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Unformatted text preview: CHAPTER 8
The Characteristics and Valuation of Stock
Multiple Choice: Conceptual
Required return
1. Increase.
Decrease.
Fluctuate.
Remain constant.
Possibly increase, possibly decrease, or possibly remain unchanged. Required return Answer: d Diff: E If the expected rate of return on a stock exceeds the required rate,
a.
b.
c.
d.
e. The stock is experiencing supernormal growth.
The stock should be sold.
The company is probably not trying to maximize price per share.
The stock is a good buy.
Dividends are not being declared. Constant growth model
3. Diff: E An increase in a firm's expected growth rate would normally cause the
firm's required rate of return to
a.
b.
c.
d.
e. 2. Answer: e Answer: a Diff: E Which of the following statements is most correct?
a. The constant growth model takes into consideration the capital gains
earned on a stock.
b. It is appropriate to use the constant growth model to estimate stock
value even if the growth rate never becomes constant.
c. Two firms with the same dividend and growth rate must also have the
same stock price.
d. Statements a and c are correct.
e. All of the statements above are correct. Constant growth model
4. Answer: a Diff: E Which of the following statements is most correct.
a. The stock valuation model, P 0 = D1/(ks  g), can be used for firms
which have negative growth rates.
b. If a stock has a required rate of return k s = 12 percent, and its
dividend grows at a constant rate of 5 percent, this implies that the
stock’s dividend yield is 5 percent.
c. The price of a stock is the present value of all expected future
dividends, discounted at the dividend growth rate.
d. Statements a and c are correct.
e. All of the statements above are correct. Chapter 8 Page1 Constant growth model
5. Answer: c Diff: E A stock’s dividend is expected to grow at a constant rate of 5 percent a
year. Which of the following statements is most correct?
a. The expected return on the stock is 5 percent a year.
b. The stock’s dividend yield is 5 percent.
c. The stock’s price one year from now is expected to be 5 percent
higher.
d. Statements a and c are correct.
e. All of the statements above are correct. Miscellaneous issues
6. Answer: c Diff: E Which of the following statements is most correct?
a. If a company has two classes of common stock, Class A and Class B,
the stocks may pay different dividends, but the two classes must have
the same voting rights.
b. An IPO occurs whenever a company buys back its stock on the open
market.
c. The preemptive right is a provision in the corporate charter which
gives common stockholders the right to purchase (on a pro rata basis)
new issues of common stock.
d. Statements a and b are correct.
e. Statements a and c are correct. Preemptive right
7. Answer: b Diff: E The preemptive right is important to shareholders because it
a. Allows management to sell additional shares below the current market
price.
b. Protects the current shareholders against dilution of ownership
interests.
c. Is included in every corporate charter.
d. Will result in higher dividends per share.
e. The preemptive right is not important to shareholders. Classified stock
8. Answer: e Diff: E Companies can issue different classes of common stock.
Which of the
following statements concerning stock classes is most correct?
a.
b.
c.
d. All common stocks fall into one of three classes: A, B, and C.
Most firms have several classes of common stock outstanding.
All common stock, regardless of class, must have voting rights.
All common stock, regardless of class, must have the same dividend
privileges.
e. None of the statements above is necessarily true. Chapter 8  Page 2 Efficient markets hypothesis
9. Answer: e Diff: E Which of the following statements is most correct?
a. If a market is strongform efficient this implies that the returns on
bonds and stocks should be identical.
b. If a market is weakform efficient this implies that all public
information is rapidly incorporated into market prices.
c. If your uncle earns a return higher than the overall stock market,
this means the stock market is inefficient.
d. Both answers a and b are correct.
e. None of the above answers is correct. Market efficiency
10. Answer: c Diff: E Which of the following statements is most correct?
a. Semistrongform market efficiency implies that all private and public
information is rapidly incorporated into stock prices.
b. Market efficiency implies that all stocks should have the same
expected return.
c. Weakform market efficiency implies that recent trends in stock
prices would be of no use in selecting stocks.
d. All of the answers above are correct.
e. None of the answers above is correct. Market efficiency
11. Answer: a Diff: E Which of the following statements is most correct?
a. Semistrongform market efficiency means that stock prices reflect all
public information.
b. An individual who has information about past stock prices should be
able to profit from this information in a weakform efficient market.
c. An individual who has inside information about a publicly traded
company should be able to profit from this information in a strongform efficient market.
d. Statements a and c are correct.
e. All the statements above are correct. Chapter 8 Page3 Market efficiency
12. Answer: a Diff: E Most studies of stock market efficiency suggest that the stock market is
highly efficient in the weak form and reasonably efficient in the
semistrong form.
Based on these findings which of the following
statements are correct?
a. Information you read in The Wall Street Journal today cannot be used
to select stocks that will consistently beat the market.
b. The stock price for a company has been increasing for the past 6
months.
Based on this information it must be true that the stock
price will also increase during the current month.
c. Information disclosed in companies’ most recent annual reports can be
used to consistently beat the market.
d. Statements a and c are correct.
e. All of the statements above are correct. Preferred stock concepts
13. Answer: e Diff: E Which of the following statements is most correct?
a. Preferred stockholders have priority over common stockholders.
b. A big advantage of preferred stock is that preferred stock dividends
are tax deductible for the issuing corporation.
c. Most preferred stock is owned by corporations.
d. Statements a and b are correct.
e. Statements a and c are correct. Preferred stock concepts
14. Answer: e Diff: E Which of the following statements is most correct?
a. One of the advantages to the firm associated with financing using
preferred stock rather than common stock is that control of the firm
is not diluted.
b. Preferred stock provides steadier and more reliable income to
investors than common stock.
c. One of the advantages to the firm of financing with preferred stock
is that 70 percent of the dividends paid out are tax deductible.
d. Statements a and c are correct.
e. Statements a and b are correct. Common stock concepts
15. Answer: d Diff: E Which of the following statements is most correct?
a. One of the advantages of financing with stock is that a greater
proportion of stock in the capital structure can reduce the risk of a
takeover bid.
b. A firm with classified stock can pay different dividends to each
class of shares.
c. One of the advantages of financing with stock is that a firm’s debt
ratio will decrease.
d. Both statements b and c are correct.
e. All of the statements above are correct. Chapter 8  Page 4 Declining growth stock
16. Answer: e Diff: E A stock expects to pay a yearend dividend of $2.00 a share (i.e., D 1 =
$2.00; assume that last year’s dividend has already been paid).
The
dividend is expected to fall 5 percent a year, forever (i.e., g = 5%).
The company’s expected and required rate of return is 15 percent. Which
of the following statements is most correct?
a. The company’s stock price is $10.
b. The company’s expected dividend yield 5 years from now will be 20
percent.
c. The company’s stock price 5 years from now is expected to be $7.74.
d. Both answers b and c are correct.
e. All of the above answers are correct. Market efficiency and stock returns
17. Answer: c Diff: M Which of the following statements is most correct?
a. If a stock's beta increased but its growth rate remained the same,
then the new equilibrium price of the stock will be higher (assuming
dividends continue to grow at the constant growth rate).
b. Market efficiency says that the actual realized returns on all stocks
will be equal to the expected rates of return.
c. An implication of the semistrong form of the efficient markets
hypothesis is that you cannot consistently benefit from trading on
information reported in The Wall Street Journal .
d. Statements a and b are correct.
e. All of the statements above are correct. Efficient markets hypothesis
18. Answer: e Diff: M Which of the following statements is most correct?
a. If the stock market is weakform efficient this means you cannot use
private information to outperform the market.
b. If the stock market is semistrongform efficient, this means the
expected return on stocks and bonds should be the same.
c. If the stock market is semistrongform efficient, this means that
high beta stocks should have the same expected return as low beta
stocks.
d. Statements b and c are correct.
e. None of the statements above is correct. Chapter 8 Page5 Semistrongform efficiency
19. Answer: c Diff: M If the stock market is semistrong efficient, which of the following
statements is most correct?
a. All stocks should have the same expected returns; however, they may
have different realized returns.
b. In equilibrium, stocks and bonds should have the same expected
returns.
c. Investors can outperform the market if they have access to
information which has not yet been publicly revealed.
d. If the stock market has been performing strongly over the past
several months, stock prices are more likely to decline than increase
over the next several months.
e. None of the statements above is correct. Semistrongform efficiency
20. Assume that markets are semistrongform
following statements is most correct? Answer: e
efficient. Which Diff: M
of the a. All stocks should have the same expected return.
b. All stocks should have the same realized return.
c. Past stock prices can be successfully used to forecast future stock
returns.
d. Answers a and c are correct.
e. None of the answers above is correct.
