Solution Manual Of Essentials of Corporate Finance 9th Edition by Ross

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Product Details:

• ISBN-10 ‏ : ‎ 1259277216
• ISBN-13 ‏ : ‎ 978-1259277214
• Author:  Bradford D. Jordan, Stephen A. Ross, Randolph W. Westerfield

Essentials of Corporate Finance by Ross, Westerfield, and Jordan is written to convey the most important concepts and principles of corporate finance at a level that is approachable for a wide audience. The authors retain their modern approach to finance, but have distilled the subject down to the essential topics in 18 chapters. They believe that understanding the “why” is just as important, if not more so, than understanding the “how,” especially in an introductory course.

Table of Content:

part one

Chapter 1 Introduction to Financial Management

part t

CRITICAL THINKING AND CONCEPTS REVIEW

LO 1  The Financial Management Decision ;What are the three types

of financial management decisions? For each type of decision, give

an example of a business transaction that would be relevant.

LO 3  Sole Proprietorships and ;What are the four primary

disadvantages to the sole proprietorship and partnership forms of business

organization? What benefits are there to these types of business

organization as opposed to the corporate form?

LO 3  ;What is the primary disadvantage of the corporate form

of organization? Name at least two of the advantages of corporate

organization.

LO 3  Corporate Finance ;In a large corporation, what are the two

distinct groups that report to the chief financial officer? Which group is

the focus of corporate finance?

LO 2  Goal of Financial ;What goal should always motivate the

actions of the firm’s financial manager?

LO 4  Agency ;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?

LO 3  Primary versus Secondary ;You’ve probably noticed coverage

in the financial press of an initial public offering (IPO) of a company’s

securities. Social networking company Facebook is a relatively recent

example. Is an IPO a primary market transaction or a secondary market

transaction?

LO 3  Auction versus Dealer ;What does it mean when we say the

New York Stock Exchange is an auction market? How are auction markets

different from dealer markets? What kind of market is NASDAQ?

LO 2  Not-for-Profit Firm ;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?

LO 2  Ethics and Firm ;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 such as 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.

LO 2  International Firm ;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?

LO 4  Agency ;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?

LO 4  Agency Problems and Corporate ;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?

LO 4  Executive ;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, in 2014, Liberty Global

CEO Michael Fries made about $112 million and Gamco Investors CEO

Mario Gabelli made about $89 million. Are such amounts excessive? In

answering, it might be helpful to recognize that superstar athletes such as

LeBron James, top entertainers such as Oprah Winfrey, and many others

at the top of their respective fields earn at least as much, if not more.

LO 4  ;In response to the Sarbanes-Oxley Act, many small firms

in the United States have opted to “go dark” and delist their stock. Why

might a company choose this route? What are the costs of “going dark”?

Chapter 2 Financial Statements, Taxes, and Cash Flow

CHAPTER REVIEW AND SELF-TEST PROBLEM

Cash Flow for Rasputin ;This problem will give you some practice

working with financial statements and figuring cash flow. Based on the following

information for Rasputin Corporation, prepare an income statement for 2016 and

balance sheets for 2015 and 2016. Next, following our Corporation examples

in the chapter, calculate cash flow from assets for Rasputin, cash flow to creditors,

and cash flow to stockholders for 2016. Use a 34 percent tax rate throughout. You

can check your answers below. (See Problem 21.)

■ Answer to Chapter Review and Self-Test Problem

;In preparing the balance sheets, remember that shareholders’ equity is the residual.

With this in mind, Rasputin’s balance sheets are as follows:

RASPUTIN CORPORATION

Balance Sheets as of December 31, 2015 and 2016

2015 2016 2015 2016

Current assets $2,140 $2,346 Current liabilities $ 994 $1,126

Net fixed assets 6,770 7,087 Long-term debt 2,869 2,956

Equity 5,047 5,351

Total liabilities and

Total assets $8,910 $9,433 shareholders’ equity $8,910 $9,433

The income statement is straightforward:

RASPUTIN CORPORATION

2016 Income Statement

Sales $3,990

Cost of goods sold 2,137

Depreciation 1,018

Earnings before interest and taxes $ 835

Interest paid 267

Taxable income $ 568

Taxes (34%) 193

Net income $ 375

Dividends $225

Addition to retained earnings 150

Notice that we’ve used a flat 34 percent tax rate. Also, notice that the addition to

retained

earnings is just net income less cash dividends.

We can now pick up the figures we need to get operating cash flow:

RASPUTIN CORPORATION

2016 Operating Cash Flow

Earnings before interest and taxes $ 835

+ Depreciation 1,018

− Current taxes 193

Operating cash flow $1,660

Next, we get the capital spending for the year by looking at the change in fixed assets,

remembering to account for the depreciation:

Ending fixed assets $7,087

− Beginning fixed assets 6,770

+ Depreciation 1,018

Net investment in fixed assets $1,335

After calculating beginning and ending NWC, we take the difference to get the change

in NWC:

Ending NWC $1,220

− Beginning NWC 1,146

Change in NWC $ 74

We now combine operating cash flow, net capital spending, and the change in net

working capital to get the total cash flow from assets:

RASPUTIN CORPORATION

2016 Cash Flow from Assets

Operating cash flow $1,660

− Net capital spending 1,335

− Change in NWC 74

Cash flow from assets $ 251

To get cash flow to creditors, notice that long-term borrowing increased by $87 during

the year and that interest paid was $267, so:

RASPUTIN CORPORATION

2016 Cash Flow to Creditors

Interest paid $267

− Net new borrowing 87

Cash flow to creditors $180

Finally, dividends paid were $225. To get net new equity, we have to do some extra

calculating. Total equity was up by $5,351 − 5,047 = $304. Of this increase, $150 was

from additions to retained earnings, so $154 in new equity was raised during the year. Cash

flow to stockholders was thus:

RASPUTIN CORPORATION

2016 Cash Flow to Stockholders

Dividends paid $225

− Net new equity 154

Cash flow to stockholders $ 71

As a check, notice that cash flow from assets ($251) does equal cash flow to creditors plus

cash flow to stockholders ($180 + 71 = $251).

CRITICAL THINKING AND CONCEPTS REVIEW

LO 1  ;What does liquidity measure? Explain the trade-off a firm

faces between high-liquidity and low-liquidity levels.

LO 2  Accounting and Cash ;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 a period?

LO 1  Book Values versus Market ;In preparing a balance sheet, why do

you think standard accounting practice focuses on historical cost rather

than market value?

LO 2  Operating Cash ;In comparing accounting net income and

operating cash flow, what two items do you find in net income that are not

in operating cash flow? Explain what each is and why it is excluded in

operating cash flow.

LO 1  Book Values versus Market ;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?

LO 4  Cash Flow from ;Suppose a company’s cash flow from assets was

negative for a particular period. Is this necessarily a good sign or a bad

sign?

LO 4  Operating Cash ;Suppose a company’s operating cash flow was

negative for several years running. Is this necessarily a good sign or a bad

sign?

LO 4  Net Working Capital and Capital ;Could a company’s change

in NWC be negative in a given year? (Hint: Yes.) Explain how this might

come about. What about net capital spending?

LO 4  Cash Flow to Stockholders and ;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?

LO 4  Firm ;Referring back to the examples used at the beginning of the

chapter, note that we suggested that 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

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–12)

LO 1 1. Building a Balance ;Bear Tracks, Inc., has current assets of $2,030,

net fixed assets of $9,780, current liabilities of $1,640, and long-term debt

of $4,490. What is the value of the shareholders’ equity account for this

firm? How much is net working capital?

LO 2 2. Building an Income ;Pharrell, Inc., has sales of $634,000, costs

of $328,000, depreciation expense of $73,000, interest expense of $38,000,

and a tax rate of 35 percent. What is the net income for this firm?

LO 2 3. Dividends and Retained ;Suppose the firm in Problem 2 paid out

$43,000 in cash dividends. What is the addition to retained earnings?

LO 2 4. Per-Share Earnings and ;Suppose the firm in Problem 3 had

35,000 shares of common stock outstanding. What is the earnings per share,

or EPS, figure? What is the dividends per share figure?

LO 3 5. Calculating ;The SGS Co. had $243,000 in taxable income. Using the

rates from Table in the chapter, calculate the company’s income taxes.

LO 3 6. Tax ;In Problem 5, what is the average tax rate? What is the

marginal tax rate?

LO 2 7. Calculating ;Hailey, Inc., has sales of $38,530, costs of $12,750,

depreciation expense of $2,550, and interest expense of $1,850. If the tax

rate is 35 percent, what is the operating cash flow, or OCF?

LO 4 8. Calculating Net Capital ;Rotweiler Obedience School’s December

31, 2015, balance sheet showed net fixed assets of $1,975,000, and the

December 31, 2016, balance sheet showed net fixed assets of $2,134,000. The

company’s 2016 income statement showed a depreciation expense of

$325,000. What was the company’s net capital spending for 2016?

LO 4 9. Calculating Additions to ;The December 31, 2015, balance sheet of

Maria’s Tennis Shop, Inc., showed current assets of $1,530 and current

liabilities of $1,270. The December 31, 2016, balance sheet showed current

assets of $1,685 and current liabilities of $1,305. What was the company’s

2016 change in net working capital, or NWC?

LO 4 10. Cash Flow to ;The December 31, 2015, balance sheet of Schism,

Inc., showed long-term debt of $1,410,000, and the December 31, 2016,

balance sheet showed long-term debt of $1,551,000. The 2016 income

statement showed an interest expense of $102,800. What was the firm’s

cash flow to creditors during 2016?

LO 4 11. Cash Flow to ;The December 31, 2015, balance sheet of

Schism, Inc., showed $130,000 in the common stock account and

$2,332,000 in the additional paid-in surplus account. The December 31,

2016, balance sheet showed $148,000 and $2,618,000 in the same two

accounts, respectively. If the company paid out $148,500 in cash dividends

during 2016, what was the cash flow to stockholders for the year?

LO 4 12. Calculating Cash ;Given the information for Schism, Inc., in

Problems 10 and 11, suppose you also know that the firm’s net capital

spending for 2016 was $705,000, and that the firm reduced its net working

capital investment by $115,000. What was the firm’s 2016 operating cash

flow, or OCF?

INTERMEDIATE (Questions 13–23)

LO 1 13. Market Values and Book ;Klingon Widgets, Inc., purchased new

cloaking machinery three years ago for $6 million. The machinery can be

sold to the Romulans today for $ million. Klingon’s current balance sheet

shows net fixed assets of $ million, current liabilities of $850,000, and

net working capital of $220,000. If all the current accounts were liquidated

today, the company would receive $ million cash. What is the book

value of Klingon’s total assets today? What is the sum of NWC and the

market value of fixed assets?

LO 4 14. Calculating Cash ;Weiland Co. shows the following information on

its 2016 income statement: sales = $173,000; costs = $91,400; other

expenses = $5,100; depreciation expense = $12,100; interest expense =

$8,900; taxes = $21,090; dividends = $9,700. In addition, you’re told that

the firm issued $2,900 in new equity during 2016 and redeemed $4,000 in

outstanding long-term debt.

1. What is the 2016 operating cash flow?
2. What is the 2016 cash flow to creditors?
3. What is the 2016 cash flow to stockholders?
4. If net fixed assets increased by $23,140 during the year, what was the

addition to NWC?

LO 2 15. Using Income ;Given the following information for Sookie’s

Cookies Co., calculate the depreciation expense: sales = $67,000; costs =

$49,200; addition to retained earnings = $3,500; dividends paid = $2,170;

interest expense = $1,980; tax rate = 40 percent.

LO 1 16. Preparing a Balance ;Prepare a balance sheet for Alaskan

Strawberry Corp. as of December 31, 2016, based on the following

information: cash = $197,000; patents and copyrights = $863,000; accounts

payable = $288,000; accounts receivable = $265,000; tangible net fixed

assets = $5,150,000; inventory = $563,000; notes payable = $194,000;

accumulated retained earnings = $4,586,000; long-term debt = $1,590,000.

LO 1 17. Residual ;Chevelle, Inc., is obligated to pay its creditors $8,400

during the year.

1. What is the value of the shareholders’ equity if assets equal $9,300?
2. What if assets equal $6,900?

LO 3 18. Marginal versus Average Tax ;(Refer to Table ) Corporation

Growth has $76,500 in taxable income, and Corporation Income has

$7,650,000 in taxable income.

1. What is the tax bill for each firm?
2. 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?

LO 2 19. Net Income and ;During the year, Belyk Paving Co. had sales of

$2,350,000. Cost of goods sold, administrative and selling expenses, and

depreciation expense were $1,295,000, $530,000, and $420,000,

respectively. In addition, the company had an interest expense of $245,000

and a tax rate of 35 percent. (Ignore any tax loss carryback or carryforward

provisions.)

1. What is the company’s net income?
2. What is its operating cash flow?
3. Explain your results in parts (a) and (b).

LO 2 20. Accounting Values versus Cash ;In Problem 19, suppose Belyk

Paving Co. paid out $395,000 in cash dividends. Is this possible? If net

capital spending was zero, no new investments were made in net working

capital, and no new stock was issued during the year, what do you know

about the firm’s long-term debt account?

LO 4 21. Calculating Cash ;Titan Football Manufacturing had the following

operating results for 2016: sales = $28,476; cost of goods sold = $20,136;

depreciation expense = $3,408; interest expense = $497; dividends paid =

$739. At the beginning of the year, net fixed assets were $19,872, current

assets were $3,528, and current liabilities were $3,110. At the end of the

year, net fixed assets were $22,608, current assets were $4,234, and current

liabilities were $2,981. The tax rate for 2016 was 40 percent.

1. What is net income for 2016?
2. What is the operating cash flow for 2016?
3. What is the cash flow from assets for 2016? Is this possible? Explain.
4. If no new debt was issued during the year, what is the cash flow to

creditors? What is the cash flow to stockholders? Explain and interpret

the positive and negative signs of your answers in parts (a) through (d).

LO 4 22. Calculating Cash ;Consider the following abbreviated financial

statements for Cabo Wabo, Inc.:

CABO WABO, INC.

Partial Balance Sheets as of December 31, 2015 and 2016

2015 2016 2015 2016

Assets Liabilities and Owners’ Equity

Current assets $ 2,718 $ 2,881 Current liabilities $1,174 $1,726

Net fixed assets 12,602 13,175 Long-term debt 6,873 8,019

CABO WABO, INC.

2016 Income Statement

Sales $40,664

Costs 20,393

Depreciation 3,434

Interest paid 938

1. What is owners’ equity for 2015 and 2016?
2. What is the change in net working capital for 2016?
3. In 2016, Cabo Wabo purchased $7,160 in new fixed assets. How much

in fixed assets did the company sell? What is the cash flow from assets

for the year? (The tax rate is 40 percent.)

1. During 2016, Cabo Wabo raised $2,155 in new long-term debt. How

much long-term debt must the company have paid off during the year?

What is the cash flow to creditors?

LO 4 23. Cash Flow ;Graffiti Advertising, Inc., reported the following

financial statements for the last two years. Construct the cash flow identity

for the company. Explain what each number means.

2016 Income Statement

Sales $714,978

Cost of goods sold 384,591

Selling and administrative 157,787

Depreciation 69,038

EBIT $103,562

Interest 24,410

EBT $ 79,152

Taxes 27,703

Net income $ 51,449

Dividends $ 16,200

Addition to retained earnings 35,249

CHALLENGE (Questions 24–25)

LO 4 24. Net Fixed Assets and ;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.

LO 3 25. Tax ;Refer to the corporate marginal tax rate information in

Table

1. 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?

1. 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 in

taxable income? Is the same thing happening here?

1. Both the 39 percent and 38 percent tax rates represent what is

called a tax “; 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?

Chapter 3 Working with Financial Statements

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Common-Size ;Here are the most recent financial statements for

Wildhack. Prepare a common-size income statement based on this information.

How do you interpret the standardized net income? What percentage of sales goes

to cost of goods sold? (See Problem 15.)

Financial ;Based on the balance sheets and income statement in the

previous problem, calculate the following ratios for 2016: (See Problem 35.)

Current ratio

Quick ratio

Cash ratio

Inventory turnover

Receivables turnover

Days’ sales in inventory

Days’ sales in receivables

Total debt ratio

Times interest earned ratio

Cash coverage ratio

ROE and the DuPont ;Calculate the 2016 ROE for the Wildhack

Corporation and then break down your answer into its component parts using the

DuPont identity. (See Problem 36.)

Sustainable ;Based on the following information, what growth rate can

Corwin maintain if no external financing is used? What is the sustainable growth

rate? (See Problems 20, 21.)

CORWIN COMPANY

Financial Statements

Income Statement Balance Sheet

Sales $2,750 Current assets $ 600 Long-term debt $ 200

Cost of sales 2,400 Net fixed assets 800 Equity 1,200

Tax (34%) 119 Total $1,400 Total $1,400

Net income $ 231

Dividends $ 77

■ Answers to Chapter Review and Self-Test Problems

;We’ve calculated the common-size income statement below. Remember that we

simply divide each item by total sales.

Net income is percent of sales. Because this is the percentage of each sales dollar

that makes its way to the bottom line, the standardized net income is the firm’s profit

margin. Cost of goods sold is percent of sales.

;We’ve calculated the ratios below based on the ending figures. If you don’t

remember a definition, refer back to Table

Current ratio $648/$1,183 = .55 times

Quick ratio $280/$1,183 = .24 times

Cash ratio $88/$1,183 = .07 times

Inventory turnover $2,453/$368 = times

Receivables turnover $3,756/$192 = times

Days’ sales in inventory 365 = days

Days’ sales in receivables 365 = days

Total debt ratio $3,260/$6,002 =

Times interest earned ratio $813/$613 = times

Cash coverage ratio $1,303/$613 = times

;The return on equity is the ratio of net income to total equity. For Wildhack, this is

$132/$2,742 = , which is not outstanding. Given the DuPont identity, ROE can

be written as:

ROE = Profit margin × Total asset turnover × Equity multiplier

= $132/$3,756 × $3,756/$6,002 × $6,002/$2,742

= × .626 ×

=

Notice that return on assets, ROA, is × .626 =

;Corwin retains b = (1 − .33) = 2∕3 ≈ .67 of net income. Return on assets is

$231/$1,400 = The internal growth rate is:

ROA × b

1 − ROA × b =

.165 × 2∕3

1 − .165 × 2∕3

=

Return on equity for Corwin is $231/$1,200 = , so we can calculate the

sustainable growth rate as:

ROE × b

1 − ROE × b =

.1925 × 2∕3

1 − .1925 × 2∕3

=

CRITICAL THINKING AND CONCEPTS REVIEW

LO 2  Current ;What effect would the following actions have on a firm’s

current ratio? Assume that net working capital is positive.

1. Inventory is purchased.
2. A supplier is paid.
3. A short-term bank loan is repaid.
4. A long-term debt is paid off early.
5. A customer pays off a credit account.
6. Inventory is sold at cost.
7. Inventory is sold for a profit.

LO 2  Current Ratio and Quick ;In recent years, Dixie Co. has greatly

increased its current ratio. At the same time, the quick ratio has fallen.

What has happened? Has the liquidity of the company improved?

LO 2  Current ;Explain what it means for a firm to have a current ratio

equal to .50. Would the firm be better off if the current ratio were

What if it were Explain your answers.

LO 2  Financial ;Fully explain the kind of information the following

financial ratios provide about a firm:

1. Quick ratio
2. Cash ratio
3. Capital intensity ratio
4. Total asset turnover
5. Equity multiplier
6. Times interest earned ratio
7. Profit margin
8. Return on assets
9. Return on equity
10. Price–earnings ratio

LO 1  Standardized Financial ;What types of information do

common-size financial statements reveal about the firm? What is the best

use for these common-size statements?

LO 2  Peer Group ;Explain what peer group analysis means. As a

financial manager, how could you use the results of peer group analysis to

evaluate the performance of your firm? How is a peer group different from

an aspirant group?

LO 3  DuPont ;Why is the DuPont identity a valuable tool for analyzing

the performance of a firm? Discuss the types of information it reveals as

compared to ROE considered by itself.

LO 2  Industry-Specific ;Specialized ratios are sometimes used in

specific industries. For example, the so-called book-to-bill ratio is closely

watched for semiconductor manufacturers. A ratio of .93 indicates that for

every $100 worth of chips shipped over some period, only $93 worth of

new orders were received. In January 2015 the North American

semiconductor equipment industry’s book-to-bill ratio was , with

orders of $ billion and billings of $ billion. The most recent

peak in the book-to-bill ratio was in February 2010 when it reached

The most recent low occurred in January 2009 when it reached .47. What

is this ratio intended to measure? Why do you think it is so closely

followed?

LO 2  Industry-Specific ;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?

LO 2  Industry-Specific ;There are many ways of using standardized

financial information beyond those discussed in this chapter. The usual

goal is to put firms on an equal footing for comparison purposes. For

example, for auto manufacturers, it is common to express sales, costs, and

profits on a per-car basis. For each of the following industries, give an

example of an actual company and discuss one or more potentially useful

means of standardizing financial information:

1. Public utilities
2. Large retailers
3. Airlines
4. Online services
5. Hospitals
6. College textbook publishers

LO 2  Financial Statement ;You are examining the common-size

income statements for a company for the past five years and have noticed

that the cost of goods as a percentage of sales has been increasing steadily.

