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Ch 11: End-of-Chapter Problems – Stock Valuation

by | Mar 23, 2020 | Uncategorized | 0 comments

1.  Problem 11-01

eBookeBookProblem 11-01

The dividend-growth model may be used to value a stock:

Round your answers to the nearest cent.

    1. What is the value of a stock if:
      D0 = $1.30
      k = 11%
      g = 8%

$   

    1. What is the value of this stock if the dividend is increased to $2.90 and the other variables remain constant?

$   

    1. What is the value of this stock if the required return declines to 8.5 percent and the other variables remain constant?

$   

    1. What is the value of this stock if the growth rate declines to 6 percent and the other variables remain constant?

$   

    1. What is the value of this stock if the dividend is increased to $2.00, the growth rate declines to 6 percent, and the required return remains 11 percent?

$   

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Solution
  2. An increase in the dividend without a reduction in the growth rate increases the value of the stock.
  3. A reduction in the required rate of return increases the value of the stock.
  4. A reduction in the growth rate reduces the value of the stock.
  5. An increase in the dividend that comes at the expense of growth may cause the value of the stock to fall. Dividends and growth are substitutes, and the substitution of one for the other may cause the value of the stock to rise or fall depending on what stockholders desire: dividend income or capital appreciation.
Solution
Correct Response
eBookProblem 11-01

The dividend-growth model may be used to value a stock:

Round your answers to the nearest cent.

    1. What is the value of a stock if:
      D0 = $1.30
      k = 11%
      g = 8%

$  

    1. What is the value of this stock if the dividend is increased to $2.90 and the other variables remain constant?

$  

    1. What is the value of this stock if the required return declines to 8.5 percent and the other variables remain constant?

$  

    1. What is the value of this stock if the growth rate declines to 6 percent and the other variables remain constant?

$  

    1. What is the value of this stock if the dividend is increased to $2.00, the growth rate declines to 6 percent, and the required return remains 11 percent?

$  

2.  Problem 11-02

eBookeBookProblem 11-02

Last year Artworks, Inc. paid a dividend of $4.90. You anticipate that the company’s growth rate is 5 percent and have a required rate of return of 9 percent for this type of equity investment. What is the maximum price you would be willing to pay for the stock? Round your answer to the nearest cent.

$   

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Solution
The dividend-growth model is

The maximum price is
Solution
Correct Response
eBookProblem 11-02

Last year Artworks, Inc. paid a dividend of $4.90. You anticipate that the company’s growth rate is 5 percent and have a required rate of return of 9 percent for this type of equity investment. What is the maximum price you would be willing to pay for the stock? Round your answer to the nearest cent.

$  

3.  Problem 11-03

eBookeBookProblem 11-03

An investor with a required return of 14 percent for very risky investments in common stock has analyzed three firms and must decide which, if any, to purchase. The information is as follows:

Firm A B C
Current earnings $ 1.90 $ 3.20 $ 7.30
Current dividend $ 1.10 $ 3.50 $ 5.80
Expected annual growth rate in 6 % 1 % -2 %
dividends and earnings
Current market price $ 23 $ 30 $ 37
    1. What is the maximum price that the investor should pay for each stock based on the dividend-growth model? Round your answers to the nearest cent.

Stock A: $   

Stock B: $   

Stock C: $   

    1. If the investor does buy stock A, what is the implied percentage return? Round your answer to two decimal places.

  %

    1. If the appropriate P/E ratio is 15, what is the maximum price the investor should pay for each stock? Round your answers to the nearest cent.

Stock A: $   

Stock B: $   

Stock C: $   

    1. If the appropriate P/E ratio is 4, what is the maximum price the investor should pay for each stock? Round your answers to the nearest cent.

Stock A: $   

Stock B: $   

Stock C: $   

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Solution
  1. The dividend-growth model is

    Stock A:

    Stock B:

    Stock C:

    According to the dividend growth model, all three stocks are currently overvalued and should not be bought.

  2. The implied rate of return is the sum of the growth rate and the dividend yield:The implied return is less than the required return. The investor should not buy the stock.
  3. P/E ratios are an alternative means to value stock (at least by financial and securities analysis).

    The P/E (Price/Per share earnings) ratios for the stocks are

    Stock A: $23.00/$1.90 = 12.11

    Stock B: $30.00/$3.20 = 9.38

    Stock C: $37.00/$7.30 = 5.07

    If the maximum P/E should be 15, the maximum value of each stock is

    Stock A: 15 × $1.90 = $28.50

    Stock B: 15 × $3.20 = $48.00

    Stock C: 15 × $7.30 = $109.50

    The P/E of each stock is below the maximum allowed P/E of 15, and the valuation of each stock based on the desired P/E is higher than the market price. This indicates that each stock is undervalued and should be bought.