Semistrongform efficiency
21. Answer: d Diff: M Assume that markets are semistrong efficient, but not strongfrom
efficient. Which of the following statements is most correct?
a. Each common stock has an expected return equal to that of the overall
market.
b. Bonds and stocks have the same expected return.
c. Investors can expect to earn returns above those predicted by the SML
if they have access to public information.
d. Investors may be able to earn returns above those predicted by the
SML if they have access to information which has not been publicly
revealed.
e. Answers b and c are correct. Chapter 8  Page 6 Ownership and going public
22. Answer: c Diff: M Which of the following statements is false?
a. When a corporation's shares are owned by a few individuals who are
associated with or are the firm's management, we say that the firm is
"closely held."
b. A publicly owned corporation is simply a company whose shares are
held by the investing public, which may include other corporations
and institutions as well as individuals.
c. Going public establishes a true market value for the firm and ensures
that a liquid market will always exist for the firm's shares.
d. When stock in a closely held corporation is offered to the public for
the first time the transaction is called "going public" and the
market for such stock is called the new issue market.
e. It is possible for a firm to go public, and yet not raise any
additional new capital. Dividend yield and g
23. Answer: b Diff: M Which of the following statements is most correct?
a. Assume that the required rate of return on a given stock is 13
percent. If the stock’s dividend is growing at a constant rate of 5
percent, its expected dividend yield is 5 percent as well.
b. The dividend yield on a stock is equal to the expected return less
the expected capital gain.
c. A stock’s dividend yield can never exceed the expected growth rate.
d. All of the answers above are correct.
e. Answers b and c are correct. Constant growth stock
24. Answer: d Diff: M The expected rate of return on the common stock of Northwest Corporation
is 14 percent. The stock’s dividend is expected to grow at a constant
rate of 8 percent a year. The stock currently sells for $50 a share.
Which of the following statements is most correct?
a.
b.
c.
d.
e. The
The
The
The
The stock’s dividend yield is 8 percent.
stock’s dividend yield is 7 percent.
current dividend per share is $4.00.
stock price is expected to be $54 a share in one year.
stock price is expected to be $57 a share in one year. Chapter 8 Page7 Multiple Choice: Problems
Preferred stock value
25. $150
$100
$ 50
$ 25
$ 10 Preferred stock value Diff: E $125
$120
$175
$150
$200 Preferred stock yield Answer: c Diff: E A share of preferred stock pays a quarterly dividend of $2.50. If the
price of this preferred stock is currently $50, what is the nominal
annual rate of return?
a.
b.
c.
d.
e. 12%
18%
20%
23%
28% Preferred stock yield
28. Answer: d Johnston Corporation is growing at a constant rate of 6 percent per
year.
It has both common stock and nonparticipating preferred stock
outstanding. The cost of preferred stock (k ps) is 8 percent. The par
value of the preferred stock is $120, and the stock has a stated
dividend of 10 percent of par.
What is the market value of the
preferred stock?
a.
b.
c.
d.
e. 27. Diff: E The Jones Company has decided to undertake a large project.
Consequently, there is a need for additional funds.
The financial
manager plans to issue preferred stock with a perpetual annual dividend
of $5 per share and a par value of $30. If the required return on this
stock is currently 20 percent, what should be the stock's market value?
a.
b.
c.
d.
e. 26. Answer: d Answer: a Diff: E A share of preferred stock pays a dividend of $0.50 each quarter. If
you are willing to pay $20.00 for this preferred stock, what is your
nominal (not effective) annual rate of return?
a. 10%
b. 8%
c. 6%
d. 12%
e. 14% Chapter 8  Page 8 Stock price
29. $164.19
$ 75.29
$107.53
$118.35
$131.74 Constant growth stock Diff: E $57.50
$62.25
$71.86
$64.00
$44.92 Constant growth stock Answer: e Diff: E Thames Inc.’s most recent dividend was $2.40 per share (i.e., D 0 =
$2.40).
The dividend is expected to grow at a rate of 6 percent per
year. The riskfree rate is 5 percent and the return on the market is 9
percent. If the company’s beta is 1.3, what is the price of the stock
today?
a.
b.
c.
d.
e. $72.14
$57.14
$40.00
$68.06
$60.57 Constant growth stock
32. Answer: a A share of common stock has just paid a dividend of $2.00.
If the
expected longrun growth rate for this stock is 15 percent, and if
investors require a 19 percent rate of return, what is the price of the
stock?
a.
b.
c.
d.
e. 31. Diff: E Assume that you plan to buy a share of XYZ stock today and to hold it
for 2 years. Your expectations are that you will not receive a dividend
at the end of Year 1, but you will receive a dividend of $9.25 at the
end of Year 2. In addition, you expect to sell the stock for $150 at
the end of Year 2. If your expected rate of return is 16 percent, how
much should you be willing to pay for this stock today?
a.
b.
c.
d.
e. 30. Answer: d Answer: c Diff: E Albright Motors is expected to pay a yearend dividend of $3.00 a share
(D1 = $3.00). The stock currently sells for $30 a share. The required
(and expected) rate of return on the stock is 16 percent.
If the
dividend is expected to grow at a constant rate, g, what is g?
a. 13.00%
b. 10.05%
c. 6.00%
d. 5.33%
e. 7.00% Chapter 8 Page9 Nonconstant growth stock
33. Answer: d Diff: E The last dividend paid by Klein Company was $1.00. Klein's growth rate
is expected to be a constant 5 percent for 2 years, after which
dividends are expected to grow at a rate of 10 percent forever. Klein's
required rate of return on equity (k s) is 12 percent.
What is the
current price of Klein's common stock?
a.
b.
c.
d.
e. $21.00
$33.33
$42.25
$50.16
$58.75 Future stock price
Answer: a Diff: E
34.
Waters Corporation has a stock price of $20 a share. The stock’s yearend dividend is expected to be $2 a share (D 1 = $2.00).
The stock’s
required rate of return is 15 percent and the stock’s dividend is
expected to grow at the same constant rate forever.
What is the
expected price of the stock seven years from now?
a.
b.
c.
d.
e. $28
$53
$27
$23
$39 Beta coefficient
35. Answer: b Diff: E Cartwright Brothers’ stock is currently selling for $40 a share.
The
stock is expected to pay a $2 dividend at the end of the year.
The
stock’s dividend is expected to grow at a constant rate of 7 percent a
year forever. The riskfree rate (k RF) is 6 percent and the market risk
premium (kM – kRF) is also 6 percent. What is the stock’s beta?
a.
b.
c.
d.
e. 1.06
1.00
2.00
0.83
1.08 New issues and dilution
Answer: b Diff: E
36.
NOPREM Inc. is a firm whose shareholders don't possess the preemptive
right.
The firm currently has 1,000 shares of stock outstanding; the
price is $100 per share. The firm plans to issue an additional 1,000
shares at $90.00 per share.