At the same time, EBIT as a percentage of sales has been decreasing.

What might account for the trends in these ratios?

LO 2  Financial Statement ;In the previous question, what actions

might managers take to improve these ratios?

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–26)

LO 2 1. Calculating Liquidity ;SDJ, Inc., has net working capital of $1,965,

current liabilities of $5,460, and inventory of $2,170. What is the current

ratio? What is the quick ratio?

LO 2 2. Calculating Profitability ;Aguilera, Inc., has sales of $

million, total assets of $ million, and total debt of $ million. If

the profit margin is 7 percent, what is net income? What is ROA? What

is ROE?

LO 2 3. Calculating the Average Collection ;Ordonez Lumber Yard has a

current accounts receivable balance of $583,174. Credit sales for the year

just ended were $6,787,626. What is the receivables turnover? The days’

sales in receivables? How long did it take on average for credit customers to

pay off their accounts during the past year?

LO 2 4. Calculating Inventory ;Bobaflex Corporation has ending

inventory of $527,156 and cost of goods sold for the year just ended was

$8,543,132. What is the inventory turnover? The days’ sales in inventory?

How long on average did a unit of inventory sit on the shelf before it was

sold?

LO 2 5. Calculating Leverage ;Fincher, Inc., has a total debt ratio of .19.

What is its debt–equity ratio? What is its equity multiplier?

LO 2 6. Calculating Market Value ;Rossdale, Inc., had additions to retained

earnings for the year just ended of $534,000. The firm paid out $185,000

in cash dividends, and it has ending total equity of $ million. If the

company currently has 365,000 shares of common stock outstanding, what

are earnings per share? Dividends per share? What is book value per share?

If the stock currently sells for $49 per share, what is the market-to-book

ratio? The price–earnings ratio? If total sales were $ million, what is the

price–sales ratio?

LO 3 7. DuPont ;If jPhone, Inc., has an equity multiplier of , total

asset turnover of , and a profit margin of percent, what is its

ROE?

LO 3 8. DuPont ;Jiminy Cricket Removal has a profit margin of

percent, total asset turnover of , and ROE of percent. What is this

firm’s debt–equity ratio?

LO 2 9. Calculating Average Payables ;For the past year, Coach, Inc., had

a cost of goods sold of $87,386. At the end of the year, the accounts payable

balance was $19,472. How long on average did it take the company to pay

off its suppliers during the year? What might a large value for this ratio

imply?

LO 2 10. Equity Multiplier and Return on ;Shelton Company has a

debt–equity ratio of .75. Return on assets is percent, and total

equity is $815,000. What is the equity multiplier? Return on equity?

Net income?

LO 3 11. Internal ;If Williams, Inc., has an ROA of percent and a payout

ratio of 25 percent, what is its internal growth rate?

LO 3 12. Sustainable ;If the Crash Davis Driving School has an ROE of

percent and a payout ratio of 20 percent, what is its sustainable growth

rate?

LO 3 13. Sustainable ;Based on the following information, calculate the

sustainable growth rate for Southern Lights Co.:

Profit margin =

Capital intensity ratio = .45

Debt–equity ratio = .55

Net income = $120,000

Dividends = $65,000

LO 3 14. Sustainable ;Assuming the following ratios are constant, what is

the sustainable growth rate?

Total asset turnover =

Profit margin =

Equity multiplier =

Payout ratio = 55%

Bethesda Mining Company reports the following balance sheet information

for 2015 and 2016. Use this information to work Problems 15 through 17.

LO 1 15. Preparing Standardized Financial ;Prepare the 2015 and 2016

common-size balance sheets for Bethesda Mining.

LO 2 16. Calculating Financial ;Based on the balance sheets given for

Bethesda Mining, calculate the following financial ratios for each year:

1. Current ratio
2. Quick ratio
3. Cash ratio
4. Debt–equity ratio and equity multiplier
5. Total debt ratio

LO 3 17. DuPont ;Suppose that the Bethesda Mining Company had sales of

$2,945,376 and net income of $89,351 for the year ending December 31,

2016. Calculate the DuPont identity.

LO 3 18. DuPont ;The Cavo Company has an ROA of percent, a profit

margin of percent, and an ROE of 16 percent. What is the company’s

total asset turnover? What is the equity multiplier?

LO 2 19. Return on ;Beckinsale, Inc., has a profit margin of percent on

sales of $14,500,000. If the firm has debt of $7,300,000 and total assets of

$11,200,000, what is the firm’s ROA?

LO 3 20. Calculating Internal ;The most recent financial statements for

Shinoda Manufacturing Co. are shown here:

Assets and costs are proportional to sales. Debt and equity are not. The company

maintains a constant 40 percent dividend payout ratio. No external financing

is possible. What is the internal growth rate?

LO 3 21. Calculating Sustainable ;For Shinoda Manufacturing in Problem

20, what is the sustainable growth rate?

LO 2 22. Total Asset ;Kaleb’s Karate Supply had a profit margin of

percent, sales of $ million, and total assets of $ million. What

was total asset turnover? If management set a goal of increasing total asset

turnover to times, what would the new sales figure need to be,

assuming no increase in total assets?

LO 2 23. Return on ;Carroll, Inc., has a total debt ratio of .75, total debt of

$353,000, and net income of $18,750. What is the company’s return on

equity?

LO 2 24. Market Value ;Ames, Inc., has a current stock price of $58. For

the past year, the company had net income of $8,400,000, total equity of

$25,300,000, sales of $52,800,000, and million shares of stock

outstanding. What are earnings per share (EPS)? Price–earnings ratio?

Price–sales ratio? Book value per share? Market-to-book ratio?

LO 3 25. Profit ;Dimeback Co. has total assets of $7,450,000 and a total

asset turnover of times. If the return on assets is percent, what is its

profit margin?

LO 2 26. Enterprise Value–EBITDA ;The market value of the equity of

Ginger, Inc., is $635,000. The balance sheet shows $39,000 in cash and

$215,000 in debt, while the income statement has EBIT of $96,400 and a

total of $168,000 in depreciation and amortization. What is the enterprise

value–EBITDA multiple for this company?

INTERMEDIATE (Questions 27–46)

LO 3 27. Using the DuPont ;Y3K, Inc., has sales of $10,570, total assets of

$4,670, and a debt–equity ratio of .25. If its return on equity is 15 percent,

what is its net income?

LO 2 28. Ratios and Fixed ;The Smathers Company has a long-term debt

ratio (, the ratio of long-term debt to long-term debt plus equity) of .45

and a current ratio of Current liabilities are $2,435, sales are $11,610,

profit margin is 9 percent, and ROE is percent. What is the amount of

the firm’s net fixed assets?

LO 2 29. Profit ;In response to complaints about high prices, a grocery chain

runs the following advertising campaign: “If you pay your child $2 to go

buy $50 worth of groceries, then your child makes twice as much on the

trip as we ; You’ve collected the following information from the grocery

chain’s financial statements:

Evaluate the grocery chain’s claim. What is the basis for the statement? Is

this claim misleading? Why or why not?

LO 3 30. Using the DuPont ;The Dahlia Company has net income of

$162,840. There are currently days’ sales in receivables. Total assets

are $794,350, total receivables are $145,350, and the debt–equity ratio is

.25. What is the company’s profit margin? Its total asset turnover? Its ROE?

LO 2 31. Calculating the Cash Coverage ;Delectable Parsnip, ;s, net

income for the most recent year was $8,417. The tax rate was 34 percent.

The firm paid $4,632 in total interest expense and deducted $5,105 in

depreciation expense. What was the company’s cash coverage ratio for

the year?

LO 2 32. Calculating the Times Interest Earned ;For the most recent year,

Seether, Inc., had sales of $534,000, cost of goods sold of $241,680,

depreciation expense of $60,400, and additions to retained earnings of

$72,800. The firm currently has 20,000 shares of common stock outstanding,

and the previous year’s dividends per share were $ Assuming a 34

percent income tax rate, what was the times interest earned ratio?

LO 2 33. Return on ;A fire has destroyed a large percentage of the financial

records of the Excandesco Company. You have the task of piecing together

information in order to release a financial report. You have found the return

on equity to be percent. Sales were $1,840,000, the total debt ratio was

.37, and total debt was $673,000. What is the return on assets (ROA)?

LO 2 34. Ratios and Foreign ;Prince Albert Canning PLC had a net loss

of ￡27,860 on sales of ￡512,621. 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 $765,828. What was the net loss in

dollars?

Some recent financial statements for Smolira Golf, Inc., follow. Use this information

to work Problems 35 through 38.

35. Calculating Financial ;Find the following financial ratios for Smolira

Golf (use year-end figures rather than average values where appropriate):

Short-term solvency ratios

1. Current ratio ________________
2. Quick ratio ________________
3. Cash ratio ________________

Asset utilization ratios

1. Total asset turnover ________________
2. Inventory turnover ________________
3. Receivables turnover ________________

Long-term solvency ratios

1. Total debt ratio ________________
2. Debt–equity ratio ________________
3. Equity multiplier ________________
4. Times interest earned ratio ________________
5. Cash coverage ratio ________________

Profitability ratios

1. Profit margin ________________
2. Return on assets ________________
3. Return on equity ________________

LO 3 36. DuPont ;Construct the DuPont identity for Smolira Golf.

LO 2 37. Market Value ;Smolira Golf has 10,000 shares of common stock

outstanding, and the market price for a share of stock at the end of 2016 was

$73. What is the price–earnings ratio? What is the price–sales ratio? What are

the dividends per share? What is the market-to-book ratio at the end of 2016?

38. Interpreting Financial ;After calculating the ratios for Smolira Golf,

you have uncovered the following industry ratios for 2016:

Lower Quartile Median Upper Quartile

Current ratio

Total asset turnover

Debt–equity ratio .25 .50 .60

Profit margin

How is Smolira Golf performing based on these ratios?

LO 3 39. Growth and Profit ;Fulkerson Manufacturing wishes to maintain a

sustainable growth rate of 8 percent a year, a debt–equity ratio of .85, and

a dividend payout ratio of 30 percent. The ratio of total assets to sales is

constant at What profit margin must the firm achieve?

LO 2 40. Market Value ;Abercrombie & Fitch and American Eagle Outfitters

(AEO), reported the following numbers (in millions) for fiscal year 2014.

Calculate the earnings per share, market-to-book ratio, and price–earnings

ratio for each company.

Abercrombie AEO

Net income $ $

Shares outstanding

Stock price $ $

Total equity $1, $1,

LO 3 41. Growth and ;A firm wishes to maintain an internal growth rate of

percent and a dividend payout ratio of 25 percent. The current profit

margin is percent and the firm uses no external financing sources. What

must total asset turnover be?

LO 3 42. Sustainable ;Based on the following information, calculate the

sustainable growth rate for Sully, Inc.:

Profit margin =

Total asset turnover =

Total debt ratio = .30

Payout ratio = 15%

What is the ROA here?

LO 3 43. Sustainable Growth and Outside ;You’ve collected the

following information about Erna, Inc.:

Sales = $275,000

Net income = $19,000

Dividends = $8,100

Total debt = $67,000

Total equity = $91,000

What is the sustainable growth rate for the company? If it does grow at this

rate, how much new borrowing will take place in the coming year, assuming

a constant debt–equity ratio? What growth rate could be supported with no

outside financing at all?

LO 4 44. Constraints on ;High Flyer, Inc., wishes to maintain a growth rate

of 13 percent per year and a debt–equity ratio of .35. The profit margin is

6 percent, and total asset turnover is constant at Is this growth rate

possible? To answer, determine what the dividend payout ratio must be.

How do you interpret the result?

LO 3 45. Internal and Sustainable Growth ;Best Buy reported the following

numbers (in millions) for the years ending February 1, 2014, and January 31,

2015. What are the internal and sustainable growth rates? What are the

internal and sustainable growth rates using ROE × b and (ROA × b) and

the end of period equity (assets)? What are the growth rates if you use the

beginning of period equity in this equation? Why aren’t the growth rates

the same? What is your best estimate of the internal and sustainable

growth rates?

2014 2015

Net income $ 1,233

Dividends 251

Total assets $14,013 15,256

Total equity 3,986 4,995

LO 3 46. Expanded DuPont ;Hershey Co. reported the following income

statement and balance sheet (in millions) for 2014. Construct the expanded

DuPont identity similar to Figure What is the company’s return on

equity?

Chapter 4 Introduction to Valuation: The Time Value of Money

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Calculating Future ;Assume you deposit $1,000 today in an account that

pays 8 percent interest. How much will you have in four years? (See Problem 2.)

Calculating Present ;Suppose you have just celebrated your 19th birthday.

A rich uncle set up a trust fund for you that will pay you $100,000 when you turn

25. If the relevant discount rate is 11 percent, how much is this fund worth today?

(See Problem 3.)

Calculating Rates of ;You’ve been offered an investment that will double

your money in 12 years. What rate of return are you being offered? Check your

answer using the Rule of 72. (See Problem 4.)

Calculating the Number of ;You’ve been offered an investment that will

pay you 7 percent per year. If you invest $10,000, how long until you have $20,000?

How long until you have $30,000? (See Problem 5.)

■ Answers to Chapter Review and Self-Test Problems

;We need to calculate the future value of $1,000 at 8 percent for four years. The

future value factor is:

=

The future value is thus $1,000 × = $1,

;We need the present value of $100,000 to be paid in six years at 11 percent. The

discount factor is:

1 = 1 = .5346

The present value is thus about $53,460.

;Suppose you invest, say, $100. You will have $200 in 12 years with this investment.

So, $100 is the amount you have today, the present value, and $200 is the amount

you will have in 12 years, or the future value. From the basic present value

equation, we have:

$200 = $100 × (1 × r)12

2 = (1 × r)12

From here, we need to solve for r, the unknown rate. As shown in the chapter, there

are several different ways to do this. We will take the 12th root of 2 (by raising 2 to

the power of 1/12):

2(1/12) = 1 + r

= 1 + r

r =

Using the Rule of 72, we have 72/t = r%, or 72/12 = 6%, so our answer looks good

(remember that the Rule of 72 is only an approximation).

;The basic equation is:

$20,000 = $10,000 × (1 + .07)t

2 = (1 + .07)t

If we solve for t, we get that t = years. Using the Rule of 72, we get 72/7 =

years, so, once again, our answer looks good. To get $30,000, verify for

yourself that you will have to wait years.

CRITICAL THINKING AND CONCEPTS REVIEW

LO 1  ;What is compounding? What is discounting?

LO 1  Compounding and ;As you increase the length of time involved,

what happens to future values? What happens to present values?

LO 1  Compounding and Interest ;What happens to a future value if you

increase the rate, r? What happens to a present value?

LO 1  Future ;Suppose you deposit a large sum in an account that earns

a low interest rate and simultaneously deposit a small sum in an account

with a high interest rate. Which account will have the larger future value?

LO 3  Ethical ;Take a look back at Example Is it deceptive

advertising? Is it unethical to advertise a future value like this without a

disclaimer?

Use the following information for the next five questions:

On March 28, 2008, Toyota Motor Credit Corporation (TMCC), a subsidiary of

Toyota

Motor, offered some securities for sale to the public. 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.

LO 2  Time Value of ;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?

LO 3  Call ;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?

LO 3  Time Value of ;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?

LO 3  Investment ;Suppose that when TMCC offered the security

for $24,099, the Treasury had offered an essentially identical security.

Do you think it would have had a higher or lower price? Why?

LO 3  Length of ;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 2018,

do you think the price would be higher or lower than today’s price? Why?

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the Preface for more information.

BASIC (Questions 1–15)

LO 1 1. Simple Interest versus Compound ;First City Bank pays 6 percent

simple interest on its savings account balances, whereas Second City Bank

pays 6 percent interest compounded annually. If you made a deposit of

$8,100 in each bank, how much more money would you earn from your

Second City Bank account at the end of 10 years?

LO 1 2. Calculating Future ;For each of the following, compute the future value:

Present Value Years Interest Rate Future Value

$ 3,150 7 13%

8,453 16 7

89,305 19 9

227,382 26 5

LO 2 3. Calculating Present ;For each of the following, compute the

present value:

Present Value Years Interest Rate Future Value

15 7% $ 17,328

8 11 41,517

13 10 790,382

25 13 647,816

LO 3 4. Calculating Interest ;Solve for the unknown interest rate in each of

the following:

Present Value Years Interest Rate Future Value

$ 715 11 $ 1,381

905 8 1,718

15,000 23 141,832

70,300 16 312,815

5. Calculating the Number of ;Solve for the unknown number of years

in each of the following:

Present Value Years Interest Rate Future Value

$ 195 9% $ 873

2,105 7 3,500

47,800 12 326,500

38,650 19 213,380

LO 3 6. Calculating Rates of ;Assume the total cost of a college education

will be $295,000 when your child enters college in 18 years. You presently

have $53,000 to invest. What annual rate of interest must you earn on your

investment to cover the cost of your child’s college education?

LO 4 7. Calculating the Number of ;At percent interest, how long does

it take to double your money? To quadruple it?

LO 3 8. Calculating Rates of ;In 2014, an 1874 $20 double eagle sold for

$15,000. What was the rate of return on this investment?

LO 4 9. Calculating the Number of ;You’re trying to save to buy a new

$150,000 Ferrari. You have $35,000 today that can be invested at your bank.

The bank pays percent annual interest on its accounts. How long will it

be before you have enough to buy the car?

LO 2 10. Calculating Present ;Imprudential, Inc., has an unfunded pension

liability of $730 million that must be paid in 25 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 percent, what is the present value of this liability?

LO 2 11. Calculating Present ;You have just received notification that you

have won the $1 million first prize in the Centennial Lottery. However, the

prize will be awarded on your 100th birthday (assuming you’re around to

collect), 80 years from now. What is the present value of your windfall if the

appropriate discount rate is percent?

LO 1 12. Calculating Future ;Your coin collection contains fifty 1952 silver

dollars. If your grandparents purchased them for their face value when they

were new, how much will your collection be worth when you retire in 2063,

assuming they appreciate at an annual rate of percent?

LO 1 13. Calculating Growth Rates and Future ;In 1895, the first Open

Golf Championship was held. The winner’s prize money was $150. In 2014,

the winner’s check was $1,620,000. What was the annual percentage

increase in the winner’s check over this period? If the winner’s prize

increases at the same rate, what will it be in 2045?

LO 3 14. Calculating Rates of ;In 2014, an Action Comics No. 1, featuring

the first appearance of Superman, was sold at auction for $3,207,852. The

comic book was originally sold in 1938 for $.10. What was the annual

increase in the value of this comic book?

LO 3 15. Calculating Rates of ;Although appealing to more refined tastes,

art as a collectible has not always performed so profitably. During 2003,

Sotheby’s 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?

INTERMEDIATE (Questions 16–25)

LO 3 16. Calculating Rates of ;Refer back to the Series EE savings bonds we

discussed at the very beginning of the chapter.

1. Assuming you purchased a $50 face value bond, what rate of return

would you earn if you held the bond for 20 years until it doubled in

value?

1. If you purchased a $50 face value bond in early 2015 at the then current

interest rate of .10 percent per year, how much would the bond be worth

in 2025?

1. In 2025, instead of cashing the bond in for its then current value, you

decide to hold the bond until it doubles in face value in 2035. What rate

of return will you earn over the last 10 years?

LO 2 17. Calculating Present ;Suppose you are still committed to

owning a $150,000 Ferrari (see Question 9). If you believe your mutual

fund can achieve a percent annual rate of return, and you want to

buy the car in 10 years on the day you turn 30, how much must you

invest today?

LO 1 18. Calculating Future ;You have just made your first $5,000

contribution to your individual retirement account. Assuming you earn an

annual rate of return of percent and make no additional contributions,

what will your account be worth when you retire in 45 years? What if

you wait 10 years before contributing? (Does this suggest an investment

strategy?)

LO 1 19. Calculating Future ;You are scheduled to receive $13,000 in

two years. When you receive it, you will invest it for six more years at

percent per year. How much will you have in eight years?

LO 4 20. Calculating the Number of ;You expect to receive $30,000 at

graduation in two years. You plan on investing it at 9 percent until you have

$150,000. How long will you wait from now? (Better than the situation in

Question 9, but still no Ferrari.)

LO 1 21. Calculating Future ;You have $6,150 to deposit. Regency Bank

offers 12 percent per year compounded monthly (1 percent per month),

while King Bank offers 12 percent but will only compound annually. How

much will your investment be worth in 20 years at each bank?

LO 3 22. Calculating Rates of ;An investment offers to triple your money

in 24 months (don’t believe it). What rate per three months are you being

offered?

LO 4 23. Calculating the Number of ;You can earn .27 percent per month

at your bank. If you deposit $1,800, how long must you wait until your

account has grown to $3,100?

LO 2 24. Calculating Present ;You need $85,000 in 10 years. If you can earn

.65 percent per month, how much will you have to deposit today?

LO 2 25. Calculating Present ;You have decided that you want to be a

millionaire when you retire in 45 years. If you can earn an annual return of

11 percent, how much do you have to invest today? What if you can earn

percent?

