed to the difference in profit
margins.

Problems with Financial Statement Analysis
We continue our chapter by discussing some additional problems that can arise in using
financial statements. In one way or another, the basic problem with financial statement
analysis is that there is no underlying theory to help us identify which quantities to look at
and to guide us in establishing benchmarks.
As we discuss in other chapters, there are many cases in which financial theory and economic logic provide guidance in making judgments about value and risk. Little such help
exists with financial statements. This is why we can’t say which ratios matter the most and
what a high or low value might be.
One particularly severe problem is that many firms are conglomerates, owning more or
less unrelated lines of business. GE is a well-known example. The consolidated financial

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THE REAL WORLD

W H AT ’ S I N A R AT I O ?
Abraham Briloff, a well-known financial commentator, famously remarked that “financial statements are like fine
perfume; to be sniffed but not swallowed.” As you have probably figured out by now, his point is that information
gleaned from financial statements—and ratios and growth rates computed from that information—should be taken
with a grain of salt.
For example, in early 2010, shares in Green Mountain Coffee Roasters had a PE ratio of about 58 times earnings.
You would expect that this stock would have a high growth rate, and indeed analysts thought so. The estimated
earnings growth rate for Green Mountain for the next year was 68 percent. At the same time, greeting card company American Greetings also had a PE ratio of about 68, but analysts estimated an earnings growth rate of only
9 percent for the next year. Why is the PE so high? The answer is that American Greetings simply had low earnings
the previous year. The “forward” PE ratio, which uses next year’s estimated earnings instead of past earnings was
only 9. So, caution is warranted when looking at PE ratios.
U.S. Airways illustrates another issue. If you calculated its ROE in 2009, you would get about 57.7 percent, which
is quite good. What’s strange is the company reported a loss of about $205 million dollars during 2009! What’s going
on is that U.S. Airways had a book value of equity balance of negative $355 million. In this situation, the more U.S.
Airways loses, the higher the ROE becomes. Of course, U.S. Airways’ market-to-book and PE ratios are also both
negative. How do you interpret a negative PE? We’re not really sure, either. Whenever a company has a negative
book value of equity, it means that losses have been so large that book equity has been wiped out. In such cases,
the ROE, PE ratio, and market-to-book ratio are often not reported because they are meaningless.
Even if a company’s book equity is positive, you still have to be careful. For example, consider venerable consumer products company Clorox, which had a market-to-book ratio of about 53 in late 2007. Since the market-tobook ratio measures the value created by the company for shareholders, this would seem to be a good sign. But
a closer look shows that Clorox’s book value of equity per share dropped from $7.23 in 2004 to $1.03 in 2006. This
decline had to do with accounting for stock repurchases made by the company, not gains or losses, but it nonetheless dramatically increased the market-to-book ratio in that year and subsequent years as well.
Financial ratios are important tools used in evaluating companies of all types, but you cannot simply take a number
as given. Instead, before doing any analysis, the first step is to ask whether the number actually makes sense.

statements for such firms don’t really fit any neat industry category. More generally, the
kind of peer group analysis we have been describing is going to work best when the firms
are strictly in the same line of business, the industry is competitive, and there is only one
way of operating.
Another problem that is becoming increasingly common is that major competitors and
natural peer group members in an industry may be scattered around the globe. The automobile industry is an obvious example. The problem here is that financial statements from
outside the United States do not necessarily conform to GAAP. The existence of different
standards and procedures makes it difficult to compare financial statements across national
borders.
Even companies that are clearly in the same line of business may not be comparable.
For example, electric utilities engaged primarily in power generation are all classified in
the same group. This group is often thought to be relatively homogeneous. However, most
utilities operate as regulated monopolies, so they don’t compete much with each other, at
least not historically. Many have stockholders, and many are organized as cooperatives
with no stockholders. There are several different ways of generating power, ranging from
hydroelectric to nuclear, so the operating activities of these utilities can differ quite a bit.
Finally, profitability is strongly affected by the regulatory environment, so utilities in different locations can be similar but show different profits.

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Several other general problems frequently crop up. First, different firms use different
accounting procedures—for inventory, for example. This makes it difficult to compare
statements. Second, different firms end their fiscal years at different times. For firms in
seasonal businesses (such as a retailer with a large Christmas season), this can lead to
difficulties in comparing balance sheets because of fluctuations in accounts during the
year. Finally, for any particular firm, unusual or transient events, such as a one-time profit
from an asset sale, may affect financial performance. Such events can give misleading
signals as we compare firms. The nearby The Real World box discusses some issues along
these lines.

3.4

FINANCIAL MODELS

Financial planning is another important use of financial statements. Most financial planning models output pro forma financial statements, where pro forma means “as a matter of
form.” In our case, this means that financial statements are the form we use to summarize
the projected future financial status of a company.

A Simple Financial Planning Model
We can begin our discussion of financial planning models with a relatively simple example. The
Computerfield Corporation’s financial statements from the most recent year are shown below.
Unless otherwise stated, the financial planners at Computerfield assume that all variables are tied directly to sales and current relationships are optimal. This means that all
items will grow at exactly the same rate as sales. This is obviously oversimplified; we use
this assumption only to make a point.
COM PUT E R FI E LD C O R P O R AT I O N
F i na n c i a l S t a t e m e n t s
I NCOM E STAT E M E NT
Sales
Costs
Net income

$1,000
800
$ 200

B A LA N C E S H E E T

Assets

$500

Total

$500

Debt
Equity
Total

$250
250
$500

Suppose sales increase by 20 percent, rising from $1,000 to $1,200. Planners would
then also forecast a 20 percent increase in costs, from $800 to $800  1.2  $960. The
pro forma income statement would thus look like this:
Pr o F or m a I n c o m e S t a t e m e n t
Sales
Costs
Net income

$1,200
960
$ 240

The assumption that all variables will grow by 20 percent lets us easily construct the
pro forma balance sheet as well:
Pr o Fo r m a B a l a n c e S h e e t
Assets

$600 (100)

Total

$600 (100)

Debt
Equity
Total

$300 (50)
300 (50)
$600 (100)

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Planware provides
insight into cash flow
forecasting at
www.planware.org.

Notice we have simply increased every item by 20 percent. The numbers in parentheses are
the dollar changes for the different items.
Now we have to reconcile these two pro forma statements. How, for example, can net
income be equal to $240 and equity increase by only $50? The answer is that Computerfield
must have paid out the difference of $240  50  $190, possibly as a cash dividend. In this
case dividends are the “plug” variable.
Suppose Computerfield does not pay out the $190. In this case, the addition to retained
earnings is the full $240. Computerfield’s equity will thus grow to $250 (the starting
amount) plus $240 (net income), or $490, and debt must be retired to keep total assets
equal to $600.
With $600 in total assets and $490 in equity, debt will have to be $600  490  $110.
Because we started with $250 in debt, Computerfield will have to retire $250  110  $140
in debt. The resulting pro forma balance sheet would look like this:
P r o Fo r m a B a l a n c e S h e e t
Assets

$600 (100)

Total

$600 (100)

Debt
Equity
Total

$110 (140)
490 (240)
$600 (100)

In this case, debt is the plug variable used to balance projected total assets and liabilities.
This example shows the interaction between sales growth and financial policy. As sales
increase, so do total assets. This occurs because the firm must invest in net working capital
and fixed assets to support higher sales levels. Because assets are growing, total liabilities
and equity, the right side of the balance sheet, will grow as well.
The thing to notice from our simple example is that the way the liabilities and owners’
equity change depends on the firm’s financing policy and its dividend policy. The growth in
assets requires that the firm decide on how to finance that growth. This is strictly a managerial decision. Note that in our example the firm needed no outside funds. This won’t usually
be the case, so we explore a more detailed situation in the next section.

The Percentage of Sales Approach
In the previous section, we described a simple planning model in which every item increased at the same rate as sales. This may be a reasonable assumption for some elements.
For others, such as long-term borrowing, it probably is not: The amount of long-term borrowing is set by management, and it does not necessarily relate directly to the level of sales.
In this section, we describe an extended version of our simple model. The basic idea is
to separate the income statement and balance sheet accounts into two groups, those that
vary directly with sales and those that do not. Given a sales forecast, we will then be able
to calculate how much financing the firm will need to support the predicted sales level.
The financial planning model we describe next is based on the percentage of sales
approach. Our goal here is to develop a quick and practical way of generating pro forma
statements. We defer discussion of some “bells and whistles” to a later section.
The Income Statement We start out with the most recent income statement for the Rosengarten Corporation, as shown in Table 3.8. Notice that we have still simplified things by
including costs, depreciation, and interest in a single cost figure.
Rosengarten has projected a 25 percent increase in sales for the coming year, so we are
anticipating sales of $1,000  1.25  $1,250. To generate a pro forma income statement,
we assume that total costs will continue to run at $800/1,000  80 percent of sales. With
this assumption, Rosengarten’s pro forma income statement is as shown in Table 3.9. The

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TABLE 3.8

ROSE NG A R T E N C O R P O R AT I O N
Income Statement
Sales
Costs
Taxable income
Taxes (34%)
Net income
Dividends

$1,000
800
$ 200
68
$ 132

Addition to retained earnings

$44
88

TABLE 3.9

ROSE NG A R T E N C O R P O R AT I O N
Pr o F o r m a I n c o m e S t a t e m e n t
Sales (projected)
Costs (80% of sales)
Taxable income
Taxes (34%)

$1,250
1,000
$ 250
85
$ 165

Net income

effect here of assuming that costs are a constant percentage of sales is to assume that the
profit margin is constant. To check this, notice that the profit margin was $132/1,000 
13.2 percent. In our pro forma statement, the profit margin is $165/1,250  13.2 percent;
so it is unchanged.
Next, we need to project the dividend payment. This amount is up to Rosengarten’s
management. We will assume Rosengarten has a policy of paying out a constant fraction of
net income in the form of a cash dividend. For the most recent year, the dividend payout
ratio was:
Dividend payout ratio  Cash dividends/Net income
 $44/132  33 1/3%

[3.22]

We can also calculate the ratio of the addition to retained earnings to net income:
Addition to retained earnings/Net income  $88/132  66 2/3%

This ratio is called the retention ratio or plowback ratio, and it is equal to 1 minus the
dividend payout ratio because everything not paid out is retained. Assuming that the payout
ratio is constant, the projected dividends and addition to retained earnings will be:
Projected dividends paid to shareholders  $165  1/3  $ 55
Projected addition to retained earnings  $165  2/3  110
$165

To generate a pro forma balance sheet, we start with the most recent
statement, as shown in Table 3.10.
On our balance sheet, we assume that some items vary directly with sales and others
do not. For those items that vary with sales, we express each as a percentage of sales for
the year just completed. When an item does not vary directly with sales, we write “n/a” for
“not applicable.”

The Balance Sheet

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TABLE 3.10
R O S E N G A R T E N C O R P O R AT I O N
Balance Sheet
As s e t s

Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y
$

PE RCE N TA G E
OF SA LE S

$ 160
440
600
$1,200

16%
44
60
120

$1,800

180

$3,000

300%

Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in
surplus
Retained earnings
Total
Total liabilities and owners’ equity

$

P E R C E N TAGE
O F S ALES

$ 300
100
$ 400
$ 800

30%
n/a
n/a
n/a

$ 800

n/a

1,000
$1,800
$3,000

n/a
n/a
n/a

For example, on the asset side, inventory is equal to 60 percent of sales ($600/1,000)
for the year just ended. We assume this percentage applies to the coming year, so for each
$1 increase in sales, inventory will rise by $.60. More generally, the ratio of total assets to
sales for the year just ended is $3,000/1,000  3, or 300 percent.
This ratio of total assets to sales is sometimes called the capital intensity ratio. It tells
us the amount of assets needed to generate $1 in sales; the higher the ratio is, the more
capital intensive is the firm. Notice also that this ratio is just the reciprocal of the total asset
turnover ratio we defined previously.
For Rosengarten, assuming that this ratio is constant, it takes $3 in total assets to generate $1 in sales (apparently Rosengarten is in a relatively capital-intensive business). Therefore, if sales are to increase by $100, Rosengarten will have to increase total assets by three
times this amount, or $300.
On the liability side of the balance sheet, we show accounts payable varying with sales.
The reason is that we expect to place more orders with our suppliers as sales volume increases, so payables will change “spontaneously” with sales. Notes payable, on the other
hand, represents short-term debt such as bank borrowing. This will not vary unless we take
specific actions to change the amount, so we mark this item as “n/a.”
Similarly, we use “n/a” for long-term debt because it won’t automatically change with
sales. The same is true for common stock and paid-in surplus. The last item on the right
side, retained earnings, will vary with sales, but it won’t be a simple percentage of sales.
Instead, we will explicitly calculate the change in retained earnings based on our projected
net income and dividends.
We can now construct a partial pro forma balance sheet for Rosengarten. We do this by
using the percentages we have just calculated wherever possible to calculate the projected
amounts. For example, net fixed assets are 180 percent of sales; so, with a new sales level
of $1,250, the net fixed asset amount will be 1.80  $1,250  $2,250, representing an
increase of $2,250  1,800  $450 in plant and equipment. It is important to note that for
items that don’t vary directly with sales, we initially assume no change and simply write in
the original amounts. The result is shown in Table 3.11. Notice that the change in retained
earnings is equal to the $110 addition to retained earnings we calculated earlier.

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TABLE 3.11
R O S E N G A R T E N C O R P O R AT I O N
P a r t i a l P r o Fo r m a B a l a n c e S h e e t
As s e t s

Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i ty

NE XT
YE AR

CHANGE
FR O M
CURRENT
YEAR

$ 200
550
750
$1,500

$ 40
110
150
$300

$2,250

$450

$3,750

$750

Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in
surplus
Retained earnings
Total
Total liabilities and owners’ equity
External financing needed

NEXT
YEAR

C HANGE
FR OM
C UR R ENT
Y EAR

$ 375
100
$ 475
$ 800

$ 75
0
$ 75
$ 0

$ 800

$ 0

1,110
$1,910
$3,185
$ 565

110
$110
$185
$565

Inspecting our pro forma balance sheet, we notice that assets are projected to increase
by $750. However, without additional financing, liabilities and equity will increase by only
$185, leaving a shortfall of $750  185  $565. We label this amount external financing
needed (EFN).
Rather than create pro forma statements, if we were so inclined, we could calculate EFN
directly as follows:
Spontaneous liabilities
Assets  Sales  _________________________
EFN  ________
 Sales  PM
Sales
Sales
 Projected sales  (1  d )

[3.23]

In this expression, “Sales” is the projected change in sales (in dollars). In our example
projected sales for next year are $1,250, an increase of $250 over the previous year, so
Sales  $250. By “Spontaneous liabilities,” we mean liabilities that naturally move up
and down with sales. For Rosengarten, the spontaneous liabilities are the $300 in accounts
payable. Finally, PM and d are the profit margin and dividend payout ratios, which we previously calculated as 13.2 percent and 33 1/3 percent, respectively. Total assets and sales
are $3,000 and $1,000, respectively, so we have:
$3,000
$300
1  $565
EFN  ________  $250  _______  $250  .132  $1,250  1  __
1,000
1,000
3

(

)

In this calculation, notice that there are three parts. The first part is the projected
increase in assets, which is calculated using the capital intensity ratio. The second is
the spontaneous increase in liabilities. The third part is the product of profit margin and
projected sales, which is projected net income, multiplied by the retention ratio. Thus, the
third part is the projected addition to retained earnings.
A Particular Scenario Our financial planning model now reminds us of one of those good

news–bad news jokes. The good news is we’re projecting a 25 percent increase in sales. The bad
news is this isn’t going to happen unless Rosengarten can somehow raise $565 in new financing.