Since the shares will be offered to the
public at large, what is the amount per share that old shareholders will
lose if they are excluded from purchasing new shares?
a.
b.
c.
d.
e. $90.00
$ 5.00
$10.00
$
0
$ 2.50 Aftertax returns Chapter 8  Page 10 Answer: a Diff: M 37. The Stuart Corporation has excess cash to invest in one of two
securities.
The company's tax rate is 40 percent.
The first
alternative is a 10year, 10 percent coupon bond (with semiannual
interest payments) that has a current price of $1,000 and a yield of 10
percent. The second alternative is the preferred stock of Pickett Corp.
which promises to pay a beforetax return of 9 percent.
What is the
aftertax nominal return of the better investment alternative?
a.
b.
c.
d.
e. 7.92%
9.00%
7.33%
5.40%
7.00% Equilibrium stock price
38. Answer: a Diff: M Motor Homes Inc. (MHI) is presently in a stage of abnormally high growth
because of a surge in the demand for motor homes. The company expects
earnings and dividends to grow at a rate of 20 percent for the next 4
years, after which time there will be no growth (g = 0) in earnings and
dividends. The company's last dividend was $1.50. MHI's beta is 1.6, the
return on the market is currently 12.75 percent, and the riskfree rate
is 4 percent. What should be the current price per share of common
stock?
a.
b.
c.
d.
e. $15.17
$17.28
$22.21
$19.10
$24.66 Chapter 8 Page11 Equilibrium stock price
39. Answer: b Diff: M You are given the following data:
(1)
(2)
(3)
(4)
(5) The riskfree rate is 5 percent.
The required return on the market is 8 percent.
The expected growth rate for the firm is 4 percent.
The last dividend paid was $0.80 per share.
Beta is 1.3. Now assume the following changes occur:
(1)
(2) (3)
(4) The inflation premium drops by 1 percent.
An increased degree of risk aversion causes the required return on
the market to go to 10 percent after adjusting for the changed
inflation premium.
The expected growth rate increases to 6 percent.
Beta rises to 1.5. What will be the change in price per share, assuming the stock was in
equilibrium before the changes?
a.
b.
c.
d.
e. +$12.11
$ 4.87
+$ 6.28
$16.97
+$ 2.78 Changing beta and the equilibrium stock price
40. Answer: d Diff: M Ceejay Corporation’s stock is currently selling at an equilibrium price
of $30 per share. The firm has been experiencing a 6 percent annual
growth rate. Last year’s earnings per share, E 0, were $4.00 and the
dividend payout ratio is 40 percent. The riskfree rate is 8 percent,
and the market risk premium is 5 percent. If market risk (beta)
increases by 50 percent, and all other factors remain constant, what
will be the new stock price? (Use 4 decimal places in your
calculations.)
a.
b.
c.
d.
e. $16.59
$18.25
$21.39
$22.69
$53.48 Chapter 8  Page 12 Nonconstant growth stock
41. $ 7.36
$ 8.62
$ 9.89
$10.98
$11.53 Nonconstant growth stock Answer: d Diff: M Mack Industries just paid
a dividend of $1.00 per share (i.e., D 0 =
$1.00). Analysts expect the company's dividend to grow 20 percent this
year (i.e., D1 = $1.20), and 15 percent next year. After two years the
dividend is expected to grow at a constant rate of 5 percent.
The
required rate of return on the company's stock is 12 percent.
What
should be the current price of the company's stock?
a.
b.
c.
d.
e. $12.33
$16.65
$16.91
$18.67
$19.67 Nonconstant growth stock
43. Diff: M A stock is not expected to pay a dividend over the next four years. Five
years from now, the company anticipates that it will establish a
dividend of $1.00 per share (i.e., D 5 = $1.00).
Once the dividend is
established, the market expects that the dividend will grow at a
constant rate of 5 percent per year forever. The riskfree rate is 5
percent, the company's beta is 1.2, and the market risk premium is 5
percent. The required rate of return on the company’s stock is expected
to remain constant. What is the current stock price?
a.
b.
c.
d.
e. 42. Answer: d Answer: a Diff: M R. E. Lee recently took his company public through an initial public
offering. He is expanding the business quickly to take advantage of an
otherwise unexploited market. Growth for his company is expected to be
40 percent for the first three years and then he expects it to slow down
to a constant 15 percent.
The most recent dividend (D 0) was $0.75.
Based on the most recent returns, the beta for his company is
approximately 1.5. The riskfree rate is 8 percent and the market risk
premium is 6 percent. What is the current price of Lee's stock?
a.
b.
c.
d.
e. $77.14
$75.17
$67.51
$73.88
$93.20 Chapter 8 Page13 Nonconstant growth stock
44. $ 69.31
$ 72.96
$ 79.38
$ 86.38
$100.00 Nonconstant growth stock Answer: e Diff: M Stewart Industries expects to pay a $3.00 per share dividend on its
common stock at the end of the year (D 1 = $3.00).
The dividend is
expected to grow 25 percent a year until t = 3, after which time the
dividend is expected to grow at a constant rate of 5 percent a year
(i.e., D3 = $4.6875 and D4 = $4.9219).
The stock’s beta is 1.2, the
riskfree rate of interest is 6 percent, and the rate of return on the
market is 11 percent. What is the company’s current stock price?
a.
b.
c.
d.
e. $29.89
$30.64
$37.29
$53.69
$59.05 Nonconstant growth stock
46. Diff: M A stock is expected to pay no dividends for the first three years, i.e.,
D1 = $0, D2 = $0, and D3 = $0. The dividend for Year 4 is expected to be
$5.00 (i.e., D4 = $5.00), and it is anticipated that the dividend will
grow at a constant rate of 8 percent a year thereafter. The riskfree
rate is 4 percent, the market risk premium is 6 percent, and the stock's
beta is 1.5. Assuming the stock is fairly priced, what is the current
price of the stock?
a.
b.
c.
d.
e. 45. Answer: a Answer: b Diff: M McPherson Enterprises is planning to pay a dividend of $2.25 per share
at the end of the year (i.e., D 1 = $2.25). The company is planning to
pay the same dividend each of the following 2 years and will then
increase the dividend to $3.00 for the subsequent 2 years (i.e., D 4 and
D5). After that time the dividends will grow at a constant rate of 5
percent per year. If the required return on the company’s common stock
is 11 percent per year, what is the current stock price?
a.
b.
c.
d.
e. $52.50
$40.41
$37.50
$50.00
$32.94 Chapter 8  Page 14 Nonconstant growth stock
47. $49
$54
$64
$52
$89 Nonconstant growth stock Answer: e Diff: M Rogers Robotics currently (2001) does not pay a dividend. However, the
company is expected to pay a $1.00 dividend two years from today (2003).
The dividend is then expected to grow at a rate of 20 percent a year for
the following three years. After the dividend is paid in 2006, it is
expected to grow forever at a constant rate of 7 percent. Currently, the
riskfree rate is 6 percent, market risk premium (k M – kRF) is 5 percent,
and the stock’s beta is 1.4. What should be the price of the stock
today?
a.
b.
c.
d.
e. $22.91
$21.20
$30.82
$28.80
$20.16 Supernormal growth stock
49. Diff: M Hadlock Healthcare expects to pay a $3.00 dividend at the end of the
year (D1 = $3.00). The stock’s dividend is expected to grow at a rate
of 10 percent a year until three years from now (t = 3).
After this
time, the stock’s dividend is expected to grow at a constant rate of 5
percent a year.
The stock’s required rate of return is 11 percent.