26. Calculating Future ;You have $20,000 you want to invest for the

next 40 years. You are offered an investment plan that will pay you

7 percent per year for the next 20 years and 11 percent per year for the last

20 years. How much will you have at the end of the 40 years? Does it matter

if the investment plan pays you 11 percent per year for the first 20 years and

7 percent per year for the next 20 years? Why or why not?

Chapter 5 Discounted Cash Flow Valuation

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Present Values with Multiple Cash ;A first-round-draft choice quarterback

has been signed to a three-year, $10 million contract. The details provide for an

immediate cash bonus of $1 million. The player is to receive $2 million in salary at

the end of the first year, $3 million the next, and $4 million at the end of the last

year. Assuming a 10 percent discount rate, is this package worth $10 million? How

much is it worth? (See Problem 1.)

Future Value with Multiple Cash ;You plan to make a series of deposits in

an interest-bearing account. You will deposit $1,000 today, $2,000 in two years, and

$8,000 in five years. If you withdraw $3,000 in three years and $5,000 in seven

years, how much will you have after eight years if the interest rate is 9 percent?

What is the present value of these cash flows? (See Problem 3.)

Annuity Present ;You are looking into an investment that will pay you

$12,000 per year for the next 10 years. If you require a 15 percent return, what is

the most you would pay for this investment? (See Problem 2.)

APR versus ;The going rate on student loans is quoted as 9 percent APR. The

terms of the loan call for monthly payments. What is the effective annual rate, or

EAR, on such a student loan? (See Problem 14.)

It’s the Principal That ;Suppose you borrow $10,000. You are going to

repay the loan by making equal annual payments for five years. The interest rate on

the loan is 14 percent per year. Prepare an amortization schedule for the loan. How

much interest will you pay over the life of the loan? (See Problem 55.)

Just a Little Bit Each ;You’ve recently finished your MBA at the Darnit

School. Naturally, you must purchase a new BMW immediately. The car costs

about $42,000. The bank quotes an interest rate of 15 percent APR for a 72-month

loan with a 10 percent down payment. What will your monthly payment be? What

is the effective interest rate on the loan? (See Problem 20.)

■ Answers to Chapter Review and Self-Test Problems

;Obviously, the package is not worth $10 million because the payments are spread

out over three years. The bonus is paid today, so it’s worth $1 million. The present

values for the three subsequent salary payments are:

$2 + $3 + $4 = $2 + $3 + $4

= $

The package is worth a total of $ million.

;We will calculate the future value for each of the cash flows separately and then add

the results up. Notice that we treat the withdrawals as negative cash flows:

$1,000 × = $1,000 × = $ 1,

$2,000 × = $2,000 × = 3,

−$3,000 × = −$3,000 × = −4,

$8,000 × = $8,000 × = 10,

−$5,000 × = −$5,000 × = −5,

Total future value = $ 5,

This value includes a small rounding error.

To calculate the present value, we could discount each cash flow back to the

present or we could discount back a single year at a time. However, since we

already know that the future value in eight years is $5,, the easy way to get

the PV is just to discount this amount back eight years:

Present value = $5,

= $5,

= $2,

We again ignore a small rounding error. For practice, you can verify that this is

what you get if you discount each cash flow back separately.

;The most you would be willing to pay is the present value of $12,000 per year for

10 years at a 15 percent discount rate. The cash flows here are in ordinary annuity

form, so the relevant present value factor is:

Annuity present value factor = [1 − (1)]/.15

= (1 − .2472)/.15

=

The present value of the 10 cash flows is thus:

Present value = $12,000 ×

= $60,225

This is the most you would pay.

;A rate of 9 percent with monthly payments is actually 9%/12 = .75% per month.

The EAR is thus:

EAR = (1 + .09/12)12 − 1 =

;We first need to calculate the annual payment. With a present value of $10,000, an interest

rate of 14 percent, and a term of five years, the payment can be determined from:

$10,000 = Payment × (1 − 1)/.14

= Payment ×

Therefore, the payment is $10,000 = $2, (actually, it’s $2,;

this will create some small rounding errors in the accompanying schedule). We can

now prepare the amortization schedule as follows:

Beginning Total Interest Principal Ending

Year Balance Payment Paid Paid Balance

1 $10, $ 2, $1, $ 1, $8,

2 8, 2, 1, 1, 6,

3 6, 2, 1, 4,

4 4, 2, 2, 2,

5 2, 2, 2, .00

Totals $14, $4, $10,

;The cash flows on the car loan are in annuity form, so we only need to find the

payment. The interest rate is 15%/12 = per month, and there are 72 months.

The first thing we need is the annuity factor for 72 periods at percent per period:

Annuity present value factor = (1 − Present value factor)/r

= [1 − (1)]/.0125

= [1 − (1)]/.0125

= (1 − .4088)/.0125

=

The present value is the amount we finance. With a 10 percent down payment, we

will be borrowing 90 percent of $42,000, or $37,800.

So, to find the payment, we need to solve for C in the following:

$37,800 = C × Annuity present value factor

= C ×

Rearranging things a bit, we have:

C = $37,800 × (1)

= $37,800 × .02115

= $

Your payment is just under $800 per month.

The actual interest rate on this loan is percent per month. Based on our

work in the chapter, we can calculate the effective annual rate as:

EAR = − 1 =

The effective rate is about one point higher than the quoted rate.

CRITICAL THINKING AND CONCEPTS REVIEW

LO 1  Annuity ;As you increase the length of time involved, what

happens to the present value of an annuity? What happens to the future

value?

LO 1  Interest ;What happens to the future value of an annuity if you

increase the rate, r? What happens to the present value?

LO 1  Annuity Present ;Tri-State Megabucks Lottery advertises a

LO 2

$10 million grand prize. The winner receives $500,000 today and

19 annual payments of $500,000. A lump sum option of $5 million

payable immediately is also available. Is this deceptive advertising?

LO 1  Annuity Present ;Suppose you won the Tri-State Megabucks

Lottery in the previous question. What factors should you take into

account in deciding whether you should take the annuity option or the

lump sum option?

LO 1  Present ;If you were an athlete negotiating a contract, would you

want a big signing bonus payable immediately and smaller payments in

the future, or vice versa? How about looking at it from the team’s

perspective?

LO 1  Present ;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?

LO 4  APR and ;Should lending laws be changed to require lenders to

report EARs instead of APRs? Why or why not?

LO 3  Time ;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.

LO 3  Time ;In words, how would you go about valuing the subsidy on a

subsidized Stafford loan?

LO 3  Time ;Eligibility for a subsidized Stafford loan is based on current

financial need. However, both subsidized and unsubsidized Stafford loans

are repaid out of future income. Given this, do you see a possible objection

to having two types?

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–28)

LO 1 1. Present Value and Multiple Cash ;Eulis Co. has identified an

investment project with the following cash flows. If the discount rate is 10

percent, what is the present value of these cash flows? What is the present

value at 18 percent? At 24 percent?

2. Present Value and Multiple Cash ;Investment X offers to pay you

$3,400 per year for nine years, whereas Investment Y offers to pay you

$5,200 per year for five years. Which of these cash flow streams has the

higher present value if the discount rate is 6 percent? If the discount rate is

22 percent?

LO 1 3. Future Value and Multiple Cash ;Booker, Inc., has identified an

investment project with the following cash flows. If the discount rate is

8 percent, what is the future value of these cash flows in Year 4? What is

the future value at an interest rate of 11 percent? At 24 percent?

Year Cash Flow

1 $ 985

2 1,160

3 1,325

4 1,495

LO 1 4. Calculating Annuity Present ;An investment offers $5,450 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?

LO 1 5. Calculating Annuity Cash ;For each of the following annuities,

calculate the annual cash flow.

Present Value Years Interest Rate

$ 24,500 6 11%

19,700 8 7

136,400 15 8

285,650 20 6

LO 1 6. Calculating Annuity ;For each of the following annuities, calculate

the present value.

7. Calculating Annuity Cash ;For each of the following annuities,

calculate the annual cash flow.

Future Value Years Interest Rate

$ 30,000 8 5%

1,200,000 40 7

625,000 25 8

125,000 13 4

LO 1 8. Calculating Annuity ;For each of the following annuities, calculate

the future value.

Annual Payment Years Interest Rate

$1,900 10 8%

6,000 40 9

2,950 9 6

6,400 30 10

LO 1 9. Calculating Annuity ;If you deposit $5,000 at the end of each year

for the next 20 years into an account paying percent interest, how much

money will you have in the account in 20 years? How much will you have if

you make deposits for 40 years?

LO 1 10. Calculating Perpetuity ;Curly’s Life Insurance Co. is trying to sell

you an investment policy that will pay you and your heirs $30,000 per year

forever. If the required return on this investment is 6 percent, how much will

you pay for the policy?

LO 1 11. Calculating Perpetuity ;In the previous problem, suppose Curly’s

told you the policy costs $645,000. At what interest rate would this be a fair

deal?

LO 4 12. Calculating ;Find the EAR in each of the following cases:

Stated Rate (APR) Number of Times Compounded Effective Rate (EAR)

10% Quarterly

17 Monthly

13 Daily

9 Semiannually

LO 4 13. Calculating ;Find the APR, or stated rate, in each of the following

cases:

14. Calculating ;First National Bank charges percent compounded

monthly on its business loans. First United Bank charges percent

compounded semiannually. As a potential borrower, which bank would you

go to for a new loan?

LO 4 15. Calculating ;Vandermark Credit Corp. wants to earn an effective

annual return on its consumer loans of percent per year. The bank uses

daily compounding on its loans. What interest rate is the bank required by

law to report to potential borrowers? Explain why this rate is misleading to

an uninformed borrower.

LO 4 16. Calculating Future ;What is the future value of $1,345 in 16 years

assuming an interest rate of percent compounded semiannually?

LO 4 17. Calculating Future ;Bucher Credit Bank is offering percent

compounded daily on its savings accounts. If you deposit $3,650 today, how

much will you have in the account in five years? In 10 years? In 20 years?

LO 4 18. Calculating Present ;An investment will pay you $65,000 in

nine years. If the appropriate discount rate is percent compounded daily,

what is the present value?

LO 4 19. EAR versus ;Ricky Ripov’s Pawn Shop charges an interest rate of

percent per month on loans to its customers. Like all lenders, Ricky

must report an APR to consumers. What rate should the shop report? What

is the effective annual rate?

LO 2 20. Calculating Loan ;You want to buy a new sports coupe for

$73,400, and the finance office at the dealership has quoted you a loan with

an APR of percent for 60 months to buy the car. What will your monthly

payments be? What is the effective annual rate on this loan?

LO 2 21. Calculating Number of ;One of your customers is delinquent on

his accounts payable balance. You’ve mutually agreed to a repayment

schedule of $400 per month. You will charge percent per month interest

on the overdue balance. If the current balance is $14,480, how long will it

take for the account to be paid off?

LO 4 22. Calculating ;Friendly’s Quick Loans, Inc., offers you “Five for four,

or I knock on your ; This means you get $4 today and repay $5 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?

LO 1 23. Valuing ;Maybepay Life Insurance Co. is selling a perpetual

annuity contract that pays $3,300 monthly. The contract currently sells for

$425,000. What is the monthly return on this investment vehicle? What is

the APR? The effective annual return?

LO 1 24. Calculating Annuity Future ;You are to make monthly deposits of

$500 into a retirement account that pays an APR of percent compounded

monthly. If your first deposit will be made one month from now, how large

will your retirement account be in 35 years?

LO 1 25. Calculating Annuity Future ;In the previous problem, suppose you

make $6,000 annual deposits into the same retirement account. How large

will your account balance be in 35 years?

26. Calculating Annuity Present ;Beginning three months from now,

you want to be able to withdraw $2,500 each quarter from your bank

account to cover college expenses over the next four years. If the account

pays .38 percent interest per quarter, how much do you need to have in your

bank account today to meet your expense needs over the next four years?

LO 1 27. Discounted Cash Flow ;If the appropriate discount rate for the

following cash flows is percent, what is the present value of the cash

flows?

Year Cash Flow

1 $1,200

2 1,100

3 800

4 600

LO 1 28. Discounted Cash Flow ;If the appropriate discount rate for the

following cash flows is percent per year, what is the present value of

the cash flows?

Year Cash Flow

1 $1,400

2 1,900

3 3,400

4 4,300

INTERMEDIATE (Questions 29–56)

LO 4 29. Simple Interest versus Compound ;First Simple Bank pays

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?

LO 2 30. Calculating Annuities ;You want to buy a new sports car from Muscle

Motors for $58,600. The contract is in the form of a 60-month annuity due

at an APR of percent. What will your monthly payment be?

LO 4 31. Calculating Interest ;You receive a credit card application from

Shady Banks Savings and Loan offering an introductory rate of percent

per year, compounded monthly for the first six months, increasing thereafter

to percent compounded monthly. Assuming you transfer the $10,000

balance from your existing credit card and make no subsequent payments,

how much interest will you owe at the end of the first year?

LO 4 32. Calculating the Number of ;You are saving to buy a $235,000

house. There are two competing banks in your area, both offering

certificates of deposit yielding percent. How long will it take your initial

$85,000 investment to reach the desired level at First Bank, which pays

simple interest? How long at Second Bank, which compounds interest

monthly?

33. Calculating Future ;You have an investment that will pay you

percent per month. How much will you have per dollar invested in one

year? In two years?

LO 4 34. Calculating Annuity Interest ;Although you may know William

Shakespeare from his classic literature, what is not well-known is that he

was an astute investor. In 1604, when he was 40 and writing King Lear,

Shakespeare grew worried about his eventual retirement. Afraid that he

would become like King Lear in his retirement and beg hospitality from

his children, he purchased grain “tithes,” or shares in farm output, for

440 pounds. The tithes paid him 60 pounds per year for 31 years. Even

though he died at the age of 52, his children received the remaining payments.

What interest rate did the Bard of Avon receive on this investment?

LO 1 35. Comparing Cash Flow ;You’ve just joined the investment banking

firm of Dewey, Cheatum, and Howe. They’ve offered you two different

salary arrangements. You can have $6,700 per month for the next two years,

or you can have $5,400 per month for the next two years, along with a

$25,000 signing bonus today. If the interest rate is 7 percent compounded

monthly, which do you prefer?

LO 1 36. Calculating Present Value of ;Peter Lynchpin wants to sell you

an investment contract that pays equal $17,500 amounts at the end of each

year for the next 20 years. If you require an effective annual return of

8 percent on this investment, how much will you pay for the contract today?

LO 4 37. Calculating Rates of ;You’re trying to choose between two different

investments, both of which have up-front costs of $39,000. Investment G

returns $75,000 in six years. Investment H returns $105,000 in 9 years.

Which of these investments has the higher return?

LO 1 38. Present Value and Interest ;What is the relationship between the

value of an annuity and the level of interest rates? Suppose you just bought

a 10-year annuity of $7,300 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?

LO 1 39. Calculating the Number of ;You’re prepared to make monthly

payments of $250, beginning at the end of this month, into an account that

pays 8 percent interest compounded monthly. How many payments will you

have made when your account balance reaches $50,000?

LO 2 40. Calculating Annuity Present ;You want to borrow $80,000 from

your local bank to buy a new sailboat. You can afford to make monthly

payments of $1,650, but no more. Assuming monthly compounding, what is

the highest rate you can afford on a 60-month APR loan?

LO 1 41. Calculating Present ;In March 2015, the Kansas City Chiefs signed

Jeremy Maclin to a contract reportedly worth $55 million. Maclin’s salary

(including roster bonus) was to be paid as $ million in 2015, $ million

in 2016 and 2017, and $ million in 2018 and 2019. If the appropriate

interest rate is 11 percent, what kind of deal did the wide receiver snag?

Assume all payments are paid at the end of each year.

LO 1 42. Calculating Present ;The contract signed in March 2015 by

Ndamukong Suh that we discussed at the beginning of the chapter was

actually paid as a $ million signing bonus to be paid immediately and

$985,000 in salary for 2015. The remaining salary was $28,585,000 in

2016, $15,085,000 in 2017, $22,085,000 in 2018, $24,085,000 in 2019, and

$18,360,000 in 2020. If the appropriate interest rate is 11 percent, what kind

of deal did the defensive tackle sack? Assume all payments other than the

first $ million are paid at the end of each year.

LO 4 43. EAR versus ;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 $2,950,000 purchase price. The monthly payment on this loan will be

$14,300. What is the APR on this loan? The EAR?

LO 1 44. Annuity ;You are planning your retirement in 10 years. You

currently have $75,000 in a bond account and $300,000 in a stock account.

You plan to add $6,000 per year at the end of each of the next 10 years to

your bond account. The stock account will earn a return of percent and

the bond account will earn a return of 7 percent. When you retire, you plan

to withdraw an equal amount for each of the next 25 years at the end of each

year and have nothing left. Additionally, when you retire you will transfer

your money to an account that earns percent. How much can you

withdraw each year?

LO 4 45. Calculating Annuities Due Interest ;You have arranged for a loan on

your new car that will require the first payment today. The loan is for

$24,500, and the monthly payments are $465. If the loan will be paid off

over the next 60 months, what is the APR of the loan?

LO 1 46. Calculating Annuities ;Suppose you are going to receive $13,500 per

year for five years. The appropriate interest rate is percent.

1. 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?

1. Suppose you plan to invest the payments for five years. What is the

future value if the payments are an ordinary annuity? What if the

payments are an annuity due?

1. Which has the higher present value, the ordinary annuity or annuity

due? Which has the higher future value? Will this always be true?

LO 1 47. Annuity and Perpetuity ;Mary is going to receive a 30-year annuity

of $12,700. Nancy is going to receive a perpetuity of $12,700. If the appropriate

interest rate is percent, how much more is Nancy’s cash flow worth?

LO 1 48. Calculating Present ;A 6-year annuity of twelve $7,750 semiannual

payments will begin 9 years from now, with the first payment coming years

from now. If the discount rate is 9 percent compounded semiannually, 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?

LO 1 49. Present Value and Multiple Cash ;What is the present value of $2,150

per year, at a discount rate of percent, if the first payment is received six

years from now and the last payment is received 20 years from now?

LO 1 50. Variable Interest ;A 10-year annuity pays $1,450 per month, and

payments are made at the end of each month. If the interest rate is 9 percent

compounded monthly for the first four years, and 7 percent compounded

monthly thereafter, what is the present value of the annuity?

51. Comparing Cash Flow ;You have your choice of two investment

accounts. Investment A is a 10-year annuity that features end-of-month

$1,145 payments and has an interest rate of 7 percent compounded monthly.

Investment B is an annually compounded lump-sum investment with an

interest rate of 9 percent, also good for 10 years. How much money would

you need to invest in B today for it to be worth as much as Investment A 10 years

from now?

LO 1 52. Calculating Present Value of a ;Given an interest rate of

percent per year, what is the value at Year 7 of a perpetual stream of

$5,000 payments that begin at Year 20?

LO 4 53. Calculating ;A local finance company quotes an interest rate of

percent on one-year loans. So, if you borrow $25,000, the interest for

the year will be $4,300. Because you must repay a total of $29,300 in one

year, the finance company requires you to pay $29,300/12, or $2, per

month over the next 12 months. Is the interest rate on this loan percent?

What rate would legally have to be quoted? What is the effective annual

rate?

LO 1 54. Calculating Future ;If today is Year 0, what is the future value of

the following cash flows five years from now? What is the future value

10 years from now? Assume an interest rate of percent per year.

Year Cash Flow

2 $15,000

3 24,000

5 33,000

LO 3 55. Amortization with Equal ;Prepare an amortization schedule for a

three-year loan of $54,000. The interest rate is 8 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?

LO 3 56. Amortization with Equal Principal ;Rework Problem 55

assuming that the loan agreement calls for a principal reduction of $18,000

every year instead of equal annual payments.

CHALLENGE (Questions 57–60)

LO 4 57. Discount Interest ;This question illustrates what is known as

discount ;Imagine you are discussing a loan with a somewhat

unscrupulous lender. You want to borrow $18,000 for one year. The interest

rate is percent. You and the lender agree that the interest on the loan

will be .135 × $18,000 = $2,430. So, the lender deducts this interest amount

from the loan up front and gives you $15,570. In this case, we say that the

discount is $2,430. What’s wrong here?

LO 1 58. Calculating Annuity ;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: (a) The present value of two years’ back pay.

The plaintiff’s annual salary for the last two years would have been $43,000

and $46,000, respectively. (b) The present value of five years’ future salary.

You assume the salary will be $49,000 per year. (c) $200,000 for pain and

suffering. (d) $25,000 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 an EAR of 7 percent, what is the size of the settlement? If you were the

plaintiff, would you like to see a higher or lower interest rate?

LO 4 59. Calculating EAR with ;You are looking at a one-year loan of

$15,000. The interest rate is quoted as 12 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 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 10 percent interest. What rate

would you actually be paying here?

LO 1 60. Future Value and Multiple Cash ;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: $ 800

Second birthday: $ 800

Third birthday: $ 900

Fourth birthday: $ 900

Fifth birthday: $1,000

Sixth birthday: $1,000

After the child’s sixth birthday, no more payments are made. When the child

reaches age 65, he or she receives $150,000. If the relevant interest rate is

9 percent for the first six years and percent for all subsequent years, is

the policy worth buying?

