Finance Chapter 8 then an increase in investor risk aversion caused the market risk premium to

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

a. –0.190

b. –0.211

c. –0.234

d. –0.260

e. –0.286

130. You hold a diversified $100,000 portfolio consisting of 20 stocks with

$5,000 invested in each. The portfolio’s beta is 1.12. You plan to

sell a stock with b = 0.90 and use the proceeds to buy a new stock with

b = 1.80. What will the portfolio’s new beta be?

a. 1.286

b. 1.255

c. 1.224

d. 1.194

e. 1.165

131. Mikkelson Corporation’s stock had a required return of 11.75% last

year, when the risk-free rate was 5.50% and the market risk premium was

4.75%. Then an increase in investor risk aversion caused the market

risk premium to rise by 2%. The risk-free rate and the firm’s beta

remain unchanged. What is the company’s new required rate of return?

(Hint: First calculate the beta, then find the required return.)

a. 14.38%

b. 14.74%

c. 15.11%

d. 15.49%

e. 15.87%

132. Company A has a beta of 0.70, while Company B’s beta is 1.20. The

required return on the stock market is 11.00%, and the risk-free rate

is 4.25%. What is the difference between A’s and B’s required rates of

return? (Hint: First find the market risk premium, then find the

required returns on the stocks.)

a. 2.75%

b. 2.89%

c. 3.05%

d. 3.21%

e. 3.38%

133. Stock A’s stock has a beta of 1.30, and its required return is 12.00%.

Stock B’s beta is 0.80. If the risk-free rate is 4.75%, what is the

required rate of return on B’s stock? (Hint: First find the market

risk premium.)

a. 8.76%

b. 8.98%

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c. 9.21%

d. 9.44%

e. 9.68%

Chapter 8: Risk and Return M/C Problems Page 305

134. Kollo Enterprises has a beta of 1.10, the real risk-free rate is 2.00%,

investors expect a 3.00% future inflation rate, and the market risk

premium is 4.70%. What is Kollo’s required rate of return?

a. 9.43%

b. 9.67%

c. 9.92%

d. 10.17%

e. 10.42%

135. Linke Motors has a beta of 1.30, the T-bill rate is 3.00%, and the T–

bond rate is 6.5%. The annual return on the stock market during the

past 3 years was 15.00%, but investors expect the annual future stock

market return to be 13.00%. Based on the SML, what is the firm’s

required return?

a. 13.51%

b. 13.86%

c. 14.21%

d. 14.58%

e. 14.95%

136. Nagel Equipment has a beta of 0.88 and an expected dividend growth rate

of 4.00% per year. The T-bill rate is 4.00%, and the T-bond rate is

5.25%. The annual return on the stock market during the past 4 years

was 10.25%. Investors expect the average annual future return on the

market to be 12.50%. Using the SML, what is the firm’s required rate

of return?

a. 11.34%

b. 11.63%

c. 11.92%

d. 12.22%

e. 12.52%

137. Consider the following information and then calculate the required rate

of return for the Global Investment Fund, which holds 4 stocks. The

market’s required rate of return is 13.25%, the risk-free rate is

7.00%, and the Fund’s assets are as follows:

Stock Investment Beta

A $ 200,000 1.50

B 300,000 –0.50

C 500,000 1.25

D $1,000,000 0.75

a. 9.58%

b. 10.09%

c. 10.62%

d. 11.18%

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e. 11.77%

Chapter 8: Risk and Return M/C Problems Page 307

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

2012 21.00%

2011 –12.50%

2010 25.00%

a. 20.08%

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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

2008 40.00% 40.00%

2009 –10.00% 15.00%

2010 35.00% –5.00%

2011 –5.00% –10.00%

2012 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%

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

Chapter 8: Risk and Return M/C Problems Page 309

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%

b. 15.68%

c. 16.50%

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d. 17.33%

e. 18.19%

CHAPTER 8

ANSWERS AND SOLUTIONS