Chapter 13: Risk and Capital Budgeting
Calculator solution:
b.
Find the PV of cash inflow using a financial calculator at 15 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, enter 27,900 and press +|–, press the Enter key.
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.
a. Which investment should be made? (Note: In looking up present value factors for this
problem, you need to work with the concept of a deferred annuity for the Australian
mine. The returns in years 5 through 15 actually represent 11 years; the returns in
years 16 through 25 represent 10 years.)
b. If the Australian mine justifies an extra 2 percent premium over the normal cost of
capital because of its riskiness and relative uncertainty of cash flows, does the
investment decision change?
13-17. Solution:
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
5–15
$353,000
(15 – 4)
(6.462 – 2.974)
$1,231,264
16–25
$503,000
(25 – 15)
(7.330 – 6.462)
$ 436,604
The U.S. Mine
Years
Cash Flow
n Factor
PVIFA@13%
Present
Value
1–25
$282,000
(25)
7.330
$2,067,060
b. Recalculate the net present value of the Australian Mine at a
15 percent discount rate.
Years
Cash Flow
n Factor
PVIFA @ 15%
Present
Value
5–15
$353,000
(15 – 4)
(5.847 – 2.855)
$ 1,056,176
16–25
$503,000
(25 – 15)
(6.464 – 5.847)
$ 310,351
Present Value of Inflows $1,366,527
Present Value of Outflows $1,649,000
Chapter 13: Risk and Capital Budgeting
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
apartment complexes, Palmer Heights and Crenshaw Village. After conferring with the present
owners, Mr. Golff has developed the following estimates of the cash flows for these properties:
Palmer Heights
Crenshaw Village
Yearly Aftertax
Cash Inflow
(in thousands)
Probability
Yearly Aftertax
Cash Inflow
(in thousands)
Probability
$70 ……………..
.2
$75 …………….
.2
75 ……………..
.2
80 …………….
.3
90 ……………..
.2
90 …………….
.4
105 ……………
.2
100 …………..
.1
110 ……………
.2
a. Find the expected cash flow from each apartment complex.
b. What is the coefficient of variation for each apartment complex?
c. Which apartment complex has more risk?
13-18. Solution:
Mr. Sam Golff
D DP=
Palmer Heights
Crenshaw Village
D
P
DP
D
P
DP
70
.2
$14.0
75
.2
$ 15.0
75
.2
15.0
80
.3
24.0
90
.2
18.0
90
.4
36.0
105
.2
21.0
100
.1
10.0
110
.2
22.0
Chapter 13: Risk and Capital Budgeting
Expected Cash
Flow
$90.0
(thousands)
Expected Cash
Flow
$85.0
(thousands)
a. First find the standard deviation and then the coefficient of
variation.
V
D
=
Palmer Heights
D
D
()DD−
2
()DD−
P
2
()DD−
P
$70
$90
$–20
$400
.20
80
75
90
–15
225
.20
45
90
90
0
0
.20
0
105
90
+15
225
.20
45
110
90
+20
400
.20
80
250
250 $15.81 (thousands)
==
V = $15.81/$90 = .176
Crenshaw Village
D
D
()DD−
2
()DD−
P
2
()DD−
P
$75
$85
$–10
$100
.20
20.0
80
85
–5
25
.30
7.5
90
85
+5
25
.40
10.0
100
85
+15
225
.10
22.5
$60.0
60 $7.75 (thousands)
==
Chapter 13: Risk and Capital Budgeting
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?
13–26
13–19. Solution:
Allison’s Dresswear Manufacturers
a.
(1)
(2)
(3)
(4)
(5)
(6)
Expected
Sales
Probability
Present Value
of Cash Flows
from Sales
Initial Cost
NPV
(3) – (4)
Expected
NPV
(2) × (5)
Expand
Fantastic
.5
$221,000
$142,000
$79,000
$39,500
Wool
Moderate
.2
192,000
142,000
50,000
10,000
Sweaters
Low
.3
88,600
142,000
(53,400)
(16,020)
Expected
NPV
$33,480
Enter
Fantastic
.3
$341,000
$102,000
$239,000
$71,700
Cashmere
Moderate
.4
272,000
102,000
170,000
68,000
Sweaters
Low
.3
0
102,000
(102,000)
(30,600)
Expected
NPV
$109,100
b. The indicated investment, based on the expected NPV, is in the Cashmere sweater line.
