CHAPTER 10
CAPITAL BUDGETING AND RISK
ANSWERS TO QUESTIONS:
1. The net present value model handles risk by discounting expected cash flows from a project
by the firm's cost of capital. This discount rate is based upon the firm's average risk level. To
the extent that a project has more than or less than average risk, the use of the firm's cost of
capital will not make the appropriate risk adjustments. The basic model also does not
explicitly consider the variability of a project's returns.
2. Risk, in the context of capital budgeting, is the possibility that actual returns from a project
will differ from expected returns. It is often measured by the standard deviation of returns or
the coefficient of variation of returns.
3. The standard deviation is an appropriate measure of risk when independent projects are being
considered in a non-capital rationing situation. When two or more mutually exclusive
projects are being evaluated and the projects are of different size, the coefficient of variation
is a better measure.
4. The basic NPV model considers increasing risk over time by using a discount rate that is a
compound rather than a simple rate.
5. The portfolio effect of a new project on the risk of a firm should be considered when the
project is large and its returns are likely to be significantly less than perfectly correlated with
returns of the remainder of the firm. Large mergers, especially of the conglomerate type, are
one example of this type of project.
6. Advantages:
1. Explicitly recognizes the interactions among all variables that influence the NPV or IRR of a
project.
2. Provides a mean and standard deviation for a project's returns that enable a decision maker to
make explicit risk-return tradeoffs.
Disadvantages:
1. Expensive to construct detailed simulation models.
2. Difficult to model complex relationships among input variables.
7. Simulation provides the decision maker with a "best" estimate of the outcome of a project
and the ability to make probability statements about other possible outcomes. Based on this
information and the decision maker's utility function regarding risk and return, more
intelligent investment decisions may be made. If this process is used for all projects, the
average of realized returns for the firm should approximate the overall expected returns over
long periods of time.
139
140  CHAPTER 10/CAPITAL BUDGETING AND RISK
8. Insurance policies are purchased because they are a way of contractually reducing risk. The
popularity of the insurance contract indicates that many individuals and organizations have an
aversion to risk.
9. Certainty equivalent cash flow estimates are obtained by multiplying expected cash flows for
each period by a certainty equivalent factor for that period. These certainty equivalent factors
range from 1.0 (the case of certain returns or costs) to 0 (the case of maximum uncertainty).
These certainty equivalent factors are set at a level such that the decision-maker will be
indifferent between receiving the risky return and a (generally) smaller certain return.
10. No, the certainty equivalent factors which various individuals will assign to the cash flows
from a project depend upon that individual's perception of the riskiness of the projected cash
flows and the individual's relative risk aversion.
CHAPTER 10/CAPITAL BUDGETING AND RISK  141
SOLUTIONS TO PROBLEMS:
1. a
Expected annual cash flow = .1($1,000) + .2($1,500) + .4($2,000) + .2($2,500) +
.1($3,000) = $2,000
b. Standard deviation = [.1($1,000-$2,000)2
+ .2($1,500-$2,000)2 + .4($2,000 - $2,000)2
+ .2($2,500-$2,000)2 + .1($3,000-$2,000)2].5
= $547.72
c. Coefficient of variation = v = $547.72/$2,000 = 0.274
2. a. z = ($0 - $400,000)/$250,000 = -1.60
From Table V, P (z < -1.6) = 5.48%
The probability of the project having negative annual net cash flows is 5.48%.
b. z = ($575,000 - $400,000)/$250,000 = 0.70
From Table V, P (z > 0.70) = 24.20%
The probability of the project having annual net cash flows in excess of $575,000 is 24.2%.
3. z = ($0 - $100,000) / $50,000 = - 2.0
P(z < - 2.0) = 0.0228, or 2.28% from Table V
4. a
Project A is riskier using the standard deviation criterion because it has a larger standard
deviation than B.
b. Coefficient of variation calculation:
vA = $20,000/$50,000 = 0.4; vB = $7,000/$10,000 = 0.7
B is riskier using the coefficient of variation criterion.
c. Because the projects are significantly different in size, the coefficient of variation criterion, a
measure of relative risk, is more appropriate.
