Chapter 9
Valuing Stocks
9-1. Assume Evco, Inc., has a current price of $64 and will pay a $2.15 dividend in one year, and its
equity cost of capital is 11%. What price must you expect it to sell for right after paying the
dividend in one year in order to justify its current price?
9-2. Anle Corporation has a current price of $27, is expected to pay a dividend of $2 in one year, and
its expected price right after paying that dividend is $28.
a. What is Anle’s expected dividend yield?
b. What is Anle’s expected capital gain rate?
c. What is Anle’s equity cost of capital?
9-3. Suppose Acap Corporation will pay a dividend of $2.72 per share at the end of this year and
$2.99 per share next year. You expect Acap’s stock price to be $53.72 in two years. If Acap’s
equity cost of capital is 11.1%:
a. What price would you be willing to pay for a share of Acap stock today, if you planned to
hold the stock for two years?
b. Suppose instead you plan to hold the stock for one year. What price would you expect to be
able to sell a share of Acap stock for in one year?
c. Given your answer in part (b), what price would you be willing to pay for a share of Acap
stock today, if you planned to hold the stock for one year? How does this compare to your
answer in part (a)?
132 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
with an expected return of 15.1% per year. Suppose DFB will maintain the same dividend
payout rate, retention rate, and return on new investments in the future and will not change its
number of outstanding shares.
a. What growth rate of earnings would you forecast for DFB?
b. If DFB’s equity cost of capital is 12.8%, what price would you estimate for DFB stock today?
c. Suppose DFB instead paid a dividend of $3.09 per share at the end of this year and retained
only $0.92 per share in earnings. If DFB maintains this higher payout rate in the future,
what stock price would you estimate now? Should DFB raise its dividend?
9-11. Cooperton Mining just announced it will cut its dividend from $4.07 to $2.47 per share and use
the extra funds to expand. Prior to the announcement, Cooperton’s dividends were expected to
grow at a 2.8% rate, and its share price was $50.31. With the new expansion, Cooperton’s
dividends are expected to grow at a 4.9% rate. What share price would you expect after the
announcement? (Assume Cooperton’s risk is unchanged by the new expansion.) Is the expansion
a positive NPV investment?
9-12. Proctor and Gamble paid an annual dividend of $1.72 in 2009. You expect P&G to increase its
dividends by 8% per year for the next five years (through 2014), and thereafter by 3% per year.
If the appropriate equity cost of capital for Proctor and Gamble is 8% per year, use the
dividend-discount model to estimate its value per share at the end of 2009.
9-13. Colgate-Palmolive Company has just paid an annual dividend of $1.50. Analysts are predicting
dividends to grow by $0.12 per year over the next five years. After then, Colgate’s earnings are
expected to grow 6% per year, and its dividend payout rate will remain constant. If Colgate’s
equity cost of capital is 8.5% per year, what price does the dividend-discount model predict
Colgate stock should sell for today?
Chapter 9/Valuing Stocks 133
PV of the first 5 dividends:
PVfirst 5 =1.62
1.085 +1.74
1.0852+1.86
1.0853+1.98
1.0854+2.10
1.0855=$7.25.
PV of the remaining dividends in year 5:
remaining in year 5
2.10(1.06)
PV 89.04.
0.085 0.06
==
−
Discounting back to the present
Thus the price of Colgate is
P=PVfirst 5 +PVremaining =$66.47.
9-14. What is the value of a firm with initial dividend Div, growing for n years (i.e., until year n + 1) at
rate g1 and after that at rate g2 forever, when the equity cost of capital is r?
9-15. Halliford Corporation expects to have earnings this coming year of $2.77 per share. Halliford
plans to retain all of its earnings for the next two years. For the subsequent two years, the firm
will retain 48% of its earnings. It will then retain 19% of its earnings from that point onward.
Each year, retained earnings will be invested in new projects with an expected return of 27.21%
per year. Any earnings that are not retained will be paid out as dividends. Assume Halliford’s
share count remains constant and all earnings growth comes from the investment of retained
earnings. If Halliford’s equity cost of capital is 9.5%, what price would you estimate for
Halliford stock?
9-16. Suppose Amazon.com Inc. pays no dividends but spent $1.88 billion on share repurchases last
year. If Amazon’s equity cost of capital is 8.1%, and if the amount spent on repurchases is
134 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
expected to grow by 6.4% per year, estimate Amazon’s market capitalization. If Amazon has 432
million shares outstanding, what stock price does this correspond to?
9-17. Maynard Steel plans to pay a dividend of $3.03 this year. The company has an expected earnings
growth rate of 3.9% per year and an equity cost of capital of 10.9%.
a. Assuming Maynard’s dividend payout rate and expected growth rate remains constant, and
Maynard does not issue or repurchase shares, estimate Maynard’s share price.
b. Suppose Maynard decides to pay a dividend of $1.03 this year and use the remaining $2 per
share to repurchase shares. If Maynard’s total payout rate remains constant, estimate
Maynard’s share price.
c. If Maynard maintains the dividend and total payout rate given in part (b), at what rate are
Maynard’s dividends and earnings per share expected to grow?
