Solution Manual for Corporate Finance , 4th Edition

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SOLUTIONS MANUAL
For
Jonathan Berk Peter DeMarzo
Stanford University Stanford University
Accuracy Editor
Sukarnen Suwanto

iii
Contents
Chapter 1 The Corporation 1
Chapter 2 Introduction to Financial Statement Analysis 4
Chapter 3 Financial Decision Making and the Law of One Price 20
Chapter 4 The Time Value of Money 30
Chapter 5 Interest Rates 56
Chapter 6 Valuing Bonds 75
Chapter 7 Investment Decision Rules 92
Chapter 8 Fundamentals of Capital Budgeting 112
Chapter 9 Valuing Stocks 130
Chapter 10 Capital Markets and the Pricing of Risk 142
Chapter 11 Optimal Portfolio Choice and the Capital Asset Pricing Model 157
Chapter 12 Estimating the Cost of Capital 177
Chapter 13 Investor Behavior and Capital Market Efficiency 186
Chapter 14 Capital Structure in a Perfect Market 196
Chapter 15 Debt and Taxes 206
Chapter 16 Financial Distress, Managerial Incentives, and Information 215
Chapter 17 Payout Policy 231
Chapter 18 Capital Budgeting and Valuation with Leverage 242
Chapter 19 Valuation and Financial Modeling: A Case Study 262
Chapter 20 Financial Options 271
Chapter 21 Option Valuation 283
Chapter 22 Real Options 295
Chapter 23 Raising Equity Capital 321
Chapter 24 Debt Financing 329
Chapter 25 Leasing 333
Chapter 26 Working Capital Management 341
Chapter 27 Short-Term Financial Planning 348
Chapter 28 Mergers and Acquisitions 354
Chapter 29 Corporate Governance 359
Chapter 30 Risk Management 362
Chapter 31 International Corporate Finance 374

1
Chapter 1
The Corporation
1-1. What is the most important difference between a corporation and all other organizational
forms?
A corporation is a legal entity separate from its owners.
1-2. What does the phrase limited liability mean in a corporate context?
Owners’ liability is limited to the amount they invested in the firm. Stockholders are not responsible
for any encumbrances of the firm; in particular, they cannot be required to pay back any debts incurred
by the firm.
1-3. Which organizational forms give their owners limited liability?
Corporations and limited liability companies give owners limited liability. Limited partnerships
provide limited liability for the limited partners, but not for the general partners.
1-4. What are the main advantages and disadvantages of organizing a firm as a corporation?
Advantages: Limited liability, liquidity, infinite life
Disadvantages: Double taxation, separation of ownership and control
1-5. Explain the difference between an S corporation and a C corporation.
C corporations must pay corporate income taxes; S corporations do not pay corporate taxes, but must
pass through the income to shareholders to whom it is taxable. S corporations are also limited to 75
shareholders and cannot have corporate or foreign stockholders.
1-6. You are a shareholder in a C corporation. The corporation earns $2 per share before taxes. Once
it has paid taxes it will distribute the rest of its earnings to you as a dividend. The corporate tax
rate is 40% and the personal tax rate on (both dividend and non-dividend) income is 30%. How
much is left for you after all taxes are paid?
First, the corporation pays the taxes. After taxes,$2 (1 0.4) $1.20´ - = is left to pay dividends. Once
the dividend is paid, personal tax must be paid, which leaves$1.20 (1 0.3) $0.84´ - = . So, after all the
taxes are paid, you are left with 84¢.
1-7. Repeat Problem 6 assuming the corporation is an S corporation.
An S corporation does not pay corporate income tax. So it distributes $2 to its stockholders. These
stockholders must then pay personal income tax on the distribution. So they are left with$2 (1 0.3) $1.40´ - =
.

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2 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
1-8. You have decided to form a new start-up company developing applications for the iPhone. Give
examples of the three distinct types of financial decisions you will need to make.
As the manager of an iPhone applications developer, you will make three types of financial decisions.
i. You will make investment decisions such as determining which type of iPhone application
projects will offer your company a positive NPV and that your company, therefore, should
develop.
ii. You will make the decision on how to fund your iPhone application investments and what mix of
debt and equity your company will have.
iii. You will be responsible for the cash management of your company, ensuring that your company
has the necessary funds to make investments, pay interest on loans, and pay your employees.
1-9. When a pharmaceutical company develops a new drug, it often receives patent protection for
that medication, allowing it to charge a higher price. Explain how this public policy of providing
patent protection might help align the corporation’s interests with society’s interests.
Without patent protection, the developer of the drug would be forced to lower prices to compete with
generic manufacturers. Because this price competition would lower expected future profits, the
developer would be willing to spend much less in R&D to develop the drug initially, and drug
innovation would be curtailed.
Alternatively, by allowing the drug’s developer to earn higher profits that are commensurate with the
value of the drug to society, drug developers will find it in their best interests to spend more on R&D,
and drug innovation is enhanced. Thus, patent protection can align the corporation’s and society’s
interests and provide for more efficient spending on drug R&D.
1-10. Corporate managers work for the owners of the corporation. Consequently, they should make
decisions that are in the interests of the owners, rather than their own. What strategies are
available to shareholders to help ensure that managers are motivated to act this way?
Shareholders can do the following.
i. Ensure that employees are paid with company stock and/or stock options.
ii. Ensure that underperforming managers are fired.
iii. Write contracts that ensure that the interests of the managers and shareholders are closely aligned.
iv. Mount hostile takeovers.
1-11. Suppose you are considering renting an apartment. You, the renter, can be viewed as an agent
while the company that owns the apartment can be viewed as the principal. What principal-
agent conflicts do you anticipate? Suppose instead that you work for the apartment company.
What features would you put into the lease agreement that would give the renter incentives to
take good care of the apartment?
The agent (renter) will not take the same care of the apartment as the principal (owner), because the
renter does not share in the costs of repairing damage to the apartment. To mitigate this problem,
having the renter pay a deposit should motivate the renter to keep damages to a minimum. The deposit
forces the renter to share in the costs of repairing any problems that they cause.
1-12. You are the CEO of a company and you are considering entering into an agreement to have your
company buy another company. You think the price might be too high, but you will be the CEO
of the combined, much larger, company. You know that when the company gets bigger, your pay
and prestige will increase. What is the nature of the agency conflict here and how is it related to
ethical considerations?
There is an ethical dilemma when the CEO of a firm has the opposite incentives to those of the
shareholders. In this case, you (as the CEO) have an incentive to potentially overpay for another
company (which would be damaging to your shareholders) because your pay and prestige will
improve.
1-13. Are hostile takeovers necessarily bad for firms or their investors? Explain.
No. They are a way to discipline managers who are not working in the interests of shareholders.

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Chapter 1/The Corporation 3
1-14. What is the difference between a public and private corporation?
The shares of a public corporation are traded on an exchange (or “over the counter” in an electronic
trading system) while the shares of a private corporation are not traded on a public exchange.
1-15. Describe the important changes that have occurred in stock markets over the last decade.
Markets have become more fragmented, stocks no longer predominantly trade on the markets on which
they are listed, off exchange transactions in dark pools are now much more common, and official
market makers have largely disappeared, replaced now by the limit order book.
1-16. Explain why the bid-ask spread is a transaction cost.
Investors always buy at the ask and sell at the bid. Since ask prices always exceed bid prices, investors
“lose” this difference. It is one of the costs of transacting. Since the market makers take the other side
of the trade, they make this difference.
1-17. Explain how the bid-ask spread is determined today.
The bid-ask spread of a stock is determined by the outstanding limit orders. The limit sell order with
the lowest price is the ask price. The limit buy order with the highest price is the bid price.
1-18. The following quote on Yahoo! Stock appeared on July 23, 2015, on Yahoo! Finance:
If you wanted to buy Yahoo!, what price would you pay? How much would you receive if you
wanted to sell Yahoo!?
You would buy at $39.66 and sell for $39.65.
1-19. Suppose the following orders are received by an exchange for Cisco stock:
• Limit Order: Buy 200 shares at $25
• Limit Order: Sell 200 shares at $26
• Limit Order: Sell 100 shares at $25.50
• Limit Order: Buy 100 shares at $25.25
a) What are the best bid and ask prices for Cisco stock?
Best bid = $25.25, Best ask = $25.50
b) What is the current bid-ask spread for Cisco stock?
Bid-Ask spread = $25.50 – 25.25 = $0.25
c) Suppose a market order arrives to buy 200 shares of Cisco. What average price will the
buyer pay?
Buy 100 shares at $25.50 and 100 shares at $26, for an average price of $25.75
d) After the market order in (c) clears, what are the new best bid and ask prices, and what is
the new bid-ask spread for Cisco?
Best bid = $25.75, Best ask = $26, Bid-Ask spread = $0.25