142  CHAPTER 10/CAPITAL BUDGETING AND RISK
5. If reducing the variability of the firm's earnings is the desired objective, purchasing the
supermarket chain is probably best. To reach this conclusion, it was necessary to assume that
the correlation of returns between the supermarket chain and the steel firm as a whole is less
than the correlation of returns between the new continuous caster and the steel firm as a
whole. This seems to be a reasonable assumption.
6.
a. ke = 8.0% + 1.5 (14% - 8%) = 17.0%
b. ke = 8.0% + 2.0(14% - 8%) = 20.0%
7. a. ßu = 1.5/[1 + (1 - 0.4)(.333/.667)] = 1.15
ßl = 1.15[1 + (1 - 0.4)(10/90)] = 1.23
ke = 8% + 1.23(15% - 8%) = 16.6%
b. ßu = 1.6/[1 + (1 - 0.35)(.20/.80)] = 1.38
ßl = 1.38[1 + (1 - 0.4)(10/90)] = 1.47
ke = 8% + 1.47(15% - 8%) = 18.3%
8. Payback: Project A = 3 years;
Project B = 4 years
Project B is unacceptable because its payback period is too long.
Net present value:
NPVA = -$50,000 + $20,000(.909) + $20,000(.826) + $10,000(.751) + $5,000(.683) +
$5,000(.621) = -$1,270
Project A is unacceptable because it fails to meet the NPV requirement. Therefore, neither
project should be undertaken by the company.
CHAPTER 10/CAPITAL BUDGETING AND RISK  143
9. a
NPV = -$1,800,000 + $400,000( (PVIFA.15,20)
NPV = -$1,800,000 + $400,000(6.259) = $703,600 @15% cost of capital
b. NPV @ 24% = -$1,800,000 + $400,000(4.110) = -$156,000
10. Net investment calculation:
Equipment cost
$200,000
Plus: Net working capital increase
Equals: Net investment
40,000
$240,000
Depreciation = $200,000/10 years = $20,000/year
Net cash flow calculation:
NCF1-5 = ($200,000 - $90,000 - $20,000)(1 - 0.4) + $20,000
NCF1-5 = $74,000
NCF6-9 = ($210,000 - $105,000 - $20,000)(1 - .4) + $20,000
NCF6-9 = $71,000
NCF10 = $71,000 + $50,000(1 - 0.4) + $40,000 (return of working capital)
NCF10 = $141,000
a. NPV @ 15% = -$240,000 + $74,000(3.352)
+ $71,000(2.855)(.497) + $141,000(.247)
= $143,619
b. NPV @ 24% = -$240,000 + $74,000(2.745)
+ $71,000(2.404)(.341) + $141,000(.116)
= $37,689
11. a
NPV @ 15% = -$35 + $5(.870) + $8(.756) + $15(.658)
+ $20(.572) + $15(.497) + $10(.432) + $4(.376)
144  CHAPTER 10/CAPITAL BUDGETING AND RISK
= $9.987 million
At a 15% rate, the project is acceptable.
b. Certainty equivalent NPV @ 9%:
NPV = -$35(1.0) + $5(.95)(.917) + $8(.9)(.842)+ $15(.8)(.772)
+ $20(.6)(.708) + $15(.4)(.65) + $10(.35)(.596) + $4(.3)(.547)
= -$0.1795 million
c. The project is unacceptable.
12. a. z = ($0 - $1,000,000)/$800,000 = -1.25
P(z < -1.25) = .1056 or 10.56% from Table V
b. z = ($2,200,000 - $1,000,000)/$800,000 = +1.5
P(z > 1.5) = .0668 or 6.68% from Table V
13. Net investment equals the equipment cost or $250,000
Annual depreciation = $250,000/10 years = $25,000/year
NCF1-10 = [5,000($50) - 5,000($25) - $25,000](1 - .4) + $25,000
= $85,000
a. NPV = -$250,000 + $85,000(PVIFA.12,10)
= -$250,000 + $85,000(5.65) = $230,250
b. NCF1-10 = [3,000($50) - 3,000($25) - $25,000](1 - .4)
+ $25,000 = $55,000
NPV = -$250,000 + $55,000(PVIFA.12,10)
= -$250,000 + $55,000(5.65) = $60,750
The NPV declines, but the project appears acceptable.