What is the price of the stock today?
a.
b.
c.
d.
e. 48. Answer: b Answer: e Diff: M A share of stock has a dividend of D 0 = $5. The dividend is expected to
grow at a 20 percent annual rate for the next 10 years, then at a 15
percent rate for 10 more years, and then at a longrun normal growth
rate of 10 percent forever. If investors require a 10 percent return on
this stock, what is its current price?
a.
b.
c.
d.
e. $100.00
$ 82.35
$195.50
$212.62
The data given in the problem are internally inconsistent, i.e., the
situation described is impossible in that no equilibrium price can be
produced. Chapter 8 Page15 Supernormal growth stock
50. Answer: b Diff: M ABC Company has been growing at a 10 percent rate, and it just paid a
dividend of D0 = $3.00. Due to a new product, ABC expects to achieve a
dramatic increase in its shortrun growth rate, to 20 percent annually
for the next 2 years. After this time, growth is expected to return to
the longrun constant rate of 10 percent. The company's beta is 2.0,
the required return on an average stock is 11 percent, and the riskfree
rate is 7 percent. What should the dividend yield (D 1/P0) be today?
a. 3.93%
b. 4.60%
c. 10.00%
d. 7.54%
e. 2.33% Supernormal growth stock
51. Diff: M DAA's stock is selling for $15 per share. The firm's income, assets,
and stock price have been growing at an annual 15 percent rate and are
expected to continue to grow at this rate for 3 more years.
No
dividends have been declared as yet, but the firm intends to declare a
dividend of D3 = $2.00 at the end of the last year of its supernormal
growth. After that, dividends are expected to grow at the firm's normal
growth rate of 6 percent.
The firm's required rate of return is 18
percent. The stock is
a.
b.
c.
d.
e. Undervalued by $3.03.
Overvalued by $3.03.
Correctly valued.
Overvalued by $2.25.
Undervalued by $2.25. Declining growth stock
52. Answer: b Answer: d Diff: M The Textbook Production Company has been hit hard due to increased
competition.
The company's analysts predict that earnings (and
dividends) will decline at a rate of 5 percent annually forever. Assume
that ks = 11 percent and D 0 = $2.00.
What will be the price of the
company's stock three years from now?
a.
b.
c.
d.
e. $27.17
$ 6.23
$28.50
$10.18
$20.63 Chapter 8  Page 16 Stock growth rate
53. Berg Inc. has just paid a dividend
for $48 per share.
The firm is
expected return on the market is
Treasury bonds is 11 percent.
If
rate of growth is expected? Answer: d Diff: M of $2.00. Its stock is now selling
half as risky as the market.
The
14 percent, and the yield on U.S.
the market is in equilibrium, what a. 13%
b. 10%
c. 4%
d. 8%
e. 2%
Stock growth rate
54. Answer: e Diff: M Grant Corporation's stock is selling for $40 in the market.
The
company's beta is 0.8, the market risk premium is 6 percent, and the
riskfree rate is 9 percent. The previous dividend was $2 (i.e., D 0 =
$2) and dividends are expected to grow at a constant rate. What is the
growth rate for this stock?
a. 5.52%
b. 5.00%
c. 13.80%
d. 8.80%
e. 8.38% Capital gains yield
55. Answer: c Diff: M Carlson Products, a constant growth company, has a current market (and
equilibrium) stock price of $20.00.
Carlson's next dividend, D 1, is
forecasted to be $2.00, and Carlson is growing at an annual rate of 6
percent. Carlson has a beta coefficient of 1.2, and the required rate
of return on the market is 15 percent. As Carlson's financial manager,
you have access to insider information concerning a switch in product
lines which would not change the growth rate, but would cut Carlson's
beta coefficient in half. If you buy the stock at the current market
price, what is your expected percentage capital gain?
a.
b.
c.
d.
e. 23%
33%
43%
53%
There would be a capital loss. Chapter 8 Page17 Capital gains yield
56. Answer: d Given the following information, calculate the expected capital gains
yield for Chicago Bears Inc.: beta = 0.6; k M = 15%; kRF = 8%; D1 = $2.00;
P0 = $25.00. Assume the stock is in equilibrium and exhibits constant
growth.
a.
b.
c.
d.
e. 3.8%
0%
8.0%
4.2%
2.5% Capital gains yield and dividend yield
57. Answer: e Diff: M Conner Corporation has a stock price of $32.35 per share.
The last
dividend was $3.42 (i.e., D 0 = $3.42). The longrun growth rate for the
company is a constant 7 percent.
What is the company’s capital gains
yield and dividend yield?
a.
b.
c.
d.
e. Capital
Capital
Capital
Capital
Capital gains
gains
gains
gains
gains yield
yield
yield
yield
yield Stock price and P/E ratios
58. Diff: M = 7.00%; Dividend yield = 10.57%.
= 10.57%; Dividend yield = 7.00%.
= 7.00%; Dividend yield = 4.31%.
= 11.31%; Dividend yield = 7.00%.
= 7.00%; Dividend yield = 11.31%.
Answer: a Diff: M Over the past few years, Swanson Company has retained, on the average,
70 percent of its earnings in the business. The future retention rate
is expected to remain at 70 percent of earnings, and longrun earnings
growth is expected to be 10 percent. If the riskfree rate, k RF, is 8
percent, the expected return on the market, k M, is 12 percent, Swanson's
beta is 2.0, and the most recent dividend, D 0, was $1.50, what is the
most likely market price and P/E ratio (P 0/E1) for Swanson's stock
today?
a.
b.
c.
d.
e. $27.50;
$33.00;
$25.00;
$22.50;
$45.00; Chapter 8  Page 18 5.0 ×
6.0 ×
5.0 ×
4.5 ×
4.5 × Stock price
59. Answer: d Diff: M You have been given the following projections for Cali Corporation for
the coming year.
Sales
Sales price per unit
Variable cost per unit
Fixed costs
Bonds outstanding
kd on outstanding bonds
Tax rate
Shares of common stock outstanding
Beta
kRF
kM
Dividend payout ratio
Growth rate =
=
=
=
=
=
=
=
=
=
=
=
= 10,000 units
$10
$5
$10,000
$15,000
8%
40%
10,000 shares
1.4
5%
9%
60%
8% Calculate the current price per share for Cali Corporation.
a.
b.
c.
d.
e. $35.22
$46.27
$48.55
$53.72
$59.76 Stock price
60. Answer: b Diff: M Newburn Entertainment’s stock is expected to pay a yearend dividend of
$3.00 a share.
(D 1 = $3.00, the dividend at time 0, D 0, has already
been paid.) The stock’s dividend is expected to grow at a constant rate
of 5 percent a year. The riskfree rate, k RF, is 6 percent and the
market risk premium, (k M – kRF), is 5 percent. The stock has a beta of
0.8. What is the stock’s expected price five years from now?
a.
b.
c.
d.
e. $60.00
$76.58
$96.63
$72.11
$68.96 Chapter 8 Page19 Beta coefficient
61. Answer: c As financial manager of Material Supplies Inc., you have recently
participated in an executive committee decision to enter into the
plastics business.
Much to your surprise, the price of the firm's
common stock subsequently declined from $40 per share to $30 per share.
While there have been several changes in financial markets during this
period, you are anxious to determine how the market perceives the
relevant risk of your firm. Assume that the market is in equilibrium.
From the following data you find that the beta value associated with
your firm has changed from an old beta of
to a new beta of
_.
(1) The real riskfree rate is 2 percent, but the inflation premium
has increased from 4 percent to 6 percent.
The expected growth rate has been reevaluated by security
analysts, and a 10.5 percent rate is considered to be more realistic than the previous 5 percent rate. This change had nothing to
do with the move into plastics; it would have occurred anyway.
The risk aversion attitude of the market has shifted somewhat, and
now the market risk premium is 3 percent instead of 2 percent.