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TABLE 3.12
R O S E N G A R T E N C O R P O R AT I O N
P r o Fo r m a B a l a n c e S h e e t
As s e t s

Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y

NE XT
YE AR

CHANG E
F ROM
CURRE N T
YE AR

$ 200
550
750
$1,500

$ 40
110
150
$300

$2,250

$450

$3,750

$750

Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Retained earnings
Total
Total liabilities and owners’ equity

NEXT
YEAR

C H ANGE
FR OM
C U RR ENT
Y EAR

$ 375
325
$ 700
$1,140

$ 75
225
$300
$340

$ 800
1,110
$1,910
$3,750

$ 0
110
$110
$750

This is a good example of how the planning process can point out problems and potential conflicts. If, for example, Rosengarten has a goal of not borrowing any additional funds
and not selling any new equity, then a 25 percent increase in sales is probably not feasible.
If we take the need for $565 in new financing as given, we know that Rosengarten has
three possible sources: short-term borrowing, long-term borrowing, and new equity. The
choice of some combination among these three is up to management; we will illustrate only
one of the many possibilities.
Suppose Rosengarten decides to borrow the needed funds. In this case, the firm might
choose to borrow some over the short term and some over the long term. For example, current assets increased by $300 whereas current liabilities rose by only $75. Rosengarten could
borrow $300  75  $225 in short-term notes payable and leave total net working capital
unchanged. With $565 needed, the remaining $565  225  $340 would have to come from
long-term debt. Table 3.12 shows the completed pro forma balance sheet for Rosengarten.
We have used a combination of short- and long-term debt as the plug here, but we
emphasize that this is just one possible strategy; it is not necessarily the best one by any
means. We could (and should) investigate many other scenarios. The various ratios we discussed earlier come in handy here. For example, with the scenario we have just examined,
we would surely want to examine the current ratio and the total debt ratio to see if we were
comfortable with the new projected debt levels.

3.5

EXTERNAL FINANCING AND GROWTH

External financing needed and growth are obviously related. All other things staying the
same, the higher the rate of growth in sales or assets, the greater will be the need for external financing. In the previous section, we took a growth rate as given, and then we determined the amount of external financing needed to support that growth. In this section, we
turn things around a bit. We will take the firm’s financial policy as given and then examine
the relationship between that financial policy and the firm’s ability to finance new investments and thereby grow.
We emphasize that we are focusing on growth not because growth is an appropriate goal; instead, for our purposes, growth is simply a convenient means of examining

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the interactions between investment and financing decisions. In effect, we assume that the
use of growth as a basis for planning is just a reflection of the very high level of aggregation
used in the planning process.

EFN and Growth
The first thing we need to do is establish the relationship between EFN and growth. To
do this, we introduce the simplified income statement and balance sheet for the Hoffman
Company in Table 3.13. Notice that we have simplified the balance sheet by combining
short-term and long-term debt into a single total debt figure. Effectively, we are assuming
that none of the current liabilities vary spontaneously with sales. This assumption isn’t as
restrictive as it sounds. If any current liabilities (such as accounts payable) vary with sales,
we can assume that any such accounts have been netted out in current assets. Also, we continue to combine depreciation, interest, and costs on the income statement.
Suppose the Hoffman Company is forecasting next year’s sales level at $600, a $100
increase. Notice that the percentage increase in sales is $100/500  20 percent. Using the
percentage of sales approach and the figures in Table 3.13, we can prepare a pro forma income statement and balance sheet as in Table 3.14. As Table 3.14 illustrates, at a 20 percent
growth rate, Hoffman needs $100 in new assets. The projected addition to retained earnings
is $52.8, so the external financing needed, EFN, is $100  52.8  $47.2.
Notice that the debt-equity ratio for Hoffman was originally (from Table 3.13) equal to
$250/250  1.0. We will assume that the Hoffman Company does not wish to sell new equity. In this case, the $47.2 in EFN will have to be borrowed. What will the new debt-equity
ratio be? From Table 3.14, we know that total owners’ equity is projected at $302.8. The
new total debt will be the original $250 plus $47.2 in new borrowing, or $297.2 total. The
debt-equity ratio thus falls slightly from 1.0 to $297.2/302.8  .98.
Table 3.15 shows EFN for several different growth rates. The projected addition to retained earnings and the projected debt-equity ratio for each scenario are also given (you
should probably calculate a few of these for practice). In determining the debt-equity ratios,
TABLE 3.13
H O FFM A N C O M PA N Y
Income Statement and Balance Sheet
I N C O M E S TAT E M E N T
Sales
Costs
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings

$500
400
$100
34
$ 66
$22
44

B A LA N C E S H E E T
As s e t s

Current assets
Net fixed assets
Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y
$

P E R C E N TA G E
O F S A LE S

$200
300
$500

40%
60
100%

Total debt
Owners’ equity
Total liabilities and owners’ equity

$

P ER C ENTAGE
OF S ALES

$250
250
$500

n/a
n/a
n/a

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TABLE 3.14
H O FFM A N C O M PA N Y
Pr o F o r ma I n c o m e S t a t e m e n t a n d B a l a n c e S h e e t
I N C O M E S TAT E M E N T
Sales (projected)
Costs (80% of sales)
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings

$600.0
480.0
$120.0
40.8
$ 79.2
$26.4
52.8

B A LA N C E S H E E T
As s e t s

Current assets
Net fixed assets
Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y
$

PE RCE N TA G E
OF SA LE S

$240.0
360.0
$600.0

40%
60
100%

Total debt
Owners’ equity
Total liabilities and owners’ equity
External financing needed

$

P E R C E N TAGE
O F S A LES

$250.0
302.8
$552.8
$ 47.2

n/a
n/a
n/a
n/a

we assumed that any needed funds were borrowed, and we also assumed any surplus funds
were used to pay off debt. Thus, for the zero growth case the debt falls by $44, from $250 to
$206. In Table 3.15, notice that the increase in assets required is simply equal to the original
assets of $500 multiplied by the growth rate. Similarly, the addition to retained earnings is
equal to the original $44 plus $44 times the growth rate.
Table 3.15 shows that for relatively low growth rates, Hoffman will run a surplus, and
its debt-equity ratio will decline. Once the growth rate increases to about 10 percent, however, the surplus becomes a deficit. Furthermore, as the growth rate exceeds approximately
20 percent, the debt-equity ratio passes its original value of 1.0.
Figure 3.1 illustrates the connection between growth in sales and external financing
needed in more detail by plotting asset needs and additions to retained earnings from
Table 3.15 against the growth rates. As shown, the need for new assets grows at a much
faster rate than the addition to retained earnings, so the internal financing provided by the
addition to retained earnings rapidly disappears.
As this discussion shows, whether a firm runs a cash surplus or deficit depends on growth.
Microsoft is a good example. Its revenue growth in the 1990s was amazing, averaging well
TABLE 3.15
Growth and Projected
EFN for the Hoffman
Company

PROJ E CT E D
SAL E S
GROW T H

INCREASE
IN ASSETS
REQUIRED

ADDITION TO
R E TA I N E D
EARNINGS

EXTERNAL
FI N A N C I N G
N E E D E D , E FN

P R O J E C TED
D E B T- E Q UITY
R AT I O

0%
5
10
15

$ 0
25
50
75
100
125

$44.0
46.2
48.4
50.6
52.8
55.0

$44.0
21.2
1.6
24.4
47.2
70.0

.70
.77
.84
.91
.98
1.05

20
25

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Asset needs and retained earnings ($)

FIGURE 3.1
Increase
in assets
required

125

Growth and Related
Financing Needed for the
Hoffman Company

100
EFN ⬎ 0
(deficit)

75
50
44
25

Projected
addition
to retained
earnings

EFN ⬍ 0
(surplus)

5

15
20
10
Projected growth in sales (%)

25

over 30 percent per year for the decade. Growth slowed down noticeably over the 2000–2009
period, but, nonetheless, Microsoft’s combination of growth and substantial profit margins
led to enormous cash surpluses. In part because Microsoft paid few dividends, the cash really
piled up; in 2010, Microsoft’s cash and short-term investment horde exceeded $36 billion.

Financial Policy and Growth
Based on our discussion just preceding, we see that there is a direct link between growth
and external financing. In this section, we discuss two growth rates that are particularly
useful in long-range planning.
The first growth rate of interest is the maximum growth rate
that can be achieved with no external financing of any kind. We will call this the internal
growth rate because this is the rate the firm can maintain with internal financing only. In
Figure 3.1, this internal growth rate is represented by the point where the two lines cross.
At this point, the required increase in assets is exactly equal to the addition to retained earnings, and EFN is therefore zero. We have seen that this happens when the growth rate is
slightly less than 10 percent. With a little algebra (see Problem 28 at the end of the chapter),
we can define this growth rate more precisely as:

The Internal Growth Rate

ROA  b
Internal growth rate  ______________
1  ROA  b

[3.24]

where ROA is the return on assets we discussed earlier, and b is the plowback, or retention,
ratio also defined earlier in this chapter.
For the Hoffman Company, net income was $66 and total assets were $500. ROA is thus
$66/500  13.2 percent. Of the $66 net income, $44 was retained, so the plowback ratio, b,
is $44/66  2/3. With these numbers, we can calculate the internal growth rate as:
ROA  b
Internal growth rate  ______________
1  ROA  b
.132  (2/3)
 _________________
1  .132  (2/3)
 9.65%

Thus, the Hoffman Company can expand at a maximum rate of 9.65 percent per year without external financing.

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The Sustainable Growth Rate We have seen that if the Hoffman Company wishes to grow
more rapidly than at a rate of 9.65 percent per year, external financing must be arranged.
The second growth rate of interest is the maximum growth rate a firm can achieve with no
external equity financing while it maintains a constant debt-equity ratio. This rate is commonly called the sustainable growth rate because it is the maximum rate of growth a firm
can maintain without increasing its financial leverage.
There are various reasons why a firm might wish to avoid equity sales. For example, new
equity sales can be expensive because of the substantial fees that may be involved. Alternatively, the current owners may not wish to bring in new owners or contribute additional
equity. Why a firm might view a particular debt-equity ratio as optimal is discussed in later
chapters; for now, we will take it as given.
Based on Table 3.15, the sustainable growth rate for Hoffman is approximately 20 percent because the debt-equity ratio is near 1.0 at that growth rate. The precise value can be
calculated as follows (see Problem 28 at the end of the chapter):
ROE  b
Sustainable growth rate  ______________
1  ROE  b

[3.25]

This is identical to the internal growth rate except that ROE, return on equity, is used instead of ROA.
For the Hoffman Company, net income was $66 and total equity was $250; ROE is thus
$66/250  26.4 percent. The plowback ratio, b, is still 2/3, so we can calculate the sustainable growth rate as:
ROE  b
Sustainable growth rate  ______________
1  ROE  b
.264  (2/3)
 _________________
1  .264  (2/3)
 21.36%

EXAMPLE

3.5

Thus, the Hoffman Company can expand at a maximum rate of 21.36 percent per year
without external equity financing.

Sustainable Growth
Suppose Hoffman grows at exactly the sustainable growth rate of 21.36 percent. What will the pro
forma statements look like?
At a 21.36 percent growth rate, sales will rise from $500 to $606.8. The pro forma income statement
will look like this:
H O FFM A N C O M PA N Y
P r o Fo r m a I n c o m e S t a t e m e n t
Sales (projected)
Costs (80% of sales)
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings

$606.8
485.4
$121.4
41.3
$ 80.1
$26.7
53.4

(continued )

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We construct the balance sheet just as we did before. Notice, in this case, that owners’ equity will rise
from $250 to $303.4 because the addition to retained earnings is $53.4.
HO FFM A N C O M PA N Y
Pr o F o r m a B a l a n c e S h e e t
As s e t s

Current assets
Net fixed assets
Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y

$

PE RCE NTA G E
OF SALE S

$242.7
364.1
$606.8

40%
60
100%

Total debt
Owners’ equity
Total liabilities and
owners’ equity
External financing
needed

$

P E R C E N TA G E
O F S A LE S

$250.0
303.4
$553.4

n/a
n/a
n/a

$ 53.4

n/a

As illustrated, EFN is $53.4. If Hoffman borrows this amount, then total debt will rise to $303.4, and the
debt-equity ratio will be exactly 1.0, which verifies our earlier calculation. At any other growth rate,
something would have to change.

Determinants of Growth Earlier in this chapter, we saw that the return on equity, ROE,
could be decomposed into its various components using the Du Pont identity. Because
ROE appears so prominently in the determination of the sustainable growth rate, it is obvious that the factors important in determining ROE are also important determinants of
growth.
From our previous discussions, we know that ROE can be written as the product of three
factors:
ROE  Profit margin  Total asset turnover  Equity multiplier

If we examine our expression for the sustainable growth rate, we see that anything that
increases ROE will increase the sustainable growth rate by making the top bigger and the
bottom smaller. Increasing the plowback ratio will have the same effect.
Putting it all together, what we have is that a firm’s ability to sustain growth depends
explicitly on the following four factors:
1. Profit margin: An increase in profit margin will increase the firm’s ability to
generate funds internally and thereby increase its sustainable growth.
2. Dividend policy: A decrease in the percentage of net income paid out as
dividends will increase the retention ratio. This increases internally generated
equity and thus increases sustainable growth.
3. Financial policy: An increase in the debt-equity ratio increases the firm’s
financial leverage. Because this makes additional debt financing available, it
increases the sustainable growth rate.
4. Total asset turnover: An increase in the firm’s total asset turnover increases the
sales generated for each dollar in assets. This decreases the firm’s need for new
assets as sales grow and thereby increases the sustainable growth rate. Notice that
increasing total asset turnover is the same thing as decreasing capital intensity.
The sustainable growth rate is a very useful planning number. What it illustrates is the
explicit relationship between the firm’s four major areas of concern: its operating efficiency

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EXAMPLE

3.6

as measured by profit margin, its asset use efficiency as measured by total asset turnover,
its dividend policy as measured by the retention ratio, and its financial policy as measured
by the debt-equity ratio.

Profit Margins and Sustainable Growth
The Sandar Co. has a debt-equity ratio of .5, a profit margin of 3 percent, a dividend payout ratio of
40 percent, and a capital intensity ratio of 1. What is its sustainable growth rate? If Sandar desired a
10 percent sustainable growth rate and planned to achieve this goal by improving profit margins, what
would you think?
ROE is .03  1  1.5  4.5 percent. The retention ratio is 1 .40  .60. Sustainable growth is
thus .045(.60)/[1  .045(.60)]  2.77 percent.
For the company to achieve a 10 percent growth rate, the profit margin will have to rise. To see
this, assume that sustainable growth is equal to 10 percent and then solve for profit margin, PM:
.10  PM(1.5)(.6)/[1  PM(1.5)(.6)]
PM  .1/.99  10.1%
For the plan to succeed, the necessary increase in profit margin is substantial, from 3 percent to
about 10 percent. This may not be feasible.

Given values for all four of these, there is only one growth rate that can be achieved.
This is an important point, so it bears restating:
If a firm does not wish to sell new equity and its profit margin, dividend policy,
financial policy, and total asset turnover (or capital intensity) are all fixed, then there
is only one possible growth rate.
One of the primary benefits of financial planning is that it ensures internal consistency
among the firm’s various goals. The concept of the sustainable growth rate captures this
element nicely. Also, we now see how a financial planning model can be used to test the
feasibility of a planned growth rate. If sales are to grow at a rate higher than the sustainable
growth rate, the firm must increase profit margins, increase total asset turnover, increase
financial leverage, increase earnings retention, or sell new shares.
The two growth rates, internal and sustainable, are summarized in Table 3.16.