9-18. Benchmark Metrics, Inc. (BMI), an all-equity financed firm, reported EPS of $4.43 in 2008.
Despite the economic downturn, BMI is confident regarding its current investment
opportunities. But due to the financial crisis, BMI does not wish to fund these investments
externally. The Board has therefore decided to suspend its stock repurchase plan and cut its
dividend to $1.44 per share (vs. almost $2 per share in 2007), and retain these funds instead. The
firm has just paid the 2008 dividend, and BMI plans to keep its dividend at $1.44 per share in
2009 as well. In subsequent years, it expects its growth opportunities to slow, and it will still be
able to fund its growth internally with a target 45% dividend payout ratio, and reinitiating its
stock repurchase plan for a total payout rate of 58%. (All dividends and repurchases occur at
the end of each year.)
Suppose BMI’s existing operations will continue to generate the current level of earnings per
share in the future. Assume further that the return on new investment is 15%, and that
reinvestments will account for all future earnings growth (if any). Finally, assume BMI’s equity
cost of capital is 10%.
a. Estimate BMI’s EPS in 2009 and 2010 (before any share repurchases).
b. What is the value of a share of BMI at the start of 2009?
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9-19. Heavy Metal Corporation is expected to generate the following free cash flows over the next five
years:
After then, the free cash flows are expected to grow at the industry average of 4.3% per year.
Using the discounted free cash flow model and a weighted average cost of capital of 14.4%:
a. Estimate the enterprise value of Heavy Metal.
b. If Heavy Metal has no excess cash, debt of $280 million, and 35 million shares outstanding,
estimate its share price.
9-20. IDX Technologies is a privately held developer of advanced security systems based in Chicago.
As part of your business development strategy, in late 2008 you initiate discussions with IDX’s
founder about the possibility of acquiring the business at the end of 2008. Estimate the value of
IDX per share using a discounted FCF approach and the following data:
■ Debt: $38 million
■ Excess cash: $118 million
■ Shares outstanding: 50 million
■ Expected FCF in 2009: $46 million
■ Expected FCF in 2010: $57 million
■ Future FCF growth rate beyond 2010: 4%
■ Weighted-average cost of capital: 9.4%
9-21. Sora Industries has 61 million outstanding shares, $121 million in debt, $49 million in cash, and
the following projected free cash flow for the next four years:
136 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
a. Suppose Sora’s revenue and free cash flow are expected to grow at a 5.7% rate beyond year
4. If Sora’s weighted average cost of capital is 11%, what is the value of Sora’s stock based
on this information?
b. Sora’s cost of goods sold was assumed to be 67% of sales. If its cost of goods sold is actually
70% of sales, how would the estimate of the stock’s value change?
c. Let’s return to the assumptions of part (a) and suppose Sora can maintain its cost of goods
sold at 67% of sales. However, now suppose Sora reduces its selling, general, and
administrative expenses from 20% of sales to 16% of sales. What stock price would you
estimate now? (Assume no other expenses, except taxes, are affected.)
*d. Sora’s net working capital needs were estimated to be 18% of sales (which is their current
level in year 0). If Sora can reduce this requirement to 12% of sales starting in year 1, but all
other assumptions remain as in part (a), what stock price do you estimate for Sora? (Hint:
This change will have the largest impact on Sora’s free cash flow in year 1.)
Chapter 9/Valuing Stocks 137
Year 0 1 2 3 4 5
Earnings Forecast ($000s) 8% 10% 6% 5% 5%
1 Sales 433.00 468.00 516.00 546.96 574.31 603.02
2 Cost of Goods Sold (313.56) (345.72) (366.46) (384.79) (404.03)
3Gross Profit 154.44 170.28 180.50 189.52 199.00
4 Selling, General & Admin. (74.88) (82.56) (87.51) (91.89) (96.48)
6 Depreciation (7.00) (7.50) (9.00) (9.45) (9.92)
7EBIT 72.56 80.22 83.98 88.18 92.59
8 Income tax at 40% (29.02) (32.09) (33.59) (35.27) (37.04)
9Unlevered Net Income 43.54 48.13 50.39 52.91 55.55
Free Cash Flow ($000s)
10 Plus: Depreciation 7.00 7.50 9.00 9.45 9.92
11 Less: Capital Expenditures (7.70) (10.00) (9.90) (10.40) (10.91)
12 Less: Increases in NWC (6.30) (8.64) (5.57) (4.92) (5.17)
13 Free Cash Flow 36.54 36.99 43.92 47.04 49.39
9-22. Consider the valuation of Kenneth Cole Productions in Example 9.7.
a. Suppose you believe KCP’s initial revenue growth rate will be between 4% and 11% (with
growth slowing in equal steps to 4% by year 2011). What range of share prices for KCP is
consistent with these forecasts?
b. Suppose you believe KCP’s EBIT margin will be between 7% and 10% of sales. What range
of share prices for KCP is consistent with these forecasts (keeping KCP’s initial revenue
growth at 9%)?
c. Suppose you believe KCP’s weighted average cost of capital is between 10% and 12%. What
range of share prices for KCP is consistent with these forecasts (keeping KCP’s initial
revenue growth and EBIT margin at 9%)?
