Chapter 13
Risk and Capital Budgeting
Discussion Questions
13-1. If corporate managers are risk-averse, does this mean they will not take risks?
Explain.
13-2. Discuss the concept of risk and how it might be measured.
Risk may be defined in terms of the variability of outcomes from a given
investment. The greater the variability, the greater the risk. Risk may be
13-3. When is the coefficient of variation a better measure of risk than the standard
deviation?
The standard deviation is an absolute measure of dispersion, while the
coefficient of variation is a relative measure and allows us to relate the standard
13-4. Explain how the concept of risk can be incorporated into the capital budgeting
process.
Risk may be introduced into the capital budgeting process by requiring higher
returns for risky investments. One method of achieving this is to use higher
13-5. If risk is to be analyzed in a qualitative way, place the following investment
decisions in order from the lowest risk to the highest risk:
New equipment
New market
Referring to Table 13-3, the following order would be correct:
13-6. Assume a company, correlated with the economy, is evaluating six projects, of
which two are positively correlated with the economy, two are negatively
correlated, and two are not correlated with it at all. Which two projects would
you select to minimize the company’s overall risk?
13-7. Assume a firm has several hundred possible investments and that it wants to
analyze the risk-return trade-off for portfolios of 20 projects. How should it
proceed with the evaluation?
The firm should attempt to construct a chart showing the risk-return
13-8. Explain the effect of the risk-return trade-off on the market value of common
stock.
High profits alone will not necessarily lead to a high market value for common
stock. To the extent large or unnecessary risks are taken, a higher discount rate
13-9. What is the purpose of using simulation analysis?
Simulation is one way of dealing with the uncertainty involved in forecasting
the outcomes of capital budgeting projects or other types of decisions. A Monte
Chapter 13
Problems
1. Risk-averse (LO13-2) Assume you are risk-averse and have the following three choices.
Which project will you select? Compute the coefficient of variation for each.
Expected
Value
Standard
Deviation
A $2,200 $1,400
B 2,730 1,960
C 2,250 1,490
13-1. Solution:
V
D
s
=
A. $1,440/$2,200 = .65
B. 1,960/2,730 = .72
C. $1,490/$2,250 = .66
Based on the coefficient of variation, you should select Project A
because it is the least risky.
2. Expected value and standard deviation (LO13-1) Myers Business Systems is evaluating
the introduction of a new product. The possible levels of unit sales and the probabilities of
their occurrence are given next:
Possible Sales
Market Reaction in Units Probabilities
Low response…………………………………….. 20 .10
Moderate response……………………………… 40 .30
High response…………………………………….. 55 .40
Very high response……………………………… 70 .20
a. What is the expected value of unit sales for the new product?
b. What is the standard deviation of unit sales?
13-2. Solution:
Myers Business Systems
a.
D DP=
å
D P DP
D
b.
2
( )D D Ps= –
å
D
D
( )D D–
2
( )D D–
P
2
( )D D–
P
3. Expected value and standard deviation (LO13-1) Sampson Corp. is evaluating the
introduction of a new product. The possible levels of unit sales and the probabilities of their
occurrence are given.
Possible
Market Reaction
Sales
in Units Probabilities
Low response…………………………………….. 30 .10
Moderate response……………………………… 50 .20
High response ……………………………………. 75 .40
Very high response …………………………….. 90 .30
a. What is the expected value of unit sales for the new product?
b. What is the standard deviation of unit sales?
13-3. Solution:
Sampson Corp
a.
D DP=
å
D P DP
370
4. Coefficient of variation (LO13-1) Shack Homebuilders Limited is evaluating a new
promotional campaign that could increase home sales. Possible outcomes and probabilities
of the outcomes are shown next. Compute the coefficient of variation.
Possible Outcomes
Additional
Sales in Units Probabilities
Ineffective campaign……………………………40 .30
Normal response…………………………………100 .30
Extremely effective……………………………..120 .40
13.4. Solution:
Shack Homebuilders Limited
Coefficient of Variation (V) = Standard Deviation / Expected
Value
D DP=
å
2
( )D D Ps= –
å
D
D
( )D D–
2
( )D D–
P
2
( )D D–
P
D
D
Standard Deviation Alternative 1
D
D
( )D D–
2
( )D D–
P
2
( )D D–
P
Coefficient of Variation (V) = Standard Deviation / Expected
Value
V
Alternative 1
32.09 .321
100 =
Alternative 1
57.00 .328
174 =
Alternative 3
91.00 .406
224 =
7. Coefficient of variation (LO1) Five investment alternatives have the following returns and
standard deviations of returns:
Alternative
Returns—
Expected Value
Standard
Deviation
A
………………………………………….. $ 5,000 $1,200
B
………………………………………….. 4,000 600
C
………………………………………….. 4,000 800
D
………………………………………….. 8,000 3,200
E
………………………………………….. 10,000 900
Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.
13-7. Solution:
Coefficient of variation (V) = Standard deviation/Mean return
Ranking from
lowest to highest
8. Coefficient of variation (LO13-1) Five investment alternatives have the following returns
and standard deviations of returns:
Alternative
Returns:
Expected Value
Standard
Deviation
A
………………………………………….. $ 1,980 $ 970
B
………………………………………….. 820 1,190
C
………………………………………….. 12,700 3,100
D
………………………………………….. 1,140 630
E
………………………………………….. 62,700 14,100
Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.