Solution Manual Of Essentials of Corporate Finance 9th Edition by Ross
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Solution Manual Of Essentials of Corporate Finance 9th Edition by Ross
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Solution Manual Of Essentials of Corporate Finance 9th Edition by Ross
SAMPLE QUESTIONS
Essentials of Corporate Finance Ninth Edition Stephen A. Ross
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.
- What is the 2016 operating cash flow?
- What is the 2016 cash flow to creditors?
- What is the 2016 cash flow to stockholders?
- 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.
- What is the value of the shareholders’ equity if assets equal $9,300?
- 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.
- What is the tax bill for each firm?
- 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.)
- What is the company’s net income?
- What is its operating cash flow?
- 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.
- What is net income for 2016?
- What is the operating cash flow for 2016?
- What is the cash flow from assets for 2016? Is this possible? Explain.
- 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
- What is owners’ equity for 2015 and 2016?
- What is the change in net working capital for 2016?
- 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.)
- 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
- 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?
- 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?
- 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.
- Inventory is purchased.
- A supplier is paid.
- A short-term bank loan is repaid.
- A long-term debt is paid off early.
- A customer pays off a credit account.
- Inventory is sold at cost.
- 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:
- Quick ratio
- Cash ratio
- Capital intensity ratio
- Total asset turnover
- Equity multiplier
- Times interest earned ratio
- Profit margin
- Return on assets
- Return on equity
- 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:
- Public utilities
- Large retailers
- Airlines
- Online services
- Hospitals
- 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:
- Current ratio
- Quick ratio
- Cash ratio
- Debt–equity ratio and equity multiplier
- 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,
- 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.
- Calculating Financial ;Find the following financial ratios for Smolira
Golf (use year-end figures rather than average values where appropriate):
Short-term solvency ratios
- Current ratio ________________
- Quick ratio ________________
- Cash ratio ________________
Asset utilization ratios
- Total asset turnover ________________
- Inventory turnover ________________
- Receivables turnover ________________
Long-term solvency ratios
- Total debt ratio ________________
- Debt–equity ratio ________________
- Equity multiplier ________________
- Times interest earned ratio ________________
- Cash coverage ratio ________________
Profitability ratios
- Profit margin ________________
- Return on assets ________________
- 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?
- 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,
- 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
- 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
- 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.
- 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?
- 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?
- 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?
- 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?
- 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.
- 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:
- 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?
- 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?
- 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.
- 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?
- 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?
- 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?
- 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.
- 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?
- 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?
- 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.
- What is the relationship between the price of a bond and its YTM?
- 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?
- 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?
- 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.
- 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?
- In 20 years, what will your company’s repayment be if you issue the
coupon bonds? What if you issue the zeroes?
- 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
- 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
- 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).
- 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?
- 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
- The security of the bond—that is, whether the
bond has collateral.
- The seniority of the bond.
- The presence of a sinking fund.
- A call provision with specified call dates and call
prices.
- A deferred call accompanying the preceding call
provision.
- A make-whole call provision.
- Any positive covenants. Also, discuss several possible
positive covenants S&S Air might consider.
- Any negative covenants. Also, discuss several
possible negative covenants S&S Air might
consider.
- A conversion feature (note that S&S Air is not a
publicly traded company).
- 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?
- 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?
- 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).
- 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.
- What is your estimate of the current stock price?
- What is the target stock price in one year?
- 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.
- 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?
- 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
- Assuming the company continues its current
growth rate, what is the value per share of the
company’s stock?
- 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:
- 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?
- What are the problems associated with using the payback period as a
means of evaluating cash flows?
- 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:
- 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?
- 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:
- 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?
- 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:
- 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?
- What is the relationship between IRR and NPV? Are there any situations
in which you might prefer one method over the other? Explain.
- 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:
- 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?
- 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:
- 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.
- 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:
- 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.
- 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?
- 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
- 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?
- 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?
- 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?
- 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
- If the company requires a return of 10 percent on its investments, should
it accept this project? Why?
- 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
- If the required return is 11 percent and the company applies the
profitability index decision rule, which project should the firm accept?
- If the company applies the NPV decision rule, which project should it
take?
- 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.
- If you apply the payback criterion, which investment will you choose?
Why?
- If you apply the NPV criterion, which investment will you choose? Why?
- If you apply the IRR criterion, which investment will you choose? Why?
- If you apply the profitability index criterion, which investment will you
choose? Why?
- 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
- What is the IRR for each project?
- What is the NPV for each project?
- 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
- What is the profitability index for each project?
- What is the NPV for each project?
- 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?
- 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
- Calculate the payback period for both projects.
- Calculate the NPV for both projects.
- 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.
- Find C in terms of I and N such that the project has a payback period
just equal to its life.
- Find C in terms of I, N, and R such that this is a profitable project
according to the NPV decision rule.
- 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.
- If Yurdone requires a return of 12 percent on such undertakings, should
the cemetery business be started?
- 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?
- 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.
- 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.
- Based on your analysis, should the company open
the mine?
- 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?
- 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?
- 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.
- 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.
- 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.
- 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?
- 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.
- What is the profitability index of the project?
- What is the IRR of the project?
- What is the NPV of the project?
- How sensitive is the NPV to changes in the price of the new smartphone? Construct
a one-way data table to help you.
- 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
- What is the payback period of the project?
- What is the profitability index of the project?
- What is the IRR of the project?
- What is the NPV of the project?
- How sensitive is the NPV to changes in the price
of the new smartphone?
- How sensitive is the NPV to changes in the quantity
sold?
- Should Conch Republic produce the new
smartphone?
- 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.
- The stock price has risen steadily each day for the past 30 days.
- 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.
- 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?
- 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.
- Assuming a $1,000 face value, what was your total dollar return on this
investment over the past year?
- What was your total nominal rate of return on this investment over the
past year?
- 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:
- In nominal terms?
- 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.
- Calculate the arithmetic average returns for large-company stocks and
T-bills over this time period.
- Calculate the standard deviation of the returns for large-company stocks
and T-bills over this time period.
- 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?
- 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.
- 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.
- What was the arithmetic average return on the stock over this fiveyear
period?
- 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.
- What was the average real return on the stock?
- 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?
- 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.
- Calculate the average return for Treasury bills and the average annual
inflation rate (consumer price index) for this period.
- Calculate the standard deviation of Treasury bill returns and inflation
over this time period.
- Calculate the real return for each year. What is the average real return
for Treasury bills?
- 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.
- 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:
- 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?
- What is the probability that in any given year, the return on T-bills
will be greater than 10 percent? Less than 0 percent?
- 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.
- Using the annual returns for large-company stocks and Treasury bills, calculate both
the 5- and 10-year rolling average return and standard deviation.
- Over how many 5-year periods did Treasury bills outperform large-company stocks?
How many 10-year periods?
- Over how many 5-year periods did Treasury bills have a larger standard deviation
than large-company stocks? Over how many 10-year periods?
- Graph the rolling 5-year and 10-year average returns for large-company stocks and
Treasury bills.
- 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:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- What advantages/disadvantages do the mutual
funds offer compared to company stock for your
retirement investing?
- 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?
- 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?
- 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?
- 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?
- Short-term interest rates increase unexpectedly.
- The interest rate a company pays on its short-term debt borrowing is
increased by its bank.
- Oil prices unexpectedly decline.
- An oil tanker ruptures, creating a large oil spill.
- A manufacturer loses a multimillion-dollar product liability suit.
- 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.
- The government announces that inflation unexpectedly jumped by
2 percent last month.
- Big Widget’s quarterly earnings report, just issued, generally fell in
line with analysts’ expectations.
- The government reports that economic growth last year was
3 percent, which generally agreed with most economists’ forecasts.
- The directors of Big Widget die in a plane crash.
- 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.
- 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
- What is the expected return on an equally weighted portfolio of these
three stocks?
- 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
- Your portfolio is invested 25 percent each in A and C and 50 percent in B.
What is the expected return of the portfolio?
- 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?
- 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.
- What is the expected return on a portfolio that is equally invested in the
two assets?
- If a portfolio of the two assets has a beta of .7, what are the portfolio
weights?
- If a portfolio of the two assets has an expected return of 9 percent, what
is its beta?
- 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?
- 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
- 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?
- 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.
- 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
- Calculate the expected return on each stock.
- 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
- 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?
- 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?
- 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.
- 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.
- 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?
- 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?
- 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?
LO 4 Company Risk versus Project ;Both Dow Chemical Company, a
large natural gas user, and Superior Oil, a major natural gas producer,
are thinking of investing in natural gas wells near Houston. Both are
all-equity–financed companies. Dow and Superior are looking at
identical projects. They’ve analyzed their respective investments, which
would involve a negative cash flow now and positive expected cash
flows in the future. These cash flows would be the same for both firms.
No debt would be used to finance the projects. Both companies
estimate that their project would have a net present value of $1 million
at an 18 percent discount rate and a −$ million NPV at a 22 percent
discount rate. Dow has a beta of , whereas Superior has a beta of
.75. The expected risk premium on the market is 8 percent, and riskfree
bonds are yielding 12 percent. Should either company proceed?
Should both? Explain.
LO 4 Divisional Cost of ;Under what circumstances would it be
appropriate for a firm to use different costs of capital for its different
operating divisions? If the overall firm WACC were used as the hurdle
rate for all divisions, would the riskier divisions or the more
conservative divisions tend to get most of the investment projects?
Why? If you were to try to estimate the appropriate cost of capital for
different divisions, what problems might you encounter? What are two
techniques you could use to develop a rough estimate for each
division’s cost of capital?
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. Calculating Cost of ;The Giuntoli Co. just issued a dividend of
$ per share on its common stock. The company is expected to maintain
a constant 5 percent growth rate in its dividends indefinitely. If the stock
sells for $43 a share, what is the company’s cost of equity?
LO 1 2. Calculating Cost of ;Halestorm Corporation’s common stock has a
beta of If the risk-free rate is percent and the expected return on
the market is 11 percent, what is the company’s cost of equity capital?
- Calculating Cost of ;Stock in CDB Industries has a beta of The
market risk premium is percent, and T-bills are currently yielding percent.
CDB’s most recent dividend was $ per share, and dividends are expected
to grow at an annual rate of 5 percent indefinitely. If the stock sells for $45 per
share, what is your best estimate of the company’s cost of equity?
LO 1 4. Estimating the DCF Growth ;Suppose Hornsby Ltd. just issued
a dividend of $ per share on its common stock. The company paid
dividends of $, $, $, and $ per share in the last four years. If
the stock currently sells for $55, what is your best estimate of the company’s
cost of equity capital using arithmetic and geometric growth rates?
LO 1 5. Calculating Cost of Preferred ;Sixth Fourth Bank has an issue of
preferred stock with a $ stated dividend that just sold for $93 per share.
What is the bank’s cost of preferred stock?
LO 2 6. Calculating Cost of ;ICU Window, Inc., is trying to determine its cost
of debt. The firm has a debt issue outstanding with seven years to maturity that
is quoted at 96 percent of face value. The issue makes semiannual payments and
has an embedded cost of percent annually. What is the company’s pretax
cost of debt? If the tax rate is 38 percent, what is the aftertax cost of debt?
LO 2 7. Calculating Cost of ;Jiminy’s Cricket Farm issued a 30-year,
percent semiannual bond 8 years ago. The bond currently sells for
107 percent of its face value. The company’s tax rate is 35 percent.
- What is the pretax cost of debt?
- What is the aftertax cost of debt?
- Which is more relevant, the pretax or the aftertax cost of debt? Why?
LO 2 8. Calculating Cost of ;For the firm in Problem 7, suppose the book value
of the debt issue is $145 million. In addition, the company has a second debt
issue, a zero coupon bond with 9 years left to maturity; the book value of this
issue is $75 million, and it sells for percent of par. What is the total book
value of debt? The total market value? What is the aftertax cost of debt now?
LO 3 9. Calculating ;Bargeron Corporation has a target capital structure of
75 percent common stock, 5 percent preferred stock, and 20 percent debt. Its
cost of equity is percent, the cost of preferred stock is percent, and
the pretax cost of debt is percent. The relevant tax rate is 35 percent.
- What is the company’s WACC?
- The company president has approached you about the company’s
capital structure. He wants to know why the company doesn’t use more
preferred stock financing, since it costs less than debt. What would you
tell the president?
LO 3 10. Taxes and ;Tulloch Manufacturing has a target debt–equity ratio
of .45. Its cost of equity is percent, and its pretax cost of debt is
percent. If the tax rate is 35 percent, what is the company’s WACC?
LO 3 11. Finding the Target Capital ;Fama’s Llamas has a WACC of
percent. The company’s cost of equity is percent, and its pretax
cost of debt is percent. The tax rate is 35 percent. What is the company’s
target debt–equity ratio?
LO 4 12. Book Value versus Market ;Bonaime, Inc., has million shares
of common stock outstanding. The current share price is $84, and the book
value per share is $11. The company also has two bond issues outstanding.
