Solution Manual of Principles of Managerial Finance
Chapter 8 Risk and the Required Rate of Return
Problems
P8-1. Rate of return A financial analyst for Smart Securities Limited, Paul Chan, wishes to
estimate the rate of return for two similar-risk investments, A and B. Paul’s research
indicates that the immediate past returns will serve as reasonable estimates of future
returns. A year ago, investment A and investment B had market values of $63,000 and
$35,000, respectively. During the year, investment A generated cash flows of $6,100, and
investment B generated cash flows of $2,800. The current market values of investments
A and B are $71,000 and $32,000, respectively.
a. Calculate the expected rate of return on investments A and B using the most recent
year’s data
Calculate the expected rate of return on investments A on the following:
𝑟=
𝐶𝑡 + 𝑃𝑡 − 𝑃𝑡−1 $6,100 + ($71,000 − $63,000)
=
= 22.38%
𝑃𝑡−1
$63,000
Calculate the expected rate of return on investments B on the following:
𝑟=
𝐶𝑡 + 𝑃𝑡 − 𝑃𝑡−1 $2,800 + ($35,000 − $32,000)
=
= 18.13%
𝑃𝑡−1
$32,000
b. Investment A should be selected because it has a higher rate of return for the same
level of risk.
P8-2. Return calculations For each of the investments shown in the following table, calculate
the rate of return earned over the unspecified time period.
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Solution Manual of Principles of Managerial Finance
Investment
Calculation
𝐾𝑡 (%)
A
−$2,800 + ($20,100 − $23,400)
$23,400
−26.07%
B
16,000 + (324,000 − 225,000)
225,000
51.11%
C
700 + (8,000 − 6,500)
6,500
33.85%
D
3,580 + (46,500 − 36,600)
36,600
36.83%
E
−500 + (52,800 − 62,700)
62,700
−16.59%
P8-3. Risk preferences Stephen So, the financial manager for Cathay Pacific Incorporation,
wishes to evaluate three prospective investments: A, B, and C. Stephen will evaluate each
of these investments to decide whether they are superior to investments that his company
already has in place, which have an expected return of 15% and a standard deviation of
8%. The expected returns and standard deviations of the investments are as follows:
a. The risk-neutral manager would accept Investments A and B because these have
higher returns than the 12% required return and the risk don’t matter.
b. The risk-averse manager would accept Investment A because it provides the highest
return and has the lowest amount of risk. Investment B offers an increase in return for
taking on more risk than what the firm currently earns.
c. The risk-seeking manager would accept Investments B and C because he or she is
willing to take greater risk without an increase in return.
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Solution Manual of Principles of Managerial Finance
d. Traditionally, financial managers are risk-averse and would choose Investment A,
since it provides the required increase in return for an increase in risk.
P8 - 9.
Rate of return, standard deviation, and coefficient of variation Mike is searching
for a stock to include in his current stock portfolio. He is interested in Hi-Tech, Inc.;
he has been impressed with the company’s computer products and believes that HiTech is an innovative market player. However, Mike realizes that any time you
consider a technology stock, risk is a major concern. The rule he follows is to include
only securities with a coefficient of variation of returns below 0.90. Mike has
obtained the following price information for the period 2012 through 2015. Hi-Tech
stock, being growth-oriented, did not pay any dividends during these 4 years.
a. T
o
c
a
l
c
a. To calculate the rate of return for each year, 2012 through 2015, for Hi-Tech
stock.
Year
2012
2013
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Computation
$21.55 − $14.36
$14.36
64.78 − 21.55
21.55
Percentage (%)
50.07%
200.60%
Solution Manual of Principles of Managerial Finance
2014
2015
72.38 − 64.78
64.78
91.80 − 72.38
72.38
11.73%
26.83%
b. To calculate the average return over this time period:
50.07% + 200.60% + 11.73% + 26.83%
= 72.31%
4
c. To calculate the standard deviation of returns over the past 4 years.
𝜎𝑟2012−2015
=√
(50.07% − 72.31%)2 + (200.60% − 72.31%)2 + (11.73% − 72.31%)2 + (26.83% − 72.31%)2
(4 − 1)
= 86.97%
d. To determine the coefficient of variation of returns for the security:
𝐶𝑉 =
86.97%
= 1.20
72.31%
e. With his rule of only including securities with a coefficient of variation 0.90 less
than, he should not include Hi – Tech in his portfolio.
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