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Page 300 M/C Problems Chapter 8: Risk and Return

c. 10.62%

d. 11.18%

e. 11.77%

138. Data for Dana Industries is shown below. Now Dana acquires some risky

assets that cause its beta to increase by 30%. In addition, expected

inflation increases by 2.00%. What is the stock’s new required rate of

return?

Initial beta 1.00

Initial required return (rs) 10.20%

Market risk premium, RPM 6.00%

Percentage increase in beta 30.00%

Increase in inflation premium, IP 2.00%

a. 14.00%

b. 14.70%

c. 15.44%

d. 16.21%

e. 17.02%

139. Mulherin’s stock has a beta of 1.23, its required return is 11.75%, and

the risk-free rate is 4.30%. What is the required rate of return on

the market? (Hint: First find the market risk premium.)

a. 10.36%

b. 10.62%

c. 10.88%

d. 11.15%

e. 11.43%

140. Suppose you hold a portfolio consisting of a $10,000 investment in each

of 8 different common stocks. The portfolio’s beta is 1.25. Now

suppose you decided to sell one of your stocks that has a beta of 1.00

and to use the proceeds to buy a replacement stock with a beta of 1.35.

What would the portfolio’s new beta be?

a. 1.17

b. 1.23

c. 1.29

d. 1.36

e. 1.43

141. Returns for the Dayton Company over the last 3 years are shown below.

What’s the standard deviation of the firm’s returns? (Hint: This is a

sample, not a complete population, so the sample standard deviation

formula should be used.)

Year Return

2011 21.00%

2010 –12.50%

Chapter 8: Risk and Return M/C Problems Page 301

2009 25.00%

a. 20.08%

b. 20.59%

c. 21.11%

d. 21.64%

e. 22.18%

142. Carson Inc.’s manager believes that economic conditions during the next

year will be strong, normal, or weak, and she thinks that the firm’s

returns will have the probability distribution shown below. What’s the

standard deviation of the estimated returns? (Hint: Use the formula

for the standard deviation of a population, not a sample.)

Economic

Conditions Prob. Return

Strong 30% 32.0%

Normal 40% 10.0%

Weak 30% –16.0%

a. 17.69%

b. 18.62%

c. 19.55%

d. 20.52%

e. 21.55%

143. Assume that your uncle holds just one stock, East Coast Bank (ECB),

which he thinks has very little risk. You agree that the stock is

relatively safe, but you want to demonstrate that his risk would be

even lower if he were more diversified. You obtain the following

returns data for West Coast Bank (WCB). Both banks have had less

variability than most other stocks over the past 5 years. Measured by

the standard deviation of returns, by how much would your uncle’s risk

have been reduced if he had held a portfolio consisting of 60% in ECB

and the remainder in WCB? (Hint: Use the sample standard deviation

formula.)

Year ECB WCB

2007 40.00% 40.00%

2008 –10.00% 15.00%

2009 35.00% –5.00%

2010 –5.00% –10.00%

2011 15.00% 35.00%

Average return = 15.00% 15.00%

Standard deviation = 22.64% 22.64%

a. 3.29%

b. 3.46%

c. 3.65%

d. 3.84%

e. 4.03%

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144. Assume that you manage a $10.00 million mutual fund that has a beta of

1.05 and a 9.50% required return. The risk-free rate is 4.20%. You

now receive another $5.00 million, which you invest in stocks with an

average beta of 0.65. What is the required rate of return on the new

portfolio? (Hint: You must first find the market risk premium, then

find the new portfolio beta.)

a. 8.83%

b. 9.05%

c. 9.27%

d. 9.51%

e. 9.74%

145. A mutual fund manager has a $40 million portfolio with a beta of 1.00.

The risk-free rate is 4.25%, and the market risk premium is 6.00%. The

manager expects to receive an additional $60 million which she plans to

invest in additional stocks. After investing the additional funds, she

wants the fund’s required and expected return to be 13.00%. What must

the average beta of the new stocks be to achieve the target required

rate of return?

a. 1.68

b. 1.76

c. 1.85

d. 1.94

e. 2.04

146. Assume that you are the portfolio manager of the SF Fund, a $3 million

hedge fund that contains the following stocks. The required rate of

return on the market is 11.00% and the risk-free rate is 5.00%. What

rate of return should investors expect (and require) on this fund?

Stock Amount Beta

A $1,075,000 1.20

B 675,000 0.50

C 750,000 1.40

D 500,000 0.75

$3,000,000

a. 10.56%

b. 10.83%

c. 11.11%

d. 11.38%

e. 11.67%

147. CCC Corp has a beta of 1.5 and is currently in equilibrium. The

required rate of return on the stock is 12.00% versus a required return

on an average stock of 10.00%. Now the required return on an average

stock increases by 30.0% (not percentage points). Neither betas nor

the risk-free rate change. What would CCC’s new required return be?

a. 14.89%

Chapter 8: Risk and Return M/C Problems Page 303

b. 15.68%

c. 16.50%

d. 17.33%

e. 18.19%

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CHAPTER 8

ANSWERS AND SOLUTIONS

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