CHAPTER 9
CAPITAL BUDGETING: DECISION
CRITERIA AND REAL OPTION
CONSIDERATIONS
ANSWERS TO QUESTIONS:
1. The net present value method computes the present worth of a project's benefits over its
costs, evaluated using the firm's cost of capital. If a project has a positive net present value it
means that investors are receiving the minimum required rate of return, as measured by the
cost of capital, plus they are receiving something extra. This positive net present value is an
additional increment to shareholder wealth.
2. In the case of mutually exclusive investments it is possible for the net present value and
internal rate of return approaches to give conflicting rankings. This is most likely to occur
when the two or more projects being considered are significantly different in size or have
very different patterns of cash flows.
3. Multiple rates of return are likely to occur when a project's cash flow stream contains more
than one sign change (from positive to negative or negative to positive). Under these
circumstances it is best to use the net present value approach.
4. The profitability index defines the number of dollars of present value benefits that are
received for each dollar of net investment. Hence it provides a measure of relative
profitability. This measure can be used to guide a ranking of investment projects in a capital
rationing situation (see Table 9-5).
5. Strengths: Easy to use; may be used to consider a project's risk or its liquidity.
Weaknesses: Does not consider cash flows beyond payback period; ignores time value of
money; provides no objective criterion for decision making.
6. The objectives of a project post-audit/review are:
a. To identify systematic biases or errors in the cash flow estimates by individuals, departments,
plants or divisions. This analysis enables decision makers to make better evaluations of
investment proposals submitted in the future.
b. To determine whether a project which has not lived up to expectations should be continued or
abandoned.
7. In an inflationary environment, the level of capital expenditures by private firms tends to
decrease, because the cost of capital generally increases with inflation. It is possible that in
119
120  CHAPTER 9/CAPITAL BUDGETING
some cases inflation might increase projected revenues from a project more than projected
costs, thereby offsetting the increasing cost of capital. To the extent that this is not the case,
there will be a decline in capital investments.
8. The major problem is placing a dollar value on all costs and benefits generated by a project.
There tends to be more intangible costs and benefits in these types of projects. This makes
analysis more difficult and less precise.
9. MACRS pushes the tax benefits of the project forward to the first 8 years of the project's life,
thereby increasing the project's after-tax net cash flows in the early years and making it a
more attractive investment.
CHAPTER 9/CAPITAL BUDGETING  121
SOLUTIONS TO PROBLEMS:
1. NPV = -$20,000 + $3,000(PVIFA0.12,10)
= - $20,000 + $3,000(5.650) = -$3,050
PI = $3,000(5.650)/$20,000 = 0.85
The project is not acceptable because it has a negative NPV and a PI
of less than 1.0.
2. a
Net Present Value
Year
Cash Flows
PVIF @ 12%
Present Value
0
-$30,000
1.000
-$30,000
1
5,000
0.893
4,465
2
8,000
0.797
6,376
3
9,000
0.712
6,408
4
8,000
0.636
5,088
5
8,000
0.567
4,536
6
5,000
0.507
2,535
7
3,000
0.452
1,356
8
-1,500
0.404
-606
Net Present Value
$158
b. Because the project has a positive NPV it should be accepted.
c. The value of the firm, and therefore the shareholders’ wealth, is increased by $158 as a result
of undertaking the project.
122  CHAPTER 9/CAPITAL BUDGETING
3. Net investment = $8,000
NCF1-10 = (_R - _O - _Dep)(1 - T) + _Dep
= (0 - (-$1,554) - $800)(1 - .4) + $800 = $1,252.40
$8,000 = $1,252.40(PVIFAi,10)
PVIFAi,10 = 6.388 (From Table IV, r is between 9% and 10%)
(9.11% using a calculator)
4. Net investment = $375,000
a. NPV = -$375,000 + $80,000(PVIFA0.12, 9) + [$80,000 + $75,000
+ $100,000(1 - 0.4)] (PVIF0.12,10)
= - $375,000 + $80,000(5.328) + $215,000(0.322)
= $120,470
b. The project is acceptable, because its NPV is positive.
c. The value of the firm, and therefore the shareholders’ wealth, is increased by $120,470 as a
result of undertaking this project.
d. The IRR of this project is 18.71% using a calculator.
e. The net present value calculation assumes the net cash flows are reinvested at 12%, the
project’s required return. The internal rate of return calculation assumes the net cash flows are
reinvested at18.71%, the project’s IRR.