CHAPTER 10/CAPITAL BUDGETING AND RISK  145
14. a
NPV calculation:
NPV = -$70,000 + $30,000(.855) + $30,000(.731) + $30,000(.624)
+ $20,000(.534) + $20,000(.456) + $10,000(.390)
= $20,000
b. Certainty equivalent NPV:
NPV = -$70,000 + $30,000(.91)(.926) + $30,000(.79)(.857) + $30,000(.65)(.794) +
$20,000(.52)(.735)
+ $20,000(.40)(.681) + $10,000(.30)(.630)
= $6,056
15. a
Net investment calculation:
Equipment cost
$100,000
Plus: Installation and shipping
$10,000
Plus: Net working capital
$15,000
Equals: Net investment
$125,000
146  CHAPTER 10/CAPITAL BUDGETING AND RISK
b. Net cash flow calculation:
Operating
Year
Revenues
Costs
Depreciation
Tax
OEAT
NCF
1
$60,000
$15,000
$15,719
$11,712
$17,569 $33,288
2
63,600
16,200
26,939
8,184
12,277
39,216
3
67,416
17,496
19,239
12,272
18,409
37,648
4
71,461
18,896
13,739
15,530
23,296
37,035
5
75,749
20,407
9,823
18,208
27,311
37,134
6
80,294
22,040
9,812
19,377
29,065
38,877
7
85,111
23,803
9,823
20,594
30,891
40,714
8*
90,218
25,707
4,906
23,842
35,763
40,669
*Operating cash flows only
NCF8 = $40,669 + $12,000 (after tax salvage) + $15,000 (return of net working capital)
= $67,669
c. NPV @ 19%: -$125,000 + $33,288(.840) + $39,216(.706) + $37,648(.593) + $37,035(.499)
+ $37,134(.419)
+ $38,877(.352) + $40,714(.296) + $67,669(.249)
= $29,599
d. Certainty equivalent NPV @ 8%:
NPV = -$125,000(1.0) + $33,288(.95)(.926) + $39,216(.90)(.857) + $37,648(.80)(.794) +
$37,035(.60)(.735) +$37,134(.50)(.681)
+ $38,877(.45)(.630) + $40,714(.40)(.583)
+ $67,669(.35)(.540) = $20,727
CHAPTER 10/CAPITAL BUDGETING AND RISK  147
16. Expected value = $100,000; Most optimistic estimate = $175,000;
Most pessimistic estimate = $25,000
Most optimistic minus expected value = $175,000- $100,000 = $75,000
A z value from Table V that leaves 10 percent in either tail is approximately z = 1.28, therefore
z = 1.28 = $75,000
= $58,594
The probability of a value less than $0 is:
z = (0 - $100,000)/$58,594 = -1.71
p(z < - 1.71) ≈ 4.36%
17. ßu = ßl/[1 + (1-T)(B/E)] = 1.7/[1 + .6(60/40)] = 0.895
ßl = ßu[1 + (1-T)(B/E)] = 0.895[1 + .66(30/70)] = 1.15
ke = 8% + 1.15(8.3%) = 17.5%
IRR = 15% = .7(17.5%) + .3(ki)
ki = 9.2%
Therefore accept the project for any after-tax cost of debt of 9.2% or less.
18. a
NPV = - $10 million + $2 million (PVIFA0.12,10)
= - $10 million + $2 million (5.650)
= $1.3 million
b. NPV = - $10 million + $2 million (PVIFA0.17,10)
= - $10 million + $2 million (4.659)
= - $0.682 million
c. The project should not be accepted because its NPV is negative, using the 17% risk-adjusted
discount rate.