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4
Chapter 2
Introduction to Financial Statement
Analysis
2-1. What four financial statements can be found in a firm’s 10-K filing? What checks are there on
the accuracy of these statements?
In a firm’s 10-K filing, four financial statements can be found: the balance sheet, income statement,
statement of cash flows, and statement of stockholders’ equity. Financial statements in form 10-K are
required to be audited by a neutral third party, who checks and ensures that the financial statements are
prepared according to GAAP and that the information contained is reliable.
2-2. Who reads financial statements? List at least three different categories of people. For each
category, provide an example of the type of information they might be interested in and discuss
why.
Users of financial statements include present and potential investors, financial analysts, and other
interested outside parties (such as lenders, suppliers and other trade creditors, and customers).
Financial managers within the firm also use the financial statements when making financial decisions.
Investors. Investors are concerned with the risk inherent in, and return provided by, their investments.
Bondholders use the firm’s financial statements to assess the ability of the company to make its debt
payments. Stockholders use the statements to assess the firm’s profitability and ability to make future
dividend payments.
Financial analysts. Financial analysts gather financial information, analyze it, and make
recommendations. They read financial statements to determine a firm’s value and project future
earnings, so that they can provide guidance to businesses and individuals to help them with their
investment decisions.
Managers. Managers use financial statements to look at trends in their own business, and to compare
their own results with that of competitors.
2-3. Find the most recent financial statements for Starbucks’ corporation (SBUX) using the following
sources:
a. From the company’s Web site www.starbucks.com (Hint: Search for “investor relations.”)
b. From the SEC Web site www.sec.gov. (Hint: Search for company filings in the EDGAR
database.)
c. From the Yahoo! Finance Web site http://finance.yahoo.com.
d. From at least one other source. (Hint: Enter “SBUX 10K” at www.google.com.)
Each method will help find the same SEC filings. Yahoo! Finance also provides some analysis such as
charts and key statistics.

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Chapter 2/Introduction to Financial Statement Analysis 5
2-4. Consider the following potential events that might have taken place at Global Conglomerate on
December 30, 2015. For each one, indicate which line items in Global’s balance sheet would be
affected and by how much. Also indicate the change to Global’s book value of equity. (In all
cases, ignore any tax consequences for simplicity.)
a. Global used $20 million of its available cash to repay $20 million of its long-term debt.
b. A warehouse fire destroyed $5 million worth of uninsured inventory.
c. Global used $5 million in cash and $5 million in new long-term debt to purchase a $10
million building.
d. A large customer owing $3 million for products it already received declared bankruptcy,
leaving no possibility that Global would ever receive payment.
e. Global’s engineers discover a new manufacturing process that will cut the cost of its flagship
product by over 50%.
f. A key competitor announces a radical new pricing policy that will drastically undercut
Global’s prices.
a. Long-term liabilities would decrease by $20 million, and cash would decrease by the same
amount. The book value of equity would be unchanged.
b. Inventory would decrease by $5 million, as would the book value of equity.
c. Long-term assets would increase by $10 million, cash would decrease by $5 million, and long-
term liabilities would increase by $5 million. There would be no change to the book value of
equity.
d. Accounts receivable would decrease by $3 million, as would the book value of equity.
e. This event would not affect the balance sheet.
f. This event would not affect the balance sheet.
2-5. What was the change in Global Conglomerate’s book value of equity from 2014 to 2015
according to Table 2.1? Does this imply that the market price of Global’s shares increased in
2015? Explain.
Global Conglomerate’s book value of equity increased by $1 million from 2014 to 2015. An increase
in book value does not necessarily indicate an increase in Global’s share price. The market value of a
stock does not depend on the historical cost of the firm’s assets, but on investors’ expectation of the
firm’s future performance. There are many events that may affect Global’s future profitability, and
hence its share price, that do not show up on the balance sheet.
2-6. Use EDGAR to find Qualcomm’s 10-K filing for 2015. From the balance sheet, answer the
following questions:
a. How much did Qualcomm have in cash and short-term investments?
b. What were Qualcomm’s total accounts receivable?
c. What were Qualcomm’s total assets?
d. What were Qualcomm’s total liabilities? How much of this was long-term debt?
e. What was the book value of Qualcomm’s equity?
a. $7,560 million (cash) and $9,761 million (short-term investments/marketable securities) for a total
of $17,321 million
b. $1,964 million
c. $50,796 million

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6 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
d. $19,382 million, $9,969 million.
e. $31,414 million.
2-7. Find online the annual 10-K report for Costco Wholesale Corporation (COST) for fiscal year
2015 (filed in October 2015). Answer the following questions from their balance sheet:
a. How much cash did Costco have at the end of the fiscal year?
b. What were Costco’s total assets?
c. What were Costco’s total liabilities? How much debt did Costco have?
d. What was the book value of Costco’s equity?
a. At the end of the fiscal year, Costco had cash and cash equivalents of $4,801 million.
b. Costco’s total assets were $33,440 million.
c. Costco’s total liabilities were $22,597 million, and it had $6,157 million in debt.
d. The book value of Costco’s equity was $10,843 million.
2-8. In early 2012, General Electric (GE) had a book value of equity of $109 billion, 10.3 billion
shares outstanding, and a market price of $9.66 per share. GE also had cash of $40 billion, and
total debt of $530 billion. Three years later, in early 2015, GE had a book value of equity of $112
billion, 10.9 billion shares outstanding with a market price of $16.59 per share, cash of $85
billion, and total debt of $417 billion. Over this period, what was the change in GE’s
a. market capitalization?
b. market-to-book ratio?
c. enterprise value?
a. 2012 Market Capitalization: 10.3 billion shares  $9.66/share = $99.5 billion. 2015 Market
Capitalization: 10.9 billion shares  $16.59/share = $180.8. The change over the period is $180.8
– $99.5 = $81.3 billion.
b. 2012 Market-to-Book = 99.5/109 = 0.91. 2015 Market-to-Book = 180.8/112 = 1.61. The change
over the period is: 1.61 – 0.91 = 0.70.
e. 2012 Enterprise Value = $109 – 40 + 530 = $599 billion. 2015 Enterprise Value = $112 – 85 +
417 = $444 billion. The change over the period is: $599 – $444 = –$155 billion.
2-9. In early-2015, Abercrombie & Fitch (ANF) had a book equity of $1390 million, a price per share
of $25.52, and 69.35 million shares outstanding. At the same time, The Gap (GPS) had a book
equity of $2983 million, a share price of $41.19, and 421 million shares outstanding.
a. What is the market-to-book ratio of each of these clothing retailers?
b. What conclusions can you draw by comparing the two ratios?
a. ANF’s market-to-book ratio = (25.52 x 69.35)/1,390 = 1.27.
GPS’s market-to-book ratio = (41.19 x 421)/2,983 = 5.81.
b. For the market, the outlook of Abercrombie and Fitch is less favorable than that of The Gap. For
every dollar of equity invested in ANF, the market values that dollar today at $1.27 versus $5.81
for a dollar invested in the GPS. Equity investors are willing to pay relatively less today for shares
of ANF than for GPS because they expect GPS to produce superior performance in the future.
2-10. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. What is Mydeco’s market capitalization at the end of each year?
b. What is Mydeco’s market-to-book ratio at the end of each year?
c. What is Mydeco’s enterprise value at the end of each year?
2012–2016 Financial Statement Data and Stock Price Data for Mydeco Corp.