5. $12,000 = PV0(FVIF0.15,25) = PV0(32.919); PV0 = $364.53
6. After tax cost of net investment:
$100,000(1 - 0.4) = $60,000
NPV = -$60,000 + $10,000(PVIFA0.12,10)
+ $22,000(PVIFA0.12,10)(PVIF0.12,10)
= -$60,000 + $10,000(5.650) + $22,000(5.650)(0.322)
= $36,525
CHAPTER 9/CAPITAL BUDGETING  123
7. a
Project A: $20,000 = $10,000(PVIFAi,4)
PVIFAi,4 = 2.000
i = 34.9% from Table IV
Project B: $20,000 = $60,000(PVIFi,4)
PVIFi,4 = 0.333
i = 31.6% from Table II
b. NPVA = -$20,000 + $10,000(3.17) = $11,700
NPVB = -$20,000 + 60,000(0.683) = $20,980
c. Project B should be chosen because it has the higher NPV. It is assumed that the firm's
reinvestment opportunities are more accurately represented by the firm's cost of capital than
by the unique internal rate of return of either project in this case.
8. a. 0%: NPV = -$1,000 + $6,000/(1+0)1 - $11,000/(1+0)2
+ $6,000/(1+0)3 = 0
b. 100%: NPV = -$1,000 + $6,000/(1+1)1 - $11,000/(1+1)2
+ $6,000/(1+1)3 = -1,000 + 3,000 - 2,750 + 750 = 0
c. 200%: NPV = -$1,000 + $6,000/(1+2)1 - $11,000/(1+2)2
+ $6,000/(1+2)3 = -1,000 + 2,000 - 1,222.22
+ 222.22 = 0
9. Computation of net investment:
New unit cost
Plus: Installation cost:
Less: Proceeds from sale of old unit
$29,000
3,000
$1,000
Plus: Tax on gain from sale of old unit
($1,000)(.4)
Equals: Net investment
400
$31,400
124  CHAPTER 9/CAPITAL BUDGETING
Computation of net cash flows:
Annual depreciation on new device =
[$29,000 + 3,000]/20 years] = $1,600
Net cash flows1-19 = (R - O - Dep)(1 - T) + Dep
= (0 -(-$9,000) - $1,600)(1 - 0.4) +$1,600
= $6,040
Net cash flow20 = $6,040 + salvage = $6,040 + $2,000(1 - 0.4)
= $7,240
NPV = -$31,400 + $6,040(PVIFA0.12,19) + $7,240(PVIF0.12,20)
= -$31,400 + $6,040(7.366) + $7,240(.104) = $13,844
Therefore, the old control device should be replaced. Note that this problem addresses the unequal
project life problem by assuming that the old device could be operated indefinitely, with
appropriate maintenance outlays.
10. $1,230 = $800/(1 + i)1 + $200/(1 + i)2 + $400/(1 + i)3
Try i = 8%
$1,230 = $800(.926) + $200(.857) + $400(.794 ) = $1,229.8
Therefore IRR = 8%
CHAPTER 9/CAPITAL BUDGETING  125
11.