Chapter 13: Risk and Capital Budgeting
20. Probability analysis with a normal curve distribution (LO13-4) When returns from a
project can be assumed to be normally distributed, such as those shown in Figure 13-6
(represented by a symmetrical, bell-shaped curve), the areas under the curve can be
determined from statistical tables based on standard deviations. For example, 68.26 percent
of the distribution will fall within one standard deviation of the expected value (
D
± 1σ).
Similarly, 95.44 percent will fall within two standard deviations (
D
± 2σ), and so on. An
abbreviated table of areas under the normal curve is shown next.
Number of σ’s
from Expected Value
+ or –
+ and –
0.5…………………..
0.1915
0.3830
1.0…………………..
0.3413
0.6826
1.5…………………..
0.4332
0.8664
1.65…………………
0.4505
0.9010
2.0 ………………….
0.4772
0.9544
Assume Project A has an expected value of $24,000 and a standard deviation (σ) of $4,800.
a. What is the probability that the outcome will be between $16,800 and $31,200?
b. What is the probability that the outcome will be between $14,400 and $33,600?
c. What is the probability that the outcome will be at least $14,400?
d. What is the probability that the outcome will be less than $31,900?
e. What is the probability that the outcome will be less than $19,200 or greater than
$26,400?
13-20. Solution:
a. Expected Value = $24,000, σ = $4,800
13-20. (Continued)
c. At least $14,400
$14,400 $24,000 $9,600 2
$4,800 $4,800
−−
d. Less than $31,900
$31,900 $24,000 $7,900 1.65
−==
$14,400
$31,900
.4772
.5000
.9772
Distribution
under the curve
.4505
.5000
Chapter 13: Risk and Capital Budgeting
13–29
13-20. (Continued)
e. Less than $19,200 or greater than $26,400
Area
$19,200 $24,000 $4,800 1 .3413 .5000 .3413 = .1587
$4,800 $4,800
$26,400 $24,000 $2,400 .3085
.5 .1915 .5000 .1915 =
$4,800 $4,800 .4672
−−
= = − −
−= = −
Distribution under the curve is .4672.
21. Increasing risk over time (LO13-1) The Oklahoma Pipeline Company projects the
following pattern of inflows from an investment. The inflows are spread over time to
reflect delayed benefits. Each year is independent of the others.
Year 1
Year 5
Year 10
Cash
Inflow
Probability
Cash Inflow
Probability
Cash
Inflow
Probability
55 …………..
.40
40 …….
.30
20 ………
.40
70 …………..
.20
70 …….
.40
70 ………
.20
85 …………..
.40
100 …….
.30
120 ………
.40
The expected value for all three years is $70.
a. Compute the standard deviation for each of the three years.
b. Diagram the expected values and standard deviations for each of the three years in a
manner similar to Figure 13-6.
c. Assuming 6 percent and 12 percent discount rates, complete the following table for
present value factors:
Year
PVIF
6%
PVIF
12%
Difference
1 ………
.943
.893
.050
5 ………
________
________
________
10 ………
________
________
________
$19,200
$26,400
Chapter 13: Risk and Capital Budgeting
13–30
d. Is the increasing risk over time, as diagrammed in part b, consistent with the larger
differences in PVIFs over time, as computed in part c?
e. Assume the initial investment is $135. What is the net present value of the investment
at a 12 percent discount rate? Should the investment be accepted?