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8 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
a.
Year 2012 2013 2014 2015 2016
Shares Outstanding (millions) 56.8 56.8 56.8 56.8 56.8
Stock Price $7.02 $3.55 $5.86 $8.33 $11.57
Market capitalization (millions) $398.7 $201.6 $332.8 $473.1 $657.2
b.
Year 2012 2013 2014 2015 2016
Market capitalization (millions) $398.7 $201.6 $332.8 $473.1 $657.2
Stockholders' Equity (millions) $255.0 $255.6 $257.8 $270.8 $279.8
Market-to-book 1.56 0.79 1.29 1.75 2.35
c.
Year 2012 2013 2014 2015 2016
Market capitalization (millions) $398.7 $201.6 $332.8 $473.1 $657.2
Cash (millions) $49.4 $68.0 $91.7 $80.4 $83.6
Long-term Debt (millions) $498.9 $498.9 $572.2 $597.5 $597.5
Enterprise value (millions) $848.2 $632.5 $813.3 $990.2 $1,171.1
2-11. Suppose that in 2016, Global launches an aggressive marketing campaign that boosts sales by
15%. However, their operating margin falls from 5.57% to 4.50%. Suppose that they have no
other income, interest expenses are unchanged, and taxes are the same percentage of pretax
income as in 2015.
a. What is Global’s EBIT in 2016?
b. What is Global’s net income in 2016?
c. If Global’s P/E ratio and number of shares outstanding remains unchanged, what is Global’s
share price in 2016?
a. Revenues in 2016 = 1.15 × 186.7 = $214.705 million.
EBIT = 4.50% × 214.705 = $9.66 million (there is no other income).
b. Net Income = EBIT – Interest Expenses – Taxes = (9.66 – 7.7) × (1 – 26%) = $1.45 million.
c. Share price = (P/E Ratio in 20015) x (EPS in 2016) = 25.2 x (1.45/3.6) = $10.15.
Note: Differences from spreadsheet solutions due to rounding.
2-12. Find online the annual 10-K report for Costco Wholesale Corporation (COST) for fiscal year
2015 (filed in October 2015). Answer the following questions from their income statement:
a. What were Costco's revenues for fiscal year 2015? By what percentage did revenues grow
from the prior year?
b. What was Costco's operating income for the fiscal year?
c. What was Costco's average tax rate for the year?
d. What were Costco's diluted earnings per share in fiscal year 2015? What number of shares
is this EPS based on?
a. Revenues = $116,199 million. Revenue growth = (116,199/112,640) – 1 = 3.16%.
b. Operating Income = $3,624 million.
c. Average tax rate = 1,195/3,604 = 33.16%.
d. The diluted earnings per share in 2015 was $5.37. The number of shares used in this calculation of
diluted EPS was 442.72 million.

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Chapter 2/Introduction to Financial Statement Analysis 9
2-13. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. By what percentage did Mydeco’s revenues grow each year from 2013 to 2016?
b. By what percentage did net income grow each year?
c. Why might the growth rates of revenues and net income differ?
a.
Year 2012 2013 2014 2015 2016
Revenue (millions) $401.9 $361.6 $429.6 $513.6 $602.6
Revenue growth –10.0% 18.8% 19.6% 17.3%
b.
Year 2012 2013 2014 2015 2016
Net Income (millions) $15.0 $4.3 $9.6 $11.8 $16.2
Net income growth –71.3% 123.3% 22.9% 37.3%
c. Net Income growth rate differs from revenue growth rate because cost of goods sold and other
expenses can move at different rates than revenues. For example, revenues declined in 2013 by
10%, however, cost of goods sold only declined by 9%.
2-14. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. Suppose
Mydeco repurchases 2.3 million shares each year from 2013 to 2016. What would its earnings
per share be in years 2013–2016? (Assume Mydeco pays for the shares using its available cash
and that Mydeco earns no interest on its cash balances.)
A repurchase does not impact earnings directly, so any change to EPS will come from a reduction in
shares outstanding.
Year 2012 2013 2014 2015 2016
Shares Outstanding (millions) 56.8 54.5 52.2 49.9 47.6
Net Income (millions) $15.0 $4.3 $9.6 $11.8 $16.2
EPS $0.26 $0.08 $0.18 $0.24 $0.34
2-15. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. Suppose
Mydeco had purchased additional equipment for $12.3 million at the end of 2013, and this
equipment was depreciated by $4.1 million per year in 2014, 2015, and 2016. Given Mydeco’s tax
rate of 35%, what impact would this additional purchase have had on Mydeco’s net income in
years 2013–2016? (Assume the equipment is paid for out of cash and that Mydeco earns no
interest on its cash balances.)
The equipment purchase does not impact net income directly, however the increased depreciation
expense and tax savings changes net income.
Year 2012 2013 2014 2015 2016
Net Income $15.0 $4.3 $9.6 $11.8 $16.2
Additional Depreciation –$4.1 –$4.1 –$4.1
Tax savings $1.4 $1.4 $1.4
New Net Income (millions) $15.0 $4.3 $6.9 $9.1 $13.5
2-16. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. Suppose
Mydeco’s costs and expenses had been the same fraction of revenues in 2013–2016 as they were
in 2012. What would Mydeco’s EPS have been each year in this case?
If Mydeco’s costs and expenses had been the same fraction of revenues in 2013–2016 as they were in
2012, then their net profit margins would have been equal.

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10 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
2012 net profit margin = 15/401.9 = 3.73%.
Year 2012 2013 2014 2015 2016
Revenue $401.9 $361.6 $429.6 $513.6 $602.6
Net Profit Margin 3.7% 3.7% 3.7% 3.7% 3.7%
New Net Income $15.0 $13.5 $16.0 $19.2 $22.5
Shares Outstanding 56.8 56.8 56.8 56.8 56.8
New EPS $0.26 $0.24 $0.28 $0.34 $0.40
2-17. Suppose a firm’s tax rate is 30%.
a. What effect would a $10 million operating expense have on this years earnings? What effect
would it have on next year’s earnings?
b. What effect would a $10 million capital expense have on this years earnings if the capital
expenditure is depreciated at a rate of $2 million per year for five years? What effect would
it have on next year’s earnings?
a. A $10 million operating expense would be immediately expensed, increasing operating expenses
by $10 million. This would lead to a reduction in taxes of 30% × $10 million = $3 million. Thus,
earnings would decline by 10 – 3 = $7 million. There would be no effect on next year’s earnings.
b. Capital expenses do not affect earnings directly. However, the depreciation of $2 million would
appear each year as an operating expense. With a reduction in taxes of 2 × 30% = $0.6 million,
earnings would be lower by 2 – 0.6 = $1.4 million for each of the next 5 years.
2-18. Quisco Systems has 6.17 billion shares outstanding and a share price of $18.96. Quisco is
considering developing a new networking product in-house at a cost of $509 million.
Alternatively, Quisco can acquire a firm that already has the technology for $893 million worth
(at the current price) of Quisco stock. Suppose that absent the expense of the new technology,
Quisco will have EPS of $0.83.
a. Suppose Quisco develops the product in-house. What impact would the development cost
have on Quisco’s EPS? Assume all costs are incurred this year and are treated as an R&D
expense, Quisco’s tax rate is 35%, and the number of shares outstanding is unchanged.
b. Suppose Quisco does not develop the product in-house but instead acquires the technology.
What effect would the acquisition have on Quisco’s EPS this year? (Note that acquisition
expenses do not appear directly on the income statement. Assume the firm was acquired at
the start of the year and has no revenues or expenses of its own, so that the only effect on
EPS is due to the change in the number of shares outstanding.)
c. Which method of acquiring the technology has a smaller impact on earnings? Is this method
cheaper? Explain.
a. If Quisco develops the product in-house, its earnings would fall by $509 × (1 – 35%) = $330.85
million. With no change to the number of shares outstanding, its EPS would decrease by
($330.9/6,170) = $0.054 to $0.776. (Assume the new product would not change this year’s
revenues.)
b. If Quisco acquires the technology for $893 million worth of its stock, it will issue $893/18.96 =
47.10 million new shares. Since earnings without this transaction are $0.83 × 6.17 billion = $5.12
billion, its EPS with the purchase is 5,121/(6,170 + 47.10) = $0.82.
c. Acquiring the technology would have a smaller impact on earnings, but this method is not
cheaper. Developing it in-house is less costly and provides an immediate tax benefit. The earnings
impact is not a good measure of the expense. In addition, note that because the acquisition
permanently increases the number of shares outstanding, it will reduce Quisco’s earnings per share
in future years as well.