EXCEL MASTER IT! PROBLEM

This is a classic retirement problem. A friend is celebrating her birthday and wants to start

saving for her anticipated retirement. She has the following years to retirement and retirement

spending goals:

Years until retirement: 30

Amount to withdraw each year: $90,000

Years to withdraw in retirement: 20

Interest rate: 8%

Because your friend is planning ahead, the first withdrawal will not take place until

one year after she retires. She wants to make equal annual deposits into her account for her

retirement fund.

1. If she starts making these deposits in one year and makes her last deposit on the day

she retires, what amount must she deposit annually to be able to make the desired

withdrawals at retirement?

1. Suppose your friend just inherited a large sum of money. Rather than making equal

annual payments, she decided to make one lump-sum deposit today to cover her

retirement needs. What amount does she have to deposit today?

1. Suppose your friend’s employer will contribute to the account each year as part of

the company’s profit-sharing plan. In addition, your friend expects a distribution

from a family trust several years from now. What amount must she deposit annually

now to be able to make the desired withdrawals at retirement?

Employer’s annual contribution: $ 1,500

Years until trust fund distribution: 20

Amount of trust fund distribution: $25,000

Chapter 6 Interest Rates and Bond Valuation

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Bond ;A Microgates Industries bond has a 10 percent coupon rate and a

$1,000 face value. Interest is paid semiannually, and the bond has 20 years to

maturity. If investors require a 12 percent yield, what is the bond’s value? What is

the effective annual yield on the bond? (See Problem 6.)

;A Macrohard Corp. bond carries an 8 percent coupon, paid semiannually.

The par value is $1,000, and the bond matures in six years. If the bond currently

sells for $, what is its yield to maturity? What is the effective annual yield?

(See Problem 21.)

■ Answers to Chapter Review and Self-Test Problems

;Because the bond has a 10 percent coupon yield and investors require a 12 percent

return, we know that the bond must sell at a discount. Notice that, because the bond

pays interest semiannually, the coupons amount to $100/2 = $50 every six months.

The required yield is 12%/2 = 6% every six months. Finally, the bond matures in

20 years, so there are a total of 40 six-month periods.

The bond’s value is thus equal to the present value of $50 every six months for

the next 40 six-month periods, plus the present value of the $1,000 face amount:

Bond value = $50 × (1 − 1)/.06 + 1,000

= $50 × + 1,000

= $

Notice that we discounted the $1,000 back 40 periods at 6 percent per period, rather

than 20 years at 12 percent. The reason is that the effective annual yield on the

bond is − 1 = , not 12 percent. We thus could have used percent

per year for 20 years when we calculated the present value of the $1,000 face

amount, and the answer would have been the same.

;The present value of the bond’s cash flows is its current price, $ The coupon

is $40 every six months for 12 periods. The face value is $1,000. So, the bond’s

yield is the unknown discount rate in the following:

$ = $40 × [1 − 1/(1 + r)12]/r + $1,000/(1 + r)12

The bond sells at a discount. Because the coupon rate is 8 percent, the yield must be

something in excess of that.

If we were to solve this by trial and error, we might try 12 percent (or 6 percent

per six months):

Bond value = $40 × (1 − 1)/.06 + $1,000

= $

This is less than the actual value, so our discount rate is too high. We now know

that the yield is somewhere between 8 and 12 percent. With further trial and error

(or a little machine assistance), the yield works out to be 10 percent, or 5 percent

every six months.

By convention, the bond’s yield to maturity would be quoted as 2 × 5% = 10%.

The effective yield is thus − 1 =

CRITICAL THINKING AND CONCEPTS REVIEW

LO 1  Treasury ;Is it true that a Treasury security is risk free?

LO 2  Interest Rate ;Which has greater interest rate risk, a 30-year

Treasury bond or a 30-year BB corporate bond?

Treasury ;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?

LO 2  Yield to ;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.

LO 1  Call ;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?

LO 1  Coupon ;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.

LO 4  Real and Nominal ;Are there any circumstances under which an

investor might be more concerned about the nominal return on an

investment than the real return?

LO 3  Bond ;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?

LO 3  Bond ;Often, junk bonds are not rated. Why?

LO 3  Crossover ;Looking back at the crossover bonds we discussed in

the chapter, why do you think split ratings such as these occur?

LO 1  Municipal ;Why is it that municipal bonds are not taxed at the

federal level, but are taxable across state lines? Why is it that

Treasury bonds are not taxable at the state level? (You may need to dust

off the history books for this one.)

LO 1  Treasury ;All Treasury bonds are relatively liquid, but some are

more liquid than others. Take a look back at Figure Which issues

appear to be the most liquid? The least liquid?

LO 3  Rating ;Several years ago, a controversy erupted regarding

bond-rating agencies when some agencies began to provide unsolicited

bond ratings. Why do you think this is controversial?

LO 1  Bonds as ;The 100-year bonds we discussed in the chapter have

something in common with junk bonds. Critics charge that, in both cases,

the issuers are really selling equity in disguise. What are the issues here?

Why would a company want to sell “equity in disguise”?

LO 2  Bond Prices versus Yields.

1. What is the relationship between the price of a bond and its YTM?
2. Explain why some bonds sell at a premium over par value while

other bonds sell at a discount. What do you know about the

relationship between the coupon rate and the YTM for premium

bonds? What about for discount bonds? For bonds selling at par

value?

1. What is the relationship between the current yield and YTM for

premium bonds? For discount bonds? For bonds selling at par

value?

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–17)

LO 2 1. Interpreting Bond ;Is the yield to maturity on a bond the same thing as

the required return? Is YTM the same thing as the coupon rate? Suppose today a

10 percent coupon bond sells at par. Two years from now, the required return on

the same bond is 8 percent. What is the coupon rate on the bond now? The YTM?

LO 2 2. Interpreting Bond ;Suppose you buy a 7 percent coupon, 20-year

bond today when it’s first issued. If interest rates suddenly rise to 15 percent,

what happens to the value of your bond? Why?

LO 2 3. Bond ;Lycan, Inc., has 7 percent coupon bonds on the market that

have 9 years left to maturity. The bonds make annual payments and have a

par value of $1,000. If the YTM on these bonds is percent, what is the

current bond price?

LO 2 4. Bond ;The Timberlake-Jackson Wardrobe Co. has 7 percent coupon

bonds on the market with 9 years left to maturity. The bonds make annual

payments and have a par value of $1,000. If the bonds currently sell for

$, what is the YTM?

LO 2 5. Coupon ;Barnes Enterprises has bonds on the market making annual

payments, with 12 years to maturity, a par value of $1,000, and a price of

$963. At this price, the bonds yield percent. What must the coupon rate

be on the bonds?

LO 2 6. Bond ;Harrison Co. issued 15-year bonds one year ago at a coupon

rate of percent. The bonds make semiannual payments. If the YTM on

these bonds is percent, what is the current dollar price assuming a

$1,000 par value?

LO 2 7. Bond ;Stein Co. issued 15-year bonds two years ago at a coupon

rate of percent. The bonds make semiannual payments. If these bonds

currently sell for 94 percent of par value, what is the YTM?

LO 2 8. Coupon ;Volbeat Corporation has bonds on the market with

years to maturity, a YTM of percent, a par value of $1,000, and a

current price of $945. The bonds make semiannual payments. What must

the coupon rate be on the bonds?

LO 4 9. Calculating Real Rates of ;If Treasury bills are currently paying

percent and the inflation rate is percent, what is the approximate real

rate of interest? The exact real rate?

LO 4 10. Inflation and Nominal ;Suppose the real rate is percent and

the inflation rate is percent. What rate would you expect to see on a

Treasury bill?

LO 4 11. Nominal and Real ;An investment offers a total return of

13 percent over the coming year. Janet Jello thinks the total real return on

this investment will be only 8 percent. What does Janet believe the inflation

rate will be over the next year?

LO 4 12. Nominal versus Real ;Say you own an asset that had a total return

last year of percent. If the inflation rate last year was percent, what

was your real return?

13. Using Treasury ;Locate the Treasury issue in Figure maturing

in August 2029. What is its coupon rate? What is the dollar bid price for a

$1,000 par value bond? What was the previous day’s asked price for a

$1,000 par value bond?

LO 2 14. Using Treasury ;Locate the Treasury bond in Figure maturing

in February 2037. Is this a premium or a discount bond? What is its current

yield? What is its yield to maturity? What is the bid-ask spread for a $1,000

par value bond?

LO 2 15. Zero Coupon ;You find a zero coupon bond with a par value of $10,000

and 17 years to maturity. If the yield to maturity on this bond is percent,

what is the price of the bond? Assume semiannual compounding periods.

LO 2 16. Valuing ;Yan Yan Corp. has a $2,000 par value bond outstanding

with a coupon rate of percent paid semiannually and 13 years to

maturity. The yield to maturity of the bond is percent. What is the price

of the bond?

LO 2 17. Valuing ;Union Local School District has bonds outstanding with a

coupon rate of percent paid semiannually and 16 years to maturity. The

yield to maturity on these bonds is percent and the bonds have a par

value of $5,000. What is the price of the bonds?

INTERMEDIATE (Questions 18–33)

LO 2 18. Bond Price ;Bond X is a premium bond making semiannual

payments. The bond has a coupon rate of percent, a YTM of 7 percent,

and has 13 years to maturity. Bond Y is a discount bond making semiannual

payments. This bond has a coupon rate of 7 percent, a YTM of percent,

and also has 13 years to maturity. What are the prices of these bonds today

assuming both bonds have a $1,000 par value? If interest rates remain

unchanged, what do you expect the prices of these bonds to be in one year? In

three years? In eight years? In 12 years? In 13 years? What’s going on here?

Illustrate your answers by graphing bond prices versus time to maturity.

LO 2 19. Interest Rate ;Both Bond Bill and Bond Ted have percent

coupons, make semiannual payments, and are priced at par value. Bond

Bill has 5 years to maturity, whereas Bond Ted has 25 years to maturity.

If interest rates suddenly rise by 2 percent, what is the percentage

change in the price of Bond Bill? Of Bond Ted? Both bonds have a par

value of $1,000. If rates were to suddenly fall by 2 percent instead,

what would the percentage change in the price of Bond Bill be then? Of

Bond Ted? Illustrate your answers by graphing bond prices versus

YTM. What does this problem tell you about the interest rate risk of

longer-term bonds?

LO 2 20. Interest Rate ;Bond J has a coupon rate of 4 percent. Bond S has a

coupon rate of 14 percent. Both bonds have 13 years to maturity, make

semiannual payments, a par value of $1,000, and have a YTM of 8 percent. If

interest rates suddenly rise by 2 percent, what is the percentage price change

of these bonds? What if rates suddenly fall by 2 percent instead? What does

this problem tell you about the interest rate risk of lower-coupon bonds?

LO 2 21. Bond ;PK Software has percent coupon bonds on the market

with 22 years to maturity. The bonds make semiannual payments and

currently sell for 97 percent of par. What is the current yield on PK’s bonds?

The YTM? The effective annual yield?

LO 2 22. Bond ;BDJ Co. wants to issue new 25-year bonds for some muchneeded

expansion projects. The company currently has percent coupon

bonds on the market that sell for $1,074, make semiannual payments, have a

$1,000 par value, and mature in 25 years. What coupon rate should the

company set on its new bonds if it wants them to sell at par?

LO 2 23. Accrued ;You purchase a bond with an invoice price of $1,043.

The bond has a coupon rate of percent, semiannual coupons, a $1,000

par value, and there are 5 months to the next coupon date. What is the clean

price of the bond?

LO 2 24. Accrued ;You purchase a bond with a coupon rate of percent,

semiannual coupons, and a clean price of $993. If the next coupon payment

is due in 2 months, what is the invoice price?

LO 2 25. Using Bond ;Suppose the following bond quote for IOU

Corporation appears in the financial page of today’s newspaper. Assume the

bond has a face value of $1,000, and the current date is April 15, 2016.

What is the yield to maturity of the bond? What is the current yield?

Company

(Ticker) Coupon Maturity

Last

Price

Last

Yield

EST Vol

(000s)

IOU (IOU) Apr 15, 2031 ?? 1,827

LO 2 26. Zero Coupon ;Suppose your company needs to raise $35 million

and you want to issue 20-year bonds for this purpose. Assume the required

return on your bond issue will be percent, and you’re evaluating two

issue alternatives: a percent semiannual coupon bond and a zero coupon

bond. Your company’s tax rate is 35 percent.

1. How many of the coupon bonds would you need to issue to raise the

$35 million? How many of the zeroes would you need to issue?

1. In 20 years, what will your company’s repayment be if you issue the

coupon bonds? What if you issue the zeroes?

1. Based on your answers in parts (a) and (b), why would you ever want to

issue the zeroes? To answer, calculate the firm’s aftertax cash outflows

for the first year under the two different scenarios. Assume that the IRS

amortization rules apply for the zero coupon bonds.

LO 2 27. Finding the ;You’ve just found a 10 percent coupon bond on the

market that sells for par value. What is the maturity on this bond? (Warning:

possible trick question.)

Use the following Treasury bond quotes to answer Questions 28–30. To calculate

the number of years until maturity, assume that it is currently May 2016. All of

the bonds have a $1,000 par value.

LO 2 28. Bond ;In the table, find the Treasury bond that matures in May

2027. What is your yield to maturity if you buy this bond?

LO 2 29. Bond ;In the table, find the Treasury bond that matures in May

2036. What is the asked price of this bond in dollars? If the bid-ask spread

for this bond is .0628, what is the bid price in dollars?

LO 2 30. Coupon ;Find the Treasury bond that matures in May 2020. What is

the coupon rate for this bond?

Use the following corporate bond quotes to answer Questions 31–33. To calculate

the number of years until maturity, assume that it is currently January 15, 2016.

All of the bonds have a $2,000 par value.

Company

(Ticker) Coupon Maturity Last Price Last Yield

EST $ Vol

(000’s)

Xenon, Inc. (XIC) Jan 15, 2020 ?? 57,362

Kenny Corp. (KCC) Jan 15, 2021 ?? 48,941

Williams Co. (WICO) ?? Jan 15, 2028 43,802

LO 2 31. Bond ;What is the yield to maturity for the bond issued by Xenon,

LO 2 32. Bond ;What price would you expect to pay for the Kenny Corp.

bond? What is the bond’s current yield?

LO 2 33. Coupon ;What is the coupon rate for the Williams Co. bond?

CHALLENGE (Questions 34–35)

LO 2 34. Components of Bond ;Bond P is a premium bond with a coupon

rate of percent. Bond D is a discount bond with a coupon rate of percent.

Both bonds make annual payments, have a YTM of 7 percent, a par value of

$1,000, and have five years to maturity. What is the current yield for Bond P?

For Bond D? If interest rates remain unchanged, what is the expected capital

gains yield over the next year for Bond P? For Bond D? Explain your answers

and the interrelationships among the various types of yields.

LO 2 35. Holding Period ;The YTM on a bond is the interest rate you earn on your

investment if interest rates don’t change. If you actually sell the bond before it

matures, your realized return is known as the holding period yield (HPY).

1. Suppose that today you buy an annual coupon bond with a coupon rate of

7 percent for $875. The bond has 10 years to maturity and a par value of

$1,000. What rate of return do you expect to earn on your investment?

1. Two years from now, the YTM on your bond has declined by 1 percent,

and you decide to sell. What price will your bond sell for? What is the

HPY on your investment? Compare this yield to the YTM when you

first bought the bond. Why are they different?

CHAPTER CASE

Financing S&S Air’s Expansion Plans with a Bond Issue

Mark Sexton and Todd Story, the owners of S&S Air,

have decided to expand their operations. They instructed

their newly hired financial analyst, Chris Guthrie,

to enlist an underwriter to help sell $20 million in new

10-year bonds to finance construction. Chris has entered

into discussions with Renata Harper, an underwriter from

the firm of Crowe & Mallard, about which bond features

S&S Air should consider and what coupon rate the issue

will likely have.

Although Chris is aware of the bond features, he is

uncertain as to the costs and benefits of some features,

so he isn’t clear on how each feature would affect the

coupon rate of the bond issue. You are Renata’s assistant,

and she has asked you to prepare a memo to Chris

describing the effect of each of the following bond features

on the coupon rate of the bond. She would also

like you to list any advantages or disadvantages of each

feature.

QUESTIONS

1. The security of the bond—that is, whether the

bond has collateral.

2. The seniority of the bond.
3. The presence of a sinking fund.
4. A call provision with specified call dates and call

prices.

5. A deferred call accompanying the preceding call

provision.

6. A make-whole call provision.
7. Any positive covenants. Also, discuss several possible

positive covenants S&S Air might consider.

8. Any negative covenants. Also, discuss several

possible negative covenants S&S Air might

consider.

9. A conversion feature (note that S&S Air is not a

publicly traded company).

10. A floating rate coupon.

Chapter 7 Equity Markets and Stock Valuation

part five

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Dividend Growth and Stock ;The Brigapenski Co. has just paid a cash

dividend of $2 per share. Investors require a 16 percent return from investments

such as this. If the dividend is expected to grow at a steady 8 percent per year, what

is the current value of the stock? What will the stock be worth in five years? (See

Problem 1.)

Required ;Suppose we observe a stock selling for $40 per share. The next

dividend will be $1 per share, and you think the dividend will grow at 12 percent

per year forever. What is the dividend yield in this case? The capital gains yield?

The total required return? (See Problem 3.)

■ Answers to Chapter Review and Self-Test Problems

;The last dividend, D0, was $2. The dividend is expected to grow steadily at

8 percent. The required return is 16 percent. Based on the dividend growth model,

we can say that the current price is:

P0 = D1/(R − g)

= D0 × (1 + g)/(R − g)

= $2 × (.16 − .08)

= $

= $27

We could calculate the price in five years by calculating the dividend in five years

and then using the growth model again. Alternatively, we could recognize that the

stock price will increase by 8 percent per year and calculate the future price

directly. We’ll do both. First, the dividend in five years will be:

D5 = D0 × (1 + g)5

= $2 ×

= $

The price in five years would therefore be:

P5 = D5 × (1 + g)/(R − g)

= $ ×

= $

= $

Once we understand the dividend model, however, it’s easier to notice that:

P5 = P0 × (1 + g)5

= $27 ×

= $27 ×

= $

Notice that both approaches yield the same price in five years.

;The dividend yield is the next dividend, D1, divided by the current price, P0, or

$1/40 = The capital gains yield is the same as the dividend growth rate,

12 percent. The total required return is the sum of the two, + 12% =

CRITICAL THINKING AND CONCEPTS REVIEW

LO 1  Stock ;Why does the value of a share of stock depend on

dividends?

LO 1  Stock ;A substantial percentage of the companies listed on the

NYSE and the NASDAQ don’t pay dividends, but investors are

nonetheless willing to buy shares in them. How is this possible given your

answer to the previous question?

LO 1  Dividend ;Referring to the previous questions, under what

circumstances might a company choose not to pay dividends?

Dividend Growth ;Under what two assumptions can we use the

dividend growth model presented in the chapter to determine the value of

a share of stock? Comment on the reasonableness of these assumptions.

LO 1  Common versus Preferred ;Suppose a company has a preferred

stock issue and a common stock issue. Both have just paid a $2 dividend.

Which do you think will have a higher price, a share of the preferred or a

share of the common?

LO 1  Dividend Growth ;Based on the dividend growth model, what are

the two components of the total return on a share of stock? Which do you

think is typically larger?

LO 1  Growth ;In the context of the dividend growth model, is it true that

the growth rate in dividends and the growth rate in the price of the stock

are identical?

LO 1  Dividends and ;Is it possible for a company to pay dividends

when it has a negative net income for the year? Could this happen for

longer periods?

LO 2  Corporate ;Is it unfair or unethical for corporations to create

classes of stock with unequal voting rights?

LO 2  Voting ;Some companies, such as Google, have created classes of

stock with little or no voting rights at all. Why would investors buy such

stock?

LO 2  Stock ;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.

LO 1  Constant Dividend Growth ;In the constant dividend growth

model, what is the highest reasonable growth rate for a stock’s dividend?

LO 3  Voting ;In the chapter, we mentioned that many companies have

been under pressure to declassify their boards of directors. Why would

investors want a board to be declassified? What are the advantages of a

classified board?

LO 3  Price Ratio ;What are the difficulties in using the PE ratio to

value stock?

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–14)

LO 1 1. Stock ;Gilmore, Inc., just paid a dividend of $ per share on its

stock. The dividends are expected to grow at a constant rate of percent

per year, indefinitely. If investors require a return of percent on this

stock, what is the current price? What will the price be in three years? In

15 years?

LO 1 2. Stock ;The next dividend payment by Dizzle, Inc., will be $

per share. The dividends are anticipated to maintain a growth rate of

percent forever. If the stock currently sells for $ per share, what is

the required return?

3. Stock ;For the company in the previous problem, what is the

dividend yield? What is the expected capital gains yield?