The next dividend, D 1, was expected to be $2 per share, assuming
the "old" 5 percent growth rate. (2) (3)
(4) a.
b.
c.
d.
e. 2.00;
1.50;
2.00;
1.67;
1.50; 1.50
3.00
3.17
2.00
1.67 Risk and stock value
62. Diff: M Answer: d Diff: M The probability distribution for k M for the coming year is as follows:
Probability kM 0.05
0.30
0.30
0.30
0.05 7%
8
9
10
12 If kRF = 6.05% and Stock X has a beta of 2.0, an expected constant
growth rate of 7 percent, and D 0 = $2, what market price gives the
investor a return consistent with the stock's risk?
a.
b.
c.
d.
e. $25.00
$37.50
$21.72
$42.38
$56.94 Chapter 8  Page 20 Future stock price
63. $24.62
$29.99
$39.40
$41.83
$47.98 Future stock price Answer: b Diff: M Graham Enterprises anticipates that its dividend at the end of the year
will be $2.00 a share (i.e., D 1 = $2.00). The dividend is expected to
grow at a constant rate of 7 percent a year. The riskfree rate is 6
percent, the market risk premium is 5 percent, and the company's beta
equals 1.2. What is the expected price of the stock five years from now?
a.
b.
c.
d.
e. $52.43
$56.10
$63.49
$70.49
$72.54 Future stock price
65. Diff: M A stock currently sells for $28 a share. Its dividend is growing at a
constant rate, and its dividend yield is 5 percent. The required rate
of return on the company’s stock is expected to remain constant at 13
percent. What is the expected stock price, seven years from now?
a.
b.
c.
d.
e. 64. Answer: e Answer: b Diff: M Kirkland Motors expects to pay a $2.00 a share dividend on its common
stock at the end of the year (i.e., D 1 = $2.00). The stock currently
sells for $20.00 a share. The required rate of return on the company’s
stock is 12 percent (i.e., k s = 0.12). The dividend is expected to grow
at some constant rate over time. What is the expected stock price five
ˆ
years from now, that is, what is P5 ?
a.
b.
c.
d.
e. $21.65
$22.08
$25.64
$35.25
$36.78 Chapter 8 Page21 Future stock price
66. $10.63
$12.32
$11.87
$13.58
$11.21 New equity and equilibrium price Answer: c Diff: M Nahanni Treasures Corporation is planning a new common stock issue of
five million shares to fund a new project. The increase in shares will
bring to 25 million the number of shares outstanding. Nahanni's longterm growth rate is 6 percent, and its current required rate of return
is 12.6 percent.
The firm just paid a $1.00 dividend and the stock
sells for $16.06 in the market. On the announcement of the new equity
issue, the firm's stock price dropped.
Nahanni estimates that the
company's growth rate will increase to 6.5 percent with the new project,
but since the project is riskier than average, the firm's cost of
capital will increase to 13.5 percent. Using the DCF growth model, what
is the change in the equilibrium stock price?
a.
b.
c.
d.
e. $1.77
$1.06
$0.85
$0.66
$0.08 Nonconstant growth stock
68. Diff: M McNally Motors has yet to pay a dividend on its common stock. However,
the company expects to pay a $1.00 dividend starting two years from now
(i.e., D2 = $1.00).
Thereafter, the stock’s dividend is expected to
grow at a constant rate of 5 percent a year. The stock’s beta is 1.4,
the riskfree rate is k RF = 0.06, and the expected market return is k M =
0.12.
What is the stock’s expected price four years from now, i.e.,
ˆ
what is P4 ?
a.
b.
c.
d.
e. 67. Answer: b Answer: d Diff: E Your company paid a dividend of $2.00 last year.
The growth rate is
expected to be 4 percent for 1 year, 5 percent the next year, then 6
percent for the following year, and then the growth rate is expected to
be a constant 7 percent thereafter.
The required rate of return on
equity (ks) is 10 percent.
What is the current price of the common
stock?
a.
b.
c.
d.
e. $53.45
$60.98
$64.49
$67.47
$69.21 Chapter 8  Page 22 CHAPTER 8
Answers and Solutions
1. Required return Answer: e Diff: E 2. Required return Answer: d Diff: E 3. Constant growth model Answer: a Diff: E Statement a is correct; the other statements are false.
The constant
growth model is not appropriate for stock valuation in the absence of a
constant growth rate. If the required rate of return differs for the two
firms due to risk differences, then the firms' stock prices would
differ. 4. Constant growth model Answer: a Diff: E Statement a is correct; the other statements are false. If a stock’s
required return is 12% and its capital gains yield is 5 percent, then
its dividend yield is 12%  5% = 7%.
The expected future dividends
should be discounted at the required rate of return.
5. Constant growth model Answer: c Diff: E Statement c is correct, the others are false. Statement a would only be
true if the dividend yield were zero. Statement b is false; we've been
given no information about the dividend yield. Statement c is true; the
constant rate at which dividends are expected to grow is also the
expected growth rate of the stock’s price.
6. Miscellaneous issues Answer: c Diff: E Statement c is correct; the others are false.
Two classes of common
stock can have different voting rights, as well as pay different
dividends. An IPO occurs when a firm goes public for the first time.
Statement c is the exact definition for a preemptive right.
7. Preemptive right Answer: b Diff: E 8. Classified stock Answer: e Diff: E 9. Efficient markets hypothesis Answer: e Diff: E Statements a through d are incorrect; therefore, statement e is correct.
Statement a is incorrect.
Strongform efficiency states that current
market prices reflect all pertinent information, whether publicly
available or privately held. If it holds, even insiders would find it
impossible to earn abnormal returns in the stock market. Statement b is
incorrect; this describes semistrong form efficiency. 10. Market efficiency Answer: c Diff: E Chapter 8 Page23 Statement c is correct; the other statements are false. Semistrongform
market efficiency implies that only public information, not private, is
rapidly incorporated into stock prices.
Markets can be efficient yet
still price securities differently depending on their risks.
11. Market efficiency Answer: a Diff: E 12. Market efficiency Answer: a Diff: E Statement a is correct; the other statements are false.
Historical
information cannot be used to beat the market under weakform
efficiency. Public information cannot be used to beat the market under
semistrongform efficiency.
13. Preferred stock concepts Answer: e Diff: E 14. Preferred stock concepts Answer: e Diff: E Both statements a and b are correct; therefore, statement e is the
correct choice.
70% of dividends received, not paid out, are tax
deductible.
15. Common stock concepts Answer: d Diff: E Statements b and c are correct; therefore, statement d is the correct
choice.
A greater proportion of stock in the capital structure
increases the likelihood of a takeover bid.
16. Declining growth stock
Statement e is
Statement a is
correct;
Div
$1.547562/$7.74 17. Answer: e Diff: E the correct choice; all the statements are correct.
correct; P 0 = $2/(0.15 + 0.05) = $10.
Statement b is
yield 5
=
D6/P5
or
($2.00(0.95) 5)/($10.00(0.95) 5)
=
= 20%. Statement c is correct; $10(0.95) 5 = $7.74. Market efficiency and stock returns Answer: c Diff: M Statement c is correct; the other statements are false.
If beta
increased, but g remained the same, the new stock price would be lower.
Market efficiency says nothing about the relationship between expected
and realized rates of return.
18. Efficient markets hypothesis Answer: e Diff: M Statement e is correct; the other statements are false. If the stock
market is weakform efficient, you could use private information to
outperform the market.
Semistrongform efficiency means that current
market prices reflect all publicly available information.
19. Semistrongform efficiency Answer: c Diff: M 20. Semistrongform efficiency Answer: e Diff: M Statement e is the correct choice.
Chapter 8  Page 24 Semistrongform efficiency implies that past stock prices cannot be used to forecast future returns.
21. Semistrongform efficiency
Answer: d Diff: M 22. Ownership and going public Answer: c Diff: M 23. Dividend yield and g Answer: b Diff: M Statement b is correct; the other statements are false.
The stock's
required return must equal the sum of its expected dividend yield and
constant growth rate. A stock's dividend yield can exceed the expected
growth rate.