A Note about Sustainable Growth Rate Calculations
Very commonly, the sustainable growth rate is calculated using just the numerator in
our expression, ROE  b. This causes some confusion, which we can clear up here. The
issue has to do with how ROE is computed. Recall that ROE is calculated as net income
divided by total equity. If total equity is taken from an ending balance sheet (as we have
done consistently, and is commonly done in practice), then our formula is the right one.
However, if total equity is from the beginning of the period, then the simpler formula is
the correct one.
In principle, you’ll get exactly the same sustainable growth rate regardless of which
way you calculate it (as long as you match up the ROE calculation with the right formula).
In reality, you may see some differences because of accounting-related complications. By
the way, if you use the average of beginning and ending equity (as some advocate), yet
another formula is needed. Also, all of our comments here apply to the internal growth
rate as well.

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TABLE 3.16

I. Internal Growth Rate

Summary of Internal
and Sustainable
Growth Rates

ROA  b
Internal growth rate  __________
1  ROA  b

where
ROA  Return on assets  Net income/Total assets
b  Plowback (retention) ratio
 Addition to retained earnings/Net income
The internal growth rate is the maximum growth rate that can be achieved with no external financing
of any kind.
II. Sustainable Growth Rate
ROE  b
Sustainable growth rate  _________
1  ROE  b

where
ROE  Return on equity  Net income/Total equity
b  Plowback (retention) ratio
 Addition to retained earnings/Net income
The sustainable growth rate is the maximum growth rate that can be achieved with no external equity
financing while maintaining a constant debt-equity ratio.

3 . 6 S O M E C A V E AT S R E G A R D I N G F I N A N C I A L
PLANNING MODELS
Financial planning models do not always ask the right questions. A primary reason is that they
tend to rely on accounting relationships and not financial relationships. In particular, the three
basic elements of firm value tend to get left out—namely, cash flow size, risk, and timing.
Because of this, financial planning models sometimes do not produce output that gives
the user many meaningful clues about what strategies will lead to increases in value. Instead, they divert the user’s attention to questions concerning the association of, say, the
debt-equity ratio and firm growth.
The financial model we used for the Hoffman Company was simple—in fact, too simple.
Our model, like many in use today, is really an accounting statement generator at heart.
Such models are useful for pointing out inconsistencies and reminding us of financial
needs, but they offer little guidance concerning what to do about these problems.
In closing our discussion, we should add that financial planning is an iterative process.
Plans are created, examined, and modified over and over. The final plan will be a result
negotiated between all the different parties to the process. In fact, long-term financial planning in most corporations relies on what might be called the Procrustes approach.5 Upperlevel management has a goal in mind, and it is up to the planning staff to rework and to
ultimately deliver a feasible plan that meets that goal.
The final plan will therefore implicitly contain different goals in different areas and also
satisfy many constraints. For this reason, such a plan need not be a dispassionate assessment of what we think the future will bring; it may instead be a means of reconciling the
planned activities of different groups and a way of setting common goals for the future.
However it is done, the important thing to remember is that financial planning should
not become a purely mechanical exercise. If it does, it will probably focus on the wrong
things. Nevertheless, the alternative to planning is stumbling into the future. Perhaps the
immortal Yogi Berra (the baseball catcher, not the cartoon character), said it best: “Ya
gotta watch out if you don’t know where you’re goin’. You just might not get there.”6
5
In Greek mythology, Procrustes is a giant who seizes travelers and ties them to an iron bed. He stretches them or cuts off their
legs as needed to make them fit the bed.
6

We’re not exactly sure what this means, either, but we like the sound of it.

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www.mhhe.com/rwj
SUMMARY AND CONCLUSIONS
This chapter focuses on working with information contained in financial statements. Specifically, we
studied standardized financial statements, ratio analysis, and long-term financial planning.
1. We explained that differences in firm size make it difficult to compare financial statements, and
we discussed how to form common-size statements to make comparisons easier and more
meaningful.
2. Evaluating ratios of accounting numbers is another way of comparing financial statement information. We defined a number of the most commonly used ratios, and we discussed the famous
Du Pont identity.
3. We showed how pro forma financial statements can be generated and used to plan for future
financing needs.
After you have studied this chapter, we hope that you have some perspective on the uses and abuses
of financial statement information. You should also find that your vocabulary of business and financial
terms has grown substantially.

CONCEPT QUESTIONS
1. Financial Ratio Analysis A financial ratio by itself tells us little about a company since financial
ratios vary a great deal across industries. There are two basic methods for analyzing financial
ratios for a company: time trend analysis and peer group analysis. Why might each of these
analysis methods be useful? What does each tell you about the company’s financial health?
2. Industry-Specific Ratios So-called “same-store sales” are a very important measure for
companies as diverse as McDonald’s and Sears. As the name suggests, examining same-store
sales means comparing revenues from the same stores or restaurants at two different points in
time. Why might companies focus on same-store sales rather than total sales?
3. Sales Forecast Why do you think most long-term financial planning begins with sales forecasts? Put differently, why are future sales the key input?
4. Sustainable Growth In the chapter, we used Rosengarten Corporation to demonstrate how
to calculate EFN. The ROE for Rosengarten is about 7.3 percent, and the plowback ratio is about
67 percent. If you calculate the sustainable growth rate for Rosengarten, you will find it is only
5.14 percent. In our calculation for EFN, we used a growth rate of 25 percent. Is this possible?
(Hint: Yes. How?)
5. EFN and Growth Rate Broslofski Co. maintains a positive retention ratio and keeps its debtequity ratio constant every year. When sales grow by 20 percent, the firm has a negative
projected EFN. What does this tell you about the firm’s sustainable growth rate? Do you know,
with certainty, if the internal growth rate is greater than or less than 20 percent? Why? What
happens to the projected EFN if the retention ratio is increased? What if the retention ratio is
decreased? What if the retention ratio is zero?
6. Common-Size Financials One tool of financial analysis is common-size financial statements.
Why do you think common-size income statements and balance sheets are used? Note that the
accounting statement of cash flows is not converted into a common-size statement. Why do you
think this is?
7. Asset Utilization and EFN One of the implicit assumptions we made in calculating the external
funds needed was that the company was operating at full capacity. If the company is operating
at less than full capacity, how will this affect the external funds needed?

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Use the following information to answer the next five questions: A small business called The
Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit,
and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company leased more space and expanded capacity, but it still could not keep up with demand. Equipment failed from overuse and quality suffered. Working capital was drained to expand production,
and, at the same time, payments from customers were often delayed until the product was shipped.
Unable to deliver on orders, the company became so strapped tor cash that employee paychecks
began to bounce Finally, out of cash, the company ceased operations entirely three years later.
8. Product Sales Do you think the company would have suffered the same fate if its product had
been less popular? Why or why not?
9. Cash Flow The Grandmother Calendar Company clearly had a cash flow problem. In the context of the cash flow analysis we developed in Chapter 2, what was the impact of customers’ not
paying until orders were shipped?
10. Corporate Borrowing If the firm was so successful at selling, why wouldn’t a bank or some
other lender step in and provide it with the cash it needed to continue?
11. Cash Flow Which is the biggest culprit here: too many orders, too little cash, or too little
production capacity?
12. Cash Flow What are some of the actions that a small company like The Grandmother Calendar
Company can take (besides expansion of capacity) if it finds itself in a situation in which growth
in sales outstrips production?
13. Comparing ROE and ROA Both ROA and ROE measure profitability. Which one is more useful
for comparing two companies? Why?
14. Ratio Analysis Consider the ratio EBITDA/Assets. What does this ratio tell us? Why might it be
more useful than ROA in comparing two companies?

QUESTIONS AND PROBLEMS
1. Du Pont Identity If Alexander, Inc., has an equity multiplier of 2.50, total asset turnover of 1.15,
and a profit margin of 6.4 percent, what is its ROE?
2. Equity Multiplier and Return on Equity Draiman Company has a debt-equity ratio of 0.75.
Return on assets is 10.4 percent, and total equity is $900,000. What is the equity multiplier?
Return on equity? Net income?

Basic
(Questions 1–10)

3. Using the Du Pont Identity Y3K, Inc., has sales of $4,350, total assets of $3,218, and a debtequity ratio of 0.65. If its return on equity is 15 percent, what is its net income?
4. EFN

The most recent financial statements for Cornell, Inc., are shown here:
I NCOM E STAT E M E NT

Sales
Costs
Taxable income
Taxes (34%)
Net income

$34,000
25,800
$ 8,200
2,788
$ 5,412

B A LA N C E S H E E T
Assets

$100,300

Total

$100,300

Debt
Equity
Total

$ 26,500
73,800
$100,300

Assets and costs are proportional to sales. Debt and equity are not. A dividend of $1,623.60
was paid, and the company wishes to maintain a constant payout ratio. Next year’s sales are
projected to be $38,420. What is the external financing needed?

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5. Sales and Growth The most recent financial statements for Weyland Co. are shown here:
I NCOM E STAT E M E N T
Sales
Costs
Taxable income
Taxes (34%)
Net income

$59,000
36,400
$22,600
7,684
$14,916

B A LA N C E S H E E T
Current assets
Fixed assets
Total

$ 17,000
139,000
$156,000

Long-term debt
Equity
Total

$ 51,000
105,000
$156,000

Assets and costs are proportional to sales. The company maintains a constant 30 percent
dividend payout ratio and a constant debt-equity ratio. What is the maximum increase in sales
that can be sustained assuming no new equity is issued?
6. Sustainable Growth If the SGS Corp. has a 13 percent ROE and a 25 percent payout ratio, what
is its sustainable growth rate?
7. Sustainable Growth Assuming the following ratios are constant, what is the sustainable
growth rate?
 2.50
 6.5%
 1.10
 60%

Total asset turnover
Profit margin
Equity multiplier
Payout ratio

8. Calculating EFN The most recent financial statements for Incredible Edibles, Inc., are shown
here (assuming no income taxes):
I NCOM E STAT E M E N T
Sales
Costs
Net income

$8,400
6,190
$2,210

B A LA N C E S H E E T
Assets

$21,500

Total

$21,500

Debt
Equity
Total

$ 4,200
17,300
$21,500

Assets and costs are proportional to sales. Debt and equity are not. No dividends are paid. Next
year’s sales are projected to be $9,660. What is the external financing needed?
9. External Funds Needed Cheryl Colby, CFO of Charming Florist Ltd., has created the firm’s
pro forma balance sheet for the next fiscal year. Sales are projected to grow by 15 percent to
$317.4 million. Current assets, fixed assets, and short-term debt are 20 percent, 90 percent,
and 15 percent of sales, respectively. Charming Florist pays out 40 percent of its net income in
dividends. The company currently has $40 million of long-term debt, and $20 million in common
stock par value. The profit margin is 10 percent.
a. Construct the current balance sheet for the firm using the projected sales figure.
b. Based on Ms. Colby’s sales growth forecast, how much does Charming Florist need in external funds for the upcoming fiscal year?
c. Construct the firm’s pro forma balance sheet for the next fiscal year and confirm the external
funds needed that you calculated in part (b).
10. Sustainable Growth Rate The Steiben Company has an ROE of 8.45 percent and a payout ratio
of 30 percent.
a. What is the company’s sustainable growth rate?

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b. Can the company’s actual growth rate be different from its sustainable growth rate? Why or
why not?
c. How can the company increase its sustainable growth rate?
11. Return on Equity Firm A and Firm B have debt / total asset ratios of 35 percent and 30 percent
and returns on total assets of 10 percent and 12 percent, respectively. Which firm has a greater
return on equity?

Intermediate
(Questions 11–23)

12. Ratios and Foreign Companies Prince Albert Canning PLC had a net loss of £18,351 on sales
of £163,184. What was the company’s profit margin? Does the fact that these figures are quoted
in a foreign currency make any difference? Why? In dollars, sales were $261,070. What was the
net loss in dollars?
13. External Funds Needed The Optical Scam Company has forecast an 18 percent sales growth
rate for next year. The current financial statements are shown below. Current assets, fixed
assets, and short-term debt are proportional to sales.

I N C O M E S TAT E M E N T
Sales
Costs
Taxable income
Taxes
Net income
Dividends
Additions to retained earnings

$37,000,000
28,900,000
$ 8,100,000
2,835,000
$ 5,265,000
$1,579,500
$3,685,500

B A LA N C E S H E E T
As s e t s
Current assets
Fixed assets

Total assets

Li a b i l i t i e s a n d E q u i t y
$10,500,000

Short-term debt
Long-term debt

$ 6,500,000
7,000,000

Common stock
Accumulated retained earnings
Total equity
Total liabilities and equity

$ 3,000,000
24,000,000
$27,000,000
$40,500,000

30,000,000

$40,500,000

a. Using the equation from the chapter, calculate the external funds needed for next year.
b. Construct the firm’s pro forma balance sheet for next year and confirm the external funds
needed you calculated in part (a).
c. Calculate the sustainable growth rate for the company.
d. Can Optical Scam eliminate the need for external funds by changing its dividend policy?
What other options are available to the company to meet its growth objectives?
14. Days’ Sales in Receivables A company has net income of $187,000, a profit margin of
6.5 percent, and an accounts receivable balance of $145,900. Assuming 80 percent of sales are
on credit, what is the company’s days’ sales in receivables?

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15. Ratios and Fixed Assets The Burk Company has a ratio of long-term debt to long-term debt
plus equity of 0.40 and a current ratio of 1.25. Current liabilities are $1,075, sales are $6,180,
profit margin is 8.5 percent, and ROE is 16.25 percent. What is the amount of the firm’s net
fixed assets?
16. Calculating the Cash Coverage Ratio FVA Inc.’s net income for the most recent year was
$17,590. The tax rate was 34 percent. The firm paid $4,150 in total interest expense and deducted
$5,820 in depreciation expense. What was FVA’s cash coverage ratio for the year?
17. Cost of Goods Sold Sexton Corp. has current liabilities of $325,000, a quick ratio of 0.85,
inventory turnover of 9.5, and a current ratio of 1.25. What is the cost of goods sold for the
company?
18. Common-Size and Common-Base Year Financial Statements In addition to common-size
financial statements, common-base year financial statements are often used. Common-base
year financial statements are constructed by dividing the current year account value by the
base year account value. Thus, the result shows the growth rate in the account. Using the
financial statements below, construct the common-size balance sheet and common-base year
balance sheet for the company. Use 2009 as the base year.

J A R R O W C O R P O R AT I O N
2009 a n d 2010 B a l a n c e S h e e t s
ASSETS

Current assets
Cash
Accounts receivable
Inventory
Total

Fixed assets
Net plant and
equipment

LI A B I LI T I E S A N D O WN E R S ’ E Q U I TY
2009

2010

$ 13,582
21,640
36,823
$ 72,045

$ 15,675
22,340
39,703
$ 77,718

$274,583

$290,586

Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and
paid-in surplus
Accumulated retained
earnings
Total

Total assets

$346,628

$368,304

Total liabilities and
owners’ equity

2009

2010

$ 19,085
24,530
$ 43,615
$ 35,000

$ 20,640
25,305
$ 45,945
$ 50,000

$ 45,000

$ 45,000

223,013

227,359

$268,013

$272,359

$346,628

$368,304

19. Full-Capacity Sales Pumpkin Mfg., Inc., is currently operating at only 92 percent of fixed asset
capacity. Current sales are $725,000. How fast can sales grow before any new fixed assets are
needed?
20. Fixed Assets and Capacity Usage For the company in the previous problem, suppose fixed assets are $645,000 and sales are projected to grow to $850,000. How much in new fixed assets is
required to support this growth in sales? Assume the company operates at full capacity.
21. Calculating EFN The most recent financial statements for Retro Machine, Inc., follow. Sales
for 2010 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate
and the dividend payout rate will also remain constant. Costs, other expenses, current assets,

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fixed assets, and accounts payable increase spontaneously with sales. If the firm is operating
at full capacity and no new debt or equity are issued, what is the external financing needed to
support the 20 percent growth rate in sales?