The first bond issue has a face value of $65 million, a coupon rate of
percent, and sells for 98 percent of par. The second issue has a face
value of $50 million, a coupon rate of percent, and sells for 97 percent
of par. The first issue matures in 20 years, the second in 12 years.
- What are the company’s capital structure weights on a book value basis?
- What are the company’s capital structure weights on a market value basis?
- Which are more relevant, the book or market value weights? Why?
LO 3 13. Calculating the ;In Problem 12, suppose the most recent dividend
was $ and the dividend growth rate is 5 percent. Assume that the overall
cost of debt is the weighted average of that implied by the two outstanding
debt issues. Both bonds make semiannual payments. The tax rate is
35 percent. What is the company’s WACC?
LO 3 14. ;Clifford, Inc., has a target debt–equity ratio of .85. Its WACC is
percent, and the tax rate is 35 percent.
- If the company’s cost of equity is 11 percent, what is its pretax cost of debt?
- If the aftertax cost of debt is percent, what is the cost of equity?
LO 3 15. Finding the ;Given the following information for Gerken Power
Co., find the WACC. Assume the company’s tax rate is 35 percent.
Debt: 15,500 percent coupon bonds outstanding, $1,000
par value, 25 years to maturity, selling for 108 percent
of par; the bonds make semiannual payments.
Common stock: 495,000 shares outstanding, selling for $81 per share;
beta is
Preferred stock: 20,000 shares of percent preferred stock
outstanding, currently selling for $92 per share.
Market: 7 percent market risk premium and percent riskfree
rate.
LO 3 16. Finding the ;Hankins Corporation has million shares of
common stock outstanding, 290,000 shares of percent preferred stock
outstanding, and 125,000 of percent semiannual bonds outstanding, par
value $1,000 each. The common stock currently sells for $64 per share and
has a beta of , the preferred stock currently sells for $103 per share,
and the bonds have 20 years to maturity and sell for 109 percent of par. The
market risk premium is percent, T-bills are yielding percent, and the
firm’s tax rate is 34 percent.
- What is the firm’s market value capital structure?
- If the firm is evaluating a new investment project that has the same risk
as the firm’s typical project, what rate should the firm use to discount
the project’s cash flows?
LO 4 17. SML and ;An all-equity firm is considering the following projects:
The T-bill rate is 4 percent, and the expected return on the market is
11 percent.
- Which projects have a higher expected return than the firm’s 11 percent
cost of capital?
- Which projects should be accepted?
- Which projects will be incorrectly accepted or rejected if the firm’s
overall cost of capital were used as a hurdle rate?
LO 3 18. Calculating the ;You are given the following information
concerning Parrothead Enterprises:
Debt: 13,000 percent coupon bonds outstanding, with
15 years to maturity and a quoted price of 107. These
bonds pay interest semiannually.
Common stock: 345,000 shares of common stock selling for $
per share. The stock has a beta of .90 and will pay a
dividend of $ next year. The dividend is expected
to grow by 5 percent per year indefinitely.
Preferred stock: 10,000 shares of percent preferred stock selling at
$86 per share.
Market: 12 percent expected return, risk-free rate of
percent, and a 35 percent tax rate.
Calculate the WACC for Parrothead Enterprises.
LO 3 19. Calculating Capital Structure ;Liu Industrial Machines issued
175,000 zero coupon bonds four years ago. The bonds originally had
30 years to maturity with a yield to maturity of percent. Interest
rates have recently decreased, and the bonds now have a yield to
maturity of percent. If the company has a $68 million market value
of equity, what weight should it use for debt when calculating the cost
of capital?
LO 3 20. Calculating the ;Gnomes R Us is considering a new project. The
company has a debt–equity ratio of .48. The company’s cost of equity is
percent, and the aftertax cost of debt is percent. The firm feels that
the project is riskier than the company as a whole and that it should use an
adjustment factor of +3 percent. What is the WACC it should use for the
project?
INTERMEDIATE (Questions 21–26)
LO 4 21. WACC and ;Hankins, Inc., is considering a project that will result in
initial aftertax cash savings of $ million at the end of the first year, and
these savings will grow at a rate of percent per year indefinitely. The
firm has a target debt–equity ratio of .25, a cost of equity of percent,
and an aftertax cost of debt of percent. The cost-saving proposal is
somewhat riskier than the usual project the firm undertakes; management
uses the subjective approach and applies an adjustment factor of +2 percent
to the cost of capital for such risky projects. Under what circumstances
should the company take on the project?
LO 2 22. Calculating the Cost of ;Ying Import has several bond issues
outstanding, each making semiannual interest payments. The bonds are
listed in the table below. If the corporate tax rate is 34 percent, what is the
aftertax cost of the company’s debt?
Bond Coupon Rate Price Quote Maturity Face Value
1 5 years $30,000,000
2 8 years 50,000,000
3 15½ years 65,000,000
4 25 years 85,000,000
LO 1 23. Calculating the Cost of ;Pierce Industries stock has a beta of
The company just paid a dividend of $, and the dividends are expected
to grow at 4 percent. The expected return on the market is percent, and
Treasury bills are yielding percent. The most recent stock price is $83.
- Calculate the cost of equity using the dividend growth model method.
- Calculate the cost of equity using the SML method.
- Why do you think your estimates in (a) and (b) are so different?
LO 3 24. Adjusted Cash Flow from ;Ward Corp. is expected to have an
EBIT of $ million next year. Depreciation, the increase in net working
capital, and capital spending are expected to be $165,000, $85,000, and
$115,000, respectively. All are expected to grow at 18 percent per year for
four years. The company currently has $13 million in debt and 800,000
shares outstanding. After Year 5, the adjusted cash flow from assets is
expected to grow at 3 percent indefinitely. The company’s WACC is
percent and the tax rate is 35 percent. What is the price per share of
the company’s stock?
LO 3 25. Adjusted Cash Flow from ;In the previous problem, instead of
a perpetual growth rate in adjusted cash flow from assets, you decide to
calculate the terminal value of the company with the price–sales ratio. You
believe that Year 5 sales will be $ million and the appropriate price–sales
ratio is What is your new estimate of the current share price?
LO 3 26. Adjusted Cash Flow from ;You have looked at the current financial
statements for Reigle Homes, Co. The company has an EBIT of $ million
this year. Depreciation, the increase in net working capital, and capital
spending were $235,000, $105,000, and $475,000, respectively. You
expect that over the next five years, EBIT will grow at 15 percent per year,
depreciation and capital spending will grow at 20 percent per year, and
NWC will grow at 10 percent per year. The company has $ million in
debt and 400,000 shares outstanding. After Year 5, the adjusted cash flow
from assets is expected to grow at percent indefinitely. The company’s
WACC is percent, and the tax rate is 35 percent. What is the price per
share of the company’s stock?
CHALLENGE (Questions 27–28)
LO 3 27. WACC and ;Photochronograph Corporation (PC) manufactures time
series photographic equipment. It is currently at its target debt–equity ratio
of .45. It’s considering building a new $37 million manufacturing facility.
This new plant is expected to generate aftertax cash flows of $ million in
perpetuity. There are three financing options:
- A new issue of common stock: The required return on the company’s
new equity is 15 percent.
- A new issue of 20-year bonds: If the company issues these new bonds
at an annual coupon rate of 7 percent, they will sell at par.
- Increased use of accounts payable financing: Because this financing is
part of the company’s ongoing daily business, the company assigns it a
cost that is the same as the overall firm WACC. Management has a
target ratio of accounts payable to long-term debt of .15. (Assume there
is no difference between the pretax and aftertax accounts payable cost.)
What is the NPV of the new plant? Assume that the company has a 35 percent
tax rate.
LO 3 28. Project ;This is a comprehensive project evaluation problem
bringing together much of what you have learned in this and previous
chapters. Suppose you have been hired as a financial consultant to Defense
Electronics, Inc. (DEI), a large, publicly traded firm that is the market
share leader in radar detection systems (RDSs). The company is looking at
setting up a manufacturing plant overseas to produce a new line of RDSs.
This will be a five-year project. The company bought some land three
years ago for $ million in anticipation of using it as a toxic dump site for
waste chemicals, but it built a piping system to safely discard the chemicals
instead. If the land were sold today, the net proceeds would be $5 million
after taxes. In five years, the land will be worth $ million after taxes.
The company wants to build its new manufacturing plant on this land; the
plant will cost $ million to build. The following market data on DEI’s
securities are current:
Debt: 60,000 percent coupon bonds outstanding,
25 years to maturity, selling for 95 percent of par; the
bonds have a $1,000 par value each and make
semiannual payments.
Common stock: 1,250,000 shares outstanding, selling for $97 per
share; the beta is
Preferred stock: 90,000 shares of percent preferred stock
outstanding, selling for $95 per share.
Market: 7 percent expected market risk premium; percent
risk-free rate.
DEI’s tax rate is 34 percent. The project requires $825,000 in initial net
working capital investment to get operational.
- Calculate the project’s Time 0 cash flow, taking into account all side
effects.
- The new RDS project is somewhat riskier than a typical project for
DEI, primarily because the plant is being located overseas.
Management has told you to use an adjustment factor of +2 percent to
account for this increased riskiness. Calculate the appropriate discount
rate to use when evaluating DEI’s project.
- The manufacturing plant has an eight-year tax life, and DEI uses
straight-line depreciation. At the end of the project (, the end of
Year 5), the plant can be scrapped for $ million. What is the aftertax
salvage value of this manufacturing plant?
- The company will incur $3,500,000 in annual fixed costs. The plan is to
manufacture 13,000 RDSs per year and sell them at $10,800 per
machine; the variable production costs are $9,900 per RDS. What is the
annual operating cash flow, OCF, from this project?
- Finally, DEI’s president wants you to throw all your calculations, all
your assumptions, and everything else into a report for the chief
financial officer; all he wants to know is what the RDS project’s
internal rate of return, IRR, and net present value, NPV, are. What will
you report?
EXCEL MASTER IT! PROBLEM
You want to calculate the WACC for auto parts retailer AutoZone (AZO). Complete the
following steps to construct a spreadsheet that can be updated.
- Using an input for the ticker symbol, create hyperlinks to the web pages that you will
need to find all of the information necessary to calculate the cost of equity. Use a
market risk premium of seven percent when using CAPM.
- Create hyperlinks to go to the FINRA bond quote website and the SEC EDGAR
database and find the information for the company’s bonds. Create a table that
calculates the cost of debt for the company. Assume the tax rate is 35 percent.
- Finally, calculate the market value weights for debt and equity. What is the WACC
for AutoZone?
CHAPTER CASE
Cost of Capital for Layton Motors
You have recently been hired by Layton Motors, Inc.
(LMI), in its relatively new treasury management department.
LMI was founded eight years ago by Rachel
Layton. Rachel found a method to manufacture a
cheaper battery that will hold a larger charge, giving a
car powered by the battery a range of 700 miles before
requiring a recharge. The cars manufactured by LMI are
midsized and carry a price that allows the company to
compete with other mainstream auto manufacturers.
The company is privately owned by Rachel and her family,
and it had sales of $197 million last year.
LMI primarily sells to customers who buy the cars online,
although it does have a limited number of companyowned
dealerships. The customer selects any
customization and makes a deposit of 20 percent of the
purchase price. After the order is taken, the car is made
to order, typically within 45 days. LMI’s growth to date has
come from its profits. When the company had sufficient
capital, it would expand production. Relatively little formal
analysis has been used in its capital budgeting process.
Rachel has just read about capital budgeting techniques
and has come to you for help. For starters, the company
has never attempted to determine its cost of capital, and
Rachel would like you to perform the analysis. Because
the company is privately owned, it is difficult to determine
the cost of equity for the company. Rachel wants you to
use the pure play approach to estimate the cost of capital
for LMI, and she has chosen Tesla Motors as a representative
company. The following questions will lead you
through the steps to calculate this estimate.
QUESTIONS
- Most publicly traded corporations are required to
submit quarterly (10Q) and annual reports (10K) to
the SEC detailing the financial operations of the
company over the past quarter or year, respectively.
These corporate filings are available on the
SEC website at Go to the SEC website,
follow the “Search EDGAR for Company Filings”
link, and search for SEC filings made by
Tesla Motors (TSLA). Find the most recent 10Q or
10K, and download the form. Look on the balance
sheet to find the book value of debt and the book
value of equity.
- To estimate the cost of equity for TSLA, go to
and enter the ticker symbol
TSLA. Follow the links to answer the following
questions: What is the most recent stock price
listed for TSLA? What is the market value of equity,
or market capitalization? How many shares of
stock does TSLA have outstanding? What is the
most recent annual dividend? Can you use the dividend
discount model in this case? What is the beta
for TSLA? Now go back to and
follow the “Bonds” link. What is the yield on
three-month Treasury bills? Using the historical
market risk premium, what is the cost of equity for
TSLA using CAPM?