13-21. Solution:
Oklahoma Pipeline Company
a. Standard deviation—year 1
D
D
()DD−
2
()DD−
P
2
()DD−
P
$55
70
–15
225
.40
90
70
70
0
0
.20
0
85
70
+15
225
.40
90
180
180 13.416
==
Standard deviation—year 5
D
D
()DD−
2
()DD−
P
2
()DD−
P
40
70
–30
900
.30
270
70
70
0
0
.40
0
100
70
+30
900
.30
270
540
540 23.24
==
Chapter 13: Risk and Capital Budgeting
13–31
13-21. (Continued)
Standard deviation—year 10
D
D
()DD−
2
()DD−
P
2
()DD−
P
20
70
–50
2,500
.40
1,000
70
70
0
0
.20
0
120
70
+50
2,500
.40
1,000
2,000
b. Risk over time
Dollars
Expected
Cash flow
($80)
$80
1 yr. 5 yr. 10 yr.
Time
c.
Year
(1)
PVIF
(2)
PVIF
(3)
PVIF
6%
12%
Difference
5
.747
.567
.180
10
.558
.322
.236
$80
($80)
Chapter 13: Risk and Capital Budgeting
13–32
13-21. (Continued)
d. Yes. The larger risk over time is consistent with the larger
differences in the present value interest factors (PVIF) over
time. In effect, future uncertainty is being penalized by a
lower present value interest factor (PVIF). This is one of the
consequences of using progressively higher discount rates
to penalize for risk.
Year
Inflow
PVIF (12%)
PV
1
$70
.893
$ 62.51
5
70
.567
$ 39.69
10
70
.322
$ 22.54
PV of Inflows
$124.74
Investment
$135.00
NPV
$ 10.26
e. Accept the investment.
22. Portfolio effect of a merger (LO13-5) Treynor Pie Company is a food company
specializing in high-calorie snack foods. It is seeking to diversify its food business and
lower its risks. It is examining three companies—a gourmet restaurant chain, a baby food
company, and a nutritional products firm. Each of these companies can be bought at the
same multiple of earnings. The following table represents information about all the
companies:
Company
Correlation
with Treynor
Pie Company
Sales
($ millions)
Expected
Earnings
($ millions)
Standard
Deviation
in Earnings
($ millions)
Treynor Pie Company ………….
+ 1.0
$126
$10
$4.0
Gourmet restaurant ………………
+ .4
63
9
1.4
Baby food company …………….
+ .3
52
5
1.6
Nutritional products
company …………………………..
− .7
77
7
3.2
a. Using the last two columns, compute the coefficient of variation for each of the four
companies. Which company is the least risky? Which company is the most risky?
b. Discuss which of the acquisition candidates is most likely to reduce Treynor Pie
Company’s risk. Explain why.
Chapter 13: Risk and Capital Budgeting
13–33
13-22. Solution:
Treynor Pie Company
a.
Standard deviation
Coefficient of variation ( ) Expected value
V=
(millions)
b. Because the nutritional products firm is highly negatively
correlated (–.7) with Treynor Pie Company, it is most likely
Chapter 13: Risk and Capital Budgeting
examining a plastics firm to add to its operations. Before the acquisition, the normal
expected outcomes for the firm were as follows:
Outcomes
($ millions)
Probability
Recession ……………………….
$20
.30
Normal economy ……………..
40
.40
Strong economy ………………
60
.30
After the acquisition, the expected outcomes for the firm would be:
Outcomes
($ millions)
Probability
Recession ……………………….
$10
.3
Normal economy ……………..
40
.4
Strong economy ………………
80
.3
a. Compute the expected value, standard deviation, and coefficient of variation before
the acquisition.
b. After the acquisition, these values are as follows:
Expected value ………………………………….
43.0 ($ millions)
Standard deviation ……………………………..
27.2 ($ millions)
Coefficient of variation ………………………
.633
Comment on whether this acquisition appears desirable to you.
c. Do you think the firm’s stock price is likely to go up as a result of this acquisition?
d. If the firm was interested in reducing its risk exposure, which of the following three
industries would you advise it to consider for an acquisition? Briefly comment on
your answer.
(1) Chemical company
(2) Oil company
(3) Computer company
13-23. Solution:
Hooper Chemical Co.
D DP=
D P PD