RETRO MACHINE INC
2 0 09 I n c o m e S t a t e m e n t
Sales
Costs
Other expenses
Earnings before interest and taxes
Interest paid
Taxable income
Taxes (35%)
Net income
Dividends
Addition to retained earnings

$929,000
723,000
19,000
$187,000
14,000
$173,000
60,550
$112,450
$ 33,735
78,715

RETRO MACHINE, INC
Ba l a n c e S h e e t a s o f D e c e m b e r 31, 2009
ASSE T S
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and
equipment
Total assets

LI A B I LI T I E S A N D O WN E R S ’ E Q U I T Y

$ 25,300
40,700
86,900
$152,900
$413,000

$565,900

Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Accumulated retained earnings
Total
Total liabilities and owners’ equity

$ 68,000
17,000
$ 85,000
$158,000
$140,000
182,900
$322,900
$565,900

22. Capacity Usage and Growth In the previous problem, suppose the firm was operating at only
80 percent capacity in 2009. What is EFN now?
23. Calculating EFN In Problem 21, suppose the firm wishes to keep its debt-equity ratio constant.
What is EFN now?
24. EFN and Internal Growth Redo Problem 21 using sales growth rates of 15 and 25 percent in
addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate,
and use this graph to determine the relationship between them.

Challenge
(Questions 24–30)

25. EFN and Sustainable Growth Redo Problem 23 using sales growth rates of 30 and 35 percent
in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth
rate, and use this graph to determine the relationship between them.
26. Constraints on Growth Dahlia, Inc., wishes to maintain a growth rate of 9 percent per year
and a debt-equity ratio of 0.55. Profit margin is 6.2 percent, and the ratio of total assets to sales
is constant at 1.90. Is this growth rate possible? To answer, determine what the dividend payout
ratio must be. How do you interpret the result?

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27. EFN Define the following:
S  Previous year’s sales
A  Total assets
D  Total debt
E  Total equity
g  Projected growth in sales
PM  Profit margin
b  Retention (plowback) ratio
Show that EFN can be written as:
EFN  PM(S)b  [A  PM(S)b]  g
Hint: Asset needs will equal A  g. The addition to retained earnings will equal PM(S)b  (1  g).
28. Sustainable Growth Rate Based on the results in Problem 27, show that the internal and sustainable growth rates can be calculated as shown in equations 3.24 and 3.25. Hint: For the internal growth rate, set EFN equal to zero and solve for g.
29. Sustainable Growth Rate In the chapter, we discussed one calculation of the sustainable
growth rate as:
ROE  b
Sustainable growth rate  ___________
1  ROE  b
In practice, probably the most commonly used calculation of the sustainable growth rate is
ROE  b. This equation is identical to the two sustainable growth rate equations presented in
the chapter if the ROE is calculated using the beginning of period equity. Derive this equation
from the equation presented in the chapter.
30. Sustainable Growth Rate Use the sustainable growth rate equations from the previous problem to answer the following questions. No Return, Inc., had total assets of $380,000 and equity
of $230,000 at the beginning of the year. At the end of the year, the company had total assets
of $430,000. During the year the company sold no new equity. Net income for the year was
$95,000 and dividends were $43,000. What is the approximate sustainable growth rate for the
company? What is the exact sustainable growth rate? What is the approximate sustainable
growth rate if you calculate ROE based on the beginning of period equity? Is this number too
high or too low? Why?

W H AT ’ S O N T H E W E B ?
1. Du Pont Identity You can find financial statements for Walt Disney Company at Disney’s home
page, disney.go.com. For the three most recent years, calculate the Du Pont identity for Disney.
How has ROE changed over this period? How have changes in each component of the Du Pont
identity affected ROE over this period?
2. Ratio Analysis You want to examine the financial ratios for Dell Computer Corporation. Go to
www.reuters.com and type in the ticker symbol for the company (DELL). Now find financial ratios for Dell and the industry, sector, and S&P 500 averages for each ratio.
a. What do TTM and MRQ mean?
b. How do Dell’s recent profitability ratios compare to their values over the past five years? To
the industry averages? To the sector averages? To the S&P 500 averages? Which is the better comparison group for Dell: the industry, sector, or S&P 500 averages? Why?

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c. In what areas does Dell seem to outperform its competitors based on the financial ratios?
Where does Dell seem to lag behind its competitors?
d. Dell’s inventory turnover ratio is much larger than that for all comparison groups. Why do
you think this is?
3. Applying Percentage of Sales Locate the most recent annual financial statements for Du
Pont at www.dupont.com under the “Investor Center” link. Locate the annual report. Using the
growth in sales for the most recent year as the projected sales growth for next year, construct
a pro forma income statement and balance sheet. Based on these projections, what are the
external funds needed?
4. Growth Rates You can find the home page for Caterpillar, Inc., at www.cat.com. Go to the
Web page and find the most recent annual report. Using the information from the financial
statements, what is the sustainable growth rate?

After Dan’s analysis of East Coast Yachts’ cash flow (at the end of our previous chapter), Larissa
approached Dan about the company’s performance and future growth plans. First, Larissa wants
to find out how East Coast Yachts is performing relative to its peers. Additionally, she wants to find
out the future financing necessary to fund the company’s growth. In the past, East Coast Yachts
experienced difficulty in financing its growth plan, in large part because of poor planning. In fact,
the company had to turn down several large jobs because its facilities were unable to handle the
additional demand. Larissa hoped that Dan would be able to estimate the amount of capital the
company would have to raise next year so that East Coast Yachts would be better prepared to fund
its expansion plans.
To get Dan started with his analyses, Larissa provided the following financial statements. Dan then
gathered the industry ratios for the yacht manufacturing industry.

CLOSING CASE

R AT I O S A N D F I N A N C I A L P L A N N I N G
AT E A S T C O A S T YA C H T S

E A S T C O A S T YA C H T S
2010 Income Statement
Sales
Cost of goods sold
Selling, general, and administrative
Depreciation
EBIT
Interest expense
EBT
Taxes
Net income
Dividends
Retained earnings

$617,760,000
435,360,000
73,824,000
20,160,000
$ 88,416,000
11,112,000
$ 77,304,000
30,921,600
$ 46,382,400
$ 17,550,960
$ 28,831,440

(continued )

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E A S T C O A S T YA C H T S
2010 B a l a n c e S h e e t
Current assets
Cash and equivalents
Accounts receivable
Inventories
Other
Total current assets
Fixed assets
Property, plant, and equipment
Less accumulated depreciation
Net property, plant, and equipment
Intangible assets and others
Total fixed assets

Total assets

$ 11,232,000
20,208,000
22,656,000
1,184,000
$ 55,280,000

Current liabilities
Accounts payable
Notes payable
Accrued expenses
Total current liabilities

$ 24,546,000
18,725,000
6,185,000
$ 49,456,000

Long-term debt
$462,030,000
Total long-term liabilities
(114,996,000)
$347,034,000
6,840,000 Stockholders’ equity
$353,874,000
Preferred stock
Common stock
Capital surplus
Accumulated retained earnings
Less treasury stock
Total equity
$409,154,000 Total liabilities and shareholders’ equity

$146,560,000
$146,560,000

$ 3,000,000
40,800,000
31,200,000
186,138,000
(48,000,000)
$213,138,000
$409,154,000

Ya c h t I n d u st r y R a t i o s

Current ratio
Quick ratio
Total asset turnover
Inventory turnover
Receivables turnover
Debt ratio
Debt-equity ratio
Equity multiplier
Interest coverage
Profit margin
Return on assets
Return on equity

LOWER QUARTILE

MEDIAN

U P P E R Q U A R T I LE

0.86
0.43
1.10
12.18
10.25
0.32
0.51
1.51
5.72
5.02%
7.05%
9.06%

1.51
0.75
1.27
14.38
17.65
0.49
0.83
1.83
8.21
7.48%
10.67%
14.32%

1.97
1.01
1.46
16.43
22.43
0.61
1.03
2.03
10.83
9.05%
14.16%
22.41%

1. East Coast Yachts uses a small percentage of preferred stock as a source of financing. In calculating the ratios for the company, should preferred stock be included as part of the company’s
total equity?
2. Calculate all of the ratios listed in the industry table for East Coast Yachts.
3. Compare the performance of East Coast Yachts to the industry as a whole. For each ratio, comment on why it might be viewed as positive or negative relative to the industry. Suppose you
create an inventory ratio calculated as inventory divided by current liabilities. How would you
interpret this ratio? How does East Coast Yachts compare to the industry average for this ratio?
4. Calculate the sustainable growth rate for East Coast Yachts. Calculate external funds needed
(EFN) and prepare pro forma income statements and balance sheets assuming growth at
precisely this rate. Recalculate the ratios in the previous question. What do you observe?

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5. As a practical matter, East Coast Yachts is unlikely to be willing to raise external equity capital,
in part because the shareholders don’t want to dilute their existing ownership and control positions. However, East Coast Yachts is planning for a growth rate of 20 percent next year. What are
your conclusions and recommendations about the feasibility of East Coast’s expansion plans?
6. Most assets can be increased as a percentage of sales. For instance, cash can be increased
by any amount. However, fixed assets often must be increased in specific amounts since it is
impossible, as a practical matter, to buy part of a new plant or machine. In this case, a company
has a “staircase” or “lumpy” fixed cost structure. Assume that East Coast Yachts is currently
producing at 100 percent of capacity and sales are expected to grow at 20 percent. As a result,
to expand production, the company must set up an entirely new line at a cost of $95,000,000.
Prepare the pro forma income statement and balance sheet. What is the new EFN with these
assumptions? What does this imply about capacity utilization for East Coast Yachts next year?

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CHAPTER

4

Discounted Cash Flow
Valuation

PART TWO Valuation and Capital Budgeting

OPENING CASE

W

hat do Chris Iannetta, John Lackey, and Matt Holliday have in common? All
three are star athletes who signed big-money contracts during late 2009 or
early 2010. Their contract values were reported as $8.35 million, $82.5 million, and $120 million, respectively. But reported numbers can be misleading.
For example, catcher Chris Ianetta re-signed with the Colorado Rockies. His

deal called for salaries of $1.75 million, $2.55 million, and $3.55 million over the next three years,
respectively, with a contract buyout of $500,000 or a salary of $5,000,000 in four years. Not bad,
especially for someone who makes a living using the “tools of ignorance” (jock jargon for a catcher’s
equipment).
A closer look at the numbers shows that Chris, John, and Matt did pretty well, but nothing like the
quoted figures. Using Matt’s contract as an example, the value was reported to be $120 million, but it
was actually payable over several years. The terms called for a salary of $17 million per year for seven
years, then a club option for $17 million in 2017 or a club buyout of $1 million. However, of the $17 million annual salary, $2 million each year was to be deferred and paid annually from 2020 to 2029. Since
the payments are spread out over time, we must consider the time value of money, which means his
contract was worth less than reported. How much did he really get? This chapter gives you the “tools
of knowledge” to answer this question.

4.1

V A L U AT I O N : T H E O N E - P E R I O D C A S E

Keith Vaughan 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. Vaughan choose?

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Alternative
sale prices

Year

$10,000

$11,424

0

1

FIGURE 4.1
Cash Flow for
Mr. Vaughan’s Sale

Mike Tuttle, Keith’s financial adviser, 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
Interest
principal

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 at 12 percent is $11,200.
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 at 12 percent so that he will have $11,424 next year? We can write this
algebraically as
PV  1.12  $11,424

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
$11,424
PV  _________  $10,200
1.12

The formula for PV can be written as
Present Value of Investment:
C1
PV  ______
1r

[4.1]

where C1 is cash flow at date 1 and r is the rate of return that Keith Vaughan 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. Vaughan
is indifferent between $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. Vaughan 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.

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4.1
EXAMPLE

Present Value
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’s
choice is described in Figure 4.2 with the cash flow time chart.

FIGURE 4.2
Cash Flows for Land Investment

Cash inflow

$91,000

Time

0

1

$85,000

Cash outflow

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  .10)  $85,000  $93,500
next year.
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
$91,000
Present value  ______  $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:
$2,273



$85,000



Cost of land
today

$91,000
_________
1.10
Present value of
next year’s sales price

The formula for NPV can be written as
NPV



Cost



PV

[4.2]

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.

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EXAMPLE

4.2

Both the Vaughan and the Jennings examples deal with perfect certainty. That is, Keith
Vaughan 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.

Uncertainty and Valuation
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.

FIGURE 4.3
Cash Flows for Investment in Painting

Expected cash inflow

$480,000

Time
Cash outflow

0

1

$400,000

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?
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.
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.

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Because the choice of a discount rate is so difficult, we merely wanted to broach the
subject here. We must wait until the specific material on risk and return is covered in later
chapters before a risk-adjusted analysis can be presented.

4.2

T H E M U LT I P E R I O D C A S E

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
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 financial market, or she can leave it in and lend
it again for a second year. The process of leaving the money in the financial 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  r 2
$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 r 2, 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, r 2, is referred to as the interest on interest. In our example this
latter amount is exactly
r 2  ($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 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

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FIGURE 4.4

$1.295
$1.270

Simple and Compound
Interest

$1.188
$1.180

$1.09

$1

1 year

2 years

3 years

The red-shaded area represents the initial investment. The
green-shaded area represents the simple interest. The blueshaded area represents interest on interest.

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

[4.3]

EXAMPLE

4.3

where C0 is the cash to be invested at date 0 (i.e., today), r is the interest rate per period, and
T is the number of periods over which the cash is invested.

Interest on Interest
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
0

1

2
Time

3

0
$500

1

2

3

Time

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4.4
EXAMPLE

Compound Growth
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

$2.88

Dollars

$2.88
Cash inflows
$2.00

$2.40
$2.00

0

1
Time

2

0

$2.40

1
Time

2

The two previous examples can be calculated in any one of four ways. The computations could be done by hand, by calculator, by spreadsheet, or with the help of a table.
The appropriate table is Table A.3, which appears in the back of the text. This table
presents future value of $1 at the end of T periods. The table is used by locating the
appropriate interest rate on the horizontal axis and the appropriate number of periods
on the vertical axis.
For example, Suh-Pyng Ku would look at the following portion of Table A.3:

I N T E R E S T R AT E
PERIOD
1
2
3
4

6%

7%

8%

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

 $612.50
$500
1.2250
Initial investment
Future value 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.

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4.5

Finding the Rate

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 Flows for Purchase of Carl Voigt’s Car

Cash inflow

$10,000
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/$10,000  1.6105, we have
(1  r)5  1.6105
Either the table or a hand calculator solves for r.

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. In fact, compound interest has been described as the “eighth wonder of the world” and “the most powerful force in the universe.”1 Take the stock market, for
example. Ibbotson and Sinquefield have calculated what the stock market returned as a whole
from 1926 through 2009.2 They find that one dollar placed in these stocks at the beginning of
1926 would have been worth $2,591.82 at the end of 2009. This is 9.81 percent compounded
annually for 84 years, i.e., ($1.0981)84  $2,591.82, ignoring a small rounding error.
The example illustrates the great difference between compound and simple interest. At
9.81 percent, simple interest on $1 is 9.81 cents a year (i.e., $.0981). Simple interest over
84 years is $8.24 (84  $.0981). That is, an individual withdrawing .0981 cents every year
would have withdrawn $8.24 (84  $.0981) over 84 years. This is quite a bit below the
$2,591.82 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 168 years would
be twice the value of $1 at the end of 84 years, if the yearly rate of return stayed the same.
1
These quotes are often attributed to Albert Einstein (particularly the second one), but whether he really said either is not known.
The first quote is also often attributed to Baron Rothschild, John Maynard Keynes, Benjamin Franklin, and others.
2

Stocks, Bonds, Bills and Inflation [SBBI]. 2010 Yearbook, Ibbotson Associates, Chicago, 2010.