- You now need to calculate the cost of debt for
TSLA. Go to
/BondCenter/, enter TSLA as the company, and
find the yield to maturity for each of TSLA’s bonds.
What is the weighted average cost of debt for
TSLA using the book value weights and using the
market value weights? Does it make a difference
in this case if you use book value weights or market
value weights?
- You now have all the necessary information to calculate
the weighted average cost of capital for
TSLA. Calculate this using book value weights
and market value weights, assuming TSLA has a
35 percent marginal tax rate. Which number is
more relevant?
- You used TSLA as a pure play company to estimate
the cost of capital for LMI. Are there any potential
problems with this approach in this
situation?
Chapter 13 Leverage and Capital Structure
CHAPTER REVIEW AND SELF-TEST PROBLEMS
EBIT and ;Suppose the GNR Corporation has decided in favor of a capital
restructuring that involves increasing its existing $5 million in debt to $25 million. The
interest rate on the debt is 12 percent and is not expected to change. The firm currently
has 1 million shares outstanding, and the price per share is $40. If the restructuring is
expected to increase the ROE, what is the minimum level for EBIT that GNR’s
management must be expecting? Ignore taxes in your answer. (See Problem 4.)
M&M Proposition II (no taxes). The Pro Bono Corporation has a WACC of
20 percent. Its cost of debt is 12 percent. If Pro Bono’s debt–equity ratio is 2, what
is its cost of equity capital? Ignore taxes in your answer. (See Problem 10.)
M&M Proposition I (with corporate taxes). Suppose TransGlobal Co. currently has
no debt and its equity is worth $20,000. If the corporate tax rate is 30 percent, what
will the value of the firm be if TransGlobal borrows $6,000 and uses the proceeds
to buy up stock? (See Problem 14.)
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 Business Risk versus Financial ;Explain what is meant by business
and financial risk. Suppose Firm A has greater business risk than Firm B.
Is it true that Firm A also has a higher cost of equity capital? Explain.
LO 1 M&M ;How would you answer in the following debate?
Q: Isn’t it true that the riskiness of a firm’s equity will rise if the firm
increases its use of debt financing?
A: Yes, that’s the essence of M&M Proposition II.
Q: And isn’t it true that, as a firm increases its use of borrowing, the likelihood
of default increases, which increases the risk of the firm’s debt?
A: Yes.
Q: In other words, increased borrowing increases the risk of the equity
and the debt?
A: That’s right.
Q: Well, given that the firm uses only debt and equity financing, and
given that the risk of both is increased by increased borrowing, does it
not follow that increasing debt increases the overall risk of the firm
and therefore decreases the value of the firm?
A: ??
LO 1 Optimal Capital ;Is there an easily identifiable debt–equity
ratio that will maximize the value of a firm? Why or why not?
LO 1 Observed Capital ;Refer to the observed capital structures
given in Table of the text. What do you notice about the types of
industries with respect to their average debt–equity ratios? Are certain
types of industries more likely to be highly leveraged than others? What
are some possible reasons for this observed segmentation? Do the
operating results and tax history of the firms play a role? How about
their future earnings prospects? Explain.
LO 1 Financial ;Why is the use of debt financing referred to as
using financial “leverage”?
Homemade ;What is homemade leverage?
LO 3 Bankruptcy and Corporate ;As mentioned in the text, some
firms have filed for bankruptcy because of actual or likely litigationrelated
losses. Is this a proper use of the bankruptcy process?
LO 3 Bankruptcy and Corporate ;Firms sometimes use the threat of a
bankruptcy filing to force creditors to renegotiate terms. Critics argue
that in such cases, the firm is using bankruptcy laws “as a sword rather
than a ; Is this an ethical tactic?
LO 3 Bankruptcy and Corporate ;As mentioned in the text,
Continental Airlines filed for bankruptcy, at least in part, as a means of
reducing labor costs. Whether this move was ethical, or proper, was hotly
debated. Give both sides of the argument.
LO 1 Capital Structure ;What is the basic goal of financial management
with regard to capital structure?
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 1–13)
LO 1 1. EBIT and ;Kaelea, Inc., has no debt outstanding and a total market
value of $194,775. Earnings before interest and taxes, EBIT, are projected to be
$13,800 if economic conditions are normal. If there is strong expansion in the
economy, then EBIT will be 20 percent higher. If there is a recession, then EBIT
will be 35 percent lower. The company is considering a $39,750 debt issue with
an interest rate of 6 percent. The proceeds will be used to repurchase shares of
stock. There are currently 7,350 shares outstanding. Ignore taxes for this problem.
- Calculate earnings per share, EPS, under each of the three economic
scenarios before any debt is issued. Also, calculate the percentage
changes in EPS when the economy expands or enters a recession.
- Repeat part (a) assuming that the company goes through with recapitalization.
What do you observe? Assume the stock price remains constant.
LO 2 2. EBIT, Taxes, and ;Repeat parts (a) and (b) in Problem 1 assuming
the company has a tax rate of 35 percent.
LO 1 3. ROE and ;Suppose the company in Problem 1 has a market-to-
LO 2 book ratio of
- Calculate return on equity, ROE, under each of the three economic
scenarios before any debt is issued. Also, calculate the percentage changes
in ROE for economic expansion and recession, assuming no taxes.
- Repeat part (a) assuming the firm goes through with the proposed
recapitalization.
- Repeat parts (a) and (b) of this problem assuming the firm has a tax
rate of 35 percent.
LO 1 4. Break-Even ;Kyle Corporation is comparing two different capital
structures, an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I,
the company would have 300,000 shares of stock outstanding. Under Plan II,
there would be 210,000 shares of stock outstanding and $2,367,000 in debt
outstanding. The interest rate on the debt is 10 percent, and there are no taxes.
- If EBIT is $600,000, which plan will result in the higher EPS?
- If EBIT is $900,000, which plan will result in the higher EPS?
- What is the break-even EBIT?
LO 1 5. M&M and Stock ;In Problem 4, use M&M Proposition I to find the
price per share of equity under each of the two proposed plans. What is the
value of the firm?
LO 1 6. Break-Even EBIT and ;Silverton Co. is comparing two different
LO 2 capital structures. Plan I would result in 11,500 shares of stock and
$494,000 in debt. Plan II would result in 16,000 shares of stock and
$260,000 in debt. The interest rate on the debt is 10 percent.
- Ignoring taxes, compare both of these plans to an all-equity plan
assuming that EBIT will be $68,000. The all-equity plan would result
in 21,000 shares of stock outstanding. Which of the three plans has the
highest EPS? The lowest?
- In part (a), what are the break-even levels of EBIT for each plan as
compared to that for an all-equity plan? Is one higher than the other? Why?
- Ignoring taxes, when will EPS be identical for Plans I and II?
- Repeat parts (a), (b), and (c) assuming that the corporate tax rate is
35 percent. Are the break-even levels of EBIT different from before?
Why or why not?
LO 1 7. Leverage and Stock ;Ignoring taxes in Problem 6, what is the price
per share of equity under Plan I? Plan II? What principle is illustrated by
your answers?
LO 1 8. Homemade ;FCOJ, Inc., a prominent consumer products firm, is
debating whether or not to convert its all-equity capital structure to one that
is 30 percent debt. Currently, there are 6,400 shares outstanding and the
price per share is $55. EBIT is expected to remain at $19,300 per year
forever. The interest rate on new debt is 8 percent, and there are no taxes.
- Melanie, a shareholder of the firm, owns 100 shares of stock. What is
her cash flow under the current capital structure, assuming the firm has
a dividend payout rate of 100 percent?
- What will Melanie’s cash flow be under the proposed capital structure
of the firm? Assume that she keeps all 100 of her shares.
- Suppose FCOJ does convert, but Melanie prefers the current all-equity
capital structure. Show how she could unlever her shares of stock to
recreate the original capital structure.
- Using your answer to part (c), explain why FCOJ’s choice of capital
structure is irrelevant.
LO 1 9. Homemade ;Lydic Enterprises is considering a change from its
current capital structure. The company currently has an all-equity capital
structure and is considering a capital structure with 25 percent debt. There
are currently 6,400 shares outstanding at a price per share of $60. EBIT is
expected to remain constant at $47,000. The interest rate on new debt is
7 percent and there are no taxes.
- Rebecca owns $18,000 worth of stock in the company. If the firm has a
100 percent payout, what is her cash flow?
- What would her cash flow be under the new capital structure assuming
that she keeps all of her shares?
- Suppose the company does convert to the new capital structure. Show
how Rebecca can maintain her current cash flow.
- Under your answer to part (c), explain why the company’s choice of
capital structure is irrelevant.
LO 1 10. Calculating ;Crosby Industries has a debt–equity ratio of Its WACC
is percent, and its cost of debt is percent. There is no corporate tax.
- What is the company’s cost of equity capital?
- What would the cost of equity be if the debt–equity ratio were
What if it were .5? What if it were zero?
LO 1 11. Calculating ;Malkin Corp. has no debt but can borrow at percent.
The firm’s WACC is currently percent, and there is no corporate tax.
- What is the company’s cost of equity?
- If the firm converts to 30 percent debt, what will its cost of equity be?
- If the firm converts to 60 percent debt, what will its cost of equity be?
- What is the company’s WACC in part (b)? In part (c)?
LO 2 12. M&M and ;Wolfgang can borrow at percent. The company currently
has no debt, and the cost of equity is percent. The current value of the firm
is $595,000. What will the value be if the company borrows $310,000 and uses
the proceeds to repurchase shares? The corporate tax rate is 35 percent.
LO 2 13. Interest Tax ;Incite Co. has a 38 percent tax rate. Its total interest
payment for the year just ended was $ million. What is the interest tax
shield? How do you interpret this amount?
INTERMEDIATE (Questions 14–16)
LO 1 14. M&;Three Piggies Enterprises has no debt. Its current total value is
$53 million. Ignoring taxes, what will the company’s value be if it sells
$ million in debt? Suppose now that the company’s tax rate is
40 percent. What will its overall value be if it sells $ million in
debt? Assume debt proceeds are used to repurchase equity.
LO 1 15. M&;In the previous question, what is the debt–equity ratio in both cases?
LO 1 16. M&;Gamer Co. has no debt. Its cost of capital is percent. Suppose
the company converts to a debt–equity ratio of The interest rate on the
debt is percent. Ignoring taxes, what is the company’s new cost of
equity? What is its new WACC?
CHALLENGE (Questions 17–20)
LO 2 17. Firm ;Calvert Corporation expects an EBIT of $22,300 every year
forever. The company currently has no debt, and its cost of equity is 15 percent.
- What is the current value of the company?
- Suppose the company can borrow at 10 percent. If the corporate tax
rate is 35 percent, what will the value of the firm be if the company
takes on debt equal to 50 percent of its unlevered value? What if it
takes on debt equal to 100 percent of its unlevered value?
- What will the value of the firm be if the company takes on debt equal
to 50 percent of its levered value? What if the company takes on debt
equal to 100 percent of its levered value?
LO 2 18. Firm ;What is the cost of capital for a firm that is 100 percent debt
financed? What is the value of the firm?
- Cost of Equity and ;Assuming a world of corporate taxes only,
show that the cost of equity, RE, is as follows: RE = RU + (RU − RD) .
(D/E) . (1 − TC).
LO 2 20. Business and Financial ;Assume a firm’s debt is risk-free, so that
the cost of debt equals the risk-free rate, Rf . Define βA as the firm’s asset
beta—that is, the systematic risk of the firm’s assets. Define βE to be the
beta of the firm’s equity. Use the capital asset pricing model (CAPM)
along with M&M Proposition II to show that βE = βA . (1 + D/E), where
D/E is the debt–equity ratio. Assume the tax rate is zero.
EXCEL MASTER IT! PROBLEM
The TL Corporation currently has no debt outstanding. Josh Culberson, the CFO, is considering
restructuring the company by issuing debt and using the proceeds to repurchase
outstanding equity. The company’s assets are worth $40 million, the stock price is $25 per
share, and there are 1,600,000 shares outstanding. In the expected state of the economy,
EBIT is expected to be $3 million. If there is a recession, EBIT would fall to $ million;
in an expansion, EBIT would increase to $ million. If the company issues debt, it will
issue a combination of short-term debt and long-term debt. The ratio of short-term debt to
long-term debt will be .20. The short-term debt will have an interest rate of 3 percent and
the long-term debt will have an interest rate of 8 percent.
- On the applicable worksheet, fill in the values in each table. For the debt–equity
ratio, create a spinner that changes the debt–equity ratio. The resulting debt–equity
ratio should range from 0 to 10 at increments of .1.
- Graph the EBIT and EPS for the TL Corporation on the same graph using a scatter plot.
- What is the breakeven EBIT between the current capital structure and the new capital
structure?
