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Chapter 08: Risk and Rates of Return
127. Jill Angel holds a $200,000 portfolio consisting of the following stocks. The portfolio's beta is 0.88.
Stock
Investment
Beta
A
$50,000
0.50
B
$50,000
0.80
C
$50,000
1.00
D
$50,000
1.20
Total
$200,000
If Jill replaces Stock A with another stock, E, which has a beta of 1.45, what will the portfolio's new beta be? Do not
round your intermediate calculations.
a.
1.39
b.
1.28
c.
0.83
d.
1.22
e.
1.11
Chapter 08: Risk and Rates of Return
128. Mike Flannery holds the following portfolio:
Stock
Investment
Beta
A
$150,000
1.40
B
$10,000
0.80
C
$140,000
1.00
D
$75,000
1.20
Total
$375,000
What is the portfolio's beta? Do not round your intermediate calculations.
a.
1.19
b.
1.36
c.
1.30
d.
1.47
e.
1.45
129. Tom Noel holds the following portfolio:
Stock
Investment
Beta
Chapter 08: Risk and Rates of Return
A
$150,000
1.40
B
$50,000
0.80
C
$100,000
1.00
D
$75,000
1.20
Total
$375,000
Tom plans to sell Stock A and replace it with Stock E, which has a beta of 0.80. By how much will the portfolio beta
change? Do not round your intermediate calculations.
a.
–0.240
b.
–0.194
c.
–0.290
d.
–0.271
e.
–0.230
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 = 1.50. What will the
portfolio's new beta be? Do not round your intermediate calculations.
a.
1.093
b.
1.185
Chapter 08: Risk and Rates of Return
c.
1.127
d.
1.150
e.
1.242
131. Mikkelson Corporation's stock had a required return of 12.50% last year, when the risk-free rate was 3% 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.) Do not round your intermediate calculations.
a.
12.87%
b.
16.50%
c.
13.04%
d.
12.71%
e.
14.36%
Chapter 08: Risk and Rates of Return
132. Company A has a beta of 0.70, while Company B's beta is 1.45. The required return on the stock market is 11.00%,
and the risk-free rate is 2.25%. 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.) Do not round your intermediate calculations.
a.
5.06%
b.
5.01%
c.
4.71%
d.
4.30%
e.
4.25%
Chapter 08: Risk and Rates of Return
133. Stock A's stock has a beta of 1.30, and its required return is 13.75%. Stock B's beta is 0.80. If the risk-free rate is
2.75%, what is the required rate of return on B's stock? (Hint: First find the market risk premium.) Do not round your
intermediate calculations.
a.
9.33%
b.
9.52%
c.
10.66%
d.
11.33%
e.
8.57%
134. Kollo Enterprises has a beta of 0.70, 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? Do not round your intermediate
calculations.
a.
7.96%
b.
7.30%
c.
6.47%
d.
6.96%
e.
8.29%
Chapter 08: Risk and Rates of Return
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 10.00%.
Based on the SML, what is the firm's required return? Do not round your intermediate calculations.
a.
11.05%
b.
13.48%
c.
12.71%
d.
10.17%
e.
10.50%
Chapter 08: Risk and Rates of Return
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 14.75%. Using the SML, what is the firm's required rate of
return? Do not round your intermediate calculations.
a.
13.61%
b.
11.57%
c.
12.25%
d.
14.70%
e.
12.11%
Chapter 08: Risk and Rates of Return
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 17.50%, the risk-free rate is 3.00%, and the Fund's assets are
as follows (Do not round your intermediate calculations.):
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.
14.06%
b.
15.46%
c.
14.76%
d.
15.18%
e.
13.35%
Chapter 08: Risk and Rates of Return
138. Data for Dana Industries is shown below. Now Dana acquires some risky assets that cause its beta to increase by
30.0%. In addition, expected inflation increases by 0.80%. What is the stock's new required rate of return? Do not round
your intermediate calculations.
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
0.80%
a.
12.80%
b.
15.87%
c.
16.00%
d.
9.98%
e.
11.90%
Chapter 08: Risk and Rates of Return
139. Mulherin's stock has a beta of 1.23, its required return is 11.75%, and the risk-free rate is 2.30%. What is the required
rate of return on the market? (Hint: First find the market risk premium.) Do not round your intermediate calculations.
a.
7.69%
b.
8.19%
c.
9.98%
d.
12.38%
e.
10.58%
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 1.55. What would the portfolio's new beta be? Do not round your intermediate
calculations.
a.
1.60
b.
1.32
c.
1.58
d.
1.61
e.
1.38
Chapter 08: Risk and Rates of Return
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.) Do
not round your intermediate calculations.
Year
Return
2013
21.00%
2012
-
12.50%
2011
35.00%
a.
30.02%
b.
18.79%
c.
23.43%
d.
27.09%
e.
24.41%
Chapter 08: Risk and Rates of Return
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.) Do not round your
intermediate calculations.
Economic
Conditions
Prob.
Return
Strong
30%
40.0%
Normal
40%
10.0%
Weak
30%
-16.0%
a.
21.71%
b.
25.18%
c.
22.58%
d.
17.59%
e.
24.75%
Chapter 08: Risk and Rates of Return
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 54% in ECB and the remainder in WCB? (Hint: Use the sample
standard deviation formula.) Do not round your intermediate calculations.
Year
ECB
WCB
1
40.00%
40.00%
2
-
10.00%
15.00%
3
35.00%
-5.00%
4
-5.00%
-
10.00%
5
15.00%
35.00%
Average return =
15.00%
15.00%
Standard deviation =
22.64%
22.64%
a.
3.59%
b.
4.27%
c.
2.99%
d.
3.99%
e.
4.51%
Chapter 08: Risk and Rates of Return
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 2.20%. You now receive another $14.50 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.) Do not round your intermediate calculations.
a.
6.81%
b.
7.82%
c.
6.56%
d.
7.31%
e.
6.31%
Chapter 08: Risk and Rates of Return
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 $29.50 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? Do not round your
intermediate calculations.
a.
2.08
b.
2.18
c.
2.60
d.
1.66
e.
1.87
Chapter 08: Risk and Rates of Return
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 2.00%. What rate of return should
investors expect (and require) on this fund? Do not round your intermediate calculations.
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.
11.16%
b.
10.82%
c.
9.93%
d.
9.37%
Chapter 08: Risk and Rates of Return
e.
9.71%
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? Do not round
your intermediate calculations.
a.
16.34%
b.
18.15%
c.
14.19%
d.
16.50%
e.
14.69%
Chapter 08: Risk and Rates of Return
