Chapter 13: Risk and Capital Budgeting
Chapter 13
Risk and Capital Budgeting
Discussion Questions
13-2.
Discuss the concept of risk and how it might be measured.
13-3.
When is the coefficient of variation a better measure of risk than the standard
deviation?
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
Chapter 13: Risk and Capital Budgeting
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:
a. New equipment
b. New market
c. Repair of old machinery
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?
Chapter 13: Risk and Capital Budgeting
13-8.
Explain the effect of the risk-return trade-off on the market value of common
stock.
13-9.
What is the purpose of using simulation analysis?
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.
VD
=
A. $1,440/$2,200 = .65
B. 1,960/2,730 = .72
C. $1,490/$2,250 = .66
Chapter 13: Risk and Capital Budgeting
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
Market Reaction
Sales
in Units
Probabilities
Low response ............................................
20
.10
Moderate response ....................................
40
.30
High response ...........................................
55
.40
Very high response ...................................
70
.20
Myers Business Systems
a.
D DP=
D P DP
60 =
D
b.
2
()D D P
=−
D
D
()DD−
2
()DD−
P
2
()DD−
P
55
50
+5
25
.40
10
70
50
+20
400
.20
80
210
Chapter 13: Risk and Capital Budgeting
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
13-3. Solution:
90 .30 27
70 =
D
D
P
50
70
–20
400
.20
80
Chapter 13: Risk and Capital Budgeting
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.
Shack Homebuilders Limited
Coefficient of Variation (V) = Standard Deviation / Expected
Value
D DP=
90=
D
Chapter 13: Risk and Capital Budgeting
2
()D D P
=−
D
D
()DD−
2
()DD−
P
2
()DD−
P
40
90
–50
2,500
.30
750
5. Coefficient of variation (LO13-1) Al Bundy is evaluating a new advertising program that
could increase shoe sales. Possible outcomes and probabilities of the outcomes are shown
next. Compute the coefficient of variation.
13-5. Solution:
Al Bundy
140 .30 42
Chapter 13: Risk and Capital Budgeting
D
P
6. Coefficient of variation (LO13-1) Possible outcomes for three investment alternatives and
their probabilities of occurrence are given next.
Alternative 1
Alternative 2
Alternative 3
Chapter 13: Risk and Capital Budgeting
135
0.4
54
225
0.4
90
380
0.2
76
225
174
+51
2,601
.4
1040.40
$3,234.00
D
Chapter 13: Risk and Capital Budgeting
380
224
+156
24,336
.2
4,867.20
$8,244.00
7. Coefficient of variation (LO1) Five investment alternatives have the following returns and
standard deviations of returns:
Returns—
Standard
13-7. Solution:
Chapter 13: Risk and Capital Budgeting
Coefficient of variation (V) = Standard deviation/Mean return
8. Coefficient of variation (LO13-1) Five investment alternatives have the following returns
and standard deviations of returns:
Returns:
Standard
13-8. Solution:
Chapter 13: Risk and Capital Budgeting
9. Coefficient of variation and time (LO13-1) Digital Technology wishes to determine its
coefficient of variation as a company over time. The firm projects the following data (in
millions of dollars):
Year
Profits:
Expected Value
Standard Deviation
1 ......................................
$180
$62
3 ......................................
240
104
6 ......................................
300
166
9 ......................................
400
292
a. Compute the coefficient of variation (V) for each time period.
Digital Technology
a.
Year
Profits:
Expected Value
Standard
Deviation
Coefficient
of Variation
1
180
62
.34
3
240
104
.43
6
300
166
.55
9
400
292
.73
b. Yes, the risk appears to be increasing over time. This may
be related to the inability to make forecasts far into the
future. There is more uncertainty.
10. Risk-averse (LO13-2) Tim Trepid is highly risk-averse, while Mike Macho actually
enjoys taking a risk.
Chapter 13: Risk and Capital Budgeting
Coefficient of Variation (V) = Standard Deviation / Expected
Value
Buy Stocks $6,140/9,140 = .672
Buy Bonds $2,560/7,680 = .333
Buy Commodity Futures $26,700/19,100 = 1.398
Buy Options $18,200/17,700 = 1.028
a. Tim should buy the bonds because bonds have the lowest
coefficient of variation.
b. Mike should buy the commodity futures because they have
the highest coefficient of variation.