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EXAMPLE

4.6

Actually the value of $1 at the end of 168 years would be the square of the value of $1 at
the end of 84 years. That is, if the annual rate of return remained the same, a $1 investment
in common stocks should be worth $6,717,530.91 [$1  (2,591.82  2,591.82)].
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 vastly 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.
How Much for That Island?
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 from native Americans for 60 guilders’ worth of trinkets. 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, about 384 years later,
be worth about $3.3 billion. Today, Manhattan is undoubtedly worth more than $2.5 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  24  1.1384  $188 quadrillion
This is a lot of money. In fact, $188 quadrillion is more than all the real estate in the world is worth
today. Note that no one in the history of the world has ever been able to find an investment yielding
10 percent every year for 384 years.

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
$1
PV  ________  $.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.

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FIGURE 4.8

$2,500.00

Compounding and
Discounting

Dollars

$2,000.00
$1,500.00

Compound
Simple
PV

$1,000.00
$500.00
$0.00

0

1

2

3

4 5 6 7
Future years

8

9 10

The top line shows the growth of $1,000 at compound interest with the funds
invested at 9%: $1,000  (1.09)10  $2,367.36. Simple interest is shown on the
next line. It is $1,000  [10  ($1,000  .09)]  $1,900. The bottom line shows the
discounted value of $1,000 if the interest rate is 9%.

To be certain that $.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 $.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 $.84 today. Checking the exact
numbers, we get
$.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 $.84 today or $1 in two years. We have no reason to treat
these two choices differently from each other, because if we had $.84 today and loaned
it out for two years, it would return $1 to us at the end of that time. The value [1/(1.09)2]
is called the present value factor. It is the factor used to calculate the present value of a
future cash flow.
In the multiperiod case, the formula for PV can be written as
Present Value of Investment:
CT
PV  ________
(1  r )T

[4.4]

EXAMPLE

4.7

where CT is cash flow at date T and r is the appropriate discount rate.
Multiperiod Discounting
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?
1 3
PV  $10,000  ____
1.08
 $10,000  .7938
 $7,938

( )

(continued )

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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

Cash inflows

$7,938

0
0

1

2

3

$10,000
1

2
Time

3

Time

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:
I N T E R E S T R AT E
PE R I O D

7%

8%

9%

1
2
3
4

.9346
.8734
.8163
.7629

.9259
.8573
.7938
.7350

.9174
.8417
.7722
.7084

The appropriate present value factor is .7938.

EXAMPLE

4.8

In the preceding example, we gave both the interest rate and the future cash flow. Alternatively, the interest rate could have been unknown.

94

Finding the Rate
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?

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FIGURE 4.10
Cash Flows for Tugboat

Cash inflows

$50,000

Time 0

3

$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 $.7722. Table A.1 tells us that 9 percent is that interest rate.

EXAMPLE

4.9

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 examples.

Cash Flow Valuation
Dennis Draper has won the Kentucky state lottery and will receive the following set of cash flows over
the next two years:
YE A R

C A S H FLO W

1
2

$2,000
$5,000

Mr. Draper can currently earn 6 percent in his money market account, and so, the appropriate discount rate is 6 percent. The present value of the cash flows is

YE AR
1
2

CASH F L OW  PR E S E N T VA LU E FA C T O R  P R E S E N T VA LU E
1
$2,000  _
 $2,000  .943
1.06
1 2  $5,000  .890
$5,000  _
1.06
Total

( )



$1,887



$4,450
$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.

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4.10
EXAMPLE

NPV
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.
C A S H FLO WS
Year 0

$50,000

1

$25,000

2
3

P R E S E N T VA LU E FA C T O R

$20,000
$15,000

1
1
_
1.07
1
_
1.07
1
_
1.07



1



.9346

2



.8734

3



.8163

( )
( )

The present values of the cash flows are:
Cash flows  Present value factor  Present value
Year 0
1
2
3

$50,000  1
$25,000  .9346
$20,000  .8734
$15,000  .8163





Total

$50,000
$23,364.5
$17,468.8
$12,244.5
$ 3,077.8

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 $3,077.8.

The Algebraic Formula
To derive an algebraic formula for the net present value of a cash flow, recall that the PV of
receiving a cash flow one year from now is
PV  C1/(1  r)

and the PV of receiving a cash flow two years from now is
PV  C2/(1  r )2

We can write the NPV of a T-period project as
T
C1
C2
CT
Ci
NPV  C0  __
 __
     __
 C0  __
i
1r
(1  r )2
(1  r )T
i1 (1  r )

[4.5]

The initial flow, C0, is assumed to be negative because it represents an investment. The 
is shorthand for the sum of the series.
We will close out this section by answering the question we posed at the beginning of
the chapter concerning baseball player Matt Holliday’s contract. Recall that the contract
called for a salary of $17 million in each year over the next seven years, with $2 million in
deferred salary. We will also assume that the option for 2017 is not picked up so he only
receives $1 million in that year. The deferred salary payments from 2020 to 2029 could

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actually be either $2 million or $3.2 million, depending on certain factors. In this case, we
will assume that the deferred payments are $3.2 million per year. If 12 percent is the appropriate discount rate, what kind of deal did the Cardinal’s outfielder catch?
To answer, we can calculate the present value by discounting each year’s salary back
to the present as follows (notice we assumed the future salaries will be paid at the end of
the year):
Year
Year
Year
Year

1:
2:
3:
4:

$15,000,000
$15,000,000
$15,000,000
$15,000,000
.






1/1.121
1/1.122
1/1.123
1/1.124
.

.

.

.

.

$ 3,200,000  1/1.12

Year 20:






$ 13,392,857.14
$ 11,957,908.16
$10,676,703.72
$ 9,532,771.18
.
.
.

20



$

331,733.65

If you fill in the missing rows and then add (do it for practice), you will see that Matt’s
contract had a present value of about $74.68 million, which is only about 60 percent of the
$120 million value reported, but still pretty good.
As you have probably noticed, doing extensive present value calculations can get to
be pretty tedious, so a nearby Spreadsheet Techniques box shows how we recommend
doing them. As an application, we take a look at lottery payouts in a The Real World box
on page 100.

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 as

(

.10
$1,000 1  ____
2

)

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

(

.10
$1,000 1  ____
4

)

4

 $1,103.81

More generally, compounding an investment m times a year provides end-of-year
wealth of
r
C0 1  ___
m

(

m

)

[4.6]

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.

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How to Calculate Present Values with
Multiple Future Cash Flows Using a
Spreadsheet

SPREADSHEET TECHNIQUES

We can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows.
Notice that we have simply calculated the present values one at a time and added them up:
A

B

C

D

E

1

Using a spreadsheet to value multiple future cash flows

2
3
4
5
6
7
8
9

What is the present value of $200 in one year, $400 the next year, $600 the next year, and
$800 the last year if the discount rate is 12 percent?
Rate:

0.12

Year

Cash flows

1
2
3
4

10
11
12
13
14
15
16
17
18
19
20
21
22

$200
$400
$600
$800
Total PV:

Present values
$178.57
$318.88
$427.07
$508.41
$1,432.93

Formula used
=PV($B$7,A10,0,⫺B10)
=PV($B$7,A11,0,⫺B11)
=PV($B$7,A12,0,⫺B12)
=PV($B$7,A13,0,⫺B13)
=SUM(C10:C13)

Notice the negative signs inserted in the PV formulas. These just make the present values have
positive signs. Also, the discount rate in cell B7 is entered as $B$7 (an "absolute" reference)
because it is used over and over. We could have just entered ".12" instead, but our approach is more
flexible.

EXAMPLE

4.11

Banks and other financial institutions may use other names for the stated annual interest
rate. Annual percentage rate (APR) is perhaps the most common synonym.3

EARs
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 (4.6), her wealth is
.24
$1 1  ___
12

(

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 rate (EAR) or the effective annual yield (EAY). Due to compounding, the effective annual
(continued)

3
By law, lenders are required to report the APR on all loans. In this text, we compute the APR as the interest rate per period multiplied by the number of periods in a year. According to federal law, the APR is a measure of the cost of consumer credit expressed
as a yearly rate and it includes interest and certain noninterest charges and fees. In practice, the APR can be much higher than
the interest rate on the loan if the lender charges substantial fees that must be included in the federally mandated APR calculation.

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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 Rate:

( 1  __mr )

m

1

[4.7]

EXAMPLE

4.12

Students are often bothered by the subtraction of 1 in (4.7). 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 1 in (4.7).

Compounding Frequencies
If the stated annual rate of interest, 8 percent, is compounded quarterly, what is the effective annual
rate?
Using (4.7), we have

( 1  __mr )

m

4

.08  1  .0824  8.24%
 1  1  ___
4

(

)

Referring back to our earlier example where C0  $1,000 and r  10%, we can generate the following table:

C0

COM POUNDI N G
F RE QUE NCY ( m )

C1

$1,000
1,000
1,000
1,000

Yearly (m  1)
Semiannually (m  2)
Quarterly (m  4)
Daily (m  365)

$1,100.00
1,102.50
1,103.81
1,105.16

E FFE C T I V E A N N U A L
R AT E 
r m
1  _
m  1

(

)

.10
.1025
.10381
.10516

Distinction between Stated Annual Interest Rate
and Effective Annual Rate
The distinction between the stated annual interest rate (SAIR), or APR, and the effective
annual rate (EAR) 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 EAR is meaningful without a compounding interval. For example, an
EAR 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.
There can be a big difference between an SAIR and an EAR when interest rates are
large. For example, consider “payday loans.” Payday loans are short-term term loans made
to consumers, often for less than two weeks, and are offered by companies such as AmeriCash Advance and National Payday. The loans work like this: you write a check today that
is postdated. When the check date arrives, you go to the store and pay the cash for the
check, or the company cashes the check. For example, AmeriCash Advance allows you to
write a postdated check for $120 for 15 days later. In this case, they would give you $100

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THE REAL WORLD

JACKPOT!
If you or someone you know is a regular lottery player, you probably already understand that you are 20 times more
likely to get struck by lightning than you are to win a big lottery jackpot. What are your odds of winning? Below you
will find a table with your chances of winning the Mega Millions Lottery compared to other events.
Odds of winning a Mega Millions jackpot
Odds of being killed by a venomous spider
Odds of being killed by a dog bite
Odds of being killed by lightning
Odds of being killed by drowning
Odds of being killed falling from a bed or other furniture
Odds of being killed in a car crash

1:135,145,920*
1:57,018,763
1:11,403,753
1:6,479,405
1:690,300
1:388,411
1:6,029

*Source: Virginia Lottery Web site. All other odds from the National Safety Council.

Sweepstakes may have different odds than lotteries, but these odds may not be much better. Probably the
largest advertised potential grand prize ever was Pepsi’s “Play for a Billion,” which, you guessed it, had a $1 billion
(billion!) prize. Not bad for a day’s work, but you still have to read the fine print. It turns out that the winner would
be paid $5 million per year for the next 20 years, $10 million per year for years 21 through 39, and a lump sum
$710 million in 40 years. From what you have learned, you know the value of the sweepstakes wasn’t even close to
$1 billion. In fact, at an interest rate of 10 percent, the present value is about $70.7 million.
In January 2010, a 59-year-old man and his 57-year-old wife in New York won the $162 million Mega Millions
jackpot. They were given the option of receiving the jackpot as $6.231 million immediately and $6.231 million per
year for the next 25 years, or $102 million immediately. So, what discount rate does this imply? After some computational effort, we find the interest rate is about 4.15 percent. Unfortunately for the winners, nearly $1 million was
placed in an escrow account over a dispute about the mismanagement of funds at a homeless shelter the couple
had previously operated.
Some lotteries make your decision a little tougher. The Ontario Lottery will pay you either $2,000 a week for the
rest of your life or $1.3 million now. (That’s in Canadian dollars or “loonies,” by the way.) Of course, there is the
chance you might die in the near future, so the lottery guarantees that your heirs will collect the $2,000 weekly
payments until the twentieth anniversary of the first payment, or until you would have turned 91, whichever comes
first. This payout scheme complicates your decision quite a bit. If you live for only the 20-year minimum, the breakeven interest rate between the two options is about 5.13 percent per year, compounded weekly. If you expect to
live longer than the 20-year minimum, you might be better off accepting $2,000 per week for life. Of course, if you
manage to invest the $1.3 million lump sum at a rate of return of about 8 percent per year (compounded weekly),
you can have your cake and eat it too because the investment will return $2,000 at the end of each week forever!
Taxes complicate the decision in this case because the lottery payments are all on an aftertax basis. Thus, the rates
of return in this example would have to be aftertax as well.

today. So what is the APR and EAR of this arrangement? First we need to find the interest
rate, which we can find by the FV equation as:
FV
$120
1.2
r






PV (1  r)t
$100  (1  r)1
(1  r)
.20 or 20%

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That doesn’t seem too bad until you remember this is the interest rate for 15 days! The
APR of the loan is:
APR  .20  36515
APR  4.8667 or 486.67%

And the EAR for this loan is:
EAR  (1  Quoted ratem)m  1
EAR  (1  .20)36515  1
EAR  83.4780 or 8,347.80%

Now that’s an interest rate! Just to see what a difference a day makes, let’s look at another
loan by the same company. AmeriCash Advance also offers a 14-day (instead of 15-day)
option. The other terms are the same. Check for yourself that the APR of this arrangement
is 521.43 percent and the EAR is 11,497.60 percent—definitely not a loan we recommend
you take out!

Compounding over Many Years
Formula 4.6 applies for an investment over one year. For an investment over one or more
(T ) years, the formula becomes
Future Value with Compounding:
r
FV  C0 1  _
m

EXAMPLE

4.13

(

)

mT

[4.8]

Multiyear Compounding
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 (4.8), his wealth is
.12
$5,000  1  ___
4

(

45

)

 $5,000  (1.03)20  $5,000  1.8061  $9,030.50

Continuous Compounding
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 sometimes 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

[4.9]

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.

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EXAMPLE 4.14

Continuous Compounding
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 (4.9) we have
$1,000  e .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 percent and T, the value on the vertical dimension, to 1. For this problem, the relevant
portion of the table is
C O N T I N U O U S LY C O M P O U N D E D R AT E ( r )
PE RI OD
(T )

9%

10%

11%

1
2
3

1.0942
1.1972
1.3100

1.1052
1.2214
1.3499

1.1163
1.2461
1.3910

EXAMPLE 4.15

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 would not care whether her bank quoted a
continuously compounded rate of 10 percent or a 10.52-percent rate, compounded annually.

Continuous Compounding, Continued
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  e .102  $1,000  e .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.
FIGURE 4.11
4

Interest
earned

3
2

4

Interest
earned

3

Dollars

Dollars

4

Dollars

Annual, Semiannual, and
Continuous Compounding

2

0

1

2
3
Years

4

Annual compounding

5

Interest
earned

2
1

1

1

3

0

1

2
3
Years

4

5

Semiannual compounding

0

1

2
3
Years

4

5

Continuous compounding

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EXAMPLE 4.16

Present Value with 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  $726.16
1  $1,000  ______
$1,000  ____
1.3771
e .084

4.4

S I M P L I F I C AT I O N S

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
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
C  ________
C
C
PV  ______
 ________
. . .
1r
(1  r )2
(1  r )3

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.