148  CHAPTER 10/CAPITAL BUDGETING AND RISK
19. P(IRR < 12%) = 10.0%
From Table V, 10.0% corresponds to - 1.28
Therefore, (12% - 18%) = -1.28
 = 4.69%
P(IRR < 14%):
z = (14% - 18%) / 4.69% = - 0.85
P(z < - 0.85) = 0.1977 or 19.8% from Table V
20. NPV = -$5.0 million + ($7.0 million + $0.5 million) / 1.15
= $1.52 million
21. z = ($0 - $3.0 million) / $ 4.0 million = - 0.75
P (z < - 0.75) = 0.2266 or 22.66% from Table V
The probability of the NPV being negative is 22.66%, which is less than 25%. Therefore, the
project should be undertaken.
22. Calculation of beta for Financial Services Division:
1.2 = 1.1 (0.4) + 1.6 (0.3) + ßFS (0.3)
ßFS = 0.93
Calculation of unlevered beta for Financial Services Division:
ßu = 0.93 / [1 + (1 - 0.4) (0.8)/0.2)]
= 0.27
Calculation of levered beta for Financial Services Division:
ßl = 0.27 [1 + (1 - 0.4) (0.9/0.1)]
= 1.73
Calculation of required return on equity for Financial Services Division:
ke = 9.0% + 1.73 (8.3%) = 23.4%
CHAPTER 10/CAPITAL BUDGETING AND RISK  149
Calculation of weighted marginal cost of capital for "new" projects in Financial Services
Division:
ka = (0.9) (19%) (1 - 0.4) + (0.1) (23.4%)
= 12.6%
23. P(NCF1 < - $10,000) = 10.0%
From Table V, 10.0% corresponds to -1.28
Therefore, z = -1.28, and - 1.28 = (- $10,000 - $50,000)/
 = $46,875
P(NCF1 < $0):
z = ($0 - $50,000)/$46,875 = - 1.07
P(z < - 1.07) = 0.1423 or 14.2% from Table V
24. z = ($1.0 million - $4.5 million)/$3.0 million
= - 1.17
P(z < - 1.17) = 0.1210 or 12.1% from Table V
P(NPV > $1,000,000) = 100% - 12.1% = 87.9%
25. Unlever beta for Dietz:
u = 1.2 / [1 + (1 - 0.4)(0.4 / 0.60] = 0.86
Relever beta for Muench:
l = 0.86[1 + (1 - 0.4)(0.2 / 0.8)] = 0.99
Required equity return for Muench:
ke = 7% + 0.99(7.4%) = 14.3%
Risk-adjusted required return for the Retail Outlet division of Muench:
ka = 12%(1 - 0.4)(0.2) + 14.3%(0.8) = 12.9 %
150  CHAPTER 10/CAPITAL BUDGETING AND RISK
26. NPV = -$15,000 + $10,000(PVIF0.12,1) + $8,000(PVIF0.12,2) + $7,000(PVIF0.12,3)
+ $6,000(PVIF0.12,4) = $9,102 (by calculator)
(Note, the return of NWC in year 4 is included in the NCF figure of $6,000 for that year.)
z = (0 - $9,102) / $3,000 = -3.03
p (z < - 3.03) = 0.0012 or 0.12%
Hence the probability of success is %100 - 0.12% = 99.88%
27. No recommended solution.
28. Plus or minus 10% corresponds to plus or minus 1.28
$4 million – $1.5 million = 1.28

= $1.95 million
a. The probability that the project will be acceptable is equal to the probability of it having an
NPV great than $0, or:
z = [$0 - $1.5] / 1.95 = -0.77
p ( z< -0.77) = 22%
Hence, the probability of a value greater than 0 is 100% - 22% = 78%
b. z = [$1 - $1.5] / $1.95 = -0.26
p ( z< -0.26= 40
Hence, the probability of a value greater than $1 million is
100% -40% = 60%
29. a. The distance from the mean of $-5 million to the most pessimistic estimate of $-20
million is $15 million. This represents 1.645 standard deviations on a normal distribution.
Hence:
1.65$15 million
CHAPTER 10/CAPITAL BUDGETING AND RISK  151
$ 9.119 million
The probability that this project will be acceptable is the probability of having a net present
value greater than $0. The z-score calculation is:
Z = [0 – ( - 5 million)] / 9.119 million = 0.55
From Table V, the probability of having an NPV greater than 0.55 is 29.12%.
b. Other factors to consider:
 Real options to expand, cancel and for production flexibility
 Impact on existing product lines
 How does this impact the risk of bankruptcy?