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Chapter 2/Introduction to Financial Statement Analysis 11
2-19. Find online the annual 10-K report for Costco Wholesale Corporation (COST) for fiscal year
2015 (filed in October 2015). Answer the following questions from their cash flow statement:
a. How much cash did Costco generate from operating activities in fiscal year 2015?
b. What was Costco depreciation and amortization expense?
c. How much cash was invested in new property and equipment (net of any sales)?
d. How much did Costco raise from the sale of shares of its stock (net of any purchases)?
a. Net cash provided by operating activities was $4,285 million in fiscal year 2015.
b. Depreciation and amortization expenses were $1,127 million.
c. Net cash used in capital expenditures for property and equipment was $2,393 million.
d. Costco raised nothing from the sale of shares of its stock, while it spent $481 million on the
purchase of common stock. Costco raised –$481 million from the sale of its shares of stock (net of
any purchases).
2-20. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. From 2012 to 2016, what was the total cash flow from operations that Mydeco generated?
b. What fraction of the total in (a) was spent on capital expenditures?
c. What fraction of the total in (a) was spent paying dividends to shareholders?
d. What was Mydeco’s total retained earnings for this period?
a. Total cash flow from operations = 45.2 + 47.6 + 53.1 + 44 + 48.8 = $238.7 million.
b. Total fraction spent on capital expenditures = (26.6 + 23.8 + 97.5 + 75.4 + 40)/238.7 = 110.3%.
c. Total fraction spent on dividends = (5.2 × 4 + 5.6)/238.7 = 11.06%.
d. Retained earnings = Net Income – Dividends = (15 + 4.3 + 9.6 + 11.8 + 16.2) – (5.2 × 4 + 5.6) =
$30.5 million.
2-21. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. In what year was Mydeco’s net income the lowest?
b. In what year did Mydeco need to reduce its cash reserves?
c. Why did Mydeco need to reduce its cash reserves in a year when net income was reasonably
high?
a. In 2013 (net income was $4.3 million).
b. 2015 (cash was reduced from 91.7 to 80.4).
c. Mydeco needed to reduce cash (it also issued debt) to pay for large capital expenditures in 2014
and 2015. In addition, even though net income was reasonably high, cash from operations was at
the lowest amount in the five-year period due to an increase in accounts receivable and
inventories.
2-22. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. Use the
data from the balance sheet and cash flow statement in 2012 to determine the following:
a. How much cash did Mydeco have at the end of 2011?
b. What were Mydeco’s accounts receivable and inventory at the end of 2011?
c. What were Mydeco’s total liabilities at the end of 2011?
d. Assuming goodwill and intangibles were equal in 2011 and 2012, what was Mydeco’s net
property, plant, and equipment at the end of 2011?
a. 20011 Cash = 2012 Cash – 2012 Change in Cash = 49.4 – 13.4 = $36 million.

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12 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
b. 2011 Accounts Receivable = 87.6 – 3.9 = $83.7 million; 2011 inventory = 33.5 – (-2.9) = $36.4
million
c. 2011 Total Liabilities = 525.3 – 1.7 = $523.6 million.
d. 2011 net property, plant, and equipment = 2012 net property, plant, and equipment – 2012 capital
expenditures + 2012 depreciation = 244.3 – 26.6 + 27.5 = $245.2 million
2-23. Can a firm with positive net income run out of cash? Explain.
A firm can have positive net income but still run out of cash. For example, to expand its current
production, a profitable company may spend more on investment activities than it generates from
operating activities and financing activities. Net cash flow for that period would be negative, although
its net income is positive. It could also run out of cash if it spends a lot on financing activities, perhaps
by paying off other maturing long-term debt, repurchasing shares, or paying dividends.
2-24. Suppose your firm receives a $4.1 million order on the last day of the year. You fill the order
with $2.9 million worth of inventory. The customer picks up the entire order the same day and
pays $1.5 million upfront in cash; you also issue a bill for the customer to pay the remaining
balance of $2.6 million in 30 days. Suppose your firm’s tax rate is 0% (i.e., ignore taxes).
Determine the consequences of this transaction for each of the following:
a. Revenues
b. Earnings
c. Receivables
d. Inventory
e. Cash
a. Revenues: increase by $4.1 million
b. Earnings: increase by 4.1 – 2.9 = $1.2 million
c. Receivables: increase by $2.6 million
d. Inventory: decrease by $2.9 million
e. Cash: increase by $1.2 million (earnings) – $2.6 million (receivables) + $2.9 million (inventory) =
$1.5 million (cash).
2-25. Nokela Industries purchases a $38.5 million cyclo-converter. The cyclo-converter will be
depreciated by $7.7 million per year over four years, starting this year. Suppose Nokela’s tax
rate is 40%.
a. What impact will the cost of the purchase have on earnings for each of the next five years?
b. What impact will the cost of the purchase have on the firm’s cash flow for the next five
years?
a. To calculate the impact on earnings for the next five years, we would have to deduct the
depreciation expense. After taxes, this would lead to a decline of 7.7 × (1 – 40%) = $4.62 million
each year for the next five years.
b. Cash flow for the next five years: less $35.42 million (–4.62 + 7.7 – 38.5) this year, and add $3.08
million (–4.62 + 7.7) for the four following years.
2-26. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. What were Mydeco’s retained earnings each year?
b. Using the data from 2012, what was Mydeco’s total stockholders’ equity in 2011?
a. Retained earnings = Net Income – Dividends Paid

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Chapter 2/Introduction to Financial Statement Analysis 13
Year 2012 2013 2014 2015 2016
Net Income $15.0 $4.3 $9.6 $11.8 $16.2
Dividends Paid –$5.2 –$5.2 –$5.2 –$5.2 –$5.6
Retained Earnings (millions) $9.8 –$0.9 $4.4 $6.6 $10.6
b. 2011 stockholders’ equity = 2012 stockholders’ equity – 2012 retained earnings = 255 – 9.8 =
$245.2 million.
2-27. Find online the annual 10-K report for Costco Wholesale Corporation (COST) for fiscal year
2015 (filed in October 2015). Answer the following questions from the notes to their financial
statements:
a. How many stores did Costco open outside of the U.S. in 2015?
b. What property does Costco lease? What are the minimum lease payments due in 2016?
c. What was Costco’s worldwide member renewal rate for 2015? What proportion of Costco
cardholders had Gold Star memberships in 2015?
d. What fraction of Costco’s 2015 sales came from gas stations, pharmacy, food court, and
optical? What fraction came from apparel and small appliances?
a. Costco opened 11 stores outside of the U.S. in 2015.
b. Costco leases land and/or buildings at warehouses and certain other office and distribution
facilities. The minimum lease payments due in 2016 are $211 million.
c. Costco had a worldwide member renewal rate of 88% for 2015. 34,000/81,300 = 42% of Costco
cardholders had Gold Star memberships in 2015.
d. 16% of Costco’s 2015 sales came from gas stations, pharmacy, food court, and optical. 11% of
Costco’s 2015 sales came from apparel and small appliances.
2-28. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. What were Mydeco’s gross margins each year?
b. Comparing Mydeco’s gross margin, EBIT margin, and net profit margin in 2012 and 2016,
which margins improved?
a.
Year 2012 2013 2014 2015 2016
Revenue $401.9 $361.6 $429.6 $513.6 $602.6
Gross Profit $209.8 $186.2 $222.5 $265.3 $306.8
Gross Margin 52.2% 51.5% 51.8% 51.7% 50.9%
b. None of the margins improved from 2012 to 2016
Year 2012 2013 2014 2015 2016
Revenue $401.9 $361.6 $429.6 $513.6 $602.6
Gross Profit $209.8 $186.2 $222.5 $265.3 $306.8
EBIT $55.5 $38.4 $46.7 $55.2 $65.8
Net Income $15.0 $4.3 $9.6 $11.8 $16.2
Gross Margin 52.2% 51.5% 51.8% 51.7% 50.9%
EBIT Margin 13.8% 10.6% 10.9% 10.7% 10.9%
Net Profit Margin 3.7% 1.2% 2.2% 2.3% 2.7%
2-29. For fiscal year end 2015, Walmart Stores, Inc. (WMT) had revenue of $485.65 billion, gross
profit of $120.57 billion, and net income of $16.36 billion. Costco Wholesale Corporation (COST)
had revenue of $116.20 billion, gross profit of $15.13 billion, and net income of $2.38 billion.
a. Compare the gross margins for Walmart and Costco.