- To illustrate the new capital structure, you would like to create a pie chart. Another
pie chart that is available is the pie-in-pie chart. Using the pie-in-pie chart, graph the
equity and total debt in the main pie chart and the short-term debt and long-term debt
in the secondary pie chart. Note, if you right-click on a data series in the chart and
select Format Data Series, the Series Options will permit you to display the series by
a customized choice. In the customization, you can select which data series you want
displayed in the primary pie chart and the secondary pie chart.
CHAPTER CASE
Stephenson Real Estate Recapitalization
Stephenson Real Estate Company was founded
25 years ago by the current CEO, Robert Stephenson.
The company purchases real estate, including land and
buildings, and rents the property to tenants. The company
has shown a profit every year for the past 18 years,
and the shareholders are satisfied with the company’s
management. Prior to founding Stephenson Real Estate,
Robert was the founder and CEO of a failed alpaca farming
operation. The resulting bankruptcy made him extremely
averse to debt financing. As a result, the
company is entirely equity financed, with 9 million
shares of common stock outstanding. The stock currently
trades at $ per share.
Stephenson is evaluating a plan to purchase a huge
tract of land in the southeastern United States for $50 million.
The land will subsequently be leased to tenant farmers.
This purchase is expected to increase Stephenson’s
annual pretax earnings by $12 million in perpetuity. Kim
Weyand, the company’s new CFO, has been put in charge
of the project. Kim has determined that the company’s current
cost of capital is percent. She feels that the company
would be more valuable if it included debt in its
capital structure, so she is evaluating whether the company
should issue debt to entirely finance the project.
Based on some conversations with investment banks, she
thinks that the company can issue bonds at par value with
a coupon rate of 8 percent. From her analysis, she also
believes that a capital structure in the range of 70 percent
equity/30 percent debt would be optimal. If the company
goes beyond 30 percent debt, its bonds would carry a
lower rating and a much higher coupon because the possibility
of financial distress and the associated costs would
rise sharply. Stephenson has a 40 percent corporate tax
rate (state and federal).
QUESTIONS
- If Stephenson wishes to maximize its total market
value, would you recommend that it issue debt or
equity to finance the land purchase? Explain.
- Construct Stephenson’s market value balance
sheet before it announces the purchase.
- Suppose Stephenson decides to issue equity to
finance the purchase.
- What is the net present value of the project?
- Construct Stephenson’s market value balance
sheet after it announces that the firm
will finance the purchase using equity. What
would be the new price per share of the firm’s
stock? How many shares will Stephenson
need to issue to finance the purchase?
- Construct Stephenson’s market value balance
sheet after the equity issue but before
the purchase has been made. How many
shares of common stock does Stephenson
have outstanding? What is the price per share
of the firm’s stock?
- Construct Stephenson’s market value balance
sheet after the purchase has been
made.
- Suppose Stephenson decides to issue debt to finance
the purchase.
- What will the market value of the Stephenson
Company be if the purchase is financed with
debt?
- Construct Stephenson’s market value balance
sheet after both the debt issue and the
land purchase. What is the price per share of
the firm’s stock?
- Which method of financing maximizes the per-share
stock price of Stephenson’s equity?
Chapter 14 Dividends and Dividend Policy
CHAPTER REVIEW AND SELF-TEST PROBLEM
Repurchase versus Cash ;Trantor Corporation is deciding whether to
pay out $300 in excess cash in the form of an extra dividend or a share repurchase.
Current earnings are $ per share, and the stock sells for $15. The market value
balance sheet before paying out the $300 is as follows:
Market Value Balance Sheet
(before paying out excess cash)
Excess cash $ 300 Debt $ 400
Other assets 1,600 Equity 1,500
Total $1,900 Total $1,900
Evaluate the two alternatives in terms of the effect on the price per share of the stock,
the EPS, and the PE ratio. (See Problem 12.)
CRITICAL THINKING AND CONCEPTS REVIEW
LO 2 Dividend Policy ;How is it possible that dividends are so
important, but, at the same time, dividend policy is irrelevant?
LO 4 Stock ;What is the impact of a stock repurchase on a
company’s debt ratio? Does this suggest another use for excess cash?
LO 1 Life Cycle Theory of ;Explain the life cycle theory of
dividend payments. How does it explain corporate dividend payments
that are seen in the stock market?
LO 1 Dividend ;On Friday, December 8, Hometown Power
;s board of directors declares a dividend of 75 cents per share
payable on Wednesday, January 17, to shareholders of record as of
Wednesday, January 3. When is the ex-dividend date? If a shareholder
buys stock before that date, who gets the dividends on those shares, the
buyer or the seller?
LO 1 Alternative ;Some corporations, like one British company
that offers its large shareholders free crematorium use, pay dividends in
kind (, offer their services to shareholders at below-market cost).
Should mutual funds invest in stocks that pay these dividends in kind?
(The fundholders do not receive these services.)
LO 2 Dividends and Stock ;If increases in dividends tend to be followed
by (immediate) increases in share prices, how can it be said that dividend
policy is irrelevant?
LO 2 Dividends and Stock ;Last month, Central Virginia Power
Company, which had been having trouble with cost overruns on a nuclear
power plant that it had been building, announced that it was “temporarily
suspending dividend payments due to the cash flow crunch associated with
its investment ; The company’s stock price dropped from $
to $25 when this announcement was made. How would you interpret this
change in the stock price (, what would you say caused it)?
LO 1 Dividend Reinvestment ;The DRK Corporation has recently
developed a dividend reinvestment plan (DRIP). The plan allows
investors to reinvest cash dividends automatically in DRK in exchange
for new shares of stock. Over time, investors in DRK will be able to build
their holdings by reinvesting dividends to purchase additional shares of
the company.
Over 1,000 companies offer dividend reinvestment plans. Most companies
with DRIPs charge no brokerage or service fees. In fact, the shares
of DRK will be purchased at a 10 percent discount from the market price.
A consultant for DRK estimates that about 75 percent of DRK’s shareholders
will take part in this plan. This is somewhat higher than the
average.
Evaluate DRK’s dividend reinvestment plan. Will it increase shareholder
wealth? Discuss the advantages and disadvantages involved here.
LO 2 Dividend ;During 2014, 207 companies went public with
common stock offerings, raising a combined total of $ billion.
Relatively few of these 207 companies involved paid cash dividends.
Why do you think most chose not to pay dividends?
LO 1 Investment and ;The Phew Charitable Trust pays no taxes
on its capital gains or on its dividend income or interest income. Would
it be irrational for it to have low-dividend, high-growth stocks in its
portfolio? Would it be irrational for it to have municipal bonds in its
portfolio? Explain.
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 1–11)
LO 2 1. Dividends and Stock ;Your portfolio is 150 shares of Barden, Inc.
The stock currently sells for $87 per share. The company has announced a
dividend of $ per share with an ex-dividend date of April 19. Assuming
no taxes, how much will your stock be worth on April 19?
LO 2 2. Dividends and Stock ;It is April 19. Using the information in the
previous problem, what is your total portfolio value?
LO 2 3. Dividends and ;Timsang, Inc., has declared a $ per share
dividend. Suppose capital gains are not taxed, but dividends are taxed at
15 percent. New IRS regulations require that taxes be withheld at the time the
dividend is paid. The company’s stock sells for $92 per share, and the stock
is about to go ex dividend. What do you think the ex-dividend price will be?
LO 3 4. Stock ;The owners’ equity accounts for Overby International are
shown here:
Common stock ($1 par value) $ 35,000
Capital surplus 149,000
Retained earnings 565,000
Total owners’ equity $749,000
- If the company’s stock currently sells for $42 per share and a 10 percent
stock dividend is declared, how many new shares will be distributed?
Show how the equity accounts would change.
- If the company declared a 25 percent stock dividend, how would the
accounts change?
- Stock ;For the company in Problem 4, show how the equity accounts
will change if:
- The company declares a two-for-one stock split. How many shares are
outstanding now? What is the new par value per share?
- The company declares a one-for-five reverse stock split. How
many shares are outstanding now? What is the new par value
per share?
LO 3 6. Stock Splits and Stock ;Bermuda Triangle Corporation (BTC)
currently has 465,000 shares of stock outstanding that sell for $86 per share.
Assuming no market imperfections or tax effects exist, what will the share
price be after:
- BTC has a five-for-three stock split?
- BTC has a 15 percent stock dividend?
- BTC has a percent stock dividend?
- BTC has a four-for-seven reverse stock split?
- Determine the new number of shares outstanding in parts (a)
through (d).
LO 1 7. Regular ;The balance sheet for Throwing Copper, Inc., is shown
here in market value terms. There are 23,000 shares of stock outstanding.
Market Value Balance Sheet
Cash $160,000
Fixed assets 564,500 Equity $724,500
Total $724,500 Total $724,500
The company has declared a dividend of $ per share. The stock goes ex
dividend tomorrow. Ignoring any tax effects, what is the stock selling for
today? What will it sell for tomorrow? What will the balance sheet look like
after the dividends are paid?
LO 4 8. Share ;In the previous problem, suppose the company has
announced it is going to repurchase $31,050 worth of stock instead of
paying a dividend. What effect will this transaction have on the equity of the
firm? How many shares will be outstanding? What will the price per share
be after the repurchase? Ignoring tax effects, show how the share repurchase
is effectively the same as a cash dividend.
LO 3 9. Stock ;The market value balance sheet for Tidwell
Manufacturing is shown here. The company has declared a 20 percent stock
dividend. The stock goes ex dividend tomorrow (the chronology for a stock
dividend is similar to that for a cash dividend). There are 24,000 shares of
stock outstanding. What will the ex-dividend price be?
Market Value Balance Sheet
Cash $135,000 Debt $215,000
Fixed assets 730,000 Equity 650,000
Total $865,000 Total $865,000
LO 3 10. Stock ;The company with the common equity accounts shown
here has declared a 10 percent stock dividend at a time when the market
the distribution of the stock dividend have?
Common stock ($1 par value) $ 245,000
Capital surplus 1,280,000
Retained earnings 2,932,000
Total owners’ equity $4,457,000
LO 3 11. Stock ;In the previous problem, suppose the company instead
decides on a two-for-one stock split. The firm’s 73-cent-per-share cash
dividend on the new (postsplit) shares represents an increase of 10 percent
over last year’s dividend on the presplit stock. What effect does this have on
the equity accounts? What was last year’s dividend per share?
INTERMEDIATE (Questions 12–13)
LO 4 12. Stock ;Hodgkiss Corporation is evaluating an extra dividend
versus a share repurchase. In either case, $9,065 would be spent. Current
earnings are $ per share, and the stock currently sells for $59 per share.
There are 4,900 shares outstanding. Ignore taxes and other imperfections in
answering the first two questions.
- Evaluate the two alternatives in terms of the effect on the price per
share of the stock and shareholder wealth.
- What will be the effect on the company’s EPS and PE ratio under the
two different scenarios?
- In the real world, which of these actions would you recommend? Why?
LO 2 13. Dividend ;The Quick Buck Company is an all-equity firm that
has been in existence for the past three years. Company management
expects that the company will last for two more years and then be
dissolved. The firm will generate cash flows of $550,000 next year and
$840,000 in two years, including the proceeds from the liquidation.
There are 20,000 shares of stock outstanding and shareholders require a
return of 12 percent.
- What is the current price per share of the stock?
- The board of directors is dissatisfied with the current dividend policy
and proposes that a dividend of $650,000 be paid next year. To raise the
cash necessary for the increased dividend, the company will sell new
shares of stock. How many shares of stock must be sold? What is the
new price per share of the existing shares of stock?
CHALLENGE (Questions 14–15)
LO 2 14. Expected Return, Dividends, and ;The Gecko Company and the
Gordon Company are two firms whose business risk is the same but that
have different dividend policies. Gecko pays no dividend, whereas Gordon
has an expected dividend yield of percent. Suppose the capital gains tax
rate is zero, whereas the income tax rate is 35 percent. Gecko has an
expected earnings growth rate of 12 percent annually, and its stock price is
expected to grow at this same rate. If the aftertax expected returns on the
two stocks are equal (because they are in the same risk class), what is the
pretax required return on Gordon’s stock?
- Dividends and ;As discussed in the text, in the absence of market
imperfections and tax effects, we would expect the share price to decline by
the amount of the dividend payment when the stock goes ex dividend. Once
we consider the role of taxes, however, this is not necessarily true. One
model has been proposed that incorporates tax effects into determining the
ex-dividend price:6
(P0 − Px)/D = (1 − TP)/(1 − TG)
where P0 is the price just before the stock goes ex, Px is the ex-dividend
share price, D is the amount of the dividend per share, TP is the relevant
marginal personal tax rate on dividends, and TG is the effective marginal tax
rate on capital gains.
- If TP = TG = 0, how much will the share price fall when the stock goes ex?
- If TP = 15 percent and TG = 0, how much will the share price fall?
- If TP = 15 percent and TG = 30 percent, how much will the share
price fall?
- Suppose the only owners of stock are corporations. Recall that
corporations get at least a 70 percent exemption from taxation on the
dividend income they receive, but they do not get such an exemption on
capital gains. If the corporation’s income and capital gains tax rates are
both 35 percent, what does this model predict the ex-dividend share
price will be?