11. Risk-averse (LO13-2) Mountain Ski Corp. was set up to take large risks and is willing to
take the greatest risk possible. Lakeway Train Co. is more typical of the average
corporation and is risk-averse.
a. Which of the following four projects should Mountain Ski Corp. choose? Compute
the coefficients of variation to help you make your decision.
b. Which one of the four projects should Lakeway Train Co. choose based on the same
criteria of using the coefficient of variation?
Chapter 13: Risk and Capital Budgeting
13-11. Solution:
Mountain Ski Corp. and Lakeway Train Co.
Coefficient of Variation (V) = Standard Deviation / Expected
Value
12. Coefficient of variation and investment decision (LO13-1) Kyle’s Shoe Stores Inc. is
considering opening an additional suburban outlet. An aftertax expected cash flow of $130
per week is anticipated from two stores that are being evaluated. Both stores have positive
net present values.
13-12. Solution:
Kyle’s Shoe Stores Inc.
Standard Deviations of Sites A and B
Chapter 13: Risk and Capital Budgeting
130
130
–0–
–0–
.3
–0–
160
130
+30
900
.1
90
170
130
+40
1,600
.3
480
$1,320
130
130
–0–
–0–
.3
–0–
VB = $65.08/$130 = .5006
Site A is the preferred site since it has the smallest coefficient of
Chapter 13: Risk and Capital Budgeting
5 ......................
30,000
The coefficient of variation for the project is .847.
Based on the following table of risk-adjusted discount rates, should the project be
undertaken? Select the appropriate discount rate and then compute the net present value.
Waste Industries
Year
Inflows
PVIF @ 14%
PV
1
$11,000
.877
$ 9,647
2
16,000
.769
12,304
3
21,000
.675
14,175
4
24,000
.592
14,208
5
30,000
.519
15,570
PV of Inflows
$65,904
Investment
70,000
NPV
$(4,096)
Based on the negative net present value, the project should not
be undertaken.
Calculator solution:
Find the PV of cash inflow using a financial calculator at 14 percent:
Chapter 13: Risk and Capital Budgeting
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, enter 70,000 and press +|–, press the Enter key.
Press down arrow, enter 11,000, and press Enter.
14. Risk-adjusted discount rate (LO13-3) Dixie Dynamite Company is evaluating two
methods of blowing up old buildings for commercial purposes over the next five years.
Method one (implosion) is relatively low in risk for this business and will carry a 12
percent discount rate. Method two (explosion) is less expensive to perform but more
dangerous and will call for a higher discount rate of 16 percent. Either method will require
an initial capital outlay of $75,000. The inflows from projected business over the next five
years are given next. Which method should be selected using net present value analysis?
Chapter 13: Risk and Capital Budgeting
Dixie Dynamite Co.
Method 1 Method 2
Year
Inflows
PVIF
@
12%
PV
Inflows
PVIF
@
16%
PV
1
$18,000
.893
$16,074
$20,000
.862
$17,240
2
24,000
.797
19,128
25,000
.743
18,575
3
34,000
.712
24,208
35,000
.641
22,435
4
26,000
.636
16,536
28,000
.552
15,456
5
14,000
.597
7,938
15,000
.476
7,140
NPV
$ 8,884
$ 5,846
Select Method 1
Calculator solution:
Method 1:
Find the PV of cash inflow using a financial calculator at 12 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, enter 75,000 and press +|–, press the Enter key.
Press down arrow, enter 18,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 24,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 34,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 26,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 14,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 12 and press Enter.
Chapter 13: Risk and Capital Budgeting
15. Discount rate and timing (LO13-1) Fill in the following table from Appendix B. Does a
high discount rate have a greater or lesser effect on long-term inflows compared to recent
ones?
Discount Rate
Years
5%
20%
1
.952
.833
10
.614
.162
20
.377
.026
The impact of a high discount rate is much greater on long-term
value. For example, after the first year, the high rate discount
value produces an answer that is 87.5 percent of the low
Chapter 13: Risk and Capital Budgeting
discount rate (.833/.952). However, after the 20th year, the high
rate discount rate is only 6.90 percent of the low discount rate
(.026/.377).