24. Constant growth stock
Statement d is correct; the
yield + Capital gains. 14%
yield = 6%. Dividend yield
$3. Future stock price = $50 25. Answer: d Diff: M
other statements are false. k s = Dividend
= Dividend yield + 8%; therefore, Dividend
= Dividend/Price; Dividend = 0.06 × $50 =
× 1.08 = $54. Preferred stock value Answer: d Diff: E Answer: d Diff: E Vps = Dps/kps = $5/0.20 = $25.
26. Preferred stock value The dividend is calculated as 10% × $120 = $12. We know that the cost
of preferred stock is equal to the dividend divided by the stock price
or 8% = $12/Price. Solve this expression for Price = $150. (Note: Nonparticipating preferred stockholders are entitled to just the stated
dividend rate. There is no growth in the dividend.)
27. Preferred stock yield Answer: c Diff: E Answer: a Diff: E Answer: d Diff: E Annual dividend = $2.50(4) = $10.
kps = Dps/Vps = $10/$50 = 0.20 = 20%.
28. Preferred stock yield
Yearly dividend = $0.50(4) = $2.00.
kps = Dps/Vps = $2.00/$20.00 = 0.10 = 10%. 29. Stock price Chapter 8 Page25 0 ks = 16%
 1

0 ˆ
P0 = ? 2
Years

ˆ
D 2 = 9.25
ˆ
P2 = 150.00
CF2 = 159.25 Numerical solution:
$159.25
ˆ
P0 =
= $118.35.
2
(1.16)
Financial calculator solution:
ˆ
Inputs: N = 2; I = 16; FV = 159.25. Output: PV = $118.35. P0 = $118.35.
30. Constant growth stock
P0 = 31. Answer: a Diff: E Answer: e Diff: E $2.00(1.15)
= $57.50.
0.19  0.15 Constant growth stock The required rate of return on the stock is 5% + (9%  5%)1.3 = 10.2%.
D1 = $2.40 × 1.06 = $2.544.
The price of the stock today is
$2.544/(0.102  0.06) = $60.57.
32. Constant growth stock
P0
$30
$4.8  $30g
$1.8
g 33. =
=
=
=
= Answer: c Answer: d 
1.00 Diff: E D1/(ks  g)
$3/(0.16 – g)
$3
$30g
6%. Nonconstant growth stock
0 Diff: E k = 12%
g = 5% 1

1.05 2
g = 5% 
1.1025 3
g = 10% Years 
1.2128 1.2128 ˆ
P2 = 0.12  0.10 = 60.6375
CFt 0 1.05 61.7400 Numerical solution:
$1.05
$61.74
+
= $50.16.
P0 =
2
(1.12)
(1.12)
Financial calculator solution:
Enter in CFLO register CF 0 = 0, CF1 = 1.05, and CF 2 = 61.74.
Then enter I = 12, and press NPV to get NPV = P 0 = $50.16.
34. Future stock price Chapter 8  Page 26 Answer: a Diff: E Step 1 Step 2 35. Find g:
P0 = D1/(ks  g)
$20 = $2/(0.15  g)
g = 5%.
Find
ˆ
P7 =
ˆ
P7 =
ˆ
P7 = P at t = 7:
P0(1 + g)7
$20(1.05)7
$28.14 ≈ $28. Beta coefficient
Step 1 36. Diff: E Answer: b Diff: E Find ks:
ks = D1/P0 + g
ks = $2/$40 + 0.07
ks = 0.12. Step 2 Answer: b Use the CAPM to find beta:
ks = kRF + (kM  kRF)b
0.12 = 0.06 + 0.06(b)
b = 1. New issues and dilution Calculate current and new market value of firm after new stock issue
1,000 shares × $100 per share
=
$100,000
Plus 1,000 new shares @ $90 each
+
90,000
New firm market value
$190,000
Calculate new market share price
$190,000/2,000 shares = $95.00 per share
Dilution Old shareholders lose $100  $95 = $5.00 per share.
37. Aftertax returns Answer: a Diff: M The aftertax yield on the bond is calculated as YTM(1  T). Thus, the
aftertax yield is 10%(1  0.4) = 6%.
The aftertax yield on the
preferred stock (remember 70% of dividends are excluded from taxes) is
9%(1  (0.3)(0.4)) = 7.92%.
Thus, the preferred stock is the best
alternative based on aftertax returns. 38. Equilibrium stock price Answer: a Diff: M Chapter 8 Page27 Time line:
ks = 18% 0 g = 20% D0 = 1.50 1 g = 20% $
D1 = 1.80 2 g = 20% $
D2 = 2.16 3 g = 20% $
D3 = 2.592 4 gn = 0% $
D4 = 3.11 5 Years ˆ
D5 = 3.11 $
P0 = ?
1.525
1.551
1.578
1.604
8.912
$
P0 = $15.17 ˆ
P4 = Required rate of return: 3.11
= 17.278
0.18 − 0 k s = 4% + 1.6(12.75%  4%) = 18%. Numerical solution:
ˆ
P0 = $1.80(PVIF 18%,1) + $2.16(PVIF 18%,2) + $2.592(PVIF 18%,3)
+ $3.11(PVIF 18%,4) + $17.278(PVIF 18%,4)
= $1.80(0.8475) + $2.16(0.7182) + $2.592(0.6086)
+ $3.11(0.5158) + $17.278(0.5158)
= $1.526 + $1.551 + $1.577 + $1.604 + $8.912 = $15.17.
Financial calculator solution:
Inputs: CF0 = 0; CF1 = 1.80; CF2 = 2.16; CF3 = 2.592; CF4 = 20.388; I = 18.
ˆ
Output: NPV = $15.17. P0 = $15.17.
39. Equilibrium stock price Answer: b Diff: M Answer: d Diff: M Numerical solution:
Before: ks = 5% + (8%  5%)1.3 = 8.9%.
$0.80(1.04)
ˆ
P0 =
= $16.98.
0.089  0.04
After:
ks = 4% + (10%  4%)1.5 = 13%.
$0.80(1.06)
ˆ
P0 =
= $12.11.
0.130  0.06 Hence, we have $12.11  $16.98 = $4.87.
40. Changing beta and the equilibrium stock price
a. Solve for
has a 40%
b. Solve for
c. Solve for
(5%)b0; b0
d. Solve for
e. Solve for
f. Solve for 41. D1: D0 = 0.40 × E0 = 0.40 × $4.00 = $1.60, since the firm
payout ratio. D 1 = D0(1 + g) = $1.60(1.06) = $1.696.
the original k s: ks = D1/P0 + g = $1.696/$30 + 6% = 11.65%.
the original beta using the CAPM formula: 11.65% = 8% +
= 0.73.
the new beta: b 1 = 1.5 × b0 = 1.5 × 0.73 = 1.095.
the new k s using the CAPM: k s = 8% + (5%)1.095 = 13.475%.
P 0 = D1 /(ks  g) = $1.696/(0.13475  0.06) = $22.69. Nonconstant growth stock Chapter 8  Page 28 Answer: d Diff: M The required return on the stock is given by:
ks = kRF + RPM(b)
ks = 5% + (5%)1.2 = 11%.
The stock price is given by:
D5
P4 =
ks − g
$1.00
=
0.11  0.05
= $16.667.
Thus, the current price is given by discounting the future price in Year
4 to the present at the required rate of return:
$16.667
ˆ
P0 =
= $10.98.
4
(1.11)
42. Nonconstant growth stock Answer: d Diff: M First, find the stock price after two years:
D1 = $1.20.
D2 = $1.20 × 1.15 = $1.38.
D3 = $1.38 × 1.05 = $1.449 ≈ $1.45.
P2 = D3/(ks  g)
= $1.449/(0.12  0.05)
= $20.70.
Discount this amount at 12% for two years to get the present value of
P2, or $16.50.
Second, calculate the present value of D 2, $1.10 (or
$1.38 discounted two years at 12%), and the present value of D 1, $1.07
(or $1.20 discounted one year at 12%). The stock price today is equal
to the sum of these three present values or $18.67.