LO 1 4. Stock ;Take Time Corporation will pay a dividend of $ per

share next year. The company pledges to increase its dividend by percent

per year, indefinitely. If you require a return of 11 percent on your

investment, how much will you pay for the company’s stock today?

LO 1 5. Stock ;Mitchell, Inc., is expected to maintain a constant

percent growth rate in its dividends, indefinitely. If the company has a

dividend yield of percent, what is the required return on the company’s

stock?

LO 1 6. Stock ;Suppose you know that a company’s stock currently sells

for $67 per share and the required return on the stock is percent. You

also know that the total return on the stock is evenly divided between capital

gains yield and 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?

LO 1 7. Stock ;Burkhardt Corp. pays a constant $ dividend on its

stock. The company will maintain this dividend for the next 9 years and will

then cease paying dividends forever. If the required return on this stock is

percent, what is the current share price?

LO 1 8. Valuing Preferred ;Smiling Elephant, Inc., has an issue of preferred

stock outstanding that pays a $ dividend every year, in perpetuity. If this

issue currently sells for $ per share, what is the required return?

LO 2 9. Voting ;After successfully completing your corporate finance class,

you feel the next challenge ahead is to serve on the board of directors of

Schenkel Enterprises. Unfortunately, you will be the only individual voting

for you. If the company has 450,000 shares outstanding and the stock

currently sells for $34, how much will it cost you to buy a seat if the

company uses straight voting? Assume that the company uses cumulative

voting and there are 4 seats in the current election; how much will it cost

you to buy a seat now?

LO 1 10. Growth ;The stock price of Baskett Co. is $73. Investors require a

return of percent on similar stocks. If the company plans to pay a

dividend of $ next year, what growth rate is expected for the company’s

stock price?

LO 1 11. Valuing Preferred ; has a new issue of preferred stock it

calls 20/20 preferred. The stock will pay a $20 dividend per year, but the

first dividend will not be paid until 20 years from today. If you require a

return of percent on this stock, how much should you pay today?

LO 1 12. Stock ;Wesen Corp. will pay a dividend of $ next year.

The company has stated that it will maintain a constant growth rate of

percent a year forever. If you want a return of 12 percent, how much will

you pay for the stock? What if you want a return of 8 percent? What does

this tell you about the relationship between the required return and the stock

price?

LO 2 13. Stock Valuation and PE ;The Sleeping Flower Co. has earnings of

$ per share. The benchmark PE for the company is 18. What stock price

would you consider appropriate? What if the benchmark PE were 21?

14. Stock Valuation and PS ;TwitterMe, Inc., is a new company and

currently has negative earnings. The company’s sales are $ million and

there are 130,000 shares outstanding. If the benchmark price–sales ratio is

, what is your estimate of an appropriate stock price? What if the

price–sales ratio were

INTERMEDIATE (Questions 15–30)

LO 1 15. Nonconstant ;Metallica Bearings, Inc., is a young start-up

company. No dividends will be paid on the stock over the next nine years,

because the firm needs to plow back its earnings to fuel growth. The

company will then pay a dividend of $19 per share 10 years from today and

will increase the dividend by 5 percent per year thereafter. If the required

return on this stock is 13 percent, what is the current share price?

LO 1 16. Nonconstant ;Hot Wings, Inc., has an odd dividend policy. The

company has just paid a dividend of $3 per share and has announced that it

will increase the dividend by $5 per share for each of the next four years,

and then never pay another dividend. If you require a return of percent

on the company’s stock, how much will you pay for a share today?

LO 1 17. Nonconstant ;Apocalyptica Corporation is expected to pay the

following dividends over the next four years: $6, $12, $17, and $

Afterward, the company pledges to maintain a constant 5 percent growth

rate in dividends, forever. If the required return on the stock is 11 percent,

what is the current share price?

LO 1 18. Supernormal ;Burton Corp. is growing quickly. Dividends are

expected to grow at a rate of 25 percent for the next three years, with the

growth rate falling off to a constant 6 percent thereafter. If the required

return is percent and the company just paid a dividend of $, what

is the current share price?

LO 1 19. Negative ;Antiques ‘R’ Us is a mature manufacturing firm. The

company just paid a dividend of $ but management expects to reduce

the payout by percent per year, indefinitely. If you require a return of

12 percent on this stock, what will you pay for a share today?

LO 1 20. Finding the ;Gontier Corporation stock currently sells for $

per share. The market requires a return of percent on the firm’s stock.

If the company maintains a constant percent growth rate in dividends,

what was the most recent dividend per share paid on the stock?

You’ve collected the following information from your favorite financial website.

Use it to answer Questions 21–25 (the 52-week Hi and Lo are the highest and

lowest stock prices over the previous 52 weeks).

21. Dividend ;Find the quote for the Laclede Group. Assume that the

dividend is constant. What was the highest dividend yield over the past

year? What was the lowest dividend yield over the past year?

LO 1 22. Stock ;According to the 2015 Value Line Investment Survey, the

growth rate in dividends for IBM for the next five years is expected to be

percent. Suppose IBM meets this growth rate in dividends for the next

five years and then the dividend growth rate falls to 5 percent indefinitely.

Assume investors require a return of 10 percent on IBM stock. Is the stock

priced correctly? What factors could affect your answer?

LO 1 23. Stock ;According to the 2015 Value Line Investment Survey, the

growth rate in dividends for Analogic for the previous 10 years has been

3 percent. If investors feel this growth rate will continue, what is the

required return for Analogic stock?

LO 1 24. Negative ;According to the 2015 Value Line Investment Survey,

the growth rate in dividends for Alcoa for the previous 10 years has been

negative 15 percent. If investors feel this growth rate will continue, what is

the required return for Alcoa stock? Does this number make sense? What

are some of the potential reasons for the negative growth in dividends?

LO 1 25. Stock ;Using the dividend yield, calculate the closing price for

Tootsie Roll on this day. The actual closing price for Tootsie Roll was

$ Why is your closing price different? The Value Line Investment

Survey projects a percent dividend growth rate for Tootsie Roll. What is

the required return for the stock using the dividend discount model and the

actual stock price?

LO 2 26. Stock Valuation and ;Sully Corp. currently has an EPS of $, and

the benchmark PE for the company is 19. Earnings are expected to grow at

7 percent per year.

1. What is your estimate of the current stock price?
2. What is the target stock price in one year?
3. Assuming the company pays no dividends, what is the implied return

on the company’s stock over the next year? What does this tell you

about the implied stock return using PE valuation?

LO 2 27. Stock Valuation and ;You have found the following historical

information for the Daniela Company:

Year 1 Year 2 Year 3 Year 4

Stock price $ $ $ $

EPS

Earnings are expected to grow at 8 percent for the next year. Using the company’s

historical average PE as a benchmark, what is the target stock price in

one year?

LO 2 28. Stock Valuation and ;In the previous problem, we assumed that the

stock had a single stock price for the year. However, if you look at stock

prices over any year, you will find a high and low stock price for the year.

Instead of a single benchmark PE ratio, we now have a high and low PE

ratio for each year. We can use these ratios to calculate a high and a low

stock price for the next year. Suppose we have the following information on

a particular company:

Year 1 Year 2 Year 3 Year 4

High price $ $ $ $

Low price

EPS

Earnings are projected to grow at 9 percent over the next year. What are your

high and low target stock prices over the next year?

LO 2 29. Stock Valuation and ;Davis, Inc., currently has an EPS of $ and an

earnings growth rate of 8 percent. If the benchmark PE ratio is 21, what is

the target share price five years from now?

LO 2 30. PE and Terminal Stock ;In practice, a common way to value a share

of stock when a company pays dividends is to value the dividends over the

next five years or so, then find the “terminal” stock price using a benchmark

PE ratio. Suppose a company just paid a dividend of $ The dividends

are expected to grow at 10 percent over the next five years. The company

has a payout ratio of 40 percent and a benchmark PE of 21. What is the

target stock price in five years? What is the stock price today assuming a

required return of 11 percent on this stock?

CHALLENGE (Questions 31–32)

LO 1 31. Capital Gains versus ;Consider four different stocks, all of which

have a required return of 17 percent and a most recent dividend of $ per

share. Stocks W, X, and Y are expected to maintain constant growth rates in

dividends for the foreseeable future of 8 percent, 0 percent, and −5 percent

per year, respectively. Stock Z is a growth stock that will increase its

dividend by 20 percent for the next two years and then maintain a constant

12 percent growth rate, thereafter. What is the dividend yield for each of

these four stocks? What is the expected capital gains yield? Discuss the

relationship among the various returns that you find for each of these stocks.

LO 1 32. Stock ;Most corporations pay quarterly dividends on their

common stock rather than annual dividends. Barring any unusual

circumstances during the year, the board raises, lowers, or maintains the

current dividend once a year and then pays this dividend out in equal

quarterly installments to its shareholders.

2. Suppose a company currently pays an annual dividend of $ on its

common stock in a single annual installment, and management plans on

raising this dividend by 6 percent per year indefinitely. If the required

return on this stock is 12 percent, what is the current share price?

1. Now suppose the company in part (a) actually pays its annual

dividend in equal quarterly installments; thus, the company has just

paid a dividend of $.55 per share, as it has for the previous three

quarters. What is your value for the current share price now? (Hint:

Find the equivalent annual end-of-year dividend for each year.)

Comment on whether you think this model of stock valuation is

appropriate.

CHAPTER CASE

Stock Valuation at Ragan, Inc.

Ragan, Inc., was founded nine years ago by brother

and sister Carrington and Genevieve Ragan. The

company manufactures and installs commercial heating,

ventilation, and cooling (HVAC) units. Ragan, Inc.,

has experienced rapid growth because of a proprietary

technology that increases the energy efficiency of its

units. The company is equally owned by Carrington

and Genevieve. The original partnership agreement

between the siblings gave each 50,000 shares of

stock. In the event either wished to sell stock, the

shares first had to be offered to the other at a discounted

price.

Although neither sibling wants to sell, they have decided

they should value their holdings in the company.

To get started, they have gathered the following information

about their main competitors:

Ragan, Inc. — Competitors

EPS Div.

Stock

Price ROE R

Arctic Cooling,

Inc.

$.84 $.39 $

National

Heating &

Cooling

.65

Expert HVAC

Corp.

−.55 .43

Industry

average

$.54 $.49 $

Expert HVAC Corporation’s negative earnings per

share were the result of an accounting write-off last year.

Without the write-off, earnings per share for the company

would have been $.54.

Last year, Ragan, Inc., had an EPS of $ and paid

a dividend to Carrington and Genevieve of $75,000

each. The company also had a return on equity of

17 percent. The siblings believe that 14 percent is an appropriate

required return for the company.

QUESTIONS

1. Assuming the company continues its current

growth rate, what is the value per share of the

company’s stock?

2. To verify their calculations, Carrington and Genevieve

have hired Josh Schlessman as a consultant. Josh

was previously an equity analyst and covered the

HVAC industry. Josh has examined the company’s

financial statements, as well as those of its competitors.

Although Ragan, Inc., currently has a technological

advantage, his research indicates that

other companies are investigating methods to improve

efficiency. Given this, Josh believes that the

company’s technological advantage will last only

for the next five years. After that period, the company’s

growth will likely slow to the industry growth

average. Additionally, Josh believes that the required

return used by the company is too high. He

believes the industry average required return is

more appropriate. Under this growth rate assumption,

what is your estimate of the stock price?

Chapter 8 Net Present Value and Other Investment Criteria

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Investment ;This problem will give you some practice calculating NPVs

and paybacks. A proposed overseas expansion has the following cash flows:

Year Cash Flow

0 −$100

1 50

2 40

3 40

4 15

Calculate the payback and NPV at a required return of 15 percent. (See Problem 21.)

Mutually Exclusive ;Consider the following two mutually exclusive

investments. Calculate the IRR for each. Under what circumstances will the IRR

and NPV criteria rank the two projects differently? (See Problem 8.)

Year Investment A Investment B

0 −$100 −$100

1 50 70

2 70 75

3 40 10

Average Accounting ;You are looking at a three-year project with a

projected net income of $1,000 in Year 1, $2,000 in Year 2, and $4,000 in Year 3.

The cost is $9,000, which will be depreciated straight-line to zero over the threeyear

life of the project. What is the average accounting return, or AAR? (See

Problem 4.)

■ Answers to Chapter Review and Self-Test Problems

;In the following table, we have listed the cash flows and their discounted values (at

15 percent).

Cash Flow

Year Undiscounted Discounted (at 15%)

1 $ 50 $

2 40

3 40

4 15

Total $145 $

Recall that the initial investment is $100. Examining the undiscounted cash flows,

we see that the payback occurs between Years 2 and 3. The cash flows for the first

two years are $90 total, so, going into the third year, we are short by $10. The total

cash flow in Year 3 is $40, so the payback is 2 + $10/40 = years.

Looking at the discounted cash flows, we see that the sum is $, so the

NPV is $

;To calculate the IRR, we might try some guesses as in the following table:

Discount Rate NPV(A) NPV(B)

0% $ $

10

20

30 −

40 − −

Several things are immediately apparent from our guesses. First, the IRR on A must

be just a little less than 30 percent (why?). With some more effort, we find that it’s

percent. For B, the IRR must be a little more than 30 percent (again, why?); it

works out to be percent. Also, notice that at 10 percent, the NPVs are very

close, indicating that the NPV profiles cross in that vicinity. Verify that the NPVs

are the same at percent.

Now, the IRR for B is always higher. As we’ve seen, A has the larger NPV for

any discount rate less than percent, so the NPV and IRR rankings will

conflict in that range. Remember, if there’s a conflict, we will go with the higher

NPV. Our decision rule is thus very simple: Take A if the required return is less

than percent, take B if the required return is between percent and

percent (the IRR on B), and take neither if the required return is more than

percent.

;Here we need to calculate the ratio of average net income to average book value to

get the AAR. Average net income is:

Average net income = ($1,000 + 2,000 + 4,000)/3

= $2,

Average book value is:

Average book value = $9,000/2 = $4,500

So, the average accounting return is:

AAR = $2,,500 =

This is an impressive return. Remember, however, that it isn’t really a rate of return

like an interest rate or an IRR, so the size doesn’t tell us a lot. In particular, our

money is probably not going to grow at percent per year, sorry to say.

CRITICAL THINKING AND CONCEPTS REVIEW

LO 4  Payback Period and Net Present ;If a project with conventional

LO 1 cash flows has a payback period less than its life, can you definitively state

the algebraic sign of the NPV? Why or why not?

LO 4  Net Present ;Suppose a project has conventional cash flows and a

positive NPV. What do you know about its payback? Its profitability

index? Its IRR? Explain.

Payback ;Concerning payback:

1. Describe how the payback period is calculated and describe the

information this measure provides about a sequence of cash flows.

What is the payback criterion decision rule?

1. What are the problems associated with using the payback period as a

means of evaluating cash flows?

1. What are the advantages of using the payback period to evaluate cash

flows? Are there any circumstances under which using payback might

be appropriate? Explain.

LO 2  Average Accounting ;Concerning AAR:

1. Describe how the average accounting return is usually calculated and

describe the information this measure provides about a sequence of

cash flows. What is the AAR criterion decision rule?

1. What are the problems associated with using the AAR as a means of

evaluating a project’s cash flows? What underlying feature of AAR is

most troubling to you from a financial perspective? Does the AAR

have any redeeming qualities?

LO 4  Net Present ;Concerning NPV:

1. Describe how NPV is calculated and describe the information this

measure provides about a sequence of cash flows. What is the NPV

criterion decision rule?

1. Why is NPV considered to be a superior method of evaluating the

cash flows from a project? Suppose the NPV for a project’s cash flows

is computed to be $2,500. What does this number represent with

respect to the firm’s shareholders?

LO 3  Internal Rate of ;Concerning IRR:

1. Describe how the IRR is calculated, and describe the information this

measure provides about a sequence of cash flows. What is the IRR

criterion decision rule?

1. What is the relationship between IRR and NPV? Are there any situations

in which you might prefer one method over the other? Explain.

1. Despite its shortcomings in some situations, why do most financial

managers use IRR along with NPV when evaluating projects? Can

you think of a situation in which IRR might be a more appropriate

measure to use than NPV? Explain.

LO 6  Profitability ;Concerning the profitability index:

1. Describe how the profitability index is calculated and describe the

information this measure provides about a sequence of cash flows.

What is the profitability index decision rule?

1. What is the relationship between the profitability index and the NPV?

Are there any situations in which you might prefer one method over

the other? Explain.

LO 3  Payback and Internal Rate of ;A project has perpetual cash flows

LO 1 of C per period, a cost of I, and a required return of ;What is the

relationship between the project’s payback and its IRR? What implications

does your answer have for long-lived projects with relatively constant cash

flows?

International Investment ;In October 2011, automobile

manufacturer Daimler AG announced plans to invest $350 million to

manufacture an entirely new Mercedes-Benz model at its Alabama plant.

Daimler AG apparently felt that it would be better able to compete and

create value with facilities. Other companies such as Fuji Film

and Swiss chemical company Lonza have reached similar conclusions and

taken similar actions. What are some of the reasons that foreign

manufacturers of products as diverse as automobiles, film, and chemicals

might arrive at this same conclusion?

LO 4  Capital Budgeting ;What are some of the difficulties that

might come up in actual applications of the various criteria we discussed

in this chapter? Which one would be the easiest to implement in actual

applications? The most difficult?

LO 4  Capital Budgeting in Not-for-Profit ;Are the capital budgeting

criteria we discussed applicable to not-for-profit corporations? How

should such entities make capital budgeting decisions? What about the

government? Should it evaluate spending proposals using these

techniques?

LO 3  Internal Rate of ;In a previous chapter, we discussed the yield to

maturity (YTM) of a bond. In what ways are the IRR and the YTM

similar? How are they different?

LO 5  Modified Internal Rate of ;One of the less flattering

interpretations of the acronym MIRR is “meaningless internal rate of

; Why do you think this term is applied to MIRR?

LO 4  Net Present ;It is sometimes stated that “the net present value

approach assumes reinvestment of the intermediate cash flows at the

required ; Is this claim correct? To answer, suppose you calculate

the NPV of a project in the usual way. Next, suppose you do the following:

1. Calculate the future value (as of the end of the project) of all the cash

flows other than the initial outlay assuming they are reinvested at the

required return, producing a single future value figure for the project.

1. Calculate the NPV of the project using the single future value

calculated in the previous step and the initial outlay. It is easy to verify

that you will get the same NPV as in your original calculation only if

you use the required return as the reinvestment rate in the previous

step.

LO 3  Internal Rate of ;It is sometimes stated that “the internal rate of

return approach assumes reinvestment of the intermediate cash flows at the

internal rate of ; Is this claim correct? To answer, suppose you

calculate the IRR of a project in the usual way. Next, suppose you do the

following:

1. Calculate the future value (as of the end of the project) of all the cash

flows other than the initial outlay assuming they are reinvested at the

IRR, producing a single future value figure for the project.

1. Calculate the IRR of the project using the single future value

calculated in the previous step and the initial outlay. It is easy to verify

that you will get the same IRR as in your original calculation only if

you use the IRR as the reinvestment rate in the previous step.

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the Preface for more information.

BASIC (Questions 1–22)

LO 1 1. Calculating ;What is the payback period for the following set of

cash flows?

Year Cash Flow

0 −$6,700

1 2,800

2 3,200

3 2,200

4 1,400

LO 1 2. Calculating ;An investment project provides cash inflows of $935

per year for eight years. What is the project payback period if the initial cost

is $3,100? What if the initial cost is $4,300? What if it is $7,900?

LO 1 3. Calculating ;Global Toys Inc. imposes a payback cutoff of three

years for its international investment projects. If the company has the

following two projects available, should it accept either of them?

Year Cash Flow (A) Cash Flow (B)

0 −$60,000 −$105,000

1 23,000 21,000

2 28,000 26,000

3 19,000 29,000

4 9,000 260,000

LO 2 4. Calculating ;You’re trying to determine whether or not to expand

your business by building a new manufacturing plant. The plant has an

installation cost of $ million, which will be depreciated straight-line to

zero over its four-year life. If the plant has projected net income of

$1,368,000, $1,935,000, $1,738,000, and $1,310,000 over these four years,

what is the project’s average accounting return (AAR)?

LO 3 5. Calculating ;A firm evaluates all of its projects by applying the IRR rule.

If the required return is 11 percent, should the firm accept the following project?

Year Cash Flow

0 −$168,500

1 86,000

2 91,000

3 53,000

LO 4 6. Calculating ;For the cash flows in the previous problem, suppose the

firm uses the NPV decision rule. At a required return of 9 percent, should

the firm accept this project? What if the required return was 21 percent?

7. Calculating NPV and ;A project that provides annual cash flows of

LO 4 $2,145 for eight years costs $8,450 today. Is this a good project if the

required return is 8 percent? What if it’s 24 percent? At what discount

rate would you be indifferent between accepting the project and

rejecting it?

LO 3 8. Calculating ;What is the IRR of the following set of cash flows?

Year Cash Flow

0 −$19,400

1 9,800

2 11,300

3 6,900

LO 4 9. Calculating ;For the cash flows in the previous problem, what is

the NPV at a discount rate of 0 percent? What if the discount rate is

10 percent? If it is 20 percent? If it is 30 percent?