 Competitive responses.
SOLUTION TO INTEGRATIVE CASE PROBLEM:
CAPITAL BUDGETING AND RISK ANALYSIS
1. Calculation of net investment:
New equipment
Plus: Installation costs
$275,000
25,000
Plus: Net working capital
150,000
Equals: Net investment
$450,000
152  CHAPTER 10/CAPITAL BUDGETING AND RISK
2.
Operating
Year
Revenues
Costs
Depreciation
Tax
OEAT
NCF
1
$842,875
$600,000
$42,870
$80,002
$120,003
$162,873
2
893,448
666,000
73,470
61,591
92,387
165,857
3
947,054
739,260
52,470
62,130
93,194
145,664
4
1,003,878
820,579
37,470
58,332
87,497
124,967
5
1,064,110
910,842
26,790
50,591
75,887
102,677
6
1,127,957
1,011,035
26,760
36,065
54,097
80,857
7
1,195,634
1,122,249
26,790
18,638
27,957
54,747
8
1,267,372
1,245,696
13,380
3,318
4,978
18,358
9
1,343,415
1,382,723
0
-15,723
-23,585
-23,585
10*
1,424,020
1,534,822
0
-44,321
-66,481
-66,481
*Operating cash flow only for year 10
NCF10 = $-66,481 + $30,000 (after tax salvage) + $150,000 (recovery of net working capital)
= $113,519
3. NPV @ 15% = $118,211 (using a calculator)
4. Yes. The project has a positive net present value.
5. Yes. Net cash flows for the first three years total $474,394, which exceeds the NINV of
$450,000. Thus the payback period is less than 3 years.
6. NPV @ 20% = $47,122 (using a calculator)
CHAPTER 10/CAPITAL BUDGETING AND RISK  153
7.
Operating
Year
Revenues
Costs
Depreciation
Tax
OEAT
NCF
1
$674,300
$600,000 $42,870
$12,572 $18,858
$61,728
2
714,758
666,000
73,470
-9,885
-14,827
58,643
3
757,643
739,260
52,470
-13,635 -20,452
32,018
4
803,102
820,579
37,470
-21,979 -32,968
4,502
5
851,288
910,842
26,790
-34,538 -51,806
-25,016
6
902,366
1,011,035 26,790
-54,172 -81,257
-54,497
7
956,507
1,122,249 26,790
-77,013 -115,519 -88,729
8
1,013,898
1,245,696 13,380
-98,071 -147,107 -133,727
9
1,074,732
1,382,723 0
-123,196 -184,795 -184,795
10*
1,139,216
1,534,822 0
-158,242 -237,364 -237,364
*Operating cash flow only for year 10
NCF10 = -$237,364 + $30,000 (after tax salvage) + $150,000 (recovery of net working
capital) = -$57,364
NPV @ 20% = -$466,382
Therefore, do not make the investment.
154  CHAPTER 10/CAPITAL BUDGETING AND RISK
8.
Operating
Year
Revenues
Costs
Depreciation
Tax
OEAT
1
$842,875
$600,000 $42,870
$80,002 $120,003 $162,873
2
893,448
678,000
73,470
56,791 85,187
158,657
3
947,054
766,140
52,470
51,378 77,066
129,536
4
1,003,878
865,738
37,470
40,268 60,402
97,872
5
1,064,110
978,284
26,790
23,614 35,422
62,212
6
1,127,957
1,105,461 26,790
-1,706
24,202
7
1,195,634
1,249,171 26,790
-32,131 -48,196
-21,406
8
1,267,372
1,411,563 13,380
-63,028 -94,543
-81,163
9
1,343,415
1,595,067 0
-100,661 -150,991 -150,991
10*
1,424,020
1,802,425 0
-151,362 -227,043 -227,043
-2,558
NCF
*Operating cash flow only for year 10
NCF10 = -$227,043 + $30,000 (after tax salvage) + $150,000 (recovery of net working
capital) = -$47,043
NPV @ 20% = -$110,536
Do not establish the collection subsidiary under these conditions.