- What does this problem tell you about real-world tax considerations
and the dividend policy of the firm?
CHAPTER CASE
Electronic Timing, Inc.
Electronic Timing, Inc. (ETI), is a small company
founded 15 years ago by electronics engineers Tom
Miller and Jessica Kerr. ETl manufactures integrated circuits
to capitalize on the complex mixed-signal design
technology and has recently entered the market for frequency
timing generators, or silicon timing devices,
which provide the timing signals or “clocks” necessary
to synchronize electronic systems. Its clock products
originally were used in PC video graphics applications,
but the market subsequently expanded to include motherboards,
PC peripheral devices, and other digital consumer
electronics, such as digital television boxes and
game consoles. ETI also designs and markets custom
application-specific integrated circuits (ASICs) for industrial
customers. The ASIC’s design combines analog and
digital, or mixed-signal, technology. In addition to Tom
and Jessica, Nolan Pittman, who provided capital for the
company, is the third primary owner. Each owns 25 percent
of the 1 million shares outstanding. The company
has several other individuals, including current employees,
who own the remaining shares.
Recently, the company designed a new computer
motherboard. The company’s design is both more efficient
and less expensive to manufacture, and the ETI
design is expected to become standard in many personal
computers. After investigating the possibility of
manufacturing the new motherboard, ETI determined
that the costs involved in building a new plant would be
prohibitive. The owners also decided that they were unwilling
to bring in another large outside owner. Instead,
ETI sold the design to an outside firm. The sale of the
motherboard design was completed for an aftertax payment
of $30 million.
QUESTIONS
- Tom believes the company should use the extra
cash to pay a special one-time dividend. How will
this proposal affect the stock price? How will it affect
the value of the company?
- Jessica believes the company should use the extra
cash to pay off debt and upgrade and expand
its existing manufacturing capability. How would
Jessica’s proposals affect the company?
- Nolan favors a share repurchase. He argues that a
repurchase will increase the company’s PE ratio,
return on assets, and return on equity. Are his arguments
correct? How will a share repurchase affect
the value of the company?
- Another option discussed by Tom, Jessica, and
Nolan would be to begin a regular dividend payment
to shareholders. How would you evaluate
this proposal?
- One way to value a share of stock is the dividend
growth, or growing perpetuity, model. Consider
the following: The dividend payout ratio is 1 – b,
where b is the “retention” or “plowback” ratio. So,
the dividend next year will be the earnings next
year, E1, × (1 – b). The most commonly used equation
to calculate the sustainable growth rate is the
return on equity times the retention ratio. Substituting
these relationships into the dividend growth
model, we get the following equation to calculate
the price of a share of stock today:
P0 =
E1(1 − b)
Rs − ROE × b
What are the implications of this result in terms of
whether the company should pay a dividend or
upgrade and expand its manufacturing capability?
Explain.
- Does the question of whether the company
should pay a dividend depend on whether the
company is organized as a corporation or an LLC?
Chapter 15 Raising Capital
CHAPTER REVIEW AND SELF-TEST PROBLEM
Flotation ;The L5 Corporation is considering an equity issue to finance a
new space station. A total of $10 million in new equity is needed. If the direct costs
are estimated at 6 percent of the amount raised, how large does the issue need to
be? What is the dollar amount of the flotation cost? (See Problem 2.)
CRITICAL THINKING AND CONCEPTS REVIEW
LO 2 Debt versus Equity Offering ;In the aggregate, debt offerings are
much more common than equity offerings and typically much larger as
well. Why?
LO 2 Debt versus Equity Flotation ;Why are the costs of selling equity
so much larger than the costs of selling debt?
Bond Ratings and Flotation ;Why do noninvestment-grade bonds
have much higher direct costs than investment-grade issues?
LO 2 Underpricing in Debt ;Why is underpricing not a great concern
with bond offerings?
Use the following information to answer the next three questions. Zipcar, the
car-sharing company, went public in April of 2011. Assisted by the investment
bank Goldman, Sachs & Co., Zipcar sold million shares at $18 each,
thereby raising a total of $ million. By the end of the first day of trading,
the stock had zipped to $28 per share, down from a high of $ On the basis
of the end-of-day numbers, Zipcar shares were apparently underpriced by about
$10 each, meaning that the company missed out on an additional $ million.
LO 3 IPO ;The Zipcar IPO was underpriced by about 56 percent.
Should Zipcar be upset at Goldman over the underpricing?
LO 3 IPO ;In the previous question, how would it affect your thinking to
know that the company was incorporated about 10 years earlier, had only
$186 million in revenues in 2010, and had never earned a profit? Additionally,
the viability of the company’s business model was still unproven.
LO 3 IPO ;In the previous two questions, how would it affect your
thinking to know that in addition to the million shares offered in the
IPO, Zipcar had an additional 30 million shares outstanding? Of those 30
million shares, million shares were owned by four venture capital
firms, and million shares were owned by the 12 directors and
executive officers.
LO 3 IPO ;In 1980, a certain assistant professor of finance bought
12 initial public offerings of common stock. He held each of these for
approximately one month and then sold. The investment rule he followed
was to submit a purchase order for every firm commitment initial public
offering of oil and gas exploration companies. There were 22 of these
offerings, and he submitted a purchase order for approximately $1,000 in
stock for each of the companies. With 10 of these, no shares were allocated
to this assistant professor. With 5 of the 12 offerings that were purchased,
fewer than the requested number of shares were allocated.
The year 1980 was very good for oil and gas exploration company owners:
On average, for the 22 companies that went public, the stocks were
selling for 80 percent above the offering price a month after the initial offering
date. The assistant professor looked at his performance record and
found that the $8,400 invested in the 12 companies had grown to $10,000,
representing a return of only about 20 percent (commissions were negligible).
Did he have bad luck, or should he have expected to do worse than
the average initial public offering investor? Explain.
LO 1 Venture ;In the chapter, we mentioned that venture capital is
very expensive. Why do you think this is true?
LO 3 IPO ;The following material represents the cover page and
summary of the prospectus for the initial public offering of the Pest
Investigation Control Corporation (PICC), which is going public
tomorrow with a firm commitment initial public offering managed by the
investment banking firm of Erlanger and Ritter. Answer the following
questions:
- Assume that you know nothing about PICC other than the information
contained in the prospectus. Based on your knowledge of finance, what
is your prediction for the price of PICC tomorrow? Provide a short
explanation of why you think this will occur.
- Assume that you have several thousand dollars to invest. When you get
home from class tonight, you find that your stockbroker, whom you
have not talked to for weeks, has called. She has left a message that
PICC is going public tomorrow and that she can get you several
hundred shares at the offering price if you call her back first thing in
the morning. Discuss the merits of this opportunity.
PROSPECTUS PICC
200,000 shares
PEST INVESTIGATION CONTROL CORPORATION
Of the shares being offered hereby, all 200,000 are being sold by the Pest Investigation Control
Corporation, Inc. (“the Company”). Before the offering there has been no public market for the shares
of PICC, and no guarantee can be given that any such market will develop.
These securities have not been approved or disapproved by the SEC nor has the commission passed upon
the accuracy or adequacy of this prospectus. Any representation to the contrary is a criminal offense.
Price to
Public
Underwriting
Discount
Proceeds to
Company*
Per share $ $ $
Total $2,200,000 $220,000 $1,980,000
*Before deducting expenses estimated at $27,000 and payable by the Company.
This is an initial public offering. The common shares are being offered, subject to prior sale, when, as,
and if delivered to and accepted by the Underwriters and subject to approval of certain legal matters
by their Counsel and by Counsel for the Company. The Underwriters reserve the right to withdraw,
cancel, or modify such offer and to reject offers in whole or in part.
Erlanger and Ritter, Investment Bankers
July 12, 2016
Prospectus Summary
The Company The Pest Investigation Control Corporation (PICC) breeds and markets toads
and tree frogs as ecologically safe insect-control mechanisms.
The Offering 200,000 shares of common stock, no par value.
Listing The Company will seek listing on NASDAQ and will trade over the counter.
Shares Outstanding As of June 30, 2016, 400,000 shares of common stock were outstanding. After
the offering, 600,000 shares of common stock will be outstanding.
Use of Proceeds To finance expansion of inventory and receivables and general working capital,
and to pay for country club memberships for certain finance professors.
Selected Financial Information
(amounts in thousands except per-share data)
Fiscal Year Ended June 30
2014 2015 2016
Revenues $ $ $
Net earnings
Earnings per share .01 .04 .09
As of June 30, 2016
Actual
As Adjusted for
This Offering
Working capital $ 8 $ 1,961
Total assets 511 2,464
Stockholders’ equity 423 2,376
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 1–7)
LO 3 1. IPO ;The Woods Co. and the McIlroy Co. have both
announced IPOs at $40 per share. One of these is undervalued by $, and
the other is overvalued by $, but you have no way of knowing which is
which. You plan on buying 1,000 shares of each issue. If an issue is
underpriced, it will be rationed, and only half your order will be filled. If
you could get 1,000 shares in Woods and 1,000 shares in McIlroy, what
would your profit be? What profit do you actually expect? What principle
have you illustrated?
LO 3 2. Calculating Flotation ;The Zuri Co. needs to raise $87 million to
finance its expansion into new markets. The company will sell new shares
of equity via a general cash offering to raise the needed funds. If the offer
price is $48 per share and the company’s underwriters charge a spread of
7 percent, how many shares need to be sold?
LO 3 3. Calculating Flotation ;In the previous problem, if the SEC filing fee
and associated administrative expenses of the offering are $1,425,000, how
many shares need to be sold now?
LO 3 4. Calculating Flotation ;The Collins Co. has just gone public.
Under a firm commitment agreement, the company received $ for
each of the million shares sold. The initial offering price was $24 per
share, and the stock rose to $ per share in the first few minutes of
trading. The company paid $1,475,000 in legal and other direct costs and
$350,000 in indirect costs. What was the flotation cost as a percentage
of funds raised?
LO 3 5. Calculating Flotation ;The Elkmont Corporation needs to raise
$ million to finance its expansion into new markets. The company
will sell new shares of equity via a general cash offering to raise the
needed funds. If the offer price is $21 per share and the company’s
underwriters charge a spread of percent, how many shares need to
be sold?
LO 3 6. Calculating Flotation ;In the previous problem, if the SEC filing fee
and associated administrative expenses of the offering are $1,450,000, how
many shares need to be sold now?
LO 3 7. Calculating Flotation ;The Wiley Oakley Co. has just gone
public. Under a firm commitment agreement, Wiley received $
for each of the million shares sold. The initial offering price was
$34 per share, and the stock rose to $ per share in the first few
minutes of trading. Wiley paid $1,350,000 in legal and other direct costs
and $210,000 in indirect costs. What was the flotation cost as a
percentage of funds raised?
CHAPTER CASE
S&S Air Goes Public
Mark Sexton and Todd Story have been discussing
the future of S&S Air. The company has been experiencing
fast growth, and the two see only clear skies in
the company’s future. However, the fast growth can no
longer be funded by internal sources, so Mark and Todd
have decided the time is right to take the company public.
To this end, they have entered into discussions with
the investment bank of Crowe & Mallard. The company
has a working relationship with Renata Harper, the underwriter
who assisted with the company’s previous
bond offering. Crowe & Mallard have assisted numerous
small companies in the IPO process, so Mark and Todd
feel confident with this choice.
Renata begins by telling Mark and Todd about the
process. Although Crowe & Mallard charged an underwriter
fee of 4 percent on the bond offering, the underwriter
fee is 7 percent on all initial stock offerings of the
size of S&S Air’s offering. Renata tells Mark and Todd
that the company can expect to pay about $1,800,000 in
legal fees and expenses, $13,500 in SEC registration
fees, and $15,000 in other filing fees. Additionally, to be
listed on the NASDAQ, the company must pay $125,000.
There are also transfer agent fees of $6,500 and engraving
expenses of $450,000. The company should
also expect to pay $75,000 for other expenses associated
with the IPO.
Finally, Renata tells Mark and Todd that to file with
the SEC, the company must provide three years’ audited
financial statements. She is unsure about the costs of
the audit. Mark tells Renata that the company provides
audited financial statements as part of the bond covenant,
and the company pays $300,000 per year for the
outside auditor.
QUESTIONS
- At the end of the discussion, Mark asks Renata
about the Dutch auction IPO process. What are
the differences in the expenses to S&S Air if it
uses a Dutch auction IPO versus a traditional IPO?
Should the company go public through a Dutch
auction or use a traditional underwritten offering?
- During the discussion of the potential IPO and S&S
Air’s future, Mark states that he feels the company
should raise $110 million. However, Renata points
out that if the company needs more cash in the
near future, a secondary offering close to the IPO
would be problematic. Instead, she suggests that
the company should raise $150 million in the IPO.
How can we calculate the optimal size of the IPO?