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14 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
b. Compare the net profit margins for Walmart and Costco.
c. Which firm was more profitable in 2015?
a. Walmart’s gross margin = 120.57/485.65 = 24.83%; Costco’s gross margin = 15.13/116.20 =
13.02%.
b. Walmart’s net margin = 16.36/485.65 = 3.37%; Costco’s net margin = 2.38/116.20 = 2.05%.
c. Walmart was more profitable in 2015.
2-30. At the end of 2015, Apple had cash and short-term investments of $41.60 billion, accounts
receivable of $35.89 billion, current assets of $89.38 billion, and current liabilities of $80.61
billion.
a. What was Apple’s current ratio?
b. What was Apple’s quick ratio?
c. What is Apple’s cash ratio?
d. At the end of 2015, HPQ had a cash ratio of 0.35, a quick ratio of 0.73 and a current ratio of
1.15. What can you say about the asset liquidity of Apple relative to HPQ?
a. Apple’s current ratio = 89.38/80.61 = 1.11.
b. Apple’s quick ratio = (41.60 + 35.89)/80.61 = 0.96.
c. Apple’s cash ratio = 41.60/80.61 = 0.52.
d. Apple generally has more liquid assets than HPQ relative to current liabilities, with the exception
of a slightly lower current ratio due to a lower proportion of inventory.
2-31. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. How did Mydeco’s accounts receivable days change over this period?
b. How did Mydeco’s inventory days change over this period?
c. Based on your analysis, has Mydeco improved its management of its working capital during
this time period?
a. 2012 accounts receivable days = 365 × 87.6 / 401.9 = 79.56.
2016 accounts receivable days = 365 × 84.2 / 602.6 = 51.00.
b. 2012 inventory days = 365 × 33.5 / 192.1 = 63.65.
2016 inventory days = 365 × 35.8 / 295.8 = 44.18.
c. Between 2012 and 2016, Mydeco improved its working capital management by reducing both
accounts receivable days and inventory days.
2-32 See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. Compare accounts payable days in 2012 and 2016.
b. Did this change in accounts payable days improve or worsen Mydeco’s cash position in
2016?
a. 2012 accounts payable days = 365 × 18.8 / 192.1 = 35.72.
2016 accounts payable days = 365 × 30.3 / 295.8 = 37.39.
b. Accounts payable days increased from 2012 to 2016, which improved the cash position of Mydeco

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Chapter 2/Introduction to Financial Statement Analysis 15
2-33. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. By how much did Mydeco increase its debt from 2012 to 2016?
b. What was Mydeco’s EBITDA/Interest coverage ratio in 2012 and 2016? Did its coverage
ratio ever fall below 2?
c. Overall, did Mydeco’s ability to meet its interest payments improve or decline over this
period?
a. Mydeco increased its debt from $498.9 million in 2012 to $595.5 million in 2016 (by $98.6
million).
b. Interest coverage ratio = (EBIT + Depreciation) / Interest expense
Year 2012 2013 2014 2015 2016
EBIT $55.5 $38.4 $46.7 $55.2 $65.8
Depreciation & Amortization $27.5 $26.3 $32.5 $38.3 $40.1
Interest Expense $32.4 $31.8 $32.0 $37.0 $40.9
Interest Coverage ratio 2.56 2.03 2.48 2.53 2.59
Mydeco’s coverage ratio did not fall below 2 between 2012 and 2016
c. Overall, Mydeco’s ability to meet its interest payments remained relatively constant, although it
experienced a slight dip in 2013.
2-34. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. How did Mydeco’s book debt-equity ratio change from 2012 to 2016?
b. How did Mydeco’s market debt-equity ratio change from 2012 to 2016?
c. Compute Mydeco’s debt-to-enterprise value ratio to assess how the fraction of its business
that is debt financed has changed over the period.
a.
Year 2012 2013 2014 2015 2016
Long-term Debt $498.9 $498.9 $572.2 $597.5 $597.5
Stockholders' Equity $255.0 $255.6 $257.8 $270.8 $279.8
Book debt-equity ratio 1.96 1.95 2.22 2.21 2.14
b.
Year 2012 2013 2014 2015 2016
Long-term Debt $498.9 $498.9 $572.2 $597.5 $597.5
Market capitalization (millions) $398.7 $201.6 $332.8 $473.1 $657.2
Market debt-equity ratio 1.25 2.47 1.72 1.26 0.91
c.
Year 2012 2013 2014 2015 2016
Long-term Debt $498.9 $498.9 $572.2 $597.5 $597.5
Enterprise value $848.2 $632.5 $813.3 $990.2 $1,171.1
Debt-to-enterprise value ratio 0.59 0.79 0.70 0.60 0.51
2-35. Use the data in Problem 8 to determine the change, from 2012 to 2015, in GE’s
a. book debt-equity ratio?
b. market debt-equity ratio?
a. 2012 book debt-equity ratio = 410/116 = 3.53.
2015 book debt-equity ratio = 302/128 = 2.36
b. 2012 market debt-equity ratio = 410/(17 x 10.6) = 2.28.
2015 market debt-equity ratio = 302/(25 x 10) = 1.21.

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16 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
2-36. You are analyzing the leverage of two firms and you note the following (all values in millions of
dollars):
a. What is the market debt-to-equity ratio of each firm?
b. What is the book debt-to-equity ratio of each firm?
c. What is the interest coverage ratio of each firm?
d. Which firm may have more difficulty meeting its debt obligations? Explain.
a. Firm A: Market debt-equity ratio = 495.8/401.1 = 1.24
Firm B: Market debt-equity ratio = 83.8/35.9 = 2.33
b. Firm A: Book debt-equity ratio = 495.8/297.9 = 1.66
Firm B: Book debt-equity ratio = 83.8/38.3 = 2.19
c. Firm A: Interest coverage ratio = 106.8/45.2 = 2.36
Firm B: Interest coverage ratio = 8.4/7.5 = 1.12
d. Firm B has a lower coverage ratio and will have more difficulty meeting its debt obligations than
Firm A.
2-37. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. Compute Mydeco’s PE ratio each year from 2012 to 2016. In which year was it the highest?
b. What was Mydeco’s Enterprise Value to EBITDA ratio each year? In which year was it the
highest?
c. What might explain the differing time pattern of the two valuation ratios?
a.
Year 2012 2013 2014 2015 2016
Stock Price $7.02 $3.55 $5.86 $8.33 $11.57
EPS $0.26 $0.08 $0.17 $0.21 $0.29
PE ratio 27.0 44.4 34.5 39.7 39.9
The PE ratio was highest in 2013.
b.
Year 2012 2013 2014 2015 2016
Enterprise value $848.2 $632.5 $813.3 $990.2 $1,171.1
EBIT $55.5 $38.4 $46.7 $55.2 $65.8
Depreciation & Amortization $27.5 $26.3 $32.5 $38.3 $40.1
Enterprise value-to-EBITDA ratio 10.2 9.8 10.3 10.6 11.1
The enterprise value/EBITDA ratio was the highest in 2016.
c. The different time patterns are caused by a change in the leverage ratio (increasing debt) that
occurred in 2014 and 2015 and reduced the earnings per share due to increased interest expense.
The PE ratio is sensitive to changes in leverage, while the enterprise value/EBITDA ratio is not.
2-38. In early-2015, United Airlines (UAL) had a market capitalization of $24.8 billion, debt of $12.8
billion, and cash of $5.5 billion. United also had annual revenues of $38.9 billion. Southwest
Airlines (LUV) had a market capitalization of $28.8 billion, debt of $2.7 billion, cash of $2.9
billion, and annual revenues of $18.6 billion.

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Chapter 2/Introduction to Financial Statement Analysis 17
a. Compare the market capitalization-to-revenue ratio (also called the price-to-sales ratio) for
United Airlines and Southwest Airlines.
b. Compare the enterprise value-to-revenue ratio for United Airlines and Southwest Airlines.
c. Which of these comparisons is more meaningful? Explain.
a. Market capitalization-to-revenue ratio:
= 24.8/38.9 = 0.64 for United Airlines.
= 28.8/18.6 = 1.55 for Southwest Airlines.
b. Enterprise value-to-revenue ratio:
= (24.8 – 5.5 + 12.8)/38.9 = 0.83 for United Airlines.
= (28.8 – 2.9 + 2.7)/18.6 = 1.54 for Southwest Airlines.
c. The market capitalization to revenue ratio cannot be meaningfully compared when the firms have
different amounts of leverage, as market capitalization measures only the value of the firm’s
equity. The enterprise value to revenue ratio is therefore more useful when firm’s leverage is quite
different, as it is here.
2-39. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp.
a. Compute Mydeco’s ROE each year from 2012 to 2016.
b. Compute Mydeco’s ROA each year from 2012 to 2016.
c. Which return is more volatile? Why?
a.
Year 2012 2013 2014 2015 2016
Net Income $15.0 $4.3 $9.6 $11.8 $16.2
Stockholders' Equity $255.0 $255.6 $257.8 $270.8 $279.8
ROE 5.9% 1.7% 3.7% 4.4% 5.8%
b.
Year 2012 2013 2014 2015 2016
Net Income $15.0 $4.3 $9.6 $11.8 $16.2
Interest Expense $32.4 $31.8 $32.0 $37.0 $40.9
Total Assets $780.3 $779.6 $859.9 $903.1 $917.0
Enterprise value-to-EBITDA ratio 6.1% 4.6% 4.8% 5.4% 6.2%
c. ROE is more volatile. Mydeco’s debt level causes a large portion of EBIT to go to interest
expense (which is relatively constant). This magnifies the volatility of earnings left over for
shareholders through net income. ROA adjusts net income by including interest expense, and thus
is less sensitive to leverage.
2-40. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. Was
Mydeco able to improve its ROIC in 2016 relative to what it was in 2012?55.5 (1 0.35)
2012 ROIC 5.12%.
255.0 498.9 49.4
 −
= =
+ −65.8 (1 0.35)
2016 ROIC 5.39%.
279.8 597.5 83.6
 −
= =
+ −
Mydeco was able to improve its ROIC in 2016 relative to 2012.
2-41. For fiscal year 2015, Costco Wholesale Corporation had a net profit margin of 2.05%, asset
turnover of 3.48, and a book equity multiplier of 3.15.