LO 3 10. NPV versus ;Zayas, LLC, has identified the following two mutually

LO 4 exclusive projects:

Year Cash Flow (A) Cash Flow (B)

0 −$78,500 −$78,500

1 43,000 21,000

2 29,000 28,000

3 23,000 34,000

4 21,000 41,000

1. What is the IRR for each of these projects? If you apply the IRR

decision rule, which project should the company accept? Is this decision

necessarily correct?

1. If the required return is 11 percent, what is the NPV for each of these

projects? Which project will you choose if you apply the NPV decision

rule?

1. Over what range of discount rates would you choose Project A? Project B?

At what discount rate would you be indifferent between these two

projects? Explain.

LO 3 11. NPV versus ;Consider the following two mutually exclusive projects:

LO 4

Year Cash Flow (X) Cash Flow (Y)

0 −$23,400 −$23,400

1 13,100 9,200

2 9,480 10,620

3 7,890 11,180

Sketch the NPV profiles for X and Y over a range of discount rates from

0 to 25 percent. What is the crossover rate for these two projects?

12. Problems with ;Howell Petroleum, Inc., is trying to evaluate a

generation project with the following cash flows:

Year Cash Flow

0 −$39,000,000

1 57,000,000

2 − 9,000,000

1. If the company requires a return of 10 percent on its investments, should

it accept this project? Why?

1. Compute the IRR for this project. How many IRRs are there? If you

apply the IRR decision rule, should you accept the project or not?

What’s going on here?

LO 6 13. Calculating Profitability ;What is the profitability index for the

following set of cash flows if the relevant discount rate is 10 percent? What

if the discount rate is 15 percent? If it is 22 percent?

Year Cash Flow

0 −$27,500

1 15,800

2 13,600

3 8,300

LO 4 14. Problems with Profitability ;The Matterhorn Corporation is trying to

LO 6 choose between the following two mutually exclusive design projects:

Year Cash Flow (I) Cash Flow (II)

0 −$78,000 −$28,800

1 28,300 9,600

2 34,800 17,400

3 43,700 15,600

1. If the required return is 11 percent and the company applies the

profitability index decision rule, which project should the firm accept?

1. If the company applies the NPV decision rule, which project should it

take?

1. Explain why your answers in parts (a) and (b) are different.

LO 1 15. Comparing Investment ;Consider the following two mutually

exclusive projects:

Whichever project you choose, if any, you require a return of 13 percent on

your investment.

1. If you apply the payback criterion, which investment will you choose?

Why?

1. If you apply the NPV criterion, which investment will you choose? Why?
2. If you apply the IRR criterion, which investment will you choose? Why?
3. If you apply the profitability index criterion, which investment will you

choose? Why?

1. Based on your answers in parts (a) through (d), which project will you

finally choose? Why?

LO 3 16. NPV and ;Reece Company is presented with the following two mutually

LO 4 exclusive projects. The required return for both projects is 15 percent.

Year Project M Project N

0 −$150,000 −$372,000

1 68,600 159,300

2 76,800 193,200

3 71,300 154,800

4 40,500 110,400

1. What is the IRR for each project?
2. What is the NPV for each project?
3. Which, if either, of the projects should the company accept?

LO 4 17. NPV and Profitability ;Robben Manufacturing has the following two

LO 6 possible projects. The required return is 12 percent.

Year Project Y Project Z

0 −$43,400 −$78,000

1 19,800 32,000

2 17,500 30,100

3 20,700 29,500

4 14,600 27,300

1. What is the profitability index for each project?
2. What is the NPV for each project?
3. Which, if either, of the projects should the company accept?

LO 3 18. Crossover ;Hodgkiss Enterprises has gathered projected cash flows

for two projects. At what interest rate would the company be indifferent

between the two projects? Which project is better if the required return is

above this interest rate? Why?

19. Payback Period and ;Suppose you have a project with a payback

period exactly equal to the life of the project. What do you know about the

IRR of the project? Suppose that the payback period is never. What do you

know about the IRR of the project now?

LO 4 20. NPV and Discount ;An investment has an installed cost of $745,382.

The cash flows over the four-year life of the investment are projected to be

$265,381, $304,172, $225,153, and $208,614. If the discount rate is zero,

what is the NPV? If the discount rate is infinite, what is the NPV? At what

discount rate is the NPV just equal to zero? Sketch the NPV profile for this

investment based on these three points.

LO 1 21. NPV and Payback ;Kaleb Konstruction, Inc., has the following

mutually exclusive projects available. The company has historically used a

three-year cutoff for projects. The required return is 10 percent.

Year Project F Project G

0 −$180,000 −$280,000

1 93,600 64,800

2 64,800 86,400

3 81,600 123,600

4 72,000 166,800

5 64,800 187,200

1. Calculate the payback period for both projects.
2. Calculate the NPV for both projects.
3. Which project, if any, should the company accept?

LO 5 22. ;Mittuch Corp. is evaluating a project with the following cash flows:

Year Cash Flow

0 −$27,500

1 10,430

2 13,850

3 11,270

4 9,830

5 − 4,050

The company uses an interest rate of 10 percent on all of its projects. Calculate

the MIRR of the project using all three methods.

INTERMEDIATE (Questions 23–27)

LO 5 23. ;Suppose the company in the previous problem uses a discount rate

of 11 percent and a reinvestment rate of 8 percent on all of its projects.

Calculate the MIRR of the project using all three methods with these rates.

LO 4 24. Crossover and ;Seether, Inc., has the following two mutually

exclusive projects available.

What is the crossover rate for these two projects? What is the NPV of each

project at the crossover rate?

LO 3 25. Calculating ;A project has the following cash flows:

Year Cash Flow

0 $91,000

1 − 55,000

2 − 46,000

What is the IRR for this project? If the required return is 10 percent,

should the firm accept the project? What is the NPV of this project? What

is the NPV of the project if the required return is 0 percent? 24 percent?

What is going on here? Sketch the NPV profile to help you with your

answer.

LO 4 26. NPV and the Profitability ;If we define the NPV index as the ratio of

NPV to cost, what is the relationship between this index and the profitability

index?

LO 1 27. Cash Flow ;A project has an initial cost of I, has a required return

of R, and pays C annually for N years.

1. Find C in terms of I and N such that the project has a payback period

just equal to its life.

1. Find C in terms of I, N, and R such that this is a profitable project

according to the NPV decision rule.

1. Find C in terms of I, N, and R such that the project has a benefit-cost

ratio of 2.

CHALLENGE (Questions 28–30)

LO 4 28. NPV ;The Yurdone Corporation wants to set up a private cemetery

business. According to the CFO, Barry M. Deep, business is “looking ; As

a result, the cemetery project will provide a net cash inflow of $135,000 for

the firm during the first year, and the cash flows are projected to grow at a

rate of percent per year forever. The project requires an initial investment

of $1,575,000.

1. If Yurdone requires a return of 12 percent on such undertakings, should

the cemetery business be started?

4. The company is somewhat unsure about the assumption of a percent

growth rate in its cash flows. At what constant growth rate would the

company just break even if it still required a return of 12 percent on its

investment?

LO 3 29. Problems with ;Rosalee Corp. has a project with the following cash

flows:

Year Cash Flow

0 $35,000

1 − 27,000

2 29,000

What is the IRR of the project? What is happening here?

30. NPV and ;Anderson International Limited is evaluating a project in

Erewhon. The project will create the following cash flows:

Year Cash Flow

0 −$862,000

1 303,800

2 219,700

3 320,000

4 288,700

All cash flows will occur in Erewhon and are expressed in dollars. In an

attempt to improve its economy, the Erewhonian government has declared

that all cash flows created by a foreign company are “blocked” and must be

reinvested with the government for one year. The reinvestment rate for these

funds is 4 percent. If Anderson uses a required return of 10 percent on this

project, what are the NPV and IRR of the project? Is the IRR you calculated

the MIRR of the project? Why or why not?

CHAPTER CASE

Bullock Gold Mining

Seth Bullock, the owner of Bullock Gold Mining, is evaluating

a new gold mine in South Dakota. Dan Dority,

the company’s geologist, has just finished his analysis of

the mine site. He has estimated that the mine would be

productive for eight years, after which the gold would be

completely mined. Dan has taken an estimate of the gold

deposits to Alma Garrett, the company’s financial officer.

Alma has been asked by Seth to perform an analysis of

the new mine and present her recommendation on

whether the company should open the new mine.

Year Cash Flow

0 −$650,000,000

1 80,000,000

2 121,000,000

3 162,000,000

4 221,000,000

5 210,000,000

6 154,000,000

7 108,000,000

8 86,000,000

9 − 72,000,000

Alma has used the estimates provided by Dan to

determine the revenues that could be expected from

the mine. She has also projected the expense of opening

the mine and the annual operating expenses. If the

company opens the mine, it will cost $650 million today,

and it will have a cash outflow of $72 million nine years

from today in costs associated with closing the mine and

reclaiming the area surrounding it. The expected cash

flows each year from the mine are shown in the table on

this page. Bullock Gold Mining has a 12 percent required

return on all of its gold mines.

1. Construct a spreadsheet to calculate the payback

period, internal rate of return, modified internal

rate of return, and net present value of the proposed

mine.

2. Based on your analysis, should the company open

the mine?

3. Bonus question: Most spreadsheets do not have a

built-in formula to calculate the payback period.

Write a VBA script that calculates the payback period

for a project.

Chapter 9 Making Capital Investment Decisions

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Calculating Operating Cash ;Mater Pasta, Inc., has projected a sales volume

of $1,432 for the second year of a proposed expansion project. Costs normally run

70 percent of sales, or about $1,002 in this case. The depreciation expense will be

$80, and the tax rate is 34 percent. What is the operating cash flow? (See Problem 9.)

Scenario ;A project under consideration costs $500,000, has a five-year

life, and has no salvage value. Depreciation is straight-line to zero. The required

return is 15 percent, and the tax rate is 34 percent. Sales are projected at 400 units

per year. Price per unit is $3,000, variable cost per unit is $1,900, and fixed costs

are $250,000 per year. No net working capital is required.

Suppose you think the unit sales, price, variable cost, and fixed cost projections

are accurate to within 5 percent. What are the upper and lower bounds for these

projections? What is the base-case NPV? What are the best- and worst-case scenario

NPVs? (See Problem 19.)

■ Answers to Chapter Review and Self-Test Problems

;First, we can calculate the project’s EBIT, its tax bill, and its net income.

EBIT = $1,432 − 1,002 − 80 = $350

Taxes = $350 × .34 = $119

Net income = $350 − 119 = $231

With these numbers, operating cash flow is:

OCF = EBIT + Depreciation − Taxes

= $350 + 80 − 119

= $311

;We can summarize the relevant information as follows:

Base Case Lower Bound Upper Bound

Unit sales 400 380 420

Price per unit $3,000 $2,850 $3,150

Variable cost per unit $1,900 $1,805 $1,995

Fixed costs $250,000 $237,500 $262,500

The depreciation is $100,000 per year, and the tax rate is 34 percent, so we can

calculate the cash flows under each scenario. Remember that we assign high costs and

low prices and volume under the worst case and just the opposite for the best case.

Scenario Unit Sales Price Variable Costs Fixed Costs Cash Flow

Base case 400 $3,000 $1,900 $250,000 $159,400

Best case 420 3,150 1,805 237,500 250,084

Worst case 380 2,850 1,995 262,500 75,184

At 15 percent, the five-year annuity factor is , so the NPVs are:

Base-case NPV = −$500,000 + 159,400 × = $34,334

Best-case NPV = −$500,000 + 250,084 × = $338,320

Worst-case NPV = −$500,000 + 75,184 × = −$247,972

CRITICAL THINKING AND CONCEPTS REVIEW

LO 1  Opportunity ;In the context of capital budgeting, what is an

opportunity cost?

LO 1  ;Given the choice, would a firm prefer to use MACRS

depreciation or straight-line depreciation? Why?

LO 1  Net Working ;In our capital budgeting examples, we assumed that

a firm would recover all of the working capital it invested in a project. Is

this a reasonable assumption? When might it not be valid?

LO 1  Stand-Alone ;Suppose a financial manager is quoted as saying,

“Our firm uses the stand-alone principle. Because we treat projects like

minifirms in our evaluation process, we include financing costs because

they are relevant at the firm ; Critically evaluate this statement.

LO 1  Cash Flow and ;“When evaluating projects, we’re only

concerned with the relevant incremental aftertax cash flows. Therefore,

because depreciation is a noncash expense, we should ignore its effects

when evaluating ; Critically evaluate this statement.

LO 1  Capital Budgeting ;A major college textbook publisher

has an existing finance textbook. The publisher is debating whether or not

to produce an “essentialized” version, meaning a shorter (and lower-priced)

book. What are some of the considerations that should come into play?

To answer the next three questions, refer to the following example. In 2003,

Porsche unveiled its new sports-utility vehicle (SUV), the Cayenne. With a price

tag of more than $40,000, the Cayenne went from zero to 62 mph in seconds.

Porsche’s decision to enter the SUV market was in response to the runaway success

of other high-priced SUVs such as the Mercedes-Benz M-class. Vehicles in

up the market, and Porsche subsequently introduced the Cayenne Turbo S, which

goes from zero to 60 mph in seconds and has a top speed of 168 mph. The

price tag for the Cayenne Turbo S? About $114,000 in 2015.

Some analysts questioned Porsche’s entry into the luxury SUV market. The

analysts were concerned not only that Porsche was a late entry into the market,

but also that the introduction of the Cayenne would damage Porsche’s reputation

as a maker of high-performance automobiles.

LO 1  ;In evaluating the Cayenne, would you consider the possible

damage to Porsche’s reputation?

LO 1  Capital ;Porsche was one of the last manufacturers to enter

the sports-utility vehicle market. Why would one company decide to

proceed with a product when other companies, at least initially, decide

not to enter the market?

LO 1  Capital ;In evaluating the Cayenne, what do you think Porsche

needs to assume regarding the substantial profit margins that exist in this

market? Is it likely they will be maintained as the market becomes more

competitive, or will Porsche be able to maintain the profit margin because

of its image and the performance of the Cayenne?

LO 2  Sensitivity Analysis and Scenario ;What is the essential

difference between sensitivity analysis and scenario analysis?

LO 1  Marginal Cash ;A co-worker claims that looking at all this marginal

this and incremental that is just a bunch of nonsense and states: “Listen, if

our average revenue doesn’t exceed our average cost, then we will have a

negative cash flow, and we will go broke!” How do you respond?

LO 1  Capital ;Going all the way back to Chapter 1, recall that we

saw that partnerships and proprietorships can face difficulties when it

comes to raising capital. In the context of this chapter, the implication is

that small businesses will generally face what problem?

LO 2  Forecasting ;What is forecasting risk? In general, would the degree of

forecasting risk be greater for a new product or a cost-cutting proposal? Why?

LO 2  Options and ;What is the option to abandon? The option to expand?

Explain why we tend to underestimate NPV when we ignore these options.

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–20)

LO 1 1. Relevant Cash ;Kenny, Inc., is looking at setting up a new

manufacturing plant in South Park. The company bought some land six years

ago for $ million in anticipation of using it as a warehouse and distribution

site, but the company has since decided to rent facilities elsewhere. The land

would net $ million if it were sold today. The company now wants to build its

new manufacturing plant on this land; the plant will cost $ million to build,

and the site requires $ million worth of grading before it is suitable for

construction. What is the proper cash flow amount to use as the initial

investment in fixed assets when evaluating this project? Why?

LO 1 2. Relevant Cash ;Winnebagel Corp. currently sells 28,000 motor

homes per year at $77,000 each and 7,000 luxury motor coaches per year at

$120,000 each. The company wants to introduce a new portable camper to

fill out its product line; it hopes to sell 29,000 of these campers per year at

$23,500 each. An independent consultant has determined that if the

company introduces the new campers, it should boost the sales of its

existing motor homes by 2,500 units per year and reduce the sales of its

motor coaches by 750 units per year. What is the amount to use as the

annual sales figure when evaluating this project? Why?

LO 2 3. Calculating Projected Net ;A proposed new investment has projected

sales of $645,000. Variable costs are 40 percent of sales, and fixed costs are

$168,000; depreciation is $83,000. Prepare a pro forma income statement

assuming a tax rate of 35 percent. What is the projected net income?

LO 2 4. Calculating ;Consider the following income statement:

Sales $558,400

Costs 346,800

Depreciation 94,500

EBIT

Taxes (35%)

Net income

Fill in the missing numbers and then calculate the OCF. What is the depreciation

tax shield?

LO 2 5. Calculating ;A piece of newly purchased industrial

equipment costs $715,000 and is classified as seven-year property under

MACRS. Calculate the annual depreciation allowances and end-of-the-year

book values for this equipment.

LO 2 6. Calculating Salvage ;Consider an asset that costs $545,000 and is

depreciated straight-line to zero over its eight-year tax life. The asset is to be

used in a five-year project; at the end of the project, the asset can be sold for

$95,000. If the relevant tax rate is 35 percent, what is the aftertax cash flow

from the sale of this asset?

LO 2 7. Calculating Salvage ;An asset used in a four-year project falls in the

five-year MACRS class for tax purposes. The asset has an acquisition cost

of $7,100,000 and will be sold for $1,460,000 at the end of the project. If

the tax rate is 34 percent, what is the aftertax salvage value of the asset?

LO 2 8. Calculating Project ;Rolston Music Company is considering the sale

of a new sound board used in recording studios. The new board would sell

for $27,300, and the company expects to sell 1,500 per year. The company

currently sells 1,850 units of its existing model per year. If the new model is

introduced, sales of the existing model will fall to 1,520 units per year. The

old board retails for $24,900. Variable costs are 55 percent of sales,

depreciation on the equipment to produce the new board will be $2,150,000

per year, and fixed costs are $3,200,000 per year. If the tax rate is 38 percent,

what is the annual OCF for the project?

9. Calculating Project ;H. Cochran, Inc., is considering a new three-year

expansion project that requires an initial fixed asset investment of

$1,950,000. The fixed asset will be depreciated straight-line to zero over its

three-year tax life, after which time it will be worthless. The project is

estimated to generate $2,145,000 in annual sales, with costs of $1,205,000.

If the tax rate is 35 percent, what is the OCF for this project?

LO 2 10. Calculating Project ;In the previous problem, suppose the required

return on the project is 14 percent. What is the project’s NPV?

LO 2 11. Calculating Project Cash Flow from ;In the previous problem,

suppose the project requires an initial investment in net working capital of

$150,000, and the fixed asset will have a market value of $175,000 at the

end of the project. What is the project’s Year 0 net cash flow? Year 1? Year

2? Year 3? What is the new NPV?

LO 2 12. NPV and Modified ;In the previous problem, suppose the fixed asset

actually falls into the three-year MACRS class. All the other facts are the

same. What is the project’s Year 1 net cash flow now? Year 2? Year 3?

What is the new NPV?

LO 2 13. Project ;Kolby’s Korndogs is looking at a new sausage system

with an installed cost of $655,000. This cost will be depreciated straight-line

to zero over the project’s five-year life, at the end of which the sausage

system can be scrapped for $85,000. The sausage system will save the firm

$183,000 per year in pretax operating costs, and the system requires an

initial investment in net working capital of $35,000. If the tax rate is 34 percent

and the discount rate is 8 percent, what is the NPV of this project?

LO 2 14. Project ;Your firm is contemplating the purchase of a new

$410,000 computer-based order entry system. The system will be

depreciated straight-line to zero over its five-year life. It will be worth

$30,000 at the end of that time. You will save $125,000 before taxes per

year in order processing costs, and you will be able to reduce working

capital by $35,000 at the beginning of the project. Working capital will

revert back to normal at the end of the project. If the tax rate is 35 percent,

what is the IRR for this project?

LO 2 15. Project ;In the previous problem, suppose your required return

on the project is 10 percent and your pretax cost savings are $145,000 per

year. Will you accept the project? What if the pretax cost savings are only

$105,000 per year?

LO 3 16. Scenario ;Automatic Transmissions, Inc., has the following

estimates for its new gear assembly project: price = $960 per unit; variable

cost = $350 per unit; fixed costs = $ million; quantity = 55,000 units.

Suppose the company believes all of its estimates are accurate only to

within ±15 percent. What values should the company use for the four

variables given here when it performs its best-case scenario analysis? What

about the worst-case scenario?

LO 3 17. Sensitivity ;For the company in the previous problem, suppose

management is most concerned about the impact of its price estimate on the

project’s profitability. How could you address this concern for Automatic

Transmissions? Describe how you would calculate your answer. What

values would you use for the other forecast variables?

18. Sensitivity ;We are evaluating a project that costs $1,720,000, has

a six-year life, and has no salvage value. Assume that depreciation is

straight-line to zero over the life of the project. Sales are projected at 91,000

units per year. Price per unit is $, variable cost per unit is $, and

fixed costs are $815,000 per year. The tax rate is 35 percent, and we require

a return of 11 percent on this project.

1. Calculate the base-case cash flow and NPV. What is the sensitivity of

NPV to changes in the sales figure? Explain what your answer tells you

about a 500-unit decrease in projected sales.