What are the advantages and disadvantages of increasing
the size of the IPO to $150 million?
- After deliberation, Mark and Todd have decided
that the company should use a firm commitment
offering with Crowe & Mallard as the lead underwriter.
The IPO will be for $125 million. Ignoring
underpricing, how much will the IPO cost the company
as a percentage of the funds received?
- Many employees of S&S Air have shares of stock
in the company because of an existing employee
stock purchase plan. To sell the stock, the employees
can tender their shares to be sold in the IPO
at the offering price, or the employees can retain
their stock and sell it in the secondary market after
S&S Air goes public. Todd asks you to advise
the employees about which option is best. What
would you suggest to the employees?
Chapter 16 Short-Term Financial Planning
CHAPTER REVIEW AND SELF-TEST PROBLEMS
The Operating and Cash ;Consider the following financial statement
information for the Glory Road Company:
Item Beginning Ending
Inventory $1,543 $1,669
Accounts receivable 4,418 3,952
Accounts payable 2,551 2,673
Net sales $11,500
Cost of goods sold 8,200
Calculate the operating and cash cycles. (See Problem 6.)
Cash Balance for Masson ;The Masson Corporation has a 60-day
average collection period and wishes to maintain a $5 million minimum cash
balance. Based on this and the information below, complete the following cash
budget. What conclusions do you draw? (See Problem 16.)
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 Operating ;What are some of the characteristics of a firm with a
long operating cycle?
LO 1 Cash ;What are some of the characteristics of a firm with a long
cash cycle?
LO 3 Sources and ;For the year just ended, you have gathered the
following information on the Holly Corporation:
- A $200 dividend was paid.
- Accounts payable increased by $500.
- Fixed asset purchases were $900.
- Inventories increased by $625.
- Long-term debt decreased by $1,200.
Label each item as a source or use of cash and describe its effect on the
firm’s cash balance.
LO 2 Cost of Current ;Kane Manufacturing, Inc., has recently installed
a just-in-time (JIT) inventory system. Describe the effect this is likely to
have on the company’s carrying costs, shortage costs, and operating cycle.
LO 1 ;Is it possible for a firm’s cash cycle to be longer than its
operating cycle? Explain why or why not.
Use the following information to answer Questions ; Last month,
BlueSky Airline announced that it would stretch out its bill payments to 45
days from 30 days. The reason given was that the company wanted to “control
costs and optimize cash ; The increased payables period will be in effect
for all of the company’s 4,000 suppliers.
Operating and Cash ;What impact did this change in payables
policy have on BlueSky’s operating cycle? Its cash cycle?
LO 1 Operating and Cash ;What impact did the announcement have
on BlueSky’s suppliers?
LO 1 Corporate ;Is it ethical for large firms to unilaterally lengthen
their payables periods, particularly when dealing with smaller suppliers?
LO 1 Payables ;Why don’t all firms simply increase their payables
periods to shorten their cash cycles?
LO 1 Payables ;BlueSky lengthened its payables period to “control
costs and optimize cash ; Exactly what is the cash benefit to
BlueSky from this change?
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 3 1. Changes in the Cash ;Indicate the impact of the following
corporate actions on cash, using the letter I for an increase, D for a decrease,
or N when no change occurs.
- A dividend is paid with funds received from a sale of debt.
- Real estate is purchased and paid for with short-term debt.
- Inventory is bought on credit.
- A short-term bank loan is repaid.
- Next year’s taxes are prepaid.
- Preferred stock is repurchased.
- Sales are made on credit.
- Interest on long-term debt is paid.
- Payments for previous sales are collected.
- The accounts payable balance is reduced.
- A dividend is paid.
- Production supplies are purchased and paid for with a short-term note.
- Utility bills are paid.
- Cash is paid for raw materials purchased for inventory.
- Marketable securities are purchased.
LO 3 2. Cash ;Sunset, Inc., has a book value of equity of $13,465.
Long-term debt is $8,200. Net working capital, other than cash, is $2,275.
Fixed assets are $18,380. How much cash does the company have? If
current liabilities are $1,630, what are current assets?
LO 1 3. Changes in the Operating ;Indicate the effect that the following will
have on the operating cycle. Use the letter I to indicate an increase, the letter
D for a decrease, and the letter N for no change.
- Average receivables go up.
- Credit payment times for customers are increased.
- Inventory turnover goes from 3 times to 7 times.
- Payables turnover goes from 6 times to 11 times.
- Receivables turnover goes from 7 times to 9 times.
- Payments to suppliers are accelerated.
LO 1 4. Changes in ;Indicate the impact of the following on the cash and
operating cycles, respectively. Use the letter I to indicate an increase, the
letter D for a decrease, and the letter N for no change.
- The terms of cash discounts offered to customers are made less
favorable.
- The cash discounts offered by suppliers are increased; thus, payments
are made earlier.
- An increased number of customers begin to pay in cash instead of with
credit.
- Fewer raw materials than usual are purchased.
- A greater percentage of raw material purchases are paid for
with credit.
- More finished goods are produced for inventory instead of for order.
LO 3 5. Calculating Cash ;The Jallouk Company has projected the
following quarterly sales amounts for the coming year:
Q1 Q2 Q3 Q4
Sales $585 $675 $630 $895
- Accounts receivable at the beginning of the year are $330. The
company has a 45-day collection period. Calculate cash collections in
each of the four quarters by completing the following:
Q1 Q2 Q3 Q4
Beginning receivables
Sales
Cash collections
Ending receivables
- Rework part (a) assuming a collection period of 60 days.
- Rework part (a) assuming a collection period of 30 days.
LO 1 6. Calculating ;Consider the following financial statement information
for the Amaryliss Corporation:
Item Beginning Ending
Inventory $9,605 $11,302
Accounts receivable 4,093 4,994
Accounts payable 4,822 5,749
Net sales $124,652
Cost of goods sold 77,681
Assume all sales are on credit. Calculate the operating and cash cycles. How
do you interpret your answer?
- Factoring ;Your firm has an average collection period of 38 days.
Current practice is to factor all receivables immediately at a 2 percent
discount. What is the effective cost of borrowing in this case? Assume that
default is extremely unlikely.
LO 3 8. Calculating ;Brunell Products has projected the following sales
for the coming year:
Q1 Q2 Q3 Q4
Sales $680 $765 $915 $840
Sales in the year following this one are projected to be 15 percent greater in
each quarter.
- Calculate payments to suppliers assuming that the company places
orders during each quarter equal to 30 percent of projected sales for the
next quarter. Assume that the company pays immediately. What is the
payables period in this case?
Q1 Q2 Q3 Q4
Payment of accounts
- Rework part (a) assuming a 90-day payables period.
- Rework part (a) assuming a 60-day payables period.
LO 3 9. Calculating ;The Sepulcro Corporation’s purchases from
suppliers in a quarter are equal to 75 percent of the next quarter’s forecast
sales. The payables period is 60 days. Wages, taxes, and other expenses are
30 percent of sales, and interest and dividends are $120 per quarter. No
capital expenditures are planned. Projected quarterly sales are:
Q1 Q2 Q3 Q4
Sales $1,825 $2,130 $2,460 $2,615
Sales for the first quarter of the following year are projected at $2,230.
Calculate
the company’s cash outlays by completing the following:
Q1 Q2 Q3 Q4
Payment of accounts
Wages, taxes, other expenses
Long-term financing expenses
(interest and dividends)
Total
LO 3 10. Calculating Cash ;The following is the sales budget for Tesoro
Azul, Inc., for the first quarter of 2016.
Credit sales are collected as follows:
65 percent in the month of the sale
20 percent in the month after the sale
15 percent in the second month after the sale
The accounts receivable balance at the end of the previous quarter was
$97,000 ($71,000 of which was uncollected December sales).
- Compute the sales for November.
- Compute the sales for December.
- Compute the cash collections from sales for each month from January
through March.
LO 3 11. Calculating the Cash ;Here are some important figures from the
budget of Marston, Inc., for the second quarter of 2016.
April May June
Credit sales $574,000 $499,000 $626,000
Credit purchases 252,000 235,000 282,000
Cash disbursements
Wages, taxes, and expenses 114,000 107,800 149,000
Interest 13,000 13,000 13,000
Equipment purchases 44,600 5,500 207,000
The company predicts that 5 percent of its credit sales will never be collected,
35 percent of its sales will be collected in the month of the sale, and
the remaining 60 percent will be collected in the following month. Credit
purchases will be paid in the month following the purchase.
In March 2016, credit sales were $468,000. Using this information,
complete the following cash budget:
April May June
Beginning cash balance $152,000
Cash receipts
Cash collections from credit sales
Total cash available
Cash disbursements
Purchases 241,000
Wages, taxes, and expenses
Interest
Equipment purchases
Total cash disbursements
Ending cash balance
LO 3 12. Calculating Cash ;The MacFarlane Company has projected the
following quarterly sales amounts for the coming year:
- Accounts receivable at the beginning of the year are $1,900. The
company has a 45-day collection period. Calculate cash collections in
each of the four quarters by completing the following:
Q1 Q2 Q3 Q4
Beginning receivables
Sales
Cash collections
Ending receivables
- Rework part (a) assuming a collection period of 60 days.
- Rework part (a) assuming a collection period of 30 days.
INTERMEDIATE (Questions 13–16)
LO 3 13. Costs of ;You’ve worked out a line of credit arrangement that
allows you to borrow up to $40 million at any time. The interest rate is
.485 percent per month. In addition, 5 percent of the amount that you
borrow must be deposited in a noninterest-bearing account. Assume that
your bank uses compound interest on its line-of-credit loans.
- What is the effective annual interest rate on this lending arrangement?
- Suppose you need $15 million today and you repay it in six months.
How much interest will you pay?
LO 3 14. Costs of ;A bank offers your firm a revolving credit
arrangement for up to $75 million at an interest rate of percent per
quarter. The bank also requires you to maintain a compensating balance
of 4 percent against the unused portion of the credit line, to be deposited
in a noninterest-bearing account. Assume you have a short-term
investment account at the bank that pays .49 percent per quarter,
and assume that the bank uses compound interest on its revolving
credit loans.
- What is your effective annual interest rate (an opportunity cost) on the
revolving credit arrangement if your firm does not use it during the
year?
- What is your effective annual interest rate on the lending
arrangement if you borrow $40 million immediately and repay
it in one year?
- What is your effective annual interest rate if you borrow $75 million
immediately and repay it in one year?
LO 3 15. Cash and Operating ;Calvani, Inc., has a cash cycle of days,
an operating cycle of days, and an inventory period of days. The
company reported cost of goods sold in the amount of $445,000, and credit
sales were $724,000. What is the company’s average balance in accounts
payable and accounts receivable?
LO 3 16. Cash ;Piano Man, Inc., has a 32-day average collection period
and wants to maintain a minimum cash balance of $20 million, which is
what the company currently has on hand. The company currently has a
receivables balance of $218 million and has developed the following sales
and cash disbursement budgets in millions:
Q1 Q2 Q3 Q4
Sales $378 $468 $570 $522
Total cash disbursement 318 408 726 450
Complete the following cash budget for the company. What conclusions do
you draw?
PIANO MAN, INC.
Cash Budget
(in millions)
Q1 Q2 Q3 Q4
Beginning receivables
Sales
Cash collections
Ending receivables
Total cash collections
Total cash disbursements
Net cash inflow
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus (deficit)
CHALLENGE (Questions 17–18)
LO 3 17. Costs of ;In exchange for a $400 million fixed commitment line
of credit, your firm has agreed to do the following:
- Pay percent per quarter on any funds actually borrowed.
- Maintain a 5 percent compensating balance on any funds actually
borrowed.
- Pay an up-front commitment fee of .25 percent of the amount of the line.
Based on this information, answer the following:
- Ignoring the commitment fee, what is the effective annual interest rate
on this line of credit?
- Suppose your firm immediately uses $210 million of the line and pays
it off in one year. What is the effective annual interest rate on this
$210 million loan?
LO 3 18. Costs of ;Come and Go Bank offers your firm a discount
interest loan with an interest rate of percent for up to $20 million, and in
addition requires you to maintain a 4 percent compensating balance against
the face amount borrowed. What is the effective annual interest rate on this
lending arrangement?
EXCEL MASTER IT! PROBLEM
Heidi Pedersen, the treasurer for Wood Products, Inc., has just been asked by Justin Wood,
the company’s president, to prepare a memo detailing the company’s ending cash balance
for the next three months. Following, you will see the relevant estimates for this period.
July August September
Credit sales $1,275,800 $1,483,500 $1,096,300
Credit purchases 765,480 890,160 657,780
Cash disbursements
Wages, taxes, and expenses 348,600 395,620 337,150
Interest 29,900 29,900 29,900
Equipment 0 158,900 96,300
Credit sales collections:
Collected in month of sale: 35%
Collected month after sale: 60%
Never collected: 5%
June credit sales: $1,135,020
June credit purchases: $ 681,012
Beginning cash balance: $ 425,000
All credit purchases are paid in the month after the purchase.