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9-23. Suppose Kenneth Cole Productions (KCP) is acquired at the end of 2012 for a purchase price of
$15.25 per share. KCP has 18.5 million shares outstanding, $45 million in cash, and no debt at
the time of the acquisition.
a. Given a weighted average cost of capital of 11%, and assuming no future growth, what level
of annual free cash flow would justify this acquisition price?
b. If KCP’s current annual sales are $480 million, assuming no net capital expenditures or
increases in net working capital, and a tax rate of 35%, what EBIT margin does your answer
in part (a) require?
9-24. You notice that PepsiCo (PEP) has a stock price of $72.62 and EPS of $3.93. Its competitor, the
Coca-Cola Company (KO), has EPS of $2.13. Estimate the value of a share of Coca-Cola stock
using only this data.
9-25. Suppose that in January 2006, Kenneth Cole Productions had EPS of $1.67 and a book value of
equity of $12.17 per share.
a. Using the average P/E multiple in Table 9.1, estimate KCP’s share price.
b. What range of share prices do you estimate based on the highest and lowest P/E multiples in
Table 9.1?
c. Using the average price to book value multiple in Table 9.1, estimate KCP’s share price.
d. What range of share prices do you estimate based on the highest and lowest price to book
value multiples in Table 9.1?
9-26. Suppose that in January 2006, Kenneth Cole Productions had sales of $531 million, EBITDA of
$51.3 million, excess cash of $107 million, $3.3 million of debt, and 23 million shares outstanding.
a. Using the average enterprise value to sales multiple in Table 9.1, estimate KCP’s share price.
b. What range of share prices do you estimate based on the highest and lowest enterprise value
to sales multiples in Table 9.1?
c. Using the average enterprise value to EBITDA multiple in Table 9.1, estimate KCP’s share
price.
d. What range of share prices do you estimate based on the highest and lowest enterprise value
to EBITDA multiples in Table 9.1?
Chapter 9/Valuing Stocks 139
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a. Estimated enterprise value for KCP = Average EV/Sales × KCP Sales = 1.06 × $531 million =
$562.86 million.
Equity Value = EV – Debt + Cash = $562.86 – 3.3 + 107 = $666.56 million.
Share price = Equity Value / Shares = $666.56 / 23 = $28.98
b. $15.36 – $55.07 (analogous to part a)
c. Estimated enterprise value for KCP = Average EV/EBITDA × KCP EBITDA = 8.49 × $51.3
million = $435.54 million.
Share Price = ($435.54 – 3.3 + 107)/23 = $23.45
d. $19.36 – $28.49
9-27. In addition to footwear, Kenneth Cole Productions designs and sells handbags, apparel, and
other accessories. You decide, therefore, to consider comparables for KCP outside the footwear
industry.
a. Suppose that Fossil, Inc., has an enterprise value to EBITDA multiple of 11.08 and a P/E
multiple of 17.09. What share price would you estimate for KCP using each of these
multiples, based on the data for KCP in Problems 25 and 26?
b. Suppose that Tommy Hilfiger Corporation has an enterprise value to EBITDA multiple of
7.07 and a P/E multiple of 17.36. What share price would you estimate for KCP using each
of these multiples, based on the data for KCP in Problems 25 and 26?
9-28. Consider the following data for the airline industry for December 2015 (EV = enterprise value,
Book = tangible book value). Discuss the challenges of using multiples to value an airline.
All the multiples show a great deal of variation across firms. This makes the use of multiples
Chapter 9/Valuing Stocks 141
a. If Coca–Cola’s equity cost of capital is 8%, what share price would you expect based on your
estimate of the dividend growth rate?
b. Given Coca-Cola’s share price, what would you conclude about your assessment of Coca–
Cola’s future dividend growth?
9-32. Roybus, Inc., a manufacturer of flash memory, just reported that its main production facility in
Taiwan was destroyed in a fire. While the plant was fully insured, the loss of production will
decrease Roybus’ free cash flow by $185 million at the end of this year and by $56 million at the
end of next year.
a. If Roybus has 38 million shares outstanding and a weighted average cost of capital of 12.8%,
what change in Roybus’ stock price would you expect upon this announcement? (Assume the
value of Roybus’ debt is not affected by the event.)
b. Would you expect to be able to sell Roybus’ stock on hearing this announcement and make a
profit? Explain.
9-33. Apnex, Inc., is a biotechnology firm that is about to announce the results of its clinical trials of a
potential new cancer drug. If the trials were successful, Apnex stock will be worth $62 per share.
If the trials were unsuccessful, Apnex stock will be worth $16 per share. Suppose that the
morning before the announcement is scheduled, Apnex shares are trading for $57 per share.
a. Based on the current share price, what sort of expectations do investors seem to have about
the success of the trials?
b. Suppose hedge fund manager Paul Kliner has hired several prominent research scientists to
examine the public data on the drug and make their own assessment of the drug’s promise.
Would Kliner’s fund be likely to profit by trading the stock in the hours prior to the
announcement?
c. What would limit the fund’s ability to profit on its information?