1. What is the sensitivity of OCF to changes in the variable cost figure?

Explain what your answer tells you about a $1 decrease in estimated

variable costs.

LO 3 19. Scenario ;In the previous problem, suppose the projections given

for price, quantity, variable costs, and fixed costs are all accurate to within

±10 percent. Calculate the best-case and worst-case NPV figures.

LO 2 20. Calculating Project Cash Flows and ;Pappy’s Potato has come up

with a new product, the Potato Pet (they are freeze-dried to last longer).

Pappy’s paid $120,000 for a marketing survey to determine the viability of

the product. It is felt that Potato Pet will generate sales of $815,000 per year.

The fixed costs associated with this will be $196,000 per year, and variable

costs will amount to 20 percent of sales. The equipment necessary for

production of the Potato Pet will cost $865,000 and will be depreciated in a

straight-line manner for the 4 years of the product life (as with all fads, it is

felt the sales will end quickly). This is the only initial cost for the

production. Pappy’s has a tax rate of 40 percent and a required return of

13 percent. Calculate the payback period, NPV, and IRR.

INTERMEDIATE (Questions 21–24)

LO 2 21. Cost-Cutting ;CSM Machine Shop is considering a four-year

project to improve its production efficiency. Buying a new machine press

for $375,000 is estimated to result in $142,000 in annual pretax cost

savings. The press falls in the MACRS five-year class, and it will have a

salvage value at the end of the project of $45,000. The press also requires an

initial investment in spare parts inventory of $15,000, along with an

additional $2,000 in inventory for each succeeding year of the project. If the

shop’s tax rate is 34 percent and its discount rate is 11 percent, should the

company buy and install the machine press?

LO 3 22. Sensitivity ;Consider a three-year project with the following

information: initial fixed asset investment = $645,000; straight-line

depreciation to zero over the five-year life; zero salvage value; price =

$; variable costs = $; fixed costs = $315,000; quantity sold =

90,000 units; tax rate = 34 percent. How sensitive is OCF to changes in

quantity sold?

LO 2 23. Project ;You are considering a new product launch. The project

will cost $780,000, have a four-year life, and have no salvage value;

depreciation is straight-line to zero. Sales are projected at 180 units per

year; price per unit will be $16,300, variable cost per unit will be $11,100,

and fixed costs will be $535,000 per year. The required return on the project

is 11 percent, and the relevant tax rate is 35 percent.

1. Based on your experience, you think the unit sales, variable cost, and fixed

cost projections given here are probably accurate to within ±10 percent.

What are the best and worst cases for these projections? What is the

base-case NPV? What are the best-case and worst-case scenarios?

1. Evaluate the sensitivity of your base-case NPV to changes in fixed costs.

LO 2 24. Project ;McGilla Golf has decided to sell a new line of golf clubs.

The clubs will sell for $825 per set and have a variable cost of $370 per set.

The company has spent $150,000 for a marketing study that determined the

company will sell 74,000 sets per year for seven years. The marketing study

also determined that the company will lose sales of 8,900 sets per year of its

high-priced clubs. The high-priced clubs sell at $1,250 and have variable

costs of $630. The company will also increase sales of its cheap clubs by

11,000 sets per year. The cheap clubs sell for $375 and have variable costs

of $140 per set. The fixed costs each year will be $14,350,000. The

company has also spent $1,000,000 on research and development for the

new clubs. The plant and equipment required will cost $29,400,000 and will

be depreciated on a straight-line basis. The new clubs will also require an

increase in net working capital of $3,500,000 that will be returned at the

end of the project. The tax rate is 40 percent, and the cost of capital is

14 percent. Calculate the payback period, the NPV, and the IRR.

CHALLENGE (Questions 25–26)

LO 2 25. Project ;Aria Acoustics, Inc. (AAI), projects unit sales for a

new seven-octave voice emulation implant as follows:

Year Unit Sales

1 67,500

2 83,900

3 98,700

4 86,000

5 72,000

Production of the implants will require $1,500,000 in net working capital to

start and additional net working capital investments each year equal to 15 percent

of the projected sales increase for the following year. Total fixed costs are

$1,950,000 per year, variable production costs are $230 per unit, and the units

are priced at $355 each. The equipment needed to begin production has an installed

cost of $18,500,000. Because the implants are intended for professional

singers, this equipment is considered industrial machinery and thus qualifies

as seven-year MACRS property. In five years, this equipment can be sold for

about 20 percent of its acquisition cost. AAI is in the 35 percent marginal tax

bracket and has a required return on all its projects of 15 percent. Based on these

preliminary project estimates, what is the NPV of the project? What is the IRR?

LO 2 26. Calculating Required ;A proposed cost-saving device has an

installed cost of $535,000. The device will be used in a five-year project but

is classified as three-year MACRS property for tax purposes. The required

initial net working capital investment is $38,000, the marginal tax rate is 35

percent, and the project discount rate is 12 percent. The device has an

estimated Year 5 salvage value of $50,000. What level of pretax cost savings

do we require for this project to be profitable?

EXCEL MASTER IT! PROBLEM

For this Master It! assignment, refer to the Conch Republic Electronics case at the end of

Chapter 9. For your convenience, we have entered the relevant values in the case, such as

the price and variable cost, already. For this project, answer the following questions.

1. What is the profitability index of the project?
2. What is the IRR of the project?
3. What is the NPV of the project?
4. How sensitive is the NPV to changes in the price of the new smartphone? Construct

a one-way data table to help you.

1. How sensitive is the NPV to changes in the quantity sold?

CHAPTER CASE

Conch Republic Electronics

Conch Republic Electronics is a midsized electronics

manufacturer located in Key West, Florida. The company

president is Shelly Couts, who inherited the company.

The company originally repaired radios and other

household appliances when it was founded more than

70 years ago. Over the years, the company has expanded,

and it is now a reputable manufacturer of various specialty

electronic items. Jay McCanless, a recent MBA graduate,

has been hired by the company in its finance department.

One of the major revenue-producing items manufactured

by Conch Republic is a smartphone. Conch

Republic currently has one smartphone model on the

market and sales have been excellent. The smartphone

is a unique item in that it comes in a variety of tropical

colors and is preprogrammed to play Jimmy Buffett music.

However, as with any electronic item, technology

changes rapidly, and the current smartphone has limited

features in comparison with newer models. Conch Republic

spent $750,000 to develop a prototype for a new

smartphone that has all the features of the existing one

but adds new features such as wifi tethering. The

company has spent a further $200,000 for a marketing

study to determine the expected sales figures for the

new smartphone.

Conch Republic can manufacture the new smartphone

for $205 each in variable costs. Fixed costs for

the operation are estimated to run $ million per year.

The estimated sales volume is 64,000, 106,000, 87,000,

78,000, and 54,000 per year for the next five years, respectively.

The unit price of the new smartphone will be

$485. The necessary equipment can be purchased for

$ million and will be depreciated on a seven-year

MACRS schedule. It is believed the value of the equipment

in five years will be $ million.

Net working capital for the smartphones will be

20 percent of sales and will occur with the timing of the

cash flows for the year (, there is no initial outlay for

NWC). Changes in NWC will thus first occur in Year 1 with

the first year’s sales. Conch Republic has a 35 percent

corporate tax rate and a required return of 12 percent.

Shelly has asked Jay to prepare a report that answers

the following questions:

QUESTIONS

1. What is the payback period of the project?
2. What is the profitability index of the project?
3. What is the IRR of the project?
4. What is the NPV of the project?
5. How sensitive is the NPV to changes in the price

of the new smartphone?

6. How sensitive is the NPV to changes in the quantity

sold?

7. Should Conch Republic produce the new

smartphone?

8. Suppose Conch Republic loses sales on other

models because of the introduction of the new

model. How would this affect your analysis?

Chapter 10 Some Lessons from Capital Market History

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Recent Return ;Use Table to calculate the average return over the

years 1997–2001 for large-company stocks, long-term government bonds, and

Treasury bills. (See Problem 9.)

More Recent Return ;Calculate the standard deviations using information

from Problem Which of the investments was the most volatile over this

period? (See Problem 7.)

;We calculate the averages as follows:

Actual Returns and Averages

Year

Large-Company

Stocks

Long-Term

Government Bonds

Treasury

Bills

1997 .3336 .1770 .0519

1998 .2858 .1922 .0486

1999 .2104 −.1276 .0480

2000 −.0910 .2216 .0598

2001 −.1189 .0530 .0333

Average: .1240 .1032 .0483

;We first need to calculate the deviations from the average returns. Using the

averages from Problem 1, we get:

Deviations from Average Returns

Year

Large-Company

Stocks

Long-Term

Government Bonds

Treasury

Bills

1997 .2096 .0738 .0036

1998 .1618 .0890 .0003

1999 .0864 −.2308 −.0003

2000 −.2150 .1184 .0115

2001 −.2429 −.0502 −.0150

Total: .0000 .0000 .0000

We square these deviations and calculate the variances and standard deviations:

Squared Deviations from Average Returns

Year

Large-Company

Stocks

Long-Term

Government Bonds

Treasury

Bills

1997 .043941 .005441 .000013

1998 .026186 .007914 .000000

1999 .007468 .053287 .000000

2000 .046216 .014009 .000132

2001 .058991 .002524 .000226

Variance: .0457 .0208 .0001

Standard deviation: .2138 .1442 .0096

To calculate the variances, we added up the squared deviations and divided by 4,

the number of returns less 1. Notice that the stocks had substantially greater

volatility with a larger average return. Once again, such investments are risky,

particularly over short periods of time.

CRITICAL THINKING AND CONCEPTS REVIEW

LO 3  Investment ;Given that RadNet, Inc., was up by 411 percent for

2014, why didn’t all investors hold RadNet?

LO 3  Investment ;Given that Transocean Ltd. was down by

63 percent for 2014, why did some investors hold the stock? Why didn’t

they sell out before the price declined so sharply?

Risk and ;We have seen that over long periods of time, stock

investments have tended to substantially outperform bond investments.

However, it is not at all uncommon to observe investors with long

horizons holding entirely bonds. Are such investors irrational?

LO 4  Market Efficiency ;Explain why a characteristic of an

efficient market is that investments in that market have zero NPVs.

LO 4  Efficient Markets ;A stock market analyst is able to identify

mispriced stocks by comparing the average price for the last 10 days to

the average price for the last 60 days. If this is true, what do you know

about the market?

LO 4  Semistrong ;If a market is semistrong form efficient, is it

also weak form efficient? Explain.

LO 4  Efficient Markets ;What are the implications of the efficient

markets hypothesis for investors who buy and sell stocks in an attempt to

“beat the market”?

LO 4  Stocks versus ;Critically evaluate the following statement:

Playing the stock market is like gambling. Such speculative investing has no

social value, other than the pleasure people get from this form of gambling.

LO 4  Efficient Markets ;There are several celebrated investors and

stock pickers frequently mentioned in the financial press who have recorded

huge returns on their investments over the past two decades. Is the success

of these particular investors an invalidation of the EMH? Explain.

LO 4  Efficient Markets ;For each of the following scenarios,

discuss whether profit opportunities exist from trading in the stock of the

firm under the conditions that (1) the market is not weak form efficient,

(2) the market is weak form but not semistrong form efficient, (3) the

market is semistrong form but not strong form efficient, and (4) the

market is strong form efficient.

1. The stock price has risen steadily each day for the past 30 days.
2. The financial statements for a company were released three days

ago, and you believe you’ve uncovered some anomalies in the

company’s inventory and cost control reporting techniques that are

causing the firm’s true liquidity strength to be understated.

1. You observe that the senior management of a company has been buying

a lot of the company’s stock on the open market over the past week.

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–18)

LO 1 1. Calculating ;Suppose a stock had an initial price of $72 per share,

paid a dividend of $ per share during the year, and had an ending share

price of $85. Compute the percentage total return. What was the dividend

yield? The capital gains yield?

2. Calculating ;Rework Problem 1 assuming the ending share price

is $62.

LO 1 3. Calculating Dollar ;You purchased 250 shares of a particular stock

at the beginning of the year at a price of $ The stock paid a dividend

of $ per share, and the stock price at the end of the year was $

What was your dollar return on this investment?

LO 1 4. Calculating ;Suppose you bought a bond with an annual

coupon rate of percent one year ago for $1,032. The bond sells for

$1,020 today.

1. Assuming a $1,000 face value, what was your total dollar return on this

investment over the past year?

1. What was your total nominal rate of return on this investment over the

past year?

1. If the inflation rate last year was 3 percent, what was your total real rate

of return on this investment?

LO 2 5. Nominal versus Real ;What was the arithmetic average annual

return on large-company stocks from 1926 through 2014:

1. In nominal terms?
2. In real terms?

LO 2 6. Bond ;What is the historical real return on long-term government

bonds? On long-term corporate bonds?

LO 1 7. Calculating Returns and ;Using the following returns,

calculate the average returns, the variances, and the standard

deviations for X and Y.

Returns

Year X Y

1 16% 36%

2 −17 − 8

3 13 21

4 15 −15

5 24 39

LO 2 8. Risk ;Refer to Table in the text and look at the period from

1973 through 1978.

1. Calculate the arithmetic average returns for large-company stocks and

T-bills over this time period.

1. Calculate the standard deviation of the returns for large-company stocks

and T-bills over this time period.

1. Calculate the observed risk premium in each year for the large-company

stocks versus the T-bills. What was the arithmetic average risk premium

over this period? What was the standard deviation of the risk premium

over this period?

1. Is it possible for the risk premium to be negative before an

investment is undertaken? Can the risk premium be negative after

the fact? Explain.

9. Calculating Returns and ;You’ve observed the following

returns on Barnett Corporation’s stock over the past five years: −12

percent, 23 percent, 18 percent, 7 percent, and 13 percent.

1. What was the arithmetic average return on the stock over this fiveyear

period?

1. What was the variance of the returns over this period? The standard

deviation?

LO 1 10. Calculating Real Returns and Risk ;For Problem 9, suppose

the average inflation rate over this period was percent and the average

T-bill rate over the period was percent.

1. What was the average real return on the stock?
2. What was the average nominal risk premium on the stock?

LO 1 11. Calculating Real ;Given the information in Problem 10, what was

the average real risk-free rate over this time period? What was the average

real risk premium?

LO 2 12. Effects of ;Look at Table and Figure in the text. When

were T-bill rates at their highest over the period from 1926 through 2014?

Why do you think they were so high during this period? What relationship

underlies your answer?

LO 1 13. Calculating ;You purchased a zero-coupon bond one year ago for

$ The market interest rate is now percent. If the bond had

20 years to maturity when you originally purchased it, what was your total

return for the past year? Assume semiannual compounding.

LO 1 14. Calculating ;You bought a share of percent preferred stock

for $ last year. The market price for your stock is now $

What is your total return for last year?

LO 1 15. Calculating ;You bought a stock three months ago for $ per

share. The stock paid no dividends. The current share price is $

What is the APR of your investment? The EAR?

LO 1 16. Calculating Real ;Refer to Table What was the average real

return for Treasury bills from 1926 through 1932?

LO 1 17. Return ;Refer back to Figure What range of returns

would you expect to see 68 percent of the time for long-term corporate

bonds? What about 95 percent of the time?

LO 3 18. Return ;Refer back to Figure What range of returns

would you expect to see 68 percent of the time for large-company stocks?

What about 95 percent of the time?

INTERMEDIATE (Questions 19–26)

LO 1 19. Calculating Returns and ;You find a certain stock that had

returns of 17 percent, −13 percent, 26 percent, and 8 percent for four of

the last five years. If the average return of the stock over this period was

10 percent, what was the stock’s return for the missing year? What is

the standard deviation of the stock’s returns?

LO 1 20. Arithmetic and Geometric ;A stock has had returns of

−23 percent, 9 percent, 37 percent, −8 percent, 28 percent, and

19 percent over the last six years. What are the arithmetic and

geometric returns for the stock?

21. Arithmetic and Geometric ;A stock has had the following

year-end prices and dividends:

Year Price Dividend

1 $ —

2 $

3

4

5

6

What are the arithmetic and geometric returns for the stock?

LO 2 22. Calculating ;Refer to Table in the text and look at the

period from 1973 through 1980.

1. Calculate the average return for Treasury bills and the average annual

inflation rate (consumer price index) for this period.

1. Calculate the standard deviation of Treasury bill returns and inflation

over this time period.

1. Calculate the real return for each year. What is the average real return

for Treasury bills?

1. Many people consider Treasury bills to be risk-free. What does this

tell you about the potential risks of Treasury bills?

LO 1 23. Calculating Investment ;You bought one of Rocky Mountain

Manufacturing ;s percent coupon bonds one year ago for

$1, These bonds make annual payments and mature nine years

from now. Suppose you decide to sell your bonds today, when the

required return on the bonds is percent. If the inflation rate was

percent over the past year, what would be your total real return on

investment?

LO 1 24. Using Return ;Suppose the returns on long-term

government bonds are normally distributed. Based on the historical record,

what is the approximate probability that your return on these bonds will be

less than − percent in a given year? What range of returns would you

expect to see 95 percent of the time? What range would you expect to see

99 percent of the time?

LO 3 25. Using Return ;Assuming that the returns from holding

small-company stocks are normally distributed, what is the approximate

probability that your money will double in value in a single year? What

about triple in value?

LO 1 26. ;In the previous problem, what is the probability that the

return is less than −100 percent (think)? What are the implications for the

distribution of returns?

CHALLENGE (Question 27–28)

LO 1 27. Using Probability ;Suppose the returns on large-company

stocks are normally distributed. Based on the historical record, use the

NORMDIST function in ExcelR to determine the probability that in any

given year you will lose money by investing in large-company common

stock.

28. Using Probability ;Suppose the returns on long-term

corporate bonds and T-bills are normally distributed. Based on the

historical record, use the NORMDIST function in ExcelR to answer the

following questions:

1. What is the probability that in any given year, the return on long-term

corporate bonds will be greater than 10 percent? Less than 0 percent?

1. What is the probability that in any given year, the return on T-bills

will be greater than 10 percent? Less than 0 percent?

4. In 1979, the return on long-term corporate bonds was – percent.

How likely is it that such a low return will recur at some point in the

future? T-bills had a return of percent in this same year. How

likely is it that such a high return on T-bills will recur at some point in

the future?

EXCEL MASTER IT! PROBLEM

As we have seen, over the 1926–2014 period, small-company stocks had the highest return

and the highest risk, while Treasury bills had the lowest return and the lowest

risk. While we certainly hope you have an 89-year holding period, it is likely your investment

will be for fewer years. One way risk and return are examined over shorter investment

periods is by using rolling returns and standard deviations. Suppose you have a

series of annual returns, and you want to calculate a three-year rolling average return. You

would calculate the first rolling average at Year 3 using the returns for the first three

years. The next rolling average would be calculated using the returns from Years 2, 3, and

4, and so on.

1. Using the annual returns for large-company stocks and Treasury bills, calculate both

the 5- and 10-year rolling average return and standard deviation.

1. Over how many 5-year periods did Treasury bills outperform large-company stocks?

How many 10-year periods?

1. Over how many 5-year periods did Treasury bills have a larger standard deviation

than large-company stocks? Over how many 10-year periods?

1. Graph the rolling 5-year and 10-year average returns for large-company stocks and

Treasury bills.

1. What conclusions do you draw from the preceding results?

CHAPTER CASE

A Job at S&S Air

You recently graduated from college, and your job

search led you to S&S Air. Because you felt the company’s

business was headed skyward, you accepted the

job offer. As you are finishing your employment paperwork,

Chris Guthrie, who works in the finance department,

stops by to inform you about the company’s new

401(k) plan.

A 401(k) is a type of retirement plan offered by many

companies. A 401(k) is tax deferred, which means that

any deposits you make into the plan are deducted from

your current income, so no current taxes are paid on the

money. For example, assume your salary will be $30,000

per year. If you contribute $1,500 to the 401(k) plan, you

will pay taxes only on $28,500 in income. No taxes will

be due on any capital gains or plan income while you

are invested in the plan, but you will pay taxes when you

withdraw the money at retirement. You can contribute

up to 15 percent of your salary to the plan. As is common,

S&S Air also has a 5 percent match program. This

means that the company will match your contribution

dollar-for-dollar up to 5 percent of your salary, but you

must contribute to get the match.

The 401(k) plan has several options for investments,

most of which are mutual funds. As you know, a mutual

fund is a portfolio of assets. When you purchase shares

in a mutual fund, you are actually purchasing partial

ownership of the fund’s assets, similar to purchasing

shares of stock in a company. The return of the fund is

the weighted average of the return of the assets owned

by the fund, minus any expenses. The largest expense

is typically the management fee paid to the fund manager,

who makes all of the investment decisions for the

fund. S&S Air uses Arias Financial Services as its 401(k)

plan administrator.

Chris Guthrie then explains that the retirement investment

options offered for employees are as follows:

1. Company stock. One option is stock in S&S Air. The

company is currently privately held. The price you

would pay for the stock is based on an annual appraisal,

less a 20 percent discount. When you interviewed

with the owners, Mark Sexton and Todd

Story, they informed you that the company stock

was expected to be publicly sold in three to five

years. If you needed to sell the stock before it became

publicly traded, the company would buy it

back at the then-current appraised value.