- Complete the cash budget for Wood Products for the next three months.
- Heidi knows that the cash budget will become a standard report completed before
each quarter. To help reduce the time preparing the report each quarter, she would
like a memo with the appropriate information in Excel linked to the memo. Prepare a
memo to Justin that will automatically update when the values are changed in Excel.
CHAPTER CASE
Piepkorn Manufacturing Working Capital Management, Part 1
You have recently been hired by Piepkorn Manufacturing
to work in its newly established treasury department.
Piepkorn Manufacturing is a small company
that produces cardboard boxes in a variety of sizes.
Gary Piepkorn, the owner of the company, works primarily
in the sales and production areas. Currently, the company
puts all receivables in one shoe box and all
payables in another. Because of the disorganized system,
the finance area needs work, and that’s what
you’ve been brought in to do.
The company currently has a cash balance of
$154,000 and plans to purchase new box folding machinery
in the fourth quarter at a cost of $325,000. The
purchase of the machinery will be made with cash because
of the discount offered. The company’s policy is
to maintain a target cash balance of $100,000. All sales
are in cash and all purchases are made on credit.
Gary Piepkorn has projected the following gross
sales for each of the next four quarters:
Q1 Q2 Q3 Q4
Gross sales $863,500 $918,500 $996,000 $924,000
Gross sales for the first quarter of next year are projected
at $908,000.
Piepkorn typically orders 50 percent of next quarter’s
projected gross sales in the current quarter, and suppliers
are typically paid in 53 days. Wages, taxes, and other costs
run about 30 percent of gross sales. The company has a
quarterly interest payment of $115,000 on its long-term debt.
The company uses a local bank for its short-term financial
needs. It pays percent per quarter on all shortterm
borrowing and maintains a money market account
that pays 1 percent per quarter on all short-term deposits.
Gary has asked you to prepare a cash budget and
short-term financial plan for the company under the current
policies. He has also asked you to prepare additional
plans based on changes in several inputs.
QUESTIONS
- Use the numbers given to complete the cash budget
and short-term financial plan.
- Rework the cash budget and short-term financial
plan assuming Piepkorn changes to a target balance
of $80,000.
PIEPKORN MANUFACTURING
Cash Budget
Q1 Q2 Q3 Q4
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus
(deficit)
PIEPKORN MANUFACTURING
Short-Term Financial Plan
Q1 Q2 Q3 Q4
Target cash balance
Net cash inflow
New short-term investments
Income from short-term
investments
Short-term investments sold
New short-term borrowing
Interest on short-term borrowing
Short-term borrowing repaid
Ending cash balance
Minimum cash balance
Cumulative surplus (deficit)
Beginning short-term
investments
Ending short-term investments
Beginning short-term debt
Ending short-term debt
Chapter 17 Working Capital Management
CHAPTER REVIEW AND SELF-TEST PROBLEMS
Calculating ;You have $10,000 on deposit with no outstanding checks
or uncleared deposits. One day you write a check for $4,000 and then deposit
a check for $3,000. What are your disbursement, collection, and net floats?
(See Problem 3.)
The ;Heusen Computer Manufacturing starts each period with 4,000 central
processing units (CPUs) in stock. This stock is depleted each month and reordered.
If the carrying cost per CPU is $1 and the fixed order cost is $10, is Heusen
following an economically advisable strategy? (See Problem 13.)
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 Cash ;Is it possible for a firm to have too much cash? Why
would shareholders care if a firm accumulates large amounts of cash?
LO 1 Cash ;What options are available to a firm if it believes it
has too much cash? How about too little?
LO 1 Agency ;Are stockholders and creditors likely to agree on how
much cash a firm should keep on hand?
LO 1 Motivations for Holding ;In the chapter opening, we discussed the cash
positions of several companies. Automobile manufacturers also have enormous
cash reserves. In the middle of 2015, Ford Motor Co. had about $ billion
in cash, General Motors had about $25 billion, and Toyota had about $43
billion. Why would firms such as these hold such large quantities of cash?
Short-Term ;Why is a preferred stock with a dividend tied
to short-term interest rates an attractive short-term investment for
corporations with excess cash?
LO 2 Collection and Disbursement ;Which would a firm prefer: a net
collection float or a net disbursement float? Why?
LO 1 ;Suppose a firm has a book balance of $2 million. At the automatic
teller machine (ATM), the cash manager finds out that the bank balance is
$ million. What is the situation here? If this is an ongoing situation,
what ethical dilemma arises?
LO 1 Short-Term ;For each of the short-term marketable
securities given here, provide an example of the potential disadvantages
the investment has for meeting a corporation’s cash management goals.
- Treasury bills
- Ordinary preferred stock
- Negotiable certificates of deposit (NCDs)
- Commercial paper
LO 1 Agency ;It is sometimes argued that excess cash held by a firm
can aggravate agency problems (discussed in Chapter 1) and, more
generally, reduce incentives for shareholder wealth maximization. How
would you frame the issue here?
LO 1 Use of Excess ;One option a firm usually has with any excess
cash is to pay its suppliers more quickly. What are the advantages and
disadvantages of this use of excess cash?
LO 1 Use of Excess ;Another option usually available for dealing with
excess cash is to reduce the firm’s outstanding debt. What are the
advantages and disadvantages of this use of excess cash?
LO 1 ;An unfortunately common practice goes like this:
(Warning: Don’t try this at home.) Suppose you are out of money in your
checking account; however, your local grocery store will, as a
convenience to you as a customer, cash a check for you. So you cash a
check for $200. Of course, this check will bounce unless you do
something. To prevent this, you go to the grocery the next day and cash
another check for $200. You take this $200 and deposit it. You repeat this
process every day, and, in doing so, you make sure that no checks bounce.
Eventually, manna from heaven arrives (perhaps in the form of money
from home) and you are able to cover your outstanding checks.
To make it interesting, suppose you are absolutely certain that no
checks will bounce along the way. Assuming this is true, and ignoring
any question of legality (what we have described is probably illegal
check kiting), is there anything unethical about this? If you say yes, then
why? In particular, who is harmed?
LO 2 Credit ;Describe each of the following:
- Sight draft
- Time draft
- Banker’s acceptance
- Promissory note
- Trade acceptance
Trade Credit ;In what form is trade credit most commonly
offered? What is the credit instrument in this case?
LO 2 Receivables ;What are the costs associated with carrying
receivables? What are the costs associated with not granting credit? What
do we call the sum of the costs for different levels of receivables?
LO 2 Five Cs of ;What are the five Cs of credit? Explain why each is
important.
LO 2 Credit Period ;What are some of the factors that determine the
length of the credit period? Why is the length of the buyer’s operating
cycle often considered an upper bound on the length of the credit period?
LO 2 Credit Period ;In each of the following pairings, indicate which
firm would probably have a longer credit period and explain your
reasoning.
- Firm A sells a miracle cure for baldness; Firm B sells toupees.
- Firm A specializes in products for landlords; Firm B specializes in
products for renters.
- Firm A sells to customers with an inventory turnover of 10 times;
Firm B sells to customers with an inventory turnover of 20 times.
- Firm A sells fresh fruit; Firm B sells canned fruit.
- Firm A sells and installs carpeting; Firm B sells rugs.
LO 3 Inventory ;What are the different inventory types? How do the
types differ? Why are some types said to have dependent demand
whereas other types are said to have independent demand?
LO 3 Just-in-Time ;If a company moves to a JIT inventory
management system, what will happen to inventory turnover? What will
happen to total asset turnover? What will happen to return on equity,
ROE? (Hint: Remember the DuPont equation from Chapter 3.)
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. Calculating ;You have $95,000 on deposit with no outstanding
checks or uncleared deposits. One day you write a check for $24,300. Does
this create a disbursement float or a collection float? What is your available
balance? Book balance?
LO 1 2. Calculating ;You have $12,700 on deposit with no outstanding
checks or uncleared deposits. If you deposit a check for $2,400, does this
create a disbursement float or a collection float? What is your available
balance? Book balance?
LO 1 3. Calculating ;You have $26,500 on deposit with no outstanding
checks or uncleared deposits. One day you write a check for $4,200 and
then deposit a check for $5,100. What are your disbursement, collection,
and net floats?
- Cash ;You place an order for 540 units of Good X at a unit
price of $62. The supplier offers terms of 1/10, net 30.
- How long do you have to pay before the account is overdue? If you take
the full period, how much should you remit?
- What is the discount being offered? How quickly must you pay to get
the discount? If you do take the discount, how much should you remit?
- If you don’t take the discount, how much interest are you paying
implicitly? How many days’ credit are you receiving?
LO 1 5. Calculating ;In a typical month, the Gulley Corporation receives 100
checks totaling $59,200. These are delayed three days on average. What is
the average daily float? Assume 30 days in a month.
LO 1 6. Calculating Net ;Each business day, on average, a company writes
checks totaling $23,400 to pay its suppliers. The usual clearing time for the
checks is four days. Meanwhile, the company is receiving payments from its
customers each day, in the form of checks, totaling $38,100. The cash from
the payments is available to the firm after two days.
- Calculate the company’s disbursement float, collection float, and
net float.
- How would your answer to part (a) change if the collected funds were
available in one day instead of two?
LO 2 7. Size of Accounts ;Essence of Skunk Fragrances, Ltd., sells
7,400 units of its perfume collection each year at a price per unit of $235.
All sales are on credit with terms of 1/10, net 30. The discount is taken by
40 percent of the customers. What is the amount of the company’s accounts
receivable? In reaction to sales by its main competitor, Sewage Spray,
Essence of Skunk is considering a change in its credit policy to terms of
3/10, net 30 to preserve its market share. How will this change in policy
affect accounts receivable?
LO 2 8. Size of Accounts ;The Bates Corporation has annual credit
sales of $ million. The average collection period is 33 days. What is the
average investment in accounts receivable as shown on the balance sheet?
LO 2 9. ACP and Accounts ;Miyagi Data, Inc., sells earnings
forecasts for Japanese securities. Its credit terms are 1/10, net 30. Based on
experience, 55 percent of all customers will take the discount.
- What is the average collection period?
- If the company sells 1,250 forecasts every month at a price of $2,300
each, what is its average balance sheet amount in accounts receivable?
LO 2 10. Size of Accounts ;Two Doors Down, Inc., has weekly credit
sales of $31,800, and the average collection period is 36 days. What is the
company’s average accounts receivable figure?
LO 2 11. Terms of ;A firm offers terms of 1/10, net 30. What effective annual
interest rate does the firm earn when a customer does not take the discount?
Without doing any calculations, explain what will happen to this effective rate if:
- The discount is changed to 2 percent.
- The credit period is increased to 40 days.
- The discount period is decreased to 20 days.
- What is the EAR for each scenario?
- ACP and Receivables ;A7X, Inc., has an average collection
period of 33 days. Its average daily investment in receivables is $87,600.
What are annual credit sales? What is the receivables turnover?
LO 3 13. ;Clap Off Manufacturing uses 1,150 switch assemblies per week
and then reorders another 1,150. If the relevant carrying cost per switch
assembly is $ and the fixed order cost is $425, is the company’s
inventory policy optimal? Why or why not?
LO 3 14. ;The Trektronics store begins each month with 765 phasers in stock.
This stock is depleted each month and reordered. If the carrying cost per
phaser is $27 per year and the fixed order cost is $385, what is the total
carrying cost? What is the restocking cost? Should the company increase
or decrease its order size? Describe an optimal inventory policy for the
company in terms of order size and order frequency.
INTERMEDIATE (Question 15)
LO 3 15. EOQ ;Prove that when carrying costs and restocking costs are
as described in the chapter, the EOQ must occur at the point where the
carrying costs and restocking costs are equal.
CHALLENGE (Question 16)
LO 3 16. Safety Stocks and Order ;Saché, Inc., expects to sell 700 of its
designer suits every week. The store is open seven days a week and expects
to sell the same number of suits every day. The company has an EOQ of 500
suits and a safety stock of 100 suits. Once an order is placed, it takes three
days for Saché to get the suits in. How many orders does the company place
per year? Assume that it is Monday morning before the store opens, and a
shipment of suits has just arrived. When will Saché place its next order?
CHAPTER CASE
Piepkorn Manufacturing Working
Capital Management, Part 2
After completing the short-term financial plan for next
year (at the end of Chapter 16), Gary Piepkorn approaches
you and asks about the company’s credit policy.
In looking at the competition, most companies in the
industry offer credit to customers, so Piepkorn Manufacturing
appears to be one of the few companies that
does not. Several customers have expressed the possibility
of changing to a different supplier because of the
lack of credit. Gary is interested in knowing how implementing
a credit policy will affect the short-term financial
plan for next year. Additionally, he would like you to inquire
as to the possibility of getting improved credit
terms for the company’s purchases.