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The amount that will give the investor C dollars each year, and therefore the present
value of the consol, is simply
C
PV  __
r

[4.10]

To confirm that this is the right answer, notice that if we lend the amount C/r, the interest
it earns each year will be
CrC
Interest  __
r

which is exactly the consol payment. To sum up, we have shown that for a consol
Formula for Present Value of Perpetuity:
C  __
C
C
PV  __
 __
 
1r
(1  r )2
(1  r )3

[4.11]

C
_
r

EXAMPLE

4.17

It is comforting to know how easily we can use a bit of financial intuition to solve this
mathematical problem.
Perpetuities
Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value
of the consol?
Using formula (4.10), we have
$100  $1,250
PV  ____
.08
Now suppose that interest rates fall to 6 percent. Using (4.10), the value of the perpetuity is
$100  $1,666.67
PV  ____
.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
$100,000(1.05)
$100,000(1.05)2
$100,000
PV  ___  ____
 ____
 
1.11
(1.11)2
(1.11)3
$100,000(1.05)N1
 
 ____
(1.11)N

Algebraically, we can write the formula as
C  (1  g )
C  (1  g )2
C  (1  g )N1
C  ___

PV  __
 ___
     ___
1r
(1  r )2
(1  r )3
(1  r )N

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, this formula reduces to the following simplification:
Formula for Present Value of Growing Perpetuity:
C
PV  ______
rg

[4.12]

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From Formula 4.12, the present value of the cash flows from the apartment building is
$100,000
___________
 $1,666,667
.11  .05

There are three important points concerning the growing perpetuity formula:

EXAMPLE

4.18

1. The Numerator. The numerator in Formula 4.12 is the cash flow one period
hence, not at date 0. Consider the following example:
Paying Dividends
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 discount rate is 11 percent. What
is the price of the stock today?
The numerator in Formula 4.12 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
__
.11  .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 4.12 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 Discount Rate and the Growth Rate. The discount 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 discount 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 4.12 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 (4.12) 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,

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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.)4
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
__
 __
     __
1r
(1  r)2
(1  r)3
(1 + r)T

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)
C
C

(T  2)
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
C
PV  __
r

[4.13]

Consol 2 is just a consol with its first payment at date T  1. From the perpetuity formula,
this consol will be worth C/r at date T.5 However, we do not want the value at date T. We
4
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.
5
Students frequently think that C /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.

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want the value now; in other words, the present value at date 0. We must discount C/r back
by T periods. Therefore, the present value of consol 2 is
C __
1
PV  _
r (1 + r)T

[

]

[4.14]

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 4.13 minus Formula 4.14. This can
be written as
C_
C __
1
_
r
r (1 + r)T

[

]

This simplifies to
Formula for Present Value of Annuity:
1  __
1
PV  C _
r
r (1  r)T

[

]

[4.15]

This can also be written as
1
1  __
(1  r)T
___
PV  C
r

EXAMPLE

4.19

[

]

Lottery Valuation
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 4.15 yields
1
Present value of
1  __
(1.08)20
Million Dollar Lottery  $50,000  __
.08
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.

The term we use to compute the present 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 Formula 4.15 is a complex formula.
For simplification, we may from time to time refer to the present value annuity factor as
PVIFAr,T

That is, the above expression stands for the present value of $1 a year for T years at an
interest rate of r.
We can also provide a formula for the future value of an annuity:
(1  r )T
(1  r)T  1
1  C ___
FV  C __
_
r
r
r

[

]

[

]

[4.16]

CHAPTER 4 Discounted Cash Flow Valuation

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As with present value factors for annuities, we have compiled future value factors in
Table A.3 in the back of this book. Of course, you can also use a spreadsheet as we illustrate below.

SPREADSHEET TECHNIQUES

Annuity Present Values

Using a spreadsheet to find annuity present values goes like this:
A

B

C

D

E

F

G

1

Using a spreadsheet to find annuity present values

2

EXAMPLE

4.20

3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

What is the present value of $500 per year for 3 years if the discount rate is 10 percent?
We need to solve for the unknown present value, so we use the formula PV(rate, nper, pmt, fv).
Payment amount per period:
Number of payments:
Discount rate:

$500
3
0.1

Annuity present value:

$1,243.43

The formula entered in cell B11 is =PV(B9,B8,-B7,0); notice that fv is zero and that
pmt has a negative sign on it. Also notice that rate is entered as a decimal, not a percentage.

Retirement Investing
Suppose you put $3,000 per year into a Roth IRA. The account pays 6 percent per year. How much will
you have when you retire in 30 years?
This question asks for the future value of an annuity of $3,000 per year for 30 years at 6 percent,
which we can calculate as follows:
(1  r)T  1
1.0630  1
 $3,000  __
FV  C __
r
.06

[

]

[

]

 $3,000  79.0582
 $237,174.56
So, you’ll have close to a quarter million dollars in the account.

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.

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4.21
EXAMPLE

Delayed Annuities
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 Formula 4.15. This is
Present Value of Annuity at Date 5:
1
1_
(1.10)4  $500  PVIFA
$500  __
10%,4
.10
 $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 in that case.
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

9
$500

10

$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.

TRICK 2: ANNUITY DUE The annuity formula of Formula 4.15 assumes that the first
annuity payment begins a full period hence. This type of annuity is sometimes called an
annuity in arrears or an ordinary annuity. What happens if the annuity begins today, in
other words, at date 0?

CHAPTER 4 Discounted Cash Flow Valuation

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4.22
EXAMPLE

Annuity Due
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

$50,000  PVIFA8%,19
Payment at date 0
19-year annuity
 $50,000  ($50,000  9.6036)
 $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 or, more commonly,
an annuity due. Always remember that Formula 4.15, as well as Table A.2, in this book refers to an
ordinary annuity.

EXAMPLE

4.23

TRICK 3: THE INFREQUENT ANNUITY The following example treats an annuity with payments occurring less frequently than once a year.
Infrequent Annuities
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
1
1  __________
(1  .1236)10
$450  ______________  $450  PVIFA12.36%,10  $2,505.57
.1236

[

]

EXAMPLE

4.24

TRICK 4: EQUATING PRESENT VALUE OF TWO ANNUITIES The following example
equates the present value of inflows with the present value of outflows.
Working with Annuities
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?

(continued)

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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 each of
her first 17 birthdays, but no deposit at date 0. This is illustrated as

Date 0
Susan’s
birth

1

2

...

17

18

19

20

21

Parents’
1st
deposit

Parents’
2nd
deposit

...

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.
1
1  _____
(1.14)4
_________
 $30,000  PVIFA14%,4
$30,000 

[

.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  PVIFA14%,17  $9,422.91
Because PVIFA14%,17  6.3729,
$9,422.91
C  ________  $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

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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 is
Formula for Present Value of Growing Annuity:
1g
1
1
______
______
PV  C ______
rgrg 1r

[

(

T

)]

1g T
1  _______
1
r
 C _____________
rg

[

(

)]

[4.17]

EXAMPLE

4.25

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.

Growing Annuities
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 (4.17), the calculation is
1.09 40
Present value
1  ____
1.20
 $711,731
of Stuart’s  $80,000  __________
.20  .09
lifetime salary

[

( )

]

EXAMPLE

4.26

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 4.17 directly.

More Growing Annuities
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?
We set the growing-annuity formula equal to $9,422.91 and solve for C.
1g
1.04
1  _____
1  ____
1  r  C __________
1.14
___________
C
rg

[

(

T

)]

[

17

( )

.14  .04
 $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.

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4.5

L O A N T Y P E S A N D L O A N A M O R T I Z AT I O N

Whenever a lender extends a loan, some provision will be made for repayment of the
principal (the original loan amount). A loan might be repaid in equal installments, for
example, or it might be repaid in a single lump sum. Because the way that the principal
and interest are paid is up to the parties involved, there are actually an unlimited number
of possibilities.
In this section, we describe a few forms of repayment that come up quite often, and
more complicated forms can usually be built up from these. The three basic types of loans
are pure discount loans, interest-only loans, and amortized loans. Working with these loans
is a very straightforward application of the present value principles that we have already
developed.

Pure Discount Loans
The pure discount loan is the simplest form of loan. With such a loan, the borrower receives
money today and repays a single lump sum at some time in the future. A one-year, 10 percent pure discount loan, for example, would require the borrower to repay $1.10 in one year
for every dollar borrowed today.
Because a pure discount loan is so simple, we already know how to value one. Suppose
a borrower was able to repay $25,000 in five years. If we, acting as the lender, wanted a
12 percent interest rate on the loan, how much would we be willing to lend? Put another
way, what value would we assign today to that $25,000 to be repaid in five years? Based on
our previous work we know the answer is just the present value of $25,000 at 12 percent
for five years:
Present value  $25,000/1.125
 $25,000/1.7623
 $14,186

EXAMPLE

4.27

Pure discount loans are common when the loan term is short, say a year or less. In recent
years, they have become increasingly common for much longer periods.

Tr e a s u r y B i l l s
When the U.S. government borrows money on a short-term basis (a year or less), it does so by selling
what are called Treasury bills, or T-bills for short. A T-bill is a promise by the government to repay a
fixed amount at some time in the future—for example, 3 months or 12 months.
Treasury bills are pure discount loans. If a T-bill promises to repay $10,000 in 12 months, and the
market interest rate is 7 percent, how much will the bill sell for in the market?
Because the going rate is 7 percent, the T-bill will sell for the present value of $10,000 to be repaid
in one year at 7 percent:
Present value  $10,000/1.07  $9,345.79

Interest-Only Loans
A second type of loan repayment plan calls for the borrower to pay interest each period and
to repay the entire principal (the original loan amount) at some point in the future. Loans
with such a repayment plan are called interest-only loans. Notice that if there is just one
period, a pure discount loan and an interest-only loan are the same thing.
For example, with a three-year, 10 percent, interest-only loan of $1,000, the borrower
would pay $1,000  .10  $100 in interest at the end of the first and second years. At the

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end of the third year, the borrower would return the $1,000 along with another $100 in
interest for that year. Similarly, a 50-year interest-only loan would call for the borrower to
pay interest every year for the next 50 years and then repay the principal. In the extreme,
the borrower pays the interest every period forever and never repays any principal. As we
discussed earlier in the chapter, the result is a perpetuity.
Most corporate bonds have the general form of an interest-only loan. Because we will
be considering bonds in some detail in the next chapter, we will defer further discussion of
them for now.

Amortized Loans
With a pure discount or interest-only loan, the principal is repaid all at once. An alternative
is an amortized loan, with which the lender may require the borrower to repay parts of the
loan amount over time. The process of providing for a loan to be paid off by making regular
principal reductions is called amortizing the loan.
A simple way of amortizing a loan is to have the borrower pay the interest each period
plus some fixed amount. This approach is common with medium-term business loans. For
example, suppose a business takes out a $5,000, five-year loan at 9 percent. The loan agreement calls for the borrower to pay the interest on the loan balance each year and to reduce
the loan balance each year by $1,000. Because the loan amount declines by $1,000 each
year, it is fully paid in five years.
In the case we are considering, notice that the total payment will decline each year. The
reason is that the loan balance goes down, resulting in a lower interest charge each year,
whereas the $1,000 principal reduction is constant. For example, the interest in the first
year will be $5,000  .09  $450. The total payment will be $1,000  450  $1,450. In
the second year, the loan balance is $4,000, so the interest is $4,000  .09  $360, and the
total payment is $1,360. We can calculate the total payment in each of the remaining years
by preparing a simple amortization schedule as follows:

YE AR
1
2
3
4
5
Totals

BE GI N N I N G
BAL A N C E

T O TA L
PAY M E N T

INTEREST
PA I D

P R I N C I PA L
PA I D

E N D ING
B A LA NC E

$5,000
4,000

$1,450
1,360
1,270
1,180
1,090
$6,350

$ 450
360
270
180
90
$1,350

$1,000
1,000
1,000
1,000
1,000
$5,000

$4,000
3,000
2,000
1,000
0

3,000
2,000
1,000

Notice that in each year, the interest paid is given by the beginning balance multiplied by
the interest rate. Also notice that the beginning balance is given by the ending balance from
the previous year.
Probably the most common way of amortizing a loan is to have the borrower make a
single, fixed payment every period. Almost all consumer loans (such as car loans) and
mortgages work this way. For example, suppose our five-year, 9 percent, $5,000 loan was
amortized this way. How would the amortization schedule look?
We first need to determine the payment. From our discussion earlier in the chapter, we
know that this loan’s cash flows are in the form of an ordinary annuity. In this case, we can
solve for the payment as follows:
$5,000  C  {[1  (1/1.095)]/.09}
 C  [(1  .6499)/.09]

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This gives us:
C  $5,000/3.8897
 $1,285.46

The borrower will therefore make five equal payments of $1,285.46. Will this pay off the
loan? We will check by filling in an amortization schedule.
In our previous example, we knew the principal reduction each year. We then calculated
the interest owed to get the total payment. In this example, we know the total payment. We
will thus calculate the interest and then subtract it from the total payment to calculate the
principal portion in each payment.
In the first year, the interest is $450, as we calculated before. Because the total payment
is $1,285.46, the principal paid in the first year must be:
Principal paid  $1,285.46  450  $835.46

The ending loan balance is thus:
Ending balance  $5,000  835.46  $4,164.54

The interest in the second year is $4,164.54  .09  $374.81, and the loan balance declines
by $1,285.46  374.81  $910.65. We can summarize all of the relevant calculations in
the following schedule:

YEAR
1
2
3
4
5
Totals

BE GI NNI NG
BAL ANCE

T OTA L
PAYM E N T

INTEREST
PA I D

P R I N C I PA L
PA I D

ENDING
B A LA N C E

$5,000.00
4,164.54

$1,285.46
1,285.46
1,285.46
1,285.46
1,285.46
$6,427.30

$ 450.00
374.81
292.85
203.51
106.14
$1,427.31

$ 835.46
910.65
992.61
1,081.95
1,179.32
$5,000.00

$4,164.54
3,253.88
2,261.27
1,179.32
0.00

3,253.88
2,261.27
1,179.32

EXAMPLE

4.28

Because the loan balance declines to zero, the five equal payments do pay off the loan. Notice
that the interest paid declines each period. This isn’t surprising because the loan balance is
going down. Given that the total payment is fixed, the principal paid must be rising each period. To see how to calculate this loan in Excel, see the upcoming Spreadsheet Strategies box.
If you compare the two loan amortizations in this section, you will see that the total
interest is greater for the equal total payment case: $1,427.31 versus $1,350. The reason
for this is that the loan is repaid more slowly early on, so the interest is somewhat higher.
This doesn’t mean that one loan is better than the other; it simply means that one is effectively paid off faster than the other. For example, the principal reduction in the first year is
$835.46 in the equal total payment case as compared to $1,000 in the first case.
Partial Amortization, or “Bite the Bullet”
A common arrangement in real estate lending might call for a 5-year loan with, say, a 15-year
amortization. What this means is that the borrower makes a payment every month of a fixed amount
based on a 15-year amortization. However, after 60 months, the borrower makes a single, much larger
payment called a “balloon” or “bullet” to pay off the loan. Because the monthly payments don’t fully
pay off the loan, the loan is said to be partially amortized.

(continued)

CHAPTER 4 Discounted Cash Flow Valuation

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Suppose we have a $100,000 commercial mortgage with a 12 percent APR and a 20-year
(240-month) amortization. Further suppose the mortgage has a five-year balloon. What will the monthly
payment be? How big will the balloon payment be?
The monthly payment can be calculated based on an ordinary annuity with a present value of
$100,000. There are 240 payments, and the interest rate is 1 percent per month. The payment is:
$100,000  C  [(1  1/1.01240)/.01]
 C  90.8194
C  $1,101.09
Now, there is an easy way and a hard way to determine the balloon payment. The hard way is to
actually amortize the loan for 60 months to see what the balance is at that time. The easy way is to
recognize that after 60 months, we have a 240  60  180-month loan. The payment is still $1,101.09
per month, and the interest rate is still 1 percent per month. The loan balance is thus the present value
of the remaining payments:
Loan balance  $1,101.09  [(1  1/1.01180)/.01]
 $1,101.09  83.3217
 $91,744.69
The balloon payment is a substantial $91,744. Why is it so large? To get an idea, consider the first
payment on the mortgage. The interest in the first month is $100,000  .01  $1,000. Your payment is
$1,101.09, so the loan balance declines by only $101.09. Because the loan balance declines so slowly,
the cumulative “pay down” over five years is not great.