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18 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
a. Use this data to compute Costco's ROE using the DuPont Identity.
b. If Costco's managers wanted to increase its ROE by one percentage point, how much higher
would their asset turnover need to be?
c. If Costco's net profit margin fell by one percentage point, by how much would their asset
turnover need to increase to maintain their ROE?
a. Costco’s ROE (DuPont) = 2.05% × 3.48 × 3.15 = 22.47%.
b. Costco's new asset turnover = 23.47%/(2.05% × 3.15) = 3.63 or an increase of 3.63 – 3.48 = 0.15.
c. Costco's new asset turnover = 22.47%/(1.05% × 3.15) = 6.79 or an increase of 6.79 – 3.48 = 3.31.
2-42. For fiscal year 2015, Walmart Stores Inc. (WMT) had total revenues of $484.65 billion, net
income of $16.36 billion, total assets of $203.49 billion, and total shareholder’s equity of $81.39
billion.
a. Calculate Wal-Mart’s ROE directly, and using the DuPont Identity.
b. Comparing with the data for Costco in problem 41, use the DuPont Identity to understand
the difference between the two firms’ ROEs.
a. Walmart’s ROE = 16.36/81.39 = 20.10%.
Walmart’s net profit margin = 16.36/484.65 = 3.38%.
Walmart’s asset turnover = 484.65/203.49 = 2.38.
Walmart’s equity multiplier = 203.49/81.39 = 2.50.
Walmart’s ROE (DuPont) = 3.38% × 2.38 × 2.50 = 20.11% (difference due to rounding).
b. Walmart has a superior profit margin, but a lower asset turnover and a lower equity multiplier
(which could represent less leverage). Despite the higher profit margin, it has a smaller ROE that
is driven by it’s lower asset turnover and leverage.
2-43. Consider a retailing firm with a net profit margin of 3.1%, a total asset turnover of 1.85, total
assets of $44.4 million, and a book value of equity of $18.2 million.
a. What is the firm’s current ROE?
b. If the firm increased its net profit margin to 3.6%, what would be its ROE?
c. If, in addition, the firm increased its revenues by 23% (while maintaining this higher profit
margin and without changing its assets or liabilities), what would be its ROE?
a. 3.1% × 1.85 × 44.4/18.2 = 14.0%.
b. 3.6% × 1.85 × 44.4/18.2 = 16.2%.
c. 3.6% × (1.85 × 1.23) × 44.4/18.2 = 20.0%.
2-44. Find online the annual 10-K report for Costco Wholesale Corporation (COST) for fiscal year
2015 (filed in October 2015).
a. Which auditing firm certified these financial statements?
b. Which officers of Costco’s certified the financial statements?
a. KPMG LLP certified Costco’s financial statements.
b. W. Craig Jelinek, President and CEO and Richard A. Galanti, Executive Vice President and CFO
certified Costco’s financial statements.
2-45. WorldCom reclassified $3.85 billion of operating expenses as capital expenditures. Explain the
effect this reclassification would have on WorldCom’s cash flows. (Hint: Consider taxes.)

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Chapter 2/Introduction to Financial Statement Analysis 19
WorldCom’s actions were illegal and clearly designed to deceive investors. But if a firm could
legitimately choose how to classify an expense for tax purposes, which choice is truly better for
the firm’s investors?
By reclassifying $3.85 billion operating expenses as capital expenditures, WorldCom increased its net
income but lowered its cash flow for that period. If a firm could legitimately choose how to classify an
expense, expensing as much as possible in a profitable period rather than capitalizing them will save
more on taxes, which results in higher cash flows, and thus is better for the firm’s investors.

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20
Chapter 3
Financial Decision Making and the Law of
One Price
3-1. Honda Motor Company is considering offering a $2500 rebate on its minivan, lowering the
vehicle’s price from $21,000 to $18,000. The marketing group estimates that this rebate will
increase sales over the next year from 31,000 to 51,000 vehicles. Suppose Honda’s profit margin
with the rebate is $6000 per vehicle. If the change in sales is the only consequence of this decision,
what are its costs and benefits? Is it a good idea?
The benefit of the rebate is that Honda will sell more vehicles and earn a profit on each additional
vehicle sold:
Benefit = Profit of $6,000 per vehicle × 20,000 additional vehicles sold = $120 million.
The cost of the rebate is that Honda will make less on the vehicles it would have sold:
Cost = Loss of $2,500 per vehicle × 31,000 vehicles that would have sold without rebate = $77.5
million.
Thus, Benefit – Cost = $120 million – $77.5 million = $42.5 million, and offering the rebate looks
attractive.
(Alternatively, we could view it in terms of total, rather than incremental, profits. The benefit as
$6000/vehicle × 51,000 sold = $306 million, and the cost is $8,500/vehicle × 31,000 sold = $263.5
million.)
3-2. You are an international shrimp trader. A food producer in the Czech Republic offers to pay you
2.2 million Czech koruna today in exchange for a year’s supply of frozen shrimp. Your Thai
supplier will provide you with the same supply for 3.6 million Thai baht today. If the current
competitive market exchange rates are 24.60 koruna per dollar and 34.99 baht per dollar, what
is the value of this deal?
Czech buyer’s offer = 2,200,000 CZK / (24.60 CZK/USD) = 89,430.89 USD.
Thai supplier’s offer = 3,600,000 THB / (34.99 THB/USD) = 102,886.54 USD.
The value of the deal is $89,430.89 – 102,886.54 = –$13,455.64 today (i.e. it is a bad deal and should
be rejected).
3-3. Suppose the current market price of corn is $4.23 per bushel. Your firm has a technology that
can convert 1 bushel of corn to 3 gallons of ethanol. If the cost of conversion is $1.47 per bushel,
at what market price of ethanol does conversion become attractive?
The price in which ethanol becomes attractive is ($4.23 + $1.47 / bushel of corn) / (3 gallons of ethanol
/ bushel of corn) = $1.90 per gallon of ethanol.

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Chapter 3/Financial Decision Making and the Law of One Price 21
3-4. Suppose your employer offers you a choice between a $5700 bonus and 120 shares of the
company stock. Whichever one you choose will be awarded today. The stock is currently trading
for $58 per share.
a. Suppose that if you receive the stock bonus, you are free to trade it. Which form of the bonus
should you choose? What is its value?
b. Suppose that if you receive the stock bonus, you are required to hold it for at least one year.
What can you say about the value of the stock bonus now? What will your decision depend
on?
a. Stock bonus = 120 × $58 = $6,960
Cash bonus = $5,700
Since you can sell the stock for $6,960 in cash today, its value is $6,960 which is better than the
cash bonus.
b. Because you could buy the stock today for $6,960 if you wanted to, the value of the stock bonus
cannot be more than $6,960. But if you are not allowed to sell the company’s stock for the next
year, its value to you could be less than $6,960. Its value will depend on what you expect the stock
to be worth in one year, as well as how you feel about the risk involved. You might decide that it
is better to take the $5,700 in cash than wait for the uncertain value of the stock in one year.
3-5. You have decided to take your daughter skiing in Utah. The best price you have been able to find
for a roundtrip air ticket is $364. You notice that you have 20,000 frequent flier miles that are
about to expire, but you need 25,000 miles to get her a free ticket. The airline offers to sell you
5000 additional miles for $0.04 per mile.
a. Suppose that if you don’t use the miles for your daughter’s ticket they will become
worthless. What should you do?
b. What additional information would your decision depend on if the miles were not expiring?
Why?
a. The price of the ticket if you purchase it is $364. The price if you purchase the miles is $0.04 ×
5000 = $200. Thus, you should purchase the miles.
b. In part a, the existing miles are worthless if you don’t use them. They are not worthless now, so
you must add in the cost of using them. Because there is no competitive market price for these
miles (you can purchase at 4¢ but not sell for that price), the decision will depend on how much
you value the existing miles (which will depend on your likelihood of using them in the future, the
cost of the equivalent ticket, the cost of additional miles you may have to buy in the future, etc.).
3-6. Suppose the risk-free interest rate is 3.9%.
a. Having $500 today is equivalent to having what amount in one year?
b. Having $500 in one year is equivalent to having what amount today?
c. Which would you prefer, $500 today or $500 in one year? Does your answer depend on when
you need the money? Why or why not?
a. Having $500 today is equivalent to having $500 × 1.039 = $519.5 in one year.
b. Having $500 in one year is equivalent to having $500 / 1.039 = $481.23 today.
c. Because money today is worth more than money in the future, $500 today is preferred to $500 in
one year. This answer is correct even if you don’t need the money today, because by investing the
$500 you receive today at the current interest rate, you will have more than $500 in one year.