To analyze the possible switch to the new credit
terms, Gary has asked you to investigate industry standard
credit terms and rework the short-term financial
plan assuming Piepkorn Manufacturing offers credit to
its customers. He would also like to investigate how better
credit terms from the company’s suppliers would affect
the short-term financial plan.
- You have looked at the credit policy offered by
your competitors and have determined that the
industry standard credit policy is 1/10, net 45. The
discount will begin to be offered on the first day of
the year. You want to examine how this credit policy
would affect the cash budget and short-term
financial plan. If this credit policy is implemented,
you believe that 60 percent of customers will take
advantage of the credit offer and the accounts receivable
period will be 24 days. Rework the cash
budget and short-term financial plan under the
new credit policy and a target cash balance of
$80,000. What interest rate are you effectively
offering customers?
- You have talked to the company’s suppliers about
the credit terms Piepkorn receives. Currently, the
company receives terms of net 45. Your suppliers
have stated that they would offer new credit terms
of 2/25, net 40. The discount would begin to be
offered on the first day of the year. What interest
rate are the suppliers offering the company? Rework
your cash budget and short-term financial
plan from the previous question assuming you
take advantage of the discount offered.
International Aspects of Financial Management
CHAPTER REVIEW AND SELF-TEST PROBLEMS
Relative Purchasing Power ;The inflation rate in the United States is
projected at 6 percent per year for the next several years. The Australian inflation
rate is projected to be 2 percent during that time. The exchange rate is currently
A$ Based on relative PPP, what is the expected exchange rate in two years?
(See Problem 12.)
Covered Interest ;The spot and 360-day forward rates on the Swiss
franc are SF and SF , respectively. The risk-free interest rate in the
United States is 8 percent, and the risk-free rate in Switzerland is 5 percent. Is
there an arbitrage opportunity here? How would you exploit it? (See Problem 7.)
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 Spot and Forward ;Suppose the exchange rate for the Swiss franc
is quoted as SF in the spot market and SF in the 90-day forward
market.
- Is the dollar selling at a premium or a discount relative to the franc?
- Does the financial market expect the franc to strengthen relative to
the dollar? Explain.
- What do you suspect is true about relative economic conditions in
the United States and Switzerland?
LO 2 Purchasing Power ;Suppose the rate of inflation in Russia will
run about 3 percent higher than the inflation rate over the next
several years. All other things being the same, what will happen to the
ruble versus dollar exchange rate? What relationship are you relying on
in answering?
LO 2 Exchange ;The exchange rate for the Australian dollar is
currently A$ This exchange rate is expected to rise by 10 percent
over the next year.
- Is the Australian dollar expected to get stronger or weaker?
- What do you think about the relative inflation rates in the
United States and Australia?
- What do you think about the relative nominal interest rates in the
United States and Australia? Relative real rates?
LO 3 Yankee ;Which of the following most accurately describes a
Yankee bond?
- A bond issued by General Motors in Japan with the interest payable
in dollars.
- A bond issued by General Motors in Japan with the interest payable
in yen.
- A bond issued by Toyota in the United States with the interest
payable in yen.
- A bond issued by Toyota in the United States with the interest
payable in dollars.
- A bond issued by Toyota worldwide with the interest payable in
dollars.
LO 1 Exchange ;Are exchange rate changes necessarily good or bad for
a particular company?
LO 4 International ;At one point, Duracell International confirmed
that it was planning to open battery-manufacturing plants in China and
India. Manufacturing in these countries would allow Duracell to avoid
import duties of between 30 and 35 percent that have made alkaline
batteries prohibitively expensive for some consumers. What additional
advantages might Duracell see in this proposal? What are some of the
risks to Duracell?
LO 3 Multinational ;Given that many multinationals based in
many countries have much greater sales outside their domestic markets
than within them, what is the particular relevance of their domestic
currency?
LO 2 Exchange Rate ;Are the following statements true or false?
Explain why.
- If the general price index in Great Britain rises faster than that in the
United States, we would expect the pound to appreciate relative to the
dollar.
- Suppose you are a German machine tool exporter and you invoice
all of your sales in foreign currency. Further suppose that the
European monetary authorities begin to undertake an
expansionary monetary policy. If it is certain that the easy money
policy will result in higher inflation rates in “Euroland” relative
to those in other countries, then you should use the forward
markets to protect yourself against future losses resulting from
the deterioration in the value of the euro.
- If you could accurately estimate differences in the relative inflation
rates of two countries over a long period of time while other market
participants were unable to do so, you could successfully speculate
in spot currency markets.
LO 2 Exchange Rate ;Some countries encourage movements in
their exchange rate relative to those of some other country as a shortterm
means of addressing foreign trade imbalances. For each of the
following scenarios, evaluate the impact the announcement would have
on an American importer and an American exporter doing business with
the foreign country.
- Officials in the administration of the United States government
announce that they are comfortable with a rising Mexican peso
relative to the dollar.
- British monetary authorities announce that they feel the pound
has been driven too low by currency speculators relative to the
dollar.
- The Brazilian government announces that it will print billions of
new reals and inject them into the economy in an effort to reduce the
country’s 40 percent unemployment rate.
LO 3 International ;If financial markets are perfectly competitive
and the Eurodollar rate is above that offered in the loan market, you
would immediately want to borrow money in the United States and invest
it in Eurodollars. True or false? Explain.
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 1–10)
LO 1 1. Using Exchange ;Take a look back at Table to answer the
following questions:
- If you have $100, how many Polish zlotys can you get?
- How much is one euro worth?
- If you have five million euros, how many dollars do you have?
- Which is worth more, a New Zealand dollar or a Singapore dollar?
- Which is worth more, a Mexican peso or a Chilean peso?
- How many Swiss francs can you get for a euro? What do you call
this rate?
- Per unit, what is the most valuable currency of those listed? The least
valuable?
LO 1 2. Using the ;Use the information in Table to answer the
following questions:
- Which would you rather have, $100 or £100? Why?
- Which would you rather have, $100 Canadian or £100? Why?
- What is the cross-rate for Canadian dollars in terms of British pounds?
For British pounds in terms of Canadian dollars?
LO 1 3. Forward Exchange ;Use the information in Table to answer the
following questions:
- What is the six-month forward rate for the Japanese yen in yen per
dollar? Is the yen selling at a premium or a discount? Explain.
- What is the three-month forward rate for the Australian dollar in
dollars per Australian dollar? Is the dollar selling at a premium or a
discount? Explain.
- What do you think will happen to the value of the dollar relative to the
yen and the Australian dollar, based on the information in the figure?
Explain.
LO 1 4. Using Spot and Forward Exchange ;Suppose the spot exchange rate
for the Canadian dollar is Can$ and the six-month forward rate is
Can$
- Which is worth more, a dollar or a Canadian dollar?
- Assuming absolute PPP holds, what is the cost in the United States of
an Elkhead beer if the price in Canada is Can$ Why might the
beer actually sell at a different price in the United States?
- Is the dollar selling at a premium or a discount relative to the
Canadian dollar?
- Which currency is expected to appreciate in value?
- Which country do you think has higher interest rates—the United States
or Canada? Explain.
LO 1 5. Cross-Rates and ;Suppose the Japanese yen exchange rate is
¥121 = $1, and the British pound exchange rate is £1 = $
- What is the cross-rate in terms of yen per pound?
- Suppose the cross-rate is ¥189 = £1. Is there an arbitrage
opportunity here? If there is, explain how to take advantage of the
mispricing.
LO 2 6. Interest Rate ;Use Table to answer the following questions.
Suppose interest rate parity holds, and the current risk-free rate in the
United States is percent per six months. What must the six-month
risk-free rate be in Australia? In Japan? In Great Britain?
LO 2 7. Interest Rates and ;The treasurer of a major firm has
$30 million to invest for three months. The interest rate in the United States
is .19 percent per month. The interest rate in Great Britain is .22 percent per
month. The spot exchange rate is £.63, and the three-month forward rate is
£.64. Ignoring transaction costs, in which country would the treasurer want
to invest the company’s funds? Why?
LO 2 8. Inflation and Exchange ;Suppose the current exchange rate for the
Russian ruble is RUB The expected exchange rate in three years is
RUB What is the difference in the annual inflation rates for the
United States and Russia over this period? Assume that the anticipated rate
is constant for both countries. What relationship are you relying on in
answering?
LO 3 9. Exchange Rate ;Suppose your company imports computer
motherboards from Singapore. The exchange rate is given in Table
You have just placed an order for 30,000 motherboards at a cost to you
of Singapore dollars each. You will pay for the shipment when it
arrives in 90 days. You can sell the motherboards for $150 each.
Calculate your profit if the exchange rate goes up or down by 10 percent
over the next 90 days. What is the break-even exchange rate? What
percentage rise or fall does this represent in terms of the Singapore
dollar versus the dollar?
LO 2 10. Exchange Rates and ;Suppose the spot and six-month forward
rates on the South Korean won are SKW 1, and SKW 1,,
respectively. The annual risk-free rate in the United States is percent,
and the annual risk-free rate in South Korea is percent.
- Is there an arbitrage opportunity here? If so, how would you
exploit it?
- What must the six-month forward rate be to prevent arbitrage?
- Spot versus Forward ;Suppose the spot and three-month forward
rates for the yen are ¥ and ¥, respectively.
- Is the yen expected to get stronger or weaker?
- What would you estimate is the difference between the inflation rates of
the United States and Japan?
LO 2 12. Expected Spot ;Suppose the spot exchange rate for the Hungarian
forint is HUF 249. Interest rates in the United States are percent per
year. They are percent in Hungary.
- What do you predict the exchange rate will be in one year?
- In two years?
- In five years? What relationship are you using?
LO 2 13. Cross-Rates and ;The British pound trades at $ in London
and $ in New York. How much profit could you earn on each trade
with $10,000?
LO 2 14. Purchasing Power Parity and Exchange ;According to purchasing
power parity, if a Big Mac sells for $ in the United States and krona
in Iceland, what is the krona/$ exchange rate?
LO 3 15. Translation ;Betancourt International has operations in Arrakis.
The balance sheet for this division in Arrakeen solaris shows assets of
40,000 solaris, debt in the amount of 12,500 solaris, and equity of 27,500
solaris.
- If the current exchange ratio is solaris per dollar, what does the
balance sheet look like in dollars?
- Assume that one year from now the balance sheet in solaris is
exactly the same as at the beginning of the year. If the exchange rate
is solaris per dollar, what does the balance sheet look like in
dollars now?
- Rework part (b) assuming the exchange rate is solaris per
dollar.
CHALLENGE (Question 16)
LO 3 16. Translation ;In the previous problem, assume the equity
increases by 1,500 solaris due to retained earnings. If the exchange rate at
the end of the year is solaris per dollar, what does the balance sheet
look like?
EXCEL MASTER IT! PROBLEM
The Federal Reserve Bank of St. Louis has historical exchange rates on its website,
Go to the website and look for the FRED® data. Then, download
the exchange rate with the dollar over the past five years for the following currencies:
Brazilian real, Canadian dollar, Hong Kong dollar, Japanese yen, Mexican
new peso, South Korean won, Indian rupee, Swiss franc, Australian dollar, and euro.
Graph the exchange rate for each of these currencies in a dashboard that can be
printed on one page.
CHAPTER CASE
S&S Air Goes International
Mark Sexton and Todd Story, the owners of S&S Air,
have been in discussions with an aircraft dealer in
Europe about selling the company’s Eagle airplane. The
Eagle sells for $98,000 and has a variable cost of
$81,000 per airplane. Amalie Diefenbaker, the dealer,
wants to add the Eagle to her current retail line. Amalie
has told Mark and Todd that she feels she will be able to
sell 15 airplanes per month in Europe. All sales will be
made in euros, and Amalie will pay the company
€75,384 for each plane. Amalie proposes that she order
15 aircraft today for the first month’s sales. She will pay
for all 15 aircraft in 90 days. This order and payment
schedule will continue each month.
Mark and Todd are confident they can handle the
extra volume with their existing facilities, but they are
unsure about the potential financial risks of selling their
aircraft in Europe. In their discussion with Amalie, they
found out that the current exchange rate is $;. This
means that they can convert the €75,384 per airplane
paid by Amalie to $98,000. Thus, the profit on the
international
sales is the same as the profit on dollardenominated
sales.
Mark and Todd decided to ask Chris Guthrie, their
financial analyst, to prepare an analysis of the proposed
international sales. Specifically, they ask Chris to answer
the following questions.
QUESTIONS
- What are the pros and cons of the international
sales? What additional risks will the company face?
- What happens to the company’s profits if the dollar
strengthens? What if the dollar weakens?
- Ignoring taxes, what are S&S Air’s projected gains or
losses from this proposed arrangement at the current
exchange rate of $;? What happens to
profits if the exchange rate changes to $;? At
what exchange rate will the company break even?
- How could the company hedge its exchange rate
risk? What are the implications of this approach?
- Taking all factors into account, should the company
pursue the international sales deal further?
Why or why not?
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