    If the maximum P/E should be 4, the maximum value of each stock is

    Stock A: 4 × $1.90 = $7.60

    Stock B: 4 × $3.20 = $12.80

    Stock C: 4 × $7.30 = $29.20

    The P/E of each stock exceeds the maximum allowed P/E of 4, and the valuation of each stock based on the desired P/E is less than the market price. This indicates that each stock is overvalued and should be avoided.
Solution
Correct Response
eBookProblem 11-03

An investor with a required return of 14 percent for very risky investments in common stock has analyzed three firms and must decide which, if any, to purchase. The information is as follows:

Firm A B C
Current earnings $ 1.90 $ 3.20 $ 7.30
Current dividend $ 1.10 $ 3.50 $ 5.80
Expected annual growth rate in 6 % 1 % -2 %
dividends and earnings
Current market price $ 23 $ 30 $ 37
    1. What is the maximum price that the investor should pay for each stock based on the dividend-growth model? Round your answers to the nearest cent.

Stock A: $  

Stock B: $  

Stock C: $  

    1. If the investor does buy stock A, what is the implied percentage return? Round your answer to two decimal places.

 %

    1. If the appropriate P/E ratio is 15, what is the maximum price the investor should pay for each stock? Round your answers to the nearest cent.

Stock A: $  

Stock B: $  

Stock C: $  

    1. If the appropriate P/E ratio is 4, what is the maximum price the investor should pay for each stock? Round your answers to the nearest cent.

Stock A: $  

Stock B: $  

Stock C: $  

4.  Problem 11-04

eBookeBookProblem 11-04

TSC, Inc. sells for $25 and pays an annual per share dividend of $2.30, which you expect to grow at 8 percent. What is your expected return on this stock? Round your answer to the two decimal places.

  %

What would be the expected return if the price were $34 a share? Round your answer to the two decimal places.

  %

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Solution
The expected return is $2.30(1.08)/$25 + 0.08 = 17.94%

If the price were $34, the expected return is

$2.30(1.08)/$34 + 0.08 = 15.31%
Solution
Correct Response
eBookProblem 11-04

TSC, Inc. sells for $25 and pays an annual per share dividend of $2.30, which you expect to grow at 8 percent. What is your expected return on this stock? Round your answer to the two decimal places.

 %

What would be the expected return if the price were $34 a share? Round your answer to the two decimal places.

 %

5.  Problem 11-05

eBookeBookProblem 11-05

Jersey Jewel Mining has a beta coefficient of 1.4. Currently the risk-free rate is 4 percent and the anticipated return on the market is 8 percent. JJM pays a $4.90 dividend that is growing at 5 percent annually. Do not round intermediate calculations.

    1. What is the required return for JJM? Round your answer to two decimal places.

  %

    1. Given the required return, what is the value of the stock? Round your answer to the nearest cent.

$   

    1. If the stock is selling for $137, what should you do?

The stock   overvalued and   be purchased.

    1. If the beta coefficient declines to 1.2, what is the new value of the stock? Round your answer to the nearest cent.

$   

    1. If the price remains $137, what course of action should you take given the valuation in d?

The stock is   and   be purchased.

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Solution
a. Required return = rf + (rm – rf)beta
= 0.04 + (0.08 – 0.04)1.4
= 9.60%
b. V =
=
= $111.85
c. The stock is overvalued ($137 > $111.85) and should not be purchased. (Should consider selling it short.)
d. Required return = rf + (rm – rf)beta
= 0.04 + (0.08 – 0.04)1.2
= 8.80%
V =
=
= $135.39
e. The stock is overvalued ($137 > $135.39) and should not be purchased.
Solution
Correct Response
eBookProblem 11-05

Jersey Jewel Mining has a beta coefficient of 1.4. Currently the risk-free rate is 4 percent and the anticipated return on the market is 8 percent. JJM pays a $4.90 dividend that is growing at 5 percent annually. Do not round intermediate calculations.

    1. What is the required return for JJM? Round your answer to two decimal places.

 %

    1. Given the required return, what is the value of the stock? Round your answer to the nearest cent.

$  

    1. If the stock is selling for $137, what should you do?

The stock  overvalued and  be purchased.

    1. If the beta coefficient declines to 1.2, what is the new value of the stock? Round your answer to the nearest cent.

$  

    1. If the price remains $137, what course of action should you take given the valuation in d?

The stock is  and  be purchased.

6.  Problem 11-06

eBookeBookProblem 11-06

The risk-free rate of return is 1 percent, and the expected return on the market is 8.9 percent. Stock A has a beta coefficient of 1.7, an earnings and dividend growth rate of 5 percent, and a current dividend of $2.80 a share. Do not round intermediate calculations. Round your answers to the nearest cent.