2. Arias S&P 500 Index Fund. This mutual fund tracks

the S&P 500. Stocks in the fund are weighted exactly

the same as they are in the S&P 500. This

means that the fund’s return is approximately the

return of the S&P 500, minus expenses. With an

index fund, the manager is not required to research

stocks and make investment decisions, so fund expenses

are usually low. The Arias S&P 500 Index

Fund charges expenses of .20 percent of assets

per year.

3. Arias Small-Cap Fund. This fund primarily invests in

small capitalization stocks. As such, the returns of

the fund are more volatile. The fund can also invest

10 percent of its assets in companies based outside

the United States. This fund charges percent of

assets in expenses per year.

4. Arias Large-Company Stock Fund. This fund invests

primarily in large capitalization stocks of companies

based in the United States. The fund is managed by

Melissa Arias and has outperformed the market

in six of the last eight years. The fund charges

percent in expenses.

5. Arias Bond Fund. This fund invests in long-term

corporate bonds issued by domiciled companies.

The fund is restricted to investments in bonds

with an investment grade credit rating. This fund

charges percent in expenses.

6. Arias Money Market Fund. This fund invests in

short-term, high credit quality debt instruments,

which include Treasury bills. As such, the return on

money market funds is only slightly higher than the

return on Treasury bills. Because of the credit quality

and short-term nature of the investments, there

is only a very slight risk of negative return. The fund

charges .60 percent in expenses.

QUESTIONS

1. What advantages/disadvantages do the mutual

funds offer compared to company stock for your

retirement investing?

2. Notice that, for every dollar you invest, S&S Air

also invests a dollar. What return on your investment

does this represent? What does your answer

suggest about matching programs?

3. Assume you decide you should invest at least part

of your money in large capitalization stocks of

companies based in the United States. What are

the advantages and disadvantages of choosing

the Arias Large-Company Stock Fund compared

to the Arias S&P 500 Index Fund?

4. The returns of the Arias Small-Cap Fund are the

most volatile of all the mutual funds offered in the

401 (k) plan. Why would you ever want to invest in

this fund? When you examine the expenses of the

mutual funds, you will notice that this fund also

has the highest expenses. Will this affect your decision

to invest in this fund?

5. A measure of risk-adjusted performance that is often

used in practice is the Sharpe ratio. The

Sharpe ratio is calculated as the risk premium of

an asset divided by its standard deviation.

The standard deviations and returns for the

funds over the past 10 years are listed here. Assuming

a risk-free rate of 4 percent, calculate the

Sharpe ratio for each of these. In broad terms,

what do you suppose the Sharpe ratio is intended

to measure?

Chapter 11 Risk and Return

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Expected Return and Standard ;This problem will give you some

practice calculating measures of prospective portfolio performance. There are two

assets and three states of the economy:

(1)

State of

Economy

(2)

Probability

of State

of Economy

(3)

Stock A

Rate of Return

If State Occurs

(4)

Stock B

Rate of Return

If State Occurs

Recession .10 −.20 .30

Normal .60 .10 .20

Boom .30 .70 .50

What are the expected returns and standard deviations for these two stocks? (See

Problem 7.)

Portfolio Risk and ;In the previous problem, suppose you have $20,000

total. If you put $6,000 in Stock A and the remainder in Stock B, what will be the

expected return and standard deviation on your portfolio? (See Problem 10.)

Risk and ;Suppose you observe the following situation:

Security Beta Expected Return

Cooley, Inc. 19%

Moyer Co. 16

If the risk-free rate is 8 percent, are these securities correctly priced? What would

the risk-free rate have to be if they are correctly priced? (See Problems 19, 20.)

;Suppose the risk-free rate is 8 percent. The expected return on the market

is 14 percent. If a particular stock has a beta of .60, what is its expected return

based on the CAPM? If another stock has an expected return of 20 percent, what

must its beta be? (See Problem 13.)

CRITICAL THINKING AND CONCEPTS REVIEW

LO 2  Diversifiable and Nondiversifiable ;In broad terms, why is some

risk diversifiable? Why are some risks nondiversifiable? Does it follow

that an investor can control the level of unsystematic risk in a portfolio,

but not the level of systematic risk?

LO 3  Information and Market ;Suppose the government announces

that, based on a just-completed survey, the growth rate in the economy is

likely to be 2 percent in the coming year, as compared to 5 percent for the

year just completed. Will security prices increase, decrease, or stay the

same following this announcement? Does it make any difference whether

or not the 2 percent figure was anticipated by the market? Explain.

LO 3  Systematic versus Unsystematic ;Classify the following events as mostly

systematic or mostly unsystematic. Is the distinction clear in every case?

1. Short-term interest rates increase unexpectedly.
2. The interest rate a company pays on its short-term debt borrowing is

increased by its bank.

1. Oil prices unexpectedly decline.
2. An oil tanker ruptures, creating a large oil spill.
3. A manufacturer loses a multimillion-dollar product liability suit.
4. A Supreme Court decision substantially broadens producer liability

for injuries suffered by product users.

LO 3  Systematic versus Unsystematic ;Indicate whether the following

events might cause stocks in general to change price, and whether they

might cause Big Widget ;s stock to change price.

1. The government announces that inflation unexpectedly jumped by

2 percent last month.

1. Big Widget’s quarterly earnings report, just issued, generally fell in

line with analysts’ expectations.

1. The government reports that economic growth last year was

3 percent, which generally agreed with most economists’ forecasts.

1. The directors of Big Widget die in a plane crash.
2. Congress approves changes to the tax code that will increase the top

marginal corporate tax rate. The legislation had been debated for the

previous six months.

LO 1  Expected Portfolio ;If a portfolio has a positive investment in

every asset, can the expected return on the portfolio be greater than that

on every asset in the portfolio? Can it be less than that on every asset in

the portfolio? If you answer yes to one or both of these questions, give an

example to support your answer.

LO 2  ;True or false: The most important characteristic in

determining the expected return of a well-diversified portfolio is the

variances of the individual assets in the portfolio. Explain.

LO 3  Portfolio ;If a portfolio has a positive investment in every asset,

can the standard deviation on the portfolio be less than that on every

asset in the portfolio? What about the portfolio beta?

LO 4  Beta and ;Is it possible that a risky asset could have a beta of

zero? Explain. Based on the CAPM, what is the expected return on such

an asset? Is it possible that a risky asset could have a negative beta? What

does the CAPM predict about the expected return on such an asset? Can

you give an explanation for your answer?

LO 2  Corporate ;In recent years, it has been common for

companies to experience significant stock price changes in reaction to

announcements of massive layoffs. Critics charge that such events

encourage companies to fire longtime employees and that Wall Street is

cheering them on. Do you agree or disagree?

LO 1  Earnings and Stock ;As indicated by a number of examples in

this chapter, earnings announcements by companies are closely followed

by, and frequently result in, share price revisions. Two issues should come

to mind. First: Earnings announcements concern past periods. If the market

values stocks based on expectations of the future, why are numbers

summarizing past performance relevant? Second: These announcements

concern accounting earnings. Going back to Chapter 2, such earnings may

have little to do with cash flow, so again, why are they relevant?

QUESTIONS AND PROBLEMS

Select problems are available in McGraw-Hill Connect. Please see the packaging

options section of the preface for more information.

BASIC (Questions 1–24)

LO 1 1. Determining Portfolio ;What are the portfolio weights for a

portfolio that has 165 shares of Stock A that sell for $69 per share and

125 shares of Stock B that sell for $44 per share?

LO 1 2. Portfolio Expected ;You own a portfolio that has $2,750 invested in

Stock A and $3,900 invested in Stock B. If the expected returns on these

stocks are 9 percent and 14 percent, respectively, what is the expected return

on the portfolio?

LO 1 3. Portfolio Expected ;You own a portfolio that is 15 percent invested

in Stock X, 40 percent in Stock Y, and 45 percent in Stock Z. The expected

returns on these three stocks are 10 percent, 13 percent, and 15 percent,

respectively. What is the expected return on the portfolio?

LO 1 4. Portfolio Expected ;You have $10,000 to invest in a stock portfolio.

Your choices are Stock X with an expected return of 13 percent and Stock Y

with an expected return of percent. If your goal is to create a portfolio

with an expected return of percent, how much money will you invest in

Stock X? In Stock Y?

LO 1 5. Calculating Expected ;Based on the following information,

calculate the expected return.

6. Calculating Expected ;Based on the following information,

calculate the expected return.

State of

Economy

Probability of

State of Economy

Rate of Return If

State Occurs

Recession .15 −.09

Normal .60 .11

Boom .25 .30

LO 1 7. Calculating Returns and Standard ;Based on the following

information, calculate the expected return and standard deviation for the

two stocks.

State of

Economy

Probability of

State of Economy

Rate of Return If State Occurs

Stock A Stock B

Recession .10 .02 −.30

Normal .50 .10 .18

Boom .40 .15 .31

LO 1 8. Calculating Expected ;A portfolio is invested 20 percent in Stock

G, 35 percent in Stock J, and 45 percent in Stock K. The expected returns on

these stocks are percent, percent, and percent, respectively.

What is the portfolio’s expected return? How do you interpret your answer?

LO 1 9. Returns and Standard ;Consider the following information:

State of

Economy

Probability of

State of Economy

Rate of Return If State Occurs

Stock A Stock B Stock C

Boom .60 .15 .02 .34

Bust .40 .03 .16 −.08

1. What is the expected return on an equally weighted portfolio of these

three stocks?

1. What is the variance of a portfolio invested 20 percent each in A and B

and 60 percent in C?

LO 1 10. Returns and Standard ;Consider the following information:

State of

Economy

Probability of

State of Economy

Rate of Return If State Occurs

Stock A Stock B Stock C

Boom .15 .35 .45 .33

Good .50 .12 .10 .17

Poor .25 .01 .02 −.05

Bust .10 −.11 −.25 −.09

1. Your portfolio is invested 25 percent each in A and C and 50 percent in B.

What is the expected return of the portfolio?

1. What is the variance of this portfolio? The standard deviation?

LO 3 11. Calculating Portfolio ;You own a stock portfolio invested 15 percent

in Stock Q, 25 percent in Stock R, 40 percent in Stock S, and 20 percent in

Stock T. The betas for these four stocks are .75, .87, , and ,

respectively. What is the portfolio beta?

12. Calculating Portfolio ;You own a portfolio equally invested in a

risk-free asset and two stocks. If one of the stocks has a beta of and the

total portfolio is equally as risky as the market, what must the beta be for the

other stock in your portfolio?

LO 4 13. Using ;A stock has a beta of , the expected return on the market

is percent, and the risk-free rate is percent. What must the expected

return on this stock be?

LO 4 14. Using ;A stock has an expected return of percent, the risk-free

rate is percent, and the market risk premium is percent. What must

the beta of this stock be?

LO 4 15. Using ;A stock has an expected return of percent, its beta is .85,

and the risk-free rate is percent. What must the expected return on the

market be?

LO 4 16. Using ;A stock has an expected return of percent and a beta of .91,

and the expected return on the market is percent. What must the

risk-free rate be?

LO 4 17. Using ;A stock has a beta of and an expected return of

percent. A risk-free asset currently earns percent.

1. What is the expected return on a portfolio that is equally invested in the

two assets?

1. If a portfolio of the two assets has a beta of .7, what are the portfolio

weights?

1. If a portfolio of the two assets has an expected return of 9 percent, what

is its beta?

2. If a portfolio of the two assets has a beta of , what are the portfolio

weights? How do you interpret the weights for the two assets in this

case? Explain.

LO 4 18. Using the ;Asset W has an expected return of percent and a

beta of If the risk-free rate is percent, complete the following

table for portfolios of Asset W and a risk-free asset. Illustrate the

relationship between portfolio expected return and portfolio beta by

plotting the expected returns against the betas. What is the slope of the

line that results?

Percentage of Portfolio

in Asset W

Portfolio

Expected Return

Portfolio

Beta

0%

25

50

75

100

125

150

LO 4 19. Reward-to-Risk ;Stock Y has a beta of and an expected return

of percent. Stock Z has a beta of .85 and an expected return of

percent. If the risk-free rate is percent and the market risk premium

is 7 percent, are these stocks correctly priced?

20. Reward-to-Risk ;In the previous problem, what would the risk-free

rate have to be for the two stocks to be correctly priced relative to each

other?

LO 1 21. Portfolio ;Using information from Table on capital market

history, determine the return on a portfolio that was equally invested in

large-company stocks and long-term corporate bonds. What was the

return on a portfolio that was equally invested in small stocks and

Treasury bills?

LO 1 22. Portfolio Expected ;You have $250,000 to invest in a stock

portfolio. Your choices are Stock H, with an expected return of percent,

and Stock L, with an expected return of percent. If your goal is to create

a portfolio with an expected return of percent, how much money will

you invest in Stock H? In Stock L?

LO 1 23. Calculating Portfolio ;Stock J has a beta of and an expected

return of percent, while Stock K has a beta of .84 and an expected

return of percent. You want a portfolio with the same risk as the

market. How much will you invest in each stock? What is the expected

return of your portfolio?

LO 1 24. Calculating Portfolio Weights and Expected ;You have a portfolio

with the following:

Stock

Number

of Shares Price

Expected

Return

W 645 $43 10%

X 830 29 15%

Y 475 94 11%

Z 765 51 14%

What is the expected return of your portfolio?

INTERMEDIATE (Questions 25–27)

LO 1 25. Portfolio Returns and ;Consider the following information on a

portfolio of three stocks:

State of

Economy

Probability of

State of

Economy

Stock A Rate

of Return

Stock B Rate

of Return

Stock C Rate

of Return

Boom .15 .02 .32 .60

Normal .60 .10 .12 .20

Bust .25 .16 −.11 −.35

1. If your portfolio is invested 40 percent each in A and B and 20 percent

in C, what is the portfolio’s expected return? The variance? The

standard deviation?

3. If the expected T-bill rate is percent, what is the expected risk

premium on the portfolio?

LO 4 26. ;Using the CAPM, show that the ratio of the risk premiums on two

assets is equal to the ratio of their betas.

27. Analyzing a ;You want to create a portfolio equally as risky as the

market, and you have $500,000 to invest. Given this information, fill in the

rest of the following table:

Asset Investment Beta

Stock A $105,000 .80

Stock B 155,000

Stock C

Risk-free asset

CHALLENGE (Questions 28–30)

LO 1 28. Analyzing a ;You have $100,000 to invest in either Stock D,

Stock F, or a risk-free asset. You must invest all of your money. Your goal is

to create a portfolio that has an expected return of percent. If D has an

expected return of percent, F has an expected return of percent, and

the risk-free rate is percent, and if you invest $50,000 in Stock D, how

much will you invest in Stock F?

LO 4 29. ;Suppose you observe the following situation:

State of

Economy

Probability

of State

Return If State Occurs

Stock A Stock B

Bust .10 −.12 −.05

Normal .65 .09 .10

Boom .25 .35 .21

1. Calculate the expected return on each stock.
2. Assuming the capital asset pricing model holds and Stock A’s beta is

greater than Stock B’s beta by .25, what is the expected market risk

premium?

LO 3 30. Systematic versus Unsystematic ;Consider the following information

on Stocks I and II:

State of

Economy

Probability of State

of Economy

Rate of Return If State Occurs

Stock I Stock II

Recession .25 .02 −.20

Normal .60 .32 .12

Irrational exuberance .15 .18 .40

The market risk premium is 7 percent, and the risk-free rate is 4 percent.

Which stock has the most systematic risk? Which one has the most

unsystematic risk? Which stock is “riskier”? Explain.

CHAPTER CASE

The Beta for FLIR Systems

Joey Moss, a recent finance graduate, has just begun

his job with the investment firm of Covili and Wyatt.

Paul Covili, one of the firm’s founders, has been talking

to Joey about the firm’s investment portfolio.

As with any investment, Paul is concerned about

the risk of the investment as well as the potential return.

More specifically, because the company holds a diversified

portfolio, Paul is concerned about the systematic

risk of current and potential investments. One position

the company currently holds is stock in FLIR Systems,

Inc. (FLIR). FLIR Systems designs, manufactures, and

markets thermal imaging and infrared camera systems.

Although better known for its military applications, the

company has divisions that design products for other

applications such as automotive night vision,

commercial products that require minute temperature

difference measurements, recreational marine usage,

and firefighting.

Covili and Wyatt currently uses a commercial data

vendor for information about its positions. Because of

this, Paul is unsure exactly how the numbers provided

are calculated. The data provider considers its methods

proprietary, and it will not disclose how stock betas and

other information are calculated. Paul is uncomfortable

with not knowing exactly how these numbers are being

computed and also believes that it could be less expensive

to calculate the necessary statistics in-house. To

explore this question, Paul has asked Joey to do the following

assignments:

QUESTIONS

1. Go to and download the ending

monthly stock prices for FLIR Systems (FLIR) for the

last 60 months. Be sure to use the adjusted closing

price to account for any stock splits and dividend

payments. Next, download the ending value of the

S&P 500 index over the same period. For the historical

risk-free rate, go to the St. Louis Federal

Reserve

website () and find the

three-month Treasury bill constant maturity rate.

Download this file. What are the monthly returns,

average monthly returns, and standard deviations

for FLIR Systems stock, the three-month Treasury

bill, and the S&P 500 for this period?

2. Beta is often estimated by linear regression. A

model often used is called the market model,

which is:

Rt − Rf t = αi + βi [RMt − Rft] + εt

In this regression, Rt is the return on the stock and

Rft is the risk-free rate for the same period. RMt is

the return on a stock market index such as the

S&P 500 index. αi is the regression intercept, and

βi is the slope (and the stock’s estimated beta). εt

represents the residuals for the regression. What

do you think is the motivation for this particular

regression?

The intercept, αi, is often called

Jensen’s

alpha. What does it measure? If an asset

has a positive Jensen’s alpha, where would it plot

with respect to the SML? What is the financial interpretation

of the residuals in the regression?

3. Use the market model to estimate the beta for

FLIR Systems using the last 60 months of returns

(the regression procedure in Excel is one easy

way to do this). Plot the monthly returns on FLIR

Systems against the index and also show the fitted

line.

4. Compare your beta for FLIR Systems to the beta

you find on How similar are

they? Why might they be different?

Chapter 12 Cost of Capital

CHAPTER REVIEW AND SELF-TEST PROBLEMS

Calculating the Cost of ;Suppose stock in Boone Corporation has a beta

of .90. The market risk premium is 7 percent, and the risk-free rate is 8 percent.

Boone’s last dividend was $ per share, and the dividend is expected to grow at

7 percent indefinitely. The stock currently sells for $25. What is Boone’s cost of

equity capital? (See Problem 1.)

Calculating the ;In addition to the information in the previous problem,

suppose Boone has a target debt–equity ratio of 50 percent. Its cost of debt is

8 percent, before taxes. If the tax rate is 34 percent, what is the WACC?

(See Problem 10.)

CRITICAL THINKING AND CONCEPTS REVIEW

LO 3  ;On the most basic level, if a firm’s WACC is 12 percent, what

does this mean?

LO 3  Book Values versus Market ;In calculating the WACC, if you had

to use book values for either debt or equity, which would you choose? Why?

LO 4  Project ;If you can borrow all the money you need for a project at

6 percent, doesn’t it follow that 6 percent is your cost of capital for the project?

LO 4  WACC and ;Why do we use an aftertax figure for cost of debt but

not for cost of equity?

LO 1  DGM Cost of Equity ;What are the advantages of using the

dividend growth model (DGM) for determining the cost of equity

capital? What are the disadvantages? What specific piece of information

do you need to find the cost of equity using this model? What are some

of the ways in which you could get an estimate of this number?

LO 1  SML Cost of Equity ;What are the advantages of using the SML

approach to finding the cost of equity capital? What are the disadvantages?

What are the specific pieces of information needed to use this method? Are

all of these variables observable, or do they need to be estimated? What are

some of the ways in which you could get these estimates?

LO 2  Cost of Debt ;How do you determine the appropriate cost of

debt for a company? Does it make a difference if the company’s debt is

privately placed as opposed to being publicly traded? How would you

estimate the cost of debt for a firm whose only debt issues are privately

held by institutional investors?

LO 4  Cost of ;Suppose Tom O’Bedlam, president of Bedlam Products,

Inc., has hired you to determine the firm’s cost of debt and cost of equity

capital.

1. The stock currently sells for $50 per share, and the dividend per share

will probably be about $5. Tom argues, “It will cost us $5 per share

to use the stockholders’ money this year, so the cost of equity is equal

to 10 percent (=$5/50).” What’s wrong with this conclusion?

1. Based on the most recent financial statements, Bedlam Products’

total liabilities are $8 million. Total interest expense for the coming

year will be about $1 million. Tom therefore reasons, “We owe

$8 million, and we will pay $1 million interest. Therefore, our cost

of debt is obviously $1 million/8 million = ; What’s wrong

with this conclusion?

1. Based on his own analysis, Tom is recommending that the company

increase its use of equity financing, because “Debt costs percent,

but equity only costs 10 percent; thus equity is ; Ignoring all

the other issues, what do you think about the conclusion that the cost

of equity is less than the cost of debt?