We will close this section with an example that may be of particular relevance. Federal
Stafford loans are an important source of financing for many college students, helping to
cover the cost of tuition, books, new cars, condominiums, and many other things. Sometimes students do not seem to fully realize that Stafford loans have a serious drawback:
they must be repaid in monthly installments, usually beginning six months after the student
leaves school.
Some Stafford loans are subsidized, meaning that the interest does not begin to accrue
until repayment begins (this is a good thing). If you are a dependent undergraduate student under this particular option, the total debt you can run up is, at most, $23,000. The
maximum interest rate is 8.25 percent, or 8.25/12  0.6875 percent per month. Under the
“standard repayment plan,” the loans are amortized over 10 years (subject to a minimum
payment of $50).
Suppose you max out borrowing under this program and also get stuck paying the maximum interest rate. Beginning six months after you graduate (or otherwise depart the ivory
tower), what will your monthly payment be? How much will you owe after making payments for four years?
Given our earlier discussions, see if you don’t agree that your monthly payment assuming a $23,000 total loan is $282.10 per month. Also, as explained in Example 4.28, after
making payments for four years, you still owe the present value of the remaining payments.
There are 120 payments in all. After you make 48 of them (the first four years), you have
72 to go. By now, it should be easy for you to verify that the present value of $282.10 per
month for 72 months at 0.6875 percent per month is just under $16,000, so you still have
a long way to go.
Of course, it is possible to rack up much larger debts. According to the Association of
American Medical Colleges, medical students who borrowed to attend medical school and
graduated in 2008 had an average student loan balance of $154,607. Ouch! How long will
it take the average student to pay off her medical school loans?

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Loan Amortization Using a Spreadsheet

SPREADSHEET TECHNIQUES

Loan amortization is a common spreadsheet application. To illustrate, we will set up the problem that we
examined earlier: a five-year, $5,000, 9 percent loan with constant payments. Our spreadsheet looks like this:
A

B

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31

C

D

E

F

G

H

Using a spreadsheet to amortize a loan
Loan amount:
Interest rate:
Loan term:
Loan payment:

$5,000
0.09
5
$1,285.46
Note: Payment is calculated using PMT(rate, nper, -pv, fv).

Amortization table:
Year
1
2
3
4
5
Totals

Beginning
Balance
$5,000.00
4,164.54
3,253.88
2,261.27
1,179.32

Total
Payment
$1,285.46
1,285.46
1,285.46
1,285.46
1,285.46
6,427.31

Interest
Paid
$450.00
374.81
292.85
203.51
106.14
1,427.31

Principal
Paid
$835.46
910.65
992.61
1,081.95
1,179.32
5,000.00

Ending
Balance
$4,164.54
3,253.88
2,261.27
1,179.32
0.00

Formulas in the amortization table:
Year
1
2
3
4
5

Beginning
Balance
=+D4
=+G13
=+G14
=+G15
=+G16

Total
Payment
=$D$7
=$D$7
=$D$7
=$D$7
=$D$7

Interest
Paid
=+$D$5*C13
=+$D$5*C14
=+$D$5*C15
=+$D$5*C16
=+$D$5*C17

Principal
Paid
=+D13-E13
=+D14-E14
=+D15-E15
=+D16-E16
=+D17-E17

Ending
Balance
=+C13-F13
=+C14-F14
=+C15-F15
=+C16-F16
=+C17-F17

Note: Totals in the amortization table are calculated using the SUM formula.

Let’s say she makes a monthly payment of $1,000, and the loan has an interest rate
of 7 percent per year, or .5833 percent per month. See if you agree that it will take
399 months, or just over 33 years, to pay off the loan. Maybe MD really stands for
“mucho debt!”

4.6

W H AT I S A F I R M W O R T H ?

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.

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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.

T H E P R E S E N T VA LU E O F T H E FI R M
E ND OF YE AR

N E T C A S H FLO W O F
T H E FI R M

P R E S E N T VA LU E
FA C T O R ( 10% )

P R E S E N T VA LU E OF
N E T C A S H FLOW S

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
.51316
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
(2,000  PVIFA
1.1

)

$5,000
10,000
10%,5
________
 $16,569.35
 _____________________  ________
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

EXAMPLE

4.29

The incremental value (NPV) of acquiring the firm is $4,569.35.

Firm Valuation
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?
The decision can be evaluated as:
$200,000
$200,000 $200,000 . . . _______


NPV  $1,000,000  _______  _______
1.15
(1.15)2
(1.15)9
 $1,000,000  $200,000  PVIFA15%,9
 $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.

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SUMMARY AND CONCLUSIONS
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 ($1/1.10) in year 0. A dollar to be received in
two years has a present value of $0.826 [$1/(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
C2
C1
CT
 ______
 C0 
 . . .  ______
NPV  C0  ______
(1  r) (1  r)2
(1  r)T

T

Ci

 ______
(1  r)
i1

i

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:
C
Perpetuity: PV  __
r
C
Growing perpetuity: PV  _____
rg
1
1  ______
(1  r)T
__________
Annuity: PV  C
r

[

]

1g T
1  _____
1r
Growing annuity: PV  C ___
rg

[

(

)]

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.
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.
6. Many loans are annuities. The process of providing for a loan to be paid off gradually is
called amortizing the loan, and we discussed how amortization schedules are prepared and
interpreted.

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CONCEPT QUESTIONS
1. Compounding and Period As you increase the length of time involved, what happens to future
values? What happens to present values?
2. Interest Rates What happens to the future value of an annuity if you increase the rate r ? What
happens to the present value?
3. Present Value Suppose two athletes sign 10-year contracts for $80 million. In one case, we’re
told that the $80 million will be paid in 10 equal installments. In the other case, we’re told that
the $80 million will be paid in 10 installments, but the installments will increase by 5 percent per
year. Who got the better deal?
4. APR and EAR Should lending laws be changed to require lenders to report EARs instead of
APRs? Why or why not?
5. Time Value On subsidized Stafford loans, a common source of financial aid for college
students, interest does not begin to accrue until repayment begins. Who receives a bigger
subsidy, a freshman or a senior? Explain.
Use the following information for Questions 6–10.
Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor Corporation, offered some
securities for sale to the public on March 28, 2008. Under the terms of the deal, TMCC promised to
repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive
nothing until then. Investors paid TMCC $24,099 for each of these securities, so they gave up $24,099
on March 28, 2008, for the promise of a $100,000 payment 30 years later.
6. Time Value of Money Why would TMCC be willing to accept such a small amount today
($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future?
7. Call Provisions TMCC has the right to buy back the securities on the anniversary date at a
price established when the securities were issued (this feature is a term of this particular deal).
What impact does this feature have on the desirability of this security as an investment?
8. Time Value of Money Would you be willing to pay $24,099 today in exchange for $100,000 in
30 years? What would be the key considerations in answering yes or no? Would your answer
depend on who is making the promise to repay?
9. Investment Comparison Suppose that when TMCC offered the security for $24,099 the U.S.
Treasury had offered an essentially identical security. Do you think it would have had a higher or
lower price? Why?
10. Length of Investment The TMCC security is bought and sold on the New York Stock Exchange.
If you looked at the price today, do you think the price would exceed the $24,099 original price?
Why? If you looked in the year 2019, do you think the price would be higher or lower than today’s
price? Why?

QUESTIONS AND PROBLEMS

Basic
(Questions 1–20)

1. Simple Interest versus Compound Interest First City Bank pays 7 percent simple interest on
its savings account balances, whereas Second City Bank pays 7 percent interest compounded
annually. If you made a $6,000 deposit in each bank, how much more money would you earn
from your Second City Bank account at the end of 10 years?
2. Calculating Future Values

Compute the future value of $2,500 compounded annually for

a. 10 years at 6 percent
b. 10 years at 8 percent

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c. 20 years at 6 percent
d. Why is the interest earned in part (c) not twice the amount earned in part (a)?
3. Calculating Present Values For each of the following, compute the present value:

PRE SE NT VAL UE

YE A R S

I N T E R E S T R AT E

FU T U R E VA LU E

9

7%

6

9

$ 15,451
51,557

21

14

886,073

27

16

550,164

4. Calculating Interest Rates Solve for the unknown interest rate in each of the following:

PRE SE NT VAL UE
$

YE A R S

I N T E R E S T R AT E

FU T U R E VA LU E

243

3

405

10

$

896

307

34,500

13

162,181

51,285

26

483,500

5. Calculating the Number of Periods Solve for the unknown number of years in each of the
following:

PRE SE NT VAL UE
$

YE A R S

I N T E R E S T R AT E

FU T U R E VA LU E

625

7%

810

8

$ 1,284
4,341

18,400

13

402,662

21,500

16

173,439

6. Calculating the Number of Periods At 8 percent interest, how long does it take to double your
money? To quadruple it?
7. Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $750 million
that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to
discount this liability back to the present. If the relevant discount rate is 6.25 percent, what is the
present value of this liability?
8. Calculating Rates of Return Although appealing to more refined tastes, art as a collectible
has not always performed so profitably. During 2003, Sothebys sold the Edgar Degas bronze
sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately
for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his
annual rate of return on this sculpture?
9. Perpetuities 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 $160 annually if the
next payment occurs one year from today? The market interest rate is 4.5 percent.

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10. Continuous Compounding

Compute the future value of $1,800 continuously compounded for

a. Five years at a stated annual interest rate of 14 percent.
b. Three years at a stated annual interest rate of 6 percent.
c. Ten years at a stated annual interest rate of 7 percent.
d. Eight years at a stated annual interest rate of 9 percent.
11. Present Value and Multiple Cash Flows Conoly Co. has identified an investment project with
the following cash flows. If the discount rate is 5 percent, what is the present value of these
cash flows? What is the present value at 13 percent? At 18 percent?
YEAR

C A S H FLO W

1

$ 850

2

740

3

1,090

4

1,310

12. Present Value and Multiple Cash Flows Investment X offers to pay you $6,000 per year for
nine years, whereas Investment Y offers to pay you $8,500 per year for five years. Which of
these cash flow streams has the higher present value if the discount rate is 9 percent? If the
discount rate is 21 percent?
13. Calculating Annuity Present Value An investment offers $7,000 per year for 15 years, with
the first payment occurring one year from now. If the required return is 8 percent, what is the
value of the investment? What would the value be if the payments occurred for 40 years? For
75 years? Forever?
14. Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you an
investment policy that will pay you and your heirs $25,000 per year forever. If the required return
on this investment is 6 percent, how much will you pay for the policy? Suppose the Perpetual
Life Insurance Co. told you the policy costs $435,000. At what interest rate would this be a fair
deal?
15. Calculating EAR

Find the EAR in each of the following cases:

STAT E D RAT E ( A P R )

NUMBER OF TIMES COMPOUNDED

15%

Quarterly

12

Monthly

9

Daily

13

16. Calculating APR

E FFE C T I V E R AT E ( EAR )

Infinite

Find the APR, or stated rate, in each of the following cases:

STAT E D RAT E ( A P R )

NUMBER OF TIMES COMPOUNDED

E FFE C T I V E R AT E ( EAR )

Semiannually

10.2%

Monthly

8.4

Weekly

15.9

Infinite

18.7

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17. Calculating EAR First National Bank charges 15.1 percent compounded monthly on its business loans. First United Bank charges 15.5 percent compounded semiannually. As a potential
borrower, which bank would you go to for a new loan?
18. Interest Rates Well-known financial writer Andrew Tobias argues that he can earn 177 percent
per year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle
of fine Bordeaux per week for the next twelve weeks. He can either pay $10 per week or buy a
case of 12 bottles today. If he buys the case, he receives a 10 percent discount, and, by doing
so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you
agree with his analysis? Do you see a problem with his numbers?
19. Calculating Number of Periods One of your customers is delinquent on his accounts payable
balance. You’ve mutually agreed to a repayment schedule of $375 per month. You will charge
0.9 percent per month interest on the overdue balance. If the current balance is $13,200, how
long will it take for the account to be paid off?
20. Calculating EAR Friendly’s Quick Loans, Inc., offers you “three for four or I knock on your
door.” This means you get $3 today and repay $4 when you get your paycheck in one week (or
else). What’s the effective annual return Friendly’s earns on this lending business? If you were
brave enough to ask, what APR would Friendly’s say you were paying?
21. Future Value What is the future value in three years of $1,800 invested in an account with a
stated annual interest rate of 10 percent,

Intermediate
(Questions 21–52)

a. Compounded annually?
b. Compounded semiannually?
c. Compounded monthly?
d. Compounded continuously?
e. Why does the future value increase as the compounding period shortens?
22. Simple Interest versus Compound Interest First Simple Bank pays 7 percent simple interest
on its investment accounts. If First Complex Bank pays interest on its accounts compounded
annually, what rate should the bank set if it wants to match First Simple Bank over an investment
horizon of 10 years?
23. Calculating Annuities You are planning to save for retirement over the next 30 years. To do
this, you will invest $700 a month in a stock account and $300 a month in a bond account. The return of the stock account is expected to be 11 percent, and the bond account will pay 6 percent.
When you retire, you will combine your money into an account with an 8 percent return. How
much can you withdraw each month from your account assuming a 25-year withdrawal period?
24. Calculating Rates of Return Suppose an investment offers to quintuple your money in
12 months (don’t believe it). What rate of return per quarter are you being offered?
25. Calculating Rates of Return You’re trying to choose between two different investments, both
of which have up-front costs of $75,000. Investment G returns $125,000 in five years. Investment
H returns $245,000 in 11 years. Which of these investments has the higher return?
26. Growing Perpetuities 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 $210,000, received three years from today. Subsequent annual cash flows will grow at 3 percent, in perpetuity. What is the present value of the technology
if the discount rate is 12 percent?
27. Perpetuities A prestigious investment bank designed a new security that pays a quarterly
dividend of $3 in perpetuity. The first dividend occurs one quarter from today. What is the price
of the security if the stated annual interest rate is 9 percent, compounded quarterly?

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28. Annuity Present Values What is the present value of an annuity of $6,000 per year, with the
first cash flow received four years from today and the last one received 18 years from today?
Use a discount rate of 8 percent.
29. Annuity Present Values What is the value today of a 15-year annuity that pays $750 a year?
The annuity’s first payment occurs six years from today. The annual interest rate is 9 percent for
years 1 through 5, and 12 percent thereafter.
30. Balloon Payments Mike Bayles has just arranged to purchase a $750,000 vacation home in
the Bahamas with a 25 percent down payment. The mortgage has a 6.5 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?
31. Calculating Interest Expense You receive a credit card application from Shady Banks Savings
and Loan offering an introductory rate of 1.80 percent per year, compounded monthly for the first
six months, increasing thereafter to 18 percent compounded monthly. Assuming you transfer
the $6,000 balance from your existing credit card and make no subsequent payments, how much
interest will you owe at the end of the first year?
32. Perpetuities Barrett Pharmaceuticals is considering a drug project that costs $875,000 today
and is expected to generate end-of-year annual cash flows of $61,000, forever. At what discount
rate would Barrett be indifferent between accepting or rejecting the project?
33. Growing Annuity Southern California Publishing Company is trying to decide whether or not
to revise its popular textbook, Financial Psychoanalysis Made Simple. It has estimated that the
revision will cost $95,000. Cash flows from increased sales will be $26,000 the first year. These
cash flows will increase by 6 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 an 11 percent return for such an investment, should it undertake the
revision?
34. Growing Annuity 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 $75,000 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 10 percent of your annual salary
in an account that will earn 9 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 35 years
from today?
35. Present Value and Interest Rates What is the relationship between the value of an annuity
and the level of interest rates? Suppose you just bought a 12-year annuity of $7,000 per
year at the current interest rate of 10 percent per year. What happens to the value of your
investment if interest rates suddenly drop to 5 percent? What if interest rates suddenly rise
to 15 percent?
36. Calculating the Number of Payments You’re prepared to make monthly payments of $125,
beginning at the end of this month, into an account that pays 10 percent interest compounded
monthly. How many payments will you have made when your account balance reaches
$25,000?
37. Calculating Annuity Present Values You want to borrow $75,000 from your local bank to
buy a new sailboat. You can afford to make monthly payments of $1,475, but no more.
Assuming monthly compounding, what is the highest rate you can afford on a 60-month
APR loan?