    1. What should be the market price of the stock?

$   

    1. If the current market price of the stock is $43.00, what should you do?

The stock   be purchased.

    1. If the expected return on the market rises to 13.4 percent and the other variables remain constant, what will be the value of the stock?

$   

    1. If the risk-free return rises to 2.5 percent and the return on the market rises to 13.6 percent, what will be the value of the stock?

$   

    1. If the beta coefficient falls to 1.5 and the other variables remain constant, what will be the value of the stock?

$   

    1. Explain why the stock’s value changes in c through e.

The increase in the return on the market   the required return and   the value of the stock.

The increase in the risk-free rate and the simultaneous increase in the return on the market cause the value of the stock to  .

The decrease in the beta coefficient causes the firm to become   risky as measured by beta, which   the value of the stock.

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Solution
a. Required return = rf + (rm – rf)beta
= 0.01 + (0.09 – 0.01)1.7
= 14.43%
V =
=
= $31.18
b. If the price of the stock is $43, the investor should not buy it, since the risk-adjusted valuation is $31.18.
c. Required return = 0.01 + (0.134 – 0.01)1.7
= 22.08%
V =
= $17.21
The increase in the return on the market increases the required return and decreases the value of the stock.
d. Required return = 0.03 + (0.136 – 0.03)1.7
= 21.37%
V =
= $17.96
The increase in the risk-free rate and the simultaneous increase in the return on the market cause the value of the stock to decrease.
e. Required return = 0.01 + (0.09 – 0.01)1.5
= 12.85%
V =
= $37.45
The firm is now less risky as measured by beta, which increases the value of the stock.
f. The explanations are given above after each calculation.
Solution
Correct Response
eBookProblem 11-06

The risk-free rate of return is 1 percent, and the expected return on the market is 8.9 percent. Stock A has a beta coefficient of 1.7, an earnings and dividend growth rate of 5 percent, and a current dividend of $2.80 a share. Do not round intermediate calculations. Round your answers to the nearest cent.

    1. What should be the market price of the stock?

$  

    1. If the current market price of the stock is $43.00, what should you do?

The stock  be purchased.

    1. If the expected return on the market rises to 13.4 percent and the other variables remain constant, what will be the value of the stock?

$  

    1. If the risk-free return rises to 2.5 percent and the return on the market rises to 13.6 percent, what will be the value of the stock?

$  

    1. If the beta coefficient falls to 1.5 and the other variables remain constant, what will be the value of the stock?

$  

    1. Explain why the stock’s value changes in c through e.

The increase in the return on the market  the required return and  the value of the stock.

The increase in the risk-free rate and the simultaneous increase in the return on the market cause the value of the stock to .

The decrease in the beta coefficient causes the firm to become  risky as measured by beta, which  the value of the stock.

7.  Problem 11-07

eBookeBookProblem 11-07

The security market line is estimated to be

k=7% + (11.5% – 7%)β.

You are considering two stocks. The beta of A is 1.0. The firm offers a dividend yield during the year of 5 percent and a growth rate of 7.9 percent. The beta of B is 1.4. The firm offers a dividend yield during the year of 6.4 percent and a growth rate of 7.3 percent.

    1. What is the required return for each security? Round your answers to two decimal places.

Stock A:   %

Stock B:   %

    1. Why are the required rates of return different?

The difference in the required rates of return is the result of   being riskier.

    1. Since A offers higher potential growth, should it be purchased?

Stock A   be purchased.

    1. Since B offers higher dividend yield, should it be purchased?

Stock B   be purchased.

    1. Which stock(s) should be purchased?

  should be purchased.

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Solution
  1. The required rates of return:
    rA = 0.07 + (0.115 – 0.07)1.0
    = 11.50%
    rB = 0.07 + (0.115 – 0.07)1.4
    = 13.30%
  2. The difference in the required rates of return is the result of Stock B being riskier. Its beta coefficient is higher (1.4 versus 1).
  3. Just because A offers higher potential growth is not sufficient evidence that the security should be bought. The investor expects to earn a 5 percent dividend yield plus 7.9 percent growth. The total return of 12.9 percent is greater than the required rate of return of 11.50 percent, so the stock should be purchased.
  4. Just because B offers higher dividend yield is not sufficient evidence that the security should be bought. The investor expects to earn a 6.4 percent dividend yield plus 7.3 percent growth. The total return of 13.7 percent is greater than the required rate of return of 13.30 percent, so the stock should be purchased.
  5. Since the expected returns on both stocks are greater than their required returns, both should be purchased.
Solution
Correct Response
eBookProblem 11-07

The security market line is estimated to be

k=7% + (11.5% – 7%)β.