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22 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
3-7. You have an investment opportunity in Japan. It requires an investment of $1.06 million today
and will produce a cash flow of ¥ 106 million in one year with no risk. Suppose the risk-free
interest rate in the United States is 4.7%, the risk-free interest rate in Japan is 2.9%, and the
current competitive exchange rate is ¥ 110 per dollar. What is the NPV of this investment? Is it a
good opportunity?
Cost = $1.06 million today
Benefit = (¥1 106) / (1.029 ¥1/¥0) / (110 ¥0/$0) = $0 0.936 million
[Note: for easy reading, I use a currency’s subscript to denote the period.]
NPV = 0.936 – 1.06 = –$0.124 million.
The NPV is negative, so it is not a good investment opportunity.
3-8. Your firm has a risk-free investment opportunity where it can invest $161,000 today and receive
$178,000 in one year. For what level of interest rates is this project attractive?
You are indifferent if r = 178,000/161,000 – 1 = 10.559%
Thus, the project is attractive if r < 10.559% (indifferent if =)
3-9. You run a construction firm. You have just won a contract to construct a government office
building. Constructing it will take one year and require an investment of $9.78 million today and
$5 million in one year. The government will pay you $22.5 million upon the building’s
completion. Suppose the cash flows and their times of payment are certain, and the risk-free
interest rate is 11%.
a. What is the NPV of this opportunity?
b. How can your firm turn this NPV into cash today?
a.Benefits CostsNPV PV PV= −Benefits
$1.10 in one year
PV = $20 million in one year ÷ $ today
= $18.18 million
 
 
 This year's costPV = $10 million todayNext year's cost
$1.10 in one year
PV = $5 million in one year ÷ $ today
= $4.55 million today
 
 
 NPV 18.18 10 4.55 $3.63 million today= − − =
b. The firm can borrow $18.18 million today, and pay it back with 10% interest using the $20 million
it will receive from the government (18.18 × 1.10 = 20). The firm can use $10 million of the 18.18
million to cover its costs today and save $4.55 million in the bank to earn 10% interest to cover its
cost of 4.55 × 1.10 = $5 million next year.
This leaves 18.18 – 10 – 4.55 = $3.63 million in cash for the firm today.
3-10. Your firm has identified three potential investment projects. The projects and their cash flows
are shown here:

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Chapter 3/Financial Decision Making and the Law of One Price 23
Suppose all cash flows are certain and the risk-free interest rate is 10%.
a. What is the NPV of each project?
b. If the firm can choose only one of these projects, which should it choose?
c. If the firm can choose any two of these projects, which should it choose?
a.A
20
NPV 10 $8.18
1.1
= − + =B
5
NPV 5 $9.55
1.1
= + =C
10
NPV 20 $10.91
1.1
= − =
b. If only one of the projects can be chosen, project C is the best choice because it has the highest
NPV.
c. If two of the projects can be chosen, projects B and C are the best choice because they offer a
higher total NPV than any other combinations.
3-11. Your computer manufacturing firm must purchase 12,000 keyboards from a supplier. One
supplier demands a payment of $144,000 today plus $12 per keyboard payable in one year.
Another supplier will charge $25 per keyboard, also payable in one year. The risk-free interest
rate is 9%.
a. What is the difference in their offers in terms of dollars today? Which offer should your firm
take?
b. Suppose your firm does not want to spend cash today. How can it take the first offer and not
spend $144,000 of its own cash today?
a.12 12, 000
Supplier 1: PV 144,000 $276,110
1.09

= − − = −25 12, 000
Supplier 2: PV $275, 229
1.09

= − = −
Costs are lower under the second supplier’s offer, so it is the better choice.
b. The firm can borrow $144,000 at 9% from a bank for one year to make the initial payment to the
first supplier. One year later, the firm will pay back the bank $156,960 (= 144,000 × 1.09) and the
first supplier $144,000 (= 12 × 12,000), for a total of $300,960 (the PV does not change).
3-12. Suppose Bank One offers a risk-free interest rate of 10.0% on both savings and loans, and Bank
Enn offers a risk-free interest rate of 10.5% on both savings and loans.
a. What arbitrage opportunity is available?
b. Which bank would experience a surge in the demand for loans? Which bank would receive a
surge in deposits?
c. What would you expect to happen to the interest rates the two banks are offering?

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24 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
a. Take a loan from Bank One at 10% and save the money in Bank Enn at 10.5%.
b. Bank One would experience a surge in the demand for loans, while Bank Enn would receive a
surge in deposits.
c. Bank One would increase the interest rate, and/or Bank Enn would decrease its rate, such that
neither bank offers a savings rate that is higher than either bank’s loan rates.
3-13. Throughout the 1990s, interest rates in Japan were lower than interest rates in the United States.
As a result, many Japanese investors were tempted to borrow in Japan and invest the proceeds
in the United States. Explain why this strategy does not represent an arbitrage opportunity.
There is exchange rate risk. Engaging in such transactions may incur a loss if the value of the dollar
falls relative to the yen. Because a profit is not guaranteed, this strategy is not an arbitrage opportunity.
3-14. An American Depositary Receipt (ADR) is security issued by a U.S. bank and traded on a U.S.
stock exchange that represents a specific number of shares of a foreign stock. For example,
Nokia Corporation trades as an ADR with symbol NOK on the NYSE. Each ADR represents one
share of Nokia Corporation stock, which trades with symbol NOK1V on the Helsinki stock
exchange. If the U.S. ADR for Nokia is trading for $5.76 per share, and Nokia stock is trading on
the Helsinki exchange for €5.25 per share, use the Law of One Price to determine the current $/€
exchange rate.
We can trade one share of Nokia stock for $5.76 per share in the U.S. and €5.24 per share in Helsinki.
By the Law of One Price, these two competitive prices must be the same at the current exchange rate.
Therefore, the exchange rate must be:$5.76/share = $1.0992/
5.24/share€ €
3-15. The promised cash flows of three securities are listed here. If the cash flows are risk-free, and the
risk-free interest rate is 4%, determine the no-arbitrage price of each security before the first
cash flow is paid.A
600
PV = 600 + = $1,176.92
1.04B
1,200
PV = = $1,153.85
1.04CPV = $1,200
While the total cash flows paid by each security are the same ($1200), securities A and B are worth
less than $1200 because some or all of the money is received in the future.
3-16. An Exchange-Traded Fund (ETF) is a security that represents a portfolio of individual stocks.
Consider an ETF for which each share represents a portfolio of two shares of Hewlett-Packard
(HPQ), one share of Sears (SHLD), and three shares of General Electric (GE). Suppose the
current stock prices of each individual stock are as shown here:

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Chapter 3/Financial Decision Making and the Law of One Price 25
a. What is the price per share of the ETF in a normal market?
b. If the ETF currently trades for $164, what arbitrage opportunity is available? What trades
would you make?
c. If the ETF currently trades for $194, what arbitrage opportunity is available? What trades
would you make?
a. We can value the portfolio by summing the value of the securities in it:
Price per share of ETF = 1 × $34 + 2 × $42 + 4 × $16 = $182
b. If the ETF currently trades for $164, an arbitrage opportunity is available. To take advantage of it,
one should buy the ETF for $164, sell one share of HPQ for $34, sell two shares of SHLD for $42
each, and sell four shares of GE for $16 each. Total profit for such transaction is $182 – $164 =
$18.
c. If the ETF trades for $194, an arbitrage opportunity is also available. To take advantage of it, one
should sell the ETF for $194, buy one share of HPQ for $34, buy two shares of SHLD for $42
each, and buy four shares of GE for $16 each. Total profit for such transaction is $194 – $182 =
$12.
3-17. Consider two securities that pay risk-free cash flows over the next two years and that have the
current market prices shown here:
a. What is the no-arbitrage price of a security that pays cash flows of $200 in one year and
$200 in two years?
b. What is the no-arbitrage price of a security that pays cash flows of $200 in one year and
$1600 in two years?
c. Suppose a security with cash flows of $100 in one year and $200 in two years is trading for a
price of $260. What arbitrage opportunity is available?
a. This security has the same cash flows as a portfolio of one share of B1 and one share of B2.
Therefore, its no-arbitrage price is 192 + 176 = $368.
b. This security has the same cash flows as a portfolio of one share of B1 and eight shares of B2.
Therefore, its no-arbitrage price is 192 + 8 × 176 = $1,600
c. There is an arbitrage opportunity because the no-arbitrage price should be $272 (= 192 / 2 + 176).
One should buy two shares of the security at $260/share and sell one share of B1 and two shares of
B2. Total profit would be $24 (–260 × 2 + 192 + 176 × 2).
3-18. Suppose a security with a risk-free cash flow of $154 in one year trades for $137 today. If there
are no arbitrage opportunities, what is the current risk-free interest rate?
The PV of the security’s cash flow is ($154 in one year)/(1 + r), where r is the one-year risk-free
interest rate. If there are no arbitrage opportunities, this PV equals the security’s price of $137 today.
Therefore,
$137 today = ($154 in one year) / (1 + r)

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26 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
r = 154 / 137 – 1 = 12.41%
3-19. Xia Corporation is a company whose sole assets are $100,000 in cash and three projects that it
will undertake. The projects are risk free and have the following cash flows:
Xia plans to invest any unused cash today at the risk-free interest rate of 9.2%. In one year, all
cash will be paid to investors and the company will be shut down.
a. What is the NPV of each project? Which projects should Xia undertake and how much cash
should it retain?
b. What is the total value of Xia’s assets (projects and cash) today?
c. What cash flows will the investors in Xia receive? Based on these cash flows, what is the
value of Xia today?
d. Suppose Xia pays any unused cash to investors today, rather than investing it. What are the
cash flows to the investors in this case? What is the value of Xia now?
e. Explain the relationship in your answers to parts (b), (c), and (d).
a.A
28, 000
NPV 20, 000 $5, 641.03
1.092
= − + =B
29, 000
NPV 13, 000 $13, 556.78
1.092
= − + =C
75, 000
NPV 56, 000 $12, 681.32
1.092
= − + =
All projects have positive NPV, and Xia has enough cash ($11,000 left over), so Xia should take
all of them.
b. Total value today = Cash + NPV(projects) = 100,000 + 5,641.03 + 13,556.78 + 12,681.32 =
$131,879.12
c. After taking the projects, Xia will have 100,000 – 20,000 – 13,000 – 56,000 = $11,000 in cash left
to invest at 9.2%. Thus, Xia’s cash flows in one year = 28,000 + 29,000 + 75,000 + 11,000 ×
1.092 = $144,012.
Value of Xia today = $144,012 / 1.092 = $131,879.12, the same as calculated in b.
d. Unused cash = $11,000
Cash flows today = $11,000
Cash flows in one year = 28,000 + 29,000 + 75,000 = $132,000
Value of Xia today = 11,000 + 132,012 / 1.092 = $131,879.12, the same as calculated in b.
e. Results from b, c, and d are the same because all methods value Xia’s assets today. Whether Xia
pays out cash now or invests it at the risk-free rate, investors get the same value today. The point
is that a firm cannot increase its value by doing what investors can do by themselves (and is the
essence of the separation principle).
3-A.1. The table here shows the no-arbitrage prices of securities A and B that we calculated.

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Chapter 3/Financial Decision Making and the Law of One Price 27
a. What are the payoffs of a portfolio of one share of security A and one share of security B?
b. What is the market price of this portfolio? What expected return will you earn from holding
this portfolio?
a. A + B pays $600 in both states of the economy (i.e., it its risk free).
b. Market price = 231 + 346 = 577. Expected return is (600 – 577) / 577 = 3.99%, which must equal
the risk-free interest rate for there to be no arbitrage.
3-A.2. Suppose security C has a payoff of $600 when the economy is weak and $1800 when the economy
is strong. The risk-free interest rate is 4%.
a. Security C has the same payoffs as which portfolio of the securities A and B in problem A-1?
b. What is the no-arbitrage price of security C?
c. What is the expected return of security C if both states are equally likely? What is its risk
premium?
d. What is the difference between the return of security C when the economy is strong and
when it is weak?
e. If security C had a risk premium of 10%, what arbitrage opportunity would be available?
a.C 3A B= +
b. Price ofC 3 231 346 1039=  + =
c. Expected payoff is600 1, 800 1, 200
2 2
+ = ; Expected return1, 200 1, 039 15.5%
1, 039
−
= =
Risk premium15.5 4 11.5%= − =
d. Return when strong1, 800 1, 039 73%
1, 039
−
= = ; return when weak600 1039 42%
1039
−
= = −
Difference( )
73 42 115%= − − =
e. Price of C given 10% risk premium1, 200 $1, 053
1.14
= =
Buy3A B+ for 1039, sell C for 1053, and earn a profit of1, 053 1, 039 $14− = .
3-A.3. You work for Innovation Partners and are considering creating a new security. This security
would pay out $2000 in one year if the last digit in the closing value of the Dow Jones Industrial
index in one year is an even number and zero if it is odd. The one-year risk-free interest rate is
5.3%. Assume that all investors are averse to risk.
a. What can you say about the price of this security if it were traded today?
b. Say the security paid out $2000 if the last digit of the Dow is odd and zero otherwise. Would
your answer to part (a) change?
c. Assume both securities (the one that paid out on even digits and the one that paid out on odd
digits) trade in the market today. Would that affect your answers?

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28 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
a. Whether the last digit in the Dow is odd or even has no correlation with the Dow index itself or
anything else in the economy. Hence the payout of this security does not vary with anything else
in the economy, so it will not have a risk premium. So the price of the security will be1 1
2000 0
2 2 $949.67
1.053
P
 + 
= =
b. No: the analysis is exactly the same and thus the price is the same.
c. The answers would remain the same; however, in this case if the actual prices departed from
949.67, an arbitrage opportunity would result because by purchasing both securities you can create
a riskless investment. The investment will only have a 5.3% return if the price of the basket of
both securities is $949.67 × 2 = $1899.34.
3-A.4. Suppose a risky security pays an expected cash flow of $83 in one year. The risk-free rate is
3.5%, and the expected return on the market index is 10.5%.
a. If the returns of this security are high when the economy is strong and low when the
economy is weak, but the returns vary by only half as much as the market index, what risk
premium is appropriate for this security?
b. What is the security’s market price?
a. If the security is half as variable, it should only earn half the risk premium of the market. The risk
premium of the market is
Market risk premium = 10.5% – 3.5% = 7%.
Thus, the security’s risk premium must equal 3.5%
b.83 83 $77.57
1 risk premium 1 3.5% 3.5%
P rf
= = =
+ + + +
3-A.5. Suppose Hewlett-Packard (HPQ) stock is currently trading on the NYSE with a bid price of
$28.12 and an ask price of $28.24. At the same time, a NASDAQ dealer posts a bid price for HPQ
of $27.98 and an ask price of $28.10.
a. Is there an arbitrage opportunity in this case? If so, how would you exploit it?
b. Suppose the NASDAQ dealer revises his quotes to a bid price of $28.10 and an ask price of
$28.22. Is there an arbitrage opportunity now? If so, how would you exploit it?
c. What must be true of the highest bid price and the lowest ask price for no arbitrage
opportunity to exist?
a. There is an arbitrage opportunity. One would buy from the NASDAQ dealer at $27.95 and sell to
NYSE dealer at $28.00, making profit of $0.05 per share.
b. There is no arbitrage opportunity.
c. To eliminate any arbitrage opportunity, the highest bid price should be lower then the lowest ask
price.
3-A.6. Consider a portfolio of two securities: one share of Johnson and Johnson (JNJ) stock and a bond
that pays $100 in one year. Suppose this portfolio is currently trading with a bid price of $141.71
and an ask price of $142.26, and the bond is trading with a bid price of $91.67 and an ask price
of $91.88. In this case, what is the no-arbitrage price range for JNJ stock?
According to the Law of One Price, the price that portfolio of securities is trading at is equal to the sum
of the price of securities within the portfolio. If the portfolio, composed of a bond and JNJ stock is
currently trading with a bid price of $141.65 and an ask price of $142.25, and the bond is trading at a

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