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38. Calculating Loan Payments You need a 30-year, fixed-rate mortgage to buy a new
home for $260,000. Your mortgage bank will lend you the money at a 6.1 percent APR for
this loan. However, you can only afford monthly payments of $1,150, so you offer to pay off
any remaining loan balance at the end of the loan in the form of a single balloon payment.
How large will this balloon payment have to be for you to keep your monthly payments at
$1,150?
39. Present and Future Values The present value of the following cash flow stream is $5,985 when
discounted at 10 percent annually. What is the value of the missing cash flow?

YE A R

C A S H FLO W

1

$1,750

2

?

3

1,380

4

2,230

40. Calculating Present Values You just won the TVM Lottery. You will receive $1 million today
plus another 10 annual payments that increase by $350,000 per year. Thus, in one year you
receive $1.35 million. In two years, you get $1.7 million, and so on. If the appropriate interest rate
is 8 percent, what is the present value of your winnings?
41. EAR versus APR You have just purchased a new warehouse. To finance the purchase,
you’ve arranged for a 30-year mortgage loan for 80 percent of the $2,400,000 purchase
price. The monthly payment on this loan will be $13,500. What is the APR on this loan?
The EAR?
42. Present Value and Break-Even Interest Consider a firm with a contract to sell an asset for
$140,000 three years from now. The asset costs $91,000 to produce today. Given a relevant discount rate on this asset of 13 percent per year, will the firm make a profit on this asset? At what
rate does the firm just break even?
43. Present Value and Multiple Cash Flows What is the present value of $2,500 per year, at a discount rate of 8 percent, if the first payment is received 7 years from now and the last payment is
received 30 years from now?
44. Variable Interest Rates A 15-year annuity pays $1,700 per month, and payments are made
at the end of each month. If the interest rate is 12 percent compounded monthly for the first
seven years, and 9 percent compounded monthly thereafter, what is the present value of the
annuity?
45. Comparing Cash Flow Streams You have your choice of two investment accounts. Investment
A is a 15-year annuity that features end-of-month $1,300 payments and has an interest rate of
8.75 percent compounded monthly. Investment B is an 8 percent continuously compounded
lump-sum investment, also good for 15 years. How much money would you need to invest in B
today for it to be worth as much as Investment A 15 years from now?
46. Calculating Present Value of a Perpetuity Given an interest rate of 8.2 percent per year,
what is the value at date t  7 of a perpetual stream of $2,100 payments that begin at date
t  15?
47. Calculating EAR A local finance company quotes a 17 percent interest rate on one-year loans.
So, if you borrow $15,000, the interest for the year will be $2,550. Because you must repay a total
of $17,550 in one year, the finance company requires you to pay $17,550/12, or $1,462.50, per month

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over the next 12 months. Is this a 17 percent loan? What rate would legally have to be quoted?
What is the effective annual rate?
48. Calculating Present Values A 5-year annuity of ten $10,000 semiannual payments will begin
9 years from now, with the first payment coming 9.5 years from now. If the discount rate is
10 percent compounded monthly, what is the value of this annuity five years from now? What is
the value three years from now? What is the current value of the annuity?
49. Calculating Annuities Due Suppose you are going to receive $8,000 per year for 10 years. The
appropriate interest rate is 9 percent.
a. What is the present value of the payments if they are in the form of an ordinary annuity?
What is the present value if the payments are an annuity due?
b. Suppose you plan to invest the payments for 10 years. What is the future value if the
payments are an ordinary annuity? What if the payments are an annuity due?
c. Which has the highest present value, the ordinary annuity or the annuity due? Which has the
highest future value? Will this always be true?
50. Calculating Annuities Due You want to buy a new sports car from Muscle Motors for $85,000.
The contract is in the form of a 60-month annuity due at a 6.8 percent APR. What will your
monthly payment be?
51. Amortization with Equal Payments Prepare an amortization schedule for a three-year loan
of $69,000. The interest rate is 9 percent per year, and the loan calls for equal annual payments.
How much interest is paid in the third year? How much total interest is paid over the life of the
loan?
52. Amortization with Equal Principal Payments Rework Problem 51 assuming that the loan agreement calls for a principal reduction of $23,000 every year instead of equal annual payments.
Challenge
(Questions 53–80)

53. Calculating Annuities Due 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 an 11.50 percent stated annual interest
rate, compounded monthly. Since the clubs cost $3,500 retail, Pings wants the PV of the lease
payments to equal $3,500. Suppose that your first payment is due immediately. What will your
monthly lease payments be?
54. Annuities 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 $55,000 per year per child, payable at the beginning of each school year. The annual interest rate is 7.25 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. Assume
four years of college.
55. Growing Annuities Tom Adams has received a job offer from a large investment bank as a
clerk to an associate banker. His base salary will be $52,000. 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 3.5 percent each year. Each year
he will receive a bonus equal to 10 percent of his salary. Mr. Adams is expected to work for
35 years. What is the present value of the offer if the discount rate is 9 percent?
56. Calculating Annuities You have recently won the super jackpot in the Set for Life lottery. On
reading the fine print, you discover that you have the following two options:
a. You will receive 31 annual payments of $400,000, with the first payment being delivered today.
The income will be taxed at a rate of 35 percent. Taxes will be withheld when the checks are
issued.

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b. You will receive $900,000 now, and you will not have to pay taxes on this amount. In addition,
beginning one year from today, you will receive $290,000 each year for 30 years. The cash
flows from this annuity will be taxed at 35 percent.
Using a discount rate of 10 percent, which option should you select?
57. Calculating Growing Annuities You have 30 years left until retirement and want to retire with
$2.2 million. Your salary is paid annually and you will receive $80,000 at the end of the current
year. Your salary will increase at 3 percent per year, and you can earn a 10 percent return on the
money you invest. If you save a constant percentage of your salary, what percentage of your
salary must you save each year?
58. Balloon Payments On September 1, 2008, Susan Chao bought a motorcycle for $30,000. She
paid $1,000 down and financed the balance with a five-year loan at a stated annual interest rate
of 7.8 percent, compounded monthly. She started the monthly payments exactly one month after
the purchase (i.e., October 1, 2008). Two years later, at the end of October 2010, 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, 2010?
59. Calculating Annuity Values Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of
$15,000 per month for 20 years, with the first payment received 30 years and 1 month from
now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated
cost of $300,000. Third, after he passes on at the end of the 20 years of withdrawals, he
would like to leave an inheritance of $1,000,000 to his nephew Frodo. He can afford to save
$2,000 per month for the next 10 years. If he can earn a 10 percent EAR before he retires
and an 8 percent EAR after he retires, how much will he have to save each month in years
11 through 30?
60. Calculating Annuity Values After deciding to buy a new car, you can either lease the car or
purchase it with a 3-year loan. The car you wish to buy costs $30,000. The dealer has a special
leasing arrangement where you pay $1,500 today and $450 per month for the next three years.
If you purchase the car, you will pay it off in monthly payments over the next three years at an
8 percent APR. You believe that you will be able to sell the car for $19,000 in three years. Should
you buy or lease the car? What break-even resale price in three years would make you indifferent between buying and leasing?
61. Calculating Annuity Values An All-Pro defensive lineman is in contract negotiations. The team
has offered the following salary structure:
TIME

S A LA RY

0

$5,000,000

1

$4,000,000

2

$4,800,000

3

$5,600,000

4

$6,200,000

5

$6,800,000

6

$7,300,000

All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate
the terms. He wants an $8 million signing bonus payable today and a contract value increase of
$1,500,000. He also wants an equal salary paid every three months, with the first paycheck three

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months from now. If the interest rate is 5 percent compounded daily, what is the amount of his
quarterly check? Assume 365 days in a year.
62. Discount Interest Loans This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow
$20,000 for one year. The interest rate is 14 percent. You and the lender agree that the interest
on the loan will be .14  $20,000  $2,800. So the lender deducts this interest amount from
the loan up front and gives you $17,200. In this case, we say that the discount is $2,800. What’s
wrong here?
63. Calculating Annuity Values You are serving on a jury. A plaintiff is suing the city for injuries
sustained after a freak street sweeper accident. In the trial, doctors testified that it will be five
years before the plaintiff is able to return to work. The jury has already decided in favor of the
plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award
to cover the following: 1) The present value of two years’ back pay. The plaintiff’s annual salary for the last two years would have been $38,000 and $40,000, respectively. 2) The present
value of five years’ future salary. You assume the salary will be $45,000 per year. 3) $200,000
for pain and suffering. 4) $30,000 for court costs. Assume that the salary payments are equal
amounts paid at the end of each month. If the interest rate you choose is a 7 percent EAR,
what is the size of the settlement? If you were the plaintiff, would you like to see a higher or
lower interest rate?
64. Calculating EAR with Points You are looking at a one-year loan of $10,000. The interest rate
is quoted as 9 percent plus two points. A point on a loan is simply 1 percent (one percentage
point) of the loan amount. Quotes similar to this one are very common with home mortgages.
The interest rate quotation in this example requires the borrower to pay two points to the lender
up front and repay the loan later with 9 percent interest. What rate would you actually be paying here?
65. Calculating EAR with Points The interest rate on a one-year loan is quoted as 13 percent plus
three points (see the previous problem). What is the EAR? Is your answer affected by the loan
amount?
66. EAR versus APR There are two banks in the area that offer 30-year, $225,000 mortgages at
7.5 percent and charge a $2,500 loan application fee. However, the application fee charged by
Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged
by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any
fees that will be refunded if the applicant is rejected be included in calculating the APR, but this
is not required with nonrefundable fees (presumably because refundable fees are part of the
loan rather than a fee). What are the EARs on these two loans? What are the APRs?
67. Calculating EAR with Add-On Interest This problem illustrates a deceptive way of quoting interest
rates called add-on interest. Imagine that you see an advertisement for Crazy Judy’s Stereo City that
reads something like this: “$2,000 Instant Credit! 17% Simple Interest! Three Years to Pay! Low, Low
Monthly Payments!” You’re not exactly sure what all this means and somebody has spilled ink over
the APR on the loan contract, so you ask the manager for clarification.
Judy explains that if you borrow $2,000 for three years at 17 percent interest, in three years
you will owe:
$2,000  1.173  $2,000  1.601613  $3,203.23
Now, Judy recognizes that coming up with $3,203.23 all at once might be a strain, so she lets you
make “low, low monthly payments” of $3,203.23/36  $88.98 per month, even though this is extra
bookkeeping work for her.
Is this a 17 percent loan? Why or why not? What is the APR on this loan? What is the EAR?
Why do you think this is called add-on interest?

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68. Calculating Annuity Payments This is a classic retirement problem. A time line will help
in solving it. Your friend is celebrating her 35th birthday today and wants to start saving
for her anticipated retirement at age 65. She wants to be able to withdraw $140,000 from
her savings account on each birthday for 20 years following her retirement; the first
withdrawal will be on her 66th birthday. Your friend intends to invest her money in the
local credit union, which offers 7 percent interest per year. She wants to make equal
annual payments on each birthday into the account established at the credit union for her
retirement fund.
a. If she starts making these deposits on her 36th birthday and continues to make deposits until
she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?
b. Suppose your friend has just inherited a large sum of money. Rather than making equal
annual payments, she has decided to make one lump-sum payment on her 35th birthday
to cover her retirement needs. What amount does she have to deposit?
c. Suppose your friend’s employer will contribute $2,000 to the account every year as part of
the company’s profit-sharing plan. In addition, your friend expects a $50,000 distribution from
a family trust fund on her 55th birthday, which she will also put into the retirement account.
What amount must she deposit annually now to be able to make the desired withdrawals at
retirement?
69. Calculating the Number of Periods Your Christmas ski vacation was great, but it unfortunately
ran a bit over budget. All is not lost, because you just received an offer in the mail to transfer
your $10,000 balance from your current credit card, which charges an annual rate of 19.2 percent, to a new credit card charging a rate of 9.2 percent. How much faster could you pay the
loan off by making your planned monthly payments of $170 with the new card? What if there was
a 3 percent fee charged on any balances transferred?
70. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its
customers. Typically, the policy is bought by a parent or grandparent 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:

$ 700

Second birthday:

$ 700

Third birthday:

$ 800

Fourth birthday:

$ 800

Fifth birthday:

$ 900

Sixth birthday:

$ 900

After the child’s sixth birthday, no more payments are made. When the child reaches age 65,
he or she receives $500,000. If the relevant interest rate is 10 percent for the first six years and
8 percent for all subsequent years, is the policy worth buying?
71. Annuity Present Values and Effective Rates You have just won the lottery. You will receive
$4,000,000 today, and then receive 40 payments of $1,000,000. These payments will start one
year from now and will be paid every six months. A representative from Greenleaf Investments
has offered to purchase all the payments from you for $20.4 million. If the appropriate interest rate is an 8 percent APR compounded daily, should you take the offer? Assume there are
365 days per year.
72. Calculating Interest Rates A financial planning service offers a college savings program. The
plan calls for you to make six annual payments of $14,000 each, with the first payment occurring

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today, your child’s 12th birthday. Beginning on your child’s 18th birthday, the plan will provide
$30,000 per year for four years. What return is this investment offering?
73. Break-Even Investment Returns Your financial planner offers you two different investment
plans. Plan X is a $10,000 annual perpetuity. Plan Y is a 10-year, $21,000 annual annuity. Both
plans will make their first payment one year from today. At what discount rate would you be
indifferent between these two plans?
74. Perpetual Cash Flows What is the value of an investment that pays $17,000 every
other year forever, if the first payment occurs one year from today and the discount rate is
12 percent compounded daily? What is the value today if the first payment occurs four years
from today?
75. Ordinary Annuities and Annuities Due As discussed in the text, an annuity due is identical to
an ordinary annuity except that the periodic payments occur at the beginning of each period
and not at the end of the period. Show that the relationship between the value of an ordinary
annuity and the value of an otherwise equivalent annuity due is:
Annuity due value  Ordinary annuity value  (1  r )
Show this for both present and future values.
76. Calculating Annuities Due A 10-year annual annuity due with the first payment occurring at
date t  7 has a current value of $85,000. If the discount rate is 9 percent per year, what is the
annuity payment amount?
77. Calculating EAR A check-cashing store is in the business of making personal loans to walk-up
customers. The store makes only one-week loans at 7 percent interest per week.
a. What APR must the store report to its customers? What is the EAR that the customers are
actually paying?
b. Now suppose the store makes one-week loans at 7 percent discount interest per week (see
Question 62). What’s the APR now? The EAR?
c. The check-cashing store also makes one-month add-on interest loans at 7 percent discount
interest per week. Thus, if you borrow $100 for one month (four weeks), the interest will be
($100  1.074)  100  $31.08. Because this is discount interest, your net loan proceeds
today will be $68.92. You must then repay the store $100 at the end of the month. To help you
out, though, the store lets you pay off this $100 in installments of $25 per week. What is the
APR of this loan? What is the EAR?
78. Present Value of a Growing Perpetuity What is the equation for the present value of a
growing perpetuity with a payment of C one period from today if the payments grow by C each
period?
79. Rule of 72 A useful rule of thumb for the time it takes an investme...


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