43. Nonconstant growth stock Answer: a Diff: M Answer: a Diff: M ks = kRF + RPM(b)
= 8% + 6%(1.5)
= 17%.
D1
D2
D3
D4 =
=
=
= $0.75(1.4) = $1.05.
$0.75(1.4) 2 = $1.47.
$0.75(1.4) 3 = $2.058.
$0.75(1.4) 3(1.15) = $2.3667. P3 = D4/ks  g
= $2.3667/(0.17  0.15)
= $118.335.
$2.058 + $118.335
$1.05
$1.47
+
+
2
3
(1.17 )
(1.17 )
1.17
= $77.14. P0 = 44. Nonconstant growth stock Chapter 8 Page29 a. Find the expected return k s:
ks = 4% + 6%(1.5) = 13%. (Using the CAPM.)
b. Value the stock at t = 3:
P3 = D4/(ks  g)
= $5/(0.13  0.08) = $100.
c. Find PV of P 3:
$100
P0 =
= $69.305.
3
(1.13)
45. Nonconstant growth stock Answer: e Diff: M To find ks, the return on the stock, we use the CAPM.
ks = 6% + (11%  6%) × 1.2 = 12%.
The value of
D1 = $3.00.
D2 = $3.00 ×
D3 = $3.75 ×
D4 = $4.6875 the dividends for Years 1  4 are:
1.25 = $3.75. (This is the only one not given in the question.)
1.25 = $4.6875.
× 1.05 = $4.9219. The value of the stock at t = 3 is:
P3 = D4/(ks  g) = $4.9219/(0.12  0.05) = $70.3129.
Now find the present value of the supernormal growth dividends and the
value of the stock at t = 3.
$3.00
$3.75
$4.6875 + $70.3129
+
+
P0 =
2
1.12
(1.12)
(1.12 3
)
= $59.05.
46. Nonconstant growth stock Answer: b Diff: M We’re given D1, D2, and D3 = $2.25. D4 and D5 = $3.00. Calculate D 6 as
$3.00 × 1.05 = $3.15. The stock price at t = 5 is P 5 = $3.15/(0.11 0.05) = $52.50. The stock price today represents the sum of the present
values of D1, D2, D3, D4, D5, and P5.
$2.25
$2.25
$2.25
$3.00
$3.00 + $52.50
+
+
+
+
P0 =
2
3
4
5
1.11
(1.11)
(1.11)
(1.11)
(1.11)
= $40.41. 47. Nonconstant growth stock Chapter 8  Page 30 Answer: b Diff: M Step 1 Step 2 Find
ˆ
P3 =
ˆ
P3 =
ˆ
P3 = Step 3 48. Calculate D 1 through D4:
Since the dividend grows at 10 percent a year for 3 years, D 1 =
$3.00, D2 = $3.30, and D3 = $3.63. The dividend starts to grow
at 5 percent after t = 3, so D 4 = $3.8115. Find the current stock price:
The current stock price (at t = 0) is the present value of the
ˆ
dividends D1, D2, D3, and the present value of P3 .
Discount
these values at 11 percent.
$3.00
$3.30
$3.63 + $63.525
P0 =
+
+
2
3
1.11
(1.11)
(1.11)
= $54.48. the stock price at t = 3 when growth becomes constant:
D4/(ks  g)
$3.8115/(0.11  0.05)
$63.525. Nonconstant growth stock 2001
 2002 2003  ks = 13% Answer: e 2004 2005 2006  2007     gs = 20% 0 1.00 g n = 7% 1.20 P0 = ? 1.44
1.728
$1.849
= 30.8167
0.13 − 0.07
32.5447 Step 1 Calculate the dividends.
D2003 = $1.00.
D2004 = $1.00(1.2) = $1.20.
D2005 = $1.00(1.2) 2 = $1.44.
D2006 = $1.00(1.2) 3 = $1.728.
D2007 = $1.00(1.2) 3(1.07) = $1.849. Step 3 Calculate P 2006 (when growth becomes constant).
D 2007
$1.849
=
P2006 =
= $30.8167.
0.13 − 0.07
ks − g Step 4 1.849 Determine k s.
ks = kRF + (kM  kRF)b
= 6% + 5%(1.4) = 13%. Step 2 49. Diff: M P0 = $0
$1.00
$1.20
$1.44
$1.728 + $30.8167
+
+
+
+
2
3
4
5
1.13 (1.13)
(1.13)
(1.13)
(1.13)
= $20.16. Supernormal growth stock Answer: e Diff: M Chapter 8 Page31 The data in the problem are unrealistic and inconsistent with the
requirements of the growth model; k less than g implies a negative stock
price. If k equals g, the denominator is zero, and the numerical result
is undefined. k must be greater than g for a reasonable application of
the model.
50. Supernormal growth stock
Time line:
0 ks = 15% Answer: b 1 2 ˆ
D 1 = 3.60 ˆ
D 2 = 4.32 g s = 20%
D 0 = 3.00 3 Diff: M
Years g n = 10% 3.13
3.27
71.86
ˆ
P0 = $78.26 ˆ
P2 = ˆ
D 3 = 4.752 4.752
= 95.04
0.15 − 0.10 ks = 0.07 + (0.11  0.07)2.0 = 0.15 = 15%.
ˆ
D
Dividend yield 1 = $3.60/$78.26 = 4.60%.
P0
Financial calculator solution:
Inputs: CF0 = 0; CF1 = 3.60; CF2 = 99.36; I = 15.
Output: NPV = $78.26.
Dividend yield = $3.60/$78.26 = 0.0460 = 4.60%. 51. Supernormal growth stock Chapter 8  Page 32 Answer: b Diff: M Time line:
0 ks = 18% 1 2 3 ˆ
D1 = 0 ˆ
D2 = 0 gs = 15%
D0 = 0 ˆ
P3 1.217 = 4 gn = 6%
ˆ
D 3 = 2 . 00
2 . 12 0 . 18 − 0 . 06 ˆ
D4 Years = 2 . 12 = 17 . 667 10.752
ˆ
P0 = $ 11 . 97 ˆ
P0 > P0 Stock is overvalued: $15.00  $11.97 = $3.03. Numerical solution:
Calculate expected price of stock, P 3, at time = 3
$2.12
D4
D3 (1 + g)
ˆ
=
=
= $17.67.
P3 =
k−g
k−g
0.18  0.06
ˆ
P0 = $2.00(PVIF 18%,3) + $17.67(PVIF 18%,3)
= $2.00(0.6086) + $17.67(0.6086) = $11.97 versus P 0 = $15.
Therefore, it is overvalued by $15.00  $11.97 = $3.03.
Financial calculator solution:
ˆ
Calculate current expected price of stock, P0
Inputs: CF0 = 0; CF1 = 0; Nj = 2; CF2 = 19.67; I = 18.
ˆ
Output: NPV = $11.97. P0 = $11.97.
52. Declining growth stock
Time line:
0 ks = 11% 1 Answer: d
2 Diff: M 4 Years 3 gn = 5% D 0 = 2 . 00 ˆ
D 1 = 1 . 90 ˆ
D 2 = 1 . 805 ˆ
D 3 = 1 . 715 ˆ
D 4 = 1 . 629 $1.90
$1.90
=
= $11.875.
0.11  0.05
0.16
$1.629
D4
=
=
= $10.18.
0.16
0.16 ˆ
P0 =
ˆ
P3 53. Stock growth rate Answer: d Diff: M Chapter 8 Page33 Numerical solution:
Required rate of return: k s = 11% + (14%  11%)0.5 = 12.5%.
Calculate growth rate using k s:
$2(1 + g)
D0 (1 + g)
P0 =
; $48 =
0.125  g
ks  g
$6  $48g = $2 + $2g
(Multiply both sides by (0.125  g))
$50g = $4
g = 0.08 = 8%.