16. Expected value with net present value (LO13-1) Debby’s Dance Studios is considering
the purchase of new sound equipment that will enhance the popularity of its aerobics
9,930..............
.2
Debby’s Dance Studios
a. Expected Cash Flow
Cash Flow P
$4,570
×
.1
$ 457
5,550
×
.3
1,665
7,400
×
.4
2,960
9,930
×
.2
1,986
$7,068
b. Net Present Value (Appendix D)
$7,068 × 3.352 (PVIFA @ 15%, n = 5) =
Chapter 13: Risk and Capital Budgeting
$23,692 Present Value of Inflows
27,900 Present Value of Outflows
$(4,208) Net Present Value
c. Debby should not buy this new equipment because the net
present value is negative.
Calculator solution:
b.
Find the PV of cash inflow using a financial calculator at 15 percent:
17. Deferred cash flows and risk-adjusted discount rate Highland Mining and Minerals Co.
is considering the purchase of two gold mines. Only one investment will be made. The
Australian gold mine will cost $1,649,000 and will produce $353,000 per year in years 5
through 15 and $503,000 per year in years 16 through 25. The U.S. gold mine will cost
$2,054,000 and will produce $282,000 per year for the next 25 years. The cost of capital is
13 percent.
Highland Mining and Minerals Co.
a. Calculate the net present value for each project.
The Australian Mine
Chapter 13: Risk and Capital Budgeting
Years
Cash
Flow
n Factor
PVIFA@13%
Present
Value
16–25
$503,000
(25 – 15)
(7.330 – 6.462)
$ 436,604
Present Value of Inflows $1,667,868
1–25
$282,000
(25)
7.330
$2,067,060
Present Value of Inflows $2,067,060
Present Value of Outflows $2,054,000
Net Present Value $ 13,060
16–25
$503,000
(25 – 15)
(6.464 – 5.847)
$ 310,351
Chapter 13: Risk and Capital Budgeting
Net Present Value $ (282,473)
Now the decision should be made to reject the purchase of the
Australian Mine and purchase the U.S. Mine.
18. Coefficient of variation and investment decision (LO13-1) Mr. Sam Golff desires to
invest a portion of his assets in rental property. He has narrowed his choices down to two
Mr. Sam Golff
D DP=
Palmer Heights
Crenshaw Village
Chapter 13: Risk and Capital Budgeting
Expected Cash
Flow
$90.0
(thousands)
Expected Cash
Flow
$85.0
(thousands)
75
90
–15
225
.20
45
90
90
0
0
.20
0
105
90
+15
225
.20
45
D
P
$60.0
Chapter 13: Risk and Capital Budgeting
b. Based on the coefficient of variation, Palmer Heights has
more risk (.176 versus .091).
19. Decision-tree analysis (LO13-4) Allison’s Dresswear Manufacturers is preparing a
strategy for the fall season. One alternative is to expand its traditional ensemble of wool
sweaters. A second option would be to enter the cashmere sweater market with a new line
of high-quality designer label products. The marketing department has determined that the
wool and cashmere sweater lines offer the following probability of outcomes and related
cash flows:
Expand Wool
Sweaters Line
Enter Cashmere
Sweaters Line
Expected
Sales
Probability
Present Value
of Cash Flows
from Sales
Probability
Present
Value of
Cash Flows
from Sales
Fantastic ....................
.5
$221,000
.3
$341,000
Moderate ...................
.2
192,000
.4
272,000
Low ...........................
.3
88,600
.3
0
The initial cost to expand the wool sweater line is $142,000. To enter the cashmere sweater
line, the initial cost in designs, inventory, and equipment is $102,000.
a. Diagram a complete decision tree of possible outcomes similar to Figure 13-8. Note
that you are dealing with thousands of dollars rather than millions. Take the analysis
all the way through the process of computing expected NPV (the last column for each
investment).
b. Given the analysis in part a, would you automatically make the investment indicated?
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
Chapter 13: Risk and Capital Budgeting