You are considering two stocks. The beta of A is 1.0. The firm offers a dividend yield during the year of 5 percent and a growth rate of 7.9 percent. The beta of B is 1.4. The firm offers a dividend yield during the year of 6.4 percent and a growth rate of 7.3 percent.

    1. What is the required return for each security? Round your answers to two decimal places.

Stock A:  %

Stock B:  %

    1. Why are the required rates of return different?

The difference in the required rates of return is the result of  being riskier.

    1. Since A offers higher potential growth, should it be purchased?

Stock A  be purchased.

    1. Since B offers higher dividend yield, should it be purchased?

Stock B  be purchased.

    1. Which stock(s) should be purchased?

 should be purchased.

8.  Problem 11-08

eBookeBookProblem 11-08

Two stocks each currently pay a dividend of $1.20 per share. It is anticipated that both firms’ dividends will grow annually at the rate of 4 percent. Firm A has a beta coefficient of 1.01 while the beta coefficient of firm B is 1.33.

    1. If U.S. Treasury bills currently yield 5.9 percent and you expect the market to increase at an annual rate of 8.2 percent, what are the valuations of these two stocks using the dividend-growth model? Do not round intermediate calculations. Round your answers to two decimal places.

Stock A: $   

Stock B: $   

    1. Why are your valuations different?

The beta coefficient of   is higher, which indicates the stock’s return is   volatile.

    1. If stock A’s price were $46 and stock B’s price were $33, what would you do?

Stock A is   and   be purchased.

Stock B is   and   be purchased.

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Solution
  1. Stock A:
    Required return = 0.059 + (0.082 – 0.059)1.01
    = 8.22%
    V =
    = $29.55

    Stock B:

    Required return = 0.059 + (0.082 – 0.059)1.33
    = 8.96%
    V =
    = $25.17
  2. The valuations are different because the systematic risk associated with each stock differs. The beta coefficient of stock B is higher (1.33 versus 1.01), which indicates that this stock’s return is more volatile. Since the growth rates and dividends are equal for the two firms, stock B’s valuation must be lower because of the increased systematic risk.
  3. If the price of stock A were $46, the stock would be overvalued and should not be bought.

    If the price of stock B were $33, the stock is overvalued and should not be bought.
Solution
Correct Response
eBookProblem 11-08

Two stocks each currently pay a dividend of $1.20 per share. It is anticipated that both firms’ dividends will grow annually at the rate of 4 percent. Firm A has a beta coefficient of 1.01 while the beta coefficient of firm B is 1.33.

    1. If U.S. Treasury bills currently yield 5.9 percent and you expect the market to increase at an annual rate of 8.2 percent, what are the valuations of these two stocks using the dividend-growth model? Do not round intermediate calculations. Round your answers to two decimal places.

Stock A: $  

Stock B: $  

    1. Why are your valuations different?

The beta coefficient of  is higher, which indicates the stock’s return is  volatile.

    1. If stock A’s price were $46 and stock B’s price were $33, what would you do?

Stock A is  and  be purchased.

Stock B is  and  be purchased.

9.  Problem 11-09

eBookeBookProblem 11-09

The dividend-growth model,

suggests that an increase in the dividend growth rate will increase the value of a stock. However, an increase in the growth may require an increase in retained earnings and a reduction in the current dividend. Thus, management may be faced with a dilemma: current dividends versus future growth. As of now, investors’ required return is 9 percent. The current dividend is $1.4 a share and is expected to grow annually by 5 percent, so the current market price of the stock is $36.75. Management may make an investment that will increase the firm’s growth rate to 7 percent, but the investment will require an increase in retained earnings, so the firm’s dividend must be cut to $1.3 a share. Should management make the investment and reduce the dividend? Round your answer to the nearest cent.

The value of the stock   to $   , so the management   make the investment and decrease the dividend.

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Solution
V =
= $69.55

The value of the stock rises, so the management should make the investment and decrease the dividend. The increase in the growth rate more than offsets the decrease in the dividend.
Solution
Correct Response
eBookProblem 11-09

The dividend-growth model,

suggests that an increase in the dividend growth rate will increase the value of a stock. However, an increase in the growth may require an increase in retained earnings and a reduction in the current dividend. Thus, management may be faced with a dilemma: current dividends versus future growth. As of now, investors’ required return is 9 percent. The current dividend is $1.4 a share and is expected to grow annually by 5 percent, so the current market price of the stock is $36.75. Management may make an investment that will increase the firm’s growth rate to 7 percent, but the investment will require an increase in retained earnings, so the firm’s dividend must be cut to $1.3 a share. Should management make the investment and reduce the dividend? Round your answer to the nearest cent.

The value of the stock  to $  , so the management  make the investment and decrease the dividend.