Required return equals total yield (Dividend yield + Capital gains
yield).
Dividend yield = $2.16/$48.00 = 4.5%; Capital gains yield = g = 8%.
54. Stock growth rate Answer: e Diff: M The required rate of return on the stock is 9% + (6%)0.8 = 13.8%. Using
the constant growth model, we can solve for the growth rate as $40 =
[$2(1 + g)]/(13.8%  g) or g = 8.38%.
55. Capital gains yield Answer: c Step 1 Calculate k RF, the riskfree rate
16% = kRF + (15%  kRF)1.2
16% = kRF  1.2kRF + 18%
0.2kRF = 2%
kRF = 10%. Step 3 56. Calculate ks, the required rate of return
$2
+ 6% = 10% + 6% = 16%.
ks =
$20 Step 2 Diff: M Calculate the new stock price and capital gain
New ks = 10% + (15%  10%)0.6 = 13%.
$2
ˆ
= $28.57.
PNew =
0.13  0.06
Therefore, the percentage capital gain is 43%
$28.57  $20.00
$8.57
=
= 43%.
$20.00
$20.00 Capital gains yield Answer: d Required rate of return, k s = 8% + (15%  8%)0.6 = 12.2%.
Chapter 8  Page 34 Diff: M Calculate dividend yield and use to calculate capital gains yield:
$2.00
D
Dividend yield = 1 =
= 0.08 = 8%.
$25.00
P0
Capital gains yield = Total yield  Dividend yield = 12.2%  8% = 4.2%.
Alternative method:
42
D1
P0 =
; $25 =
0.122  g
ks  g
$3.05  $25g = $2
(Multiply both sides by (0.122  g))
$25g = $1.05
g = 0.042 = 4.2%.
Since the stock is growing at a constant rate, g = Capital gains yield.
57. Capital gains yield and dividend yield Answer: e Diff: M Calculate D1 as $3.42 × 1.07 = $3.66.
The dividend yield is
$3.66/$32.35 = 11.31%. The capital gains yield is equal to the longrun
growth rate for this stock (since constant growth) or 7%.
58. Stock price and P/E ratios
Step 1 59. Answer: d Diff: M Calculate the current market price
$1.50(1.10)
ˆ
P0 =
= $27.50.
0.16 − 0.10 Step 3 Diff: M Calculate the required rate of return
ks = 8% + 2.0(12%  8%) = 16%. Step 2 Answer: a Calculate the earnings and P/E ratio
D1 = $1.50(1.10) = $1.65 = 0.30E 1.
E1 = $1.65/0.30 = $5.50.
ˆ
P0 = $27.50 = 5.0×.
$5.50
E1 Stock price
Step 1 Set up an income statement to find Net income:
Sales
$100,000
$10 × 10,000
Chapter 8 Page35 Variable costs
50,000
$5 × 10,000
Fixed costs
10,000
(Given)
EBIT
$ 40,000
0.08 × $15,000
Interest
1,200
EBT
$ 38,800
Taxes
15,520
0.40 × $38,800
NI
$ 23,280
Then, calculate the total amount of dividends, Div = Net income
× Payout = $23,280 × 0.6 = $13,968. Note: Dividends/Share = Total dividend/# of shares outstanding
= $13,968/10,000 = $1.3968.
Because these projections are for the coming year,
dividend is D 1, or the dividend for the coming year. this Step 2 Use the CAPM equation to find the required return on the stock:
kS = kRF + (kM  kRF)b = 0.05 + (0.09  0.05)1.4 = 0.106 = 10.6%. Step 3 Calculate stock price:
P0 = D1/(kS  g)
= $1.3968/(0.106  0.08)
= $53.72. 60. Stock price 61. First, find ks = 6%
$3.00/(0.10 – 0.05)
for 5 years to find
Beta coefficient Answer: b Diff: M + 5%(0.8) = 10%. Then, find P 0 = D1/(ks  g). P0 =
= $60. Finally, compound this at the 5% growth rate
ˆ
ˆ
P5 . P5 = $60(1.05)5 = $76.58.
Answer: c Diff: M Numerical solution:
Old required returns and beta
$2
ks(old) =
+ 0.05 = 0.10.
$40
0.10 = kRF + (RPM)bOld = 0.06 + (0.02)b Old; bOld = 2.00.
New required return and beta
$2.00
Note that D0 =
= $1.905.
$1.05
D1,New = $1.905(1.105) = $2.105.
2.105
ks,New =
+ 0.105 = 0.175.
$30
0.175 = 0.08 + (0.03)b New; bNew = 3.17. 62. Risk and stock value Answer: d Diff: M Numerical solution:
Required return on market and stock
kM = 0.05(7%) + 0.30(8%) + 0.30(9%) + 0.30(10%) + 0.05(12%) = 9.05%.
Chapter 8  Page 36 ks = 6.05% + (9.05%  6.05%)2.0 = 12.05%.
Expected equilibrium stock price
$2(1.07)
ˆ
P0 =
= $42.38.
0.1205 − 0.07
63. Future stock price Answer: e Diff: M The growth rate is the required return minus the dividend yield.
g = 0.13  0.05 = 0.08.
What is D1?
0.05 = D1/P0
D1 = $1.40.
What will be the Year 8 dividend?
D8 = D1 × (1 + g)7 = $2.399.
The Year 7 price is given by:
P7 = D8/(ks  g) = $2.399/0.05 = $47.98.
64. Future stock price
First, find D6 = $2.00(1.07)5 = $2.805.
0.05(1.2) = 0.12. Answer: b Diff: M Then, calculate k s = 0.06 + It follows that: P 5 = $2.805/(0.12  0.07) = $56.10.
65. Future stock price Answer: b Diff: M To find the growth rate:
ks = D1/P0 + g
Therefore ks  D1/P0 = g
0.12  $2/$20 = 0.02.
To find P5 we can use the following formula:
P5 = D6/(ks  g).
We therefore need D 6.
D6 = D1(1 + g)5
= $2(1.02)5 = $2.2082.
Therefore P5 = D6/(ks  g) = $2.2082/(0.12  0.02) = $22.0820.
Note that you could also get this by taking $20(1.02) 5 = $22.082. 66. Future stock price Answer: b Step 1 Find the cost of equity:
ks = 6% + (12%  6%)1.4 = 14.4%. Step 2 Diff: M Find the value of the stock at the end of Year 1:
Chapter 8 Page37 ˆ
P 1 = D2/(ks  g) = $1.00/(0.144  0.05) = $10.638.
Step 3
67. Find the value of the stock in Year 4:
ˆ
ˆ
P 4 = P 1(1.05)3 = $10.638(1.05) 3 = $12.315 ≈ $12.32. New equity and equilibrium price Answer: c Diff: M Calculate new equilibrium price and determine change:
$1.00(1.06)
D0 (1.06)
P0, Old =
=
= $16.06.
0.126  0.06
0.066
1.00(1 + g New)
$1.00(1.065)
$1.065
P0, New =
=
=
= $15.21.
ˆs, New  gNew
0.135  0.065
0.07
k
Change in price = $15.21  $16.06 = $0.85.
68. Nonconstant growth stock
Time line:
0 k = 10%
1
s


g = 4%
g = 5%
2.00
2.08 Answer: d
2

g = 6%
2.1840 3
 Diff: E 4 Years
 gn = 7%
2.3150
2.4771 2.3150 (1.07
)
ˆ
P3 =
= 82.5683
0.10 − 0.07 CFt 0 2.08 2.8140 84.8833 Enter in calculator CF0 = 0, CF1 = 2.08, CF2 = 2.1840, and CF3
84.8833. Then enter I = 10, and press NPV to get NPV = P 0 = $67.47. Chapter 8  Page 38 = ...
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 Spring '12
 Rhee
 International Finance, Valuation

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