Project
Net Investment
NPV
PI
Rank
1
$200,000
$20,000
1.100
2
2
500,000
41,000
1.082
3
3
275,000
60,000
1.218
1
4
150,000
5,000
1.033
6
5
250,000
20,000
1.080
4 (tie)
6
100,000
4,000
1.040
5
7
275,000
22,000
1.080
4 (tie)
8
200,000
-18,000
0.910
7
Project
PI
Net Investment
Cum. Net Investment
Cum. NPV
3
1.218
$275,000
$275,000
$60,000
1
1.100
200,000
475,000
80,000
2
1.082
500,000
975,000
121,000
5
1.080
250,000
1,225,000
141,000
7
1.080
275,000
1,500,000
163,000
6
1.040
100,000
1,600,000
167,000
4
1.033
150,000
1,750,000
172,000
b. Projects 3, 1, and 2 should be adopted, using a total of $975,000 and leaving $25,000 unused.
c. If projects 3, 1, 5, and 7 are adopted, all funds will be expended and the aggregate NPV is
$122,000 vs. $121,000 when projects 3, 1, and 2 are adopted.
d. The opportunity cost of the unexpended funds is the amount of the unexpended funds times the
firm's cost of capital.
126  CHAPTER 9/CAPITAL BUDGETING
12. Net investment (cost of baboon) = $12,000
Annual depreciation on baboon = $12,000 /20 years
= $600
Net cash flow calculation:
NCF1-20 = (R - O - Dep)(1 - T) + Dep
= (0 - ($4,000 - $7,000) - 600)(1 - .4) + 600 = $2,060/year
NPV = - $12,000 + $2,040(7.963) = $4,245
Yes, buy the baboon, since NPV > 0.
13. a
NPV = -$10 + $20(PVIFk,1) + $5(PVIFk,2) - $17(PVIFk,3)
NPV @ k = 5%: -$10 + $20(.952) + $5(.907) - $17(.864) = -$1.11 million
NPV @ k = 10%: -$0.46 million
NPV @ k = 15%: -$0.01 million
NPV @ k = 30%: +$0.61 million
NPV @ k = 71%: +$0.01 million NPV @ k = 80%: -$0.26 million
b. The NPV is negative at discount rates between 0% and 15%, positive from 15% to 71% and
negative beyond 71%.
c. If L-S's cost of capital is 10%, the project is unacceptable (negative NPV).
If L-S's cost of capital is 20% the project is acceptable (positive NPV).
NPV @ k = 20%: -$10 + $20(.833) + $5(.694) - $17(.579)
= +$0.29 million
14. a
Net investment calculation:
Land
Plus: Packing equipment
Equals: Net investment
Net cash flow calculation:
$150,000
20,000
$170,000
CHAPTER 9/CAPITAL BUDGETING  127
Depreciation/year = $20,000/20 = $1,000/year
NCF1-10 = [200($400) - $50,000 - $1,000](1 - .3) + $1,000 = $21,300
NCF11-19 = [200($500) - $60,000 - $1,000](1 - .3) + $1,000 = $28,300
NCF20 = $28,300 + after-tax land value
Land value in 20 years = $150,000(FVIF0.05,20) = $150,000(2.653) = $397,950
Tax on gain from land sale:
Sale price of land
$397,950
Less: Original cost
150,000
Equals: Capital gain
$247,950
Times: Capital gains tax rate
Equals: Tax on gain
.30
$74,385
Land value net of taxes = $397,950 - $74,385 = $323,565
NCF20 = $28,300 + $323,565 = $351,865
NPV = -$170,000 + $21,300(5.426) + $28,300(5.132)(.295) + $351,865(.087) = $19,031
Yes, because NPV > 0
b. NCF20 = $28,300 + $50,000 + $100,000 loss(.30) = $108,300
NPV = -$170,000 + $21,300(5.426) + $28,300(5.132)(.295)
+ $108,300(.087) = $-2,160
No, because NPV < 0
15. a
Net investment: $80,000
b. Basis for MACRS depreciation = $80,000
First year revenues = $2 x 50,000 = $100,000; Revenues increase 7%/year; operating costs
increase at 8%/year.
128  CHAPTER 9/CAPITAL BUDGETING
Year
Revenues
Operating Costs
Depreciation
Tax
OEAT
NCF
1
$100,000
$50,000
$11,432
$15,427 $23,141
$34,573
2
107,000
54,000
19,592
13,363
20,045
39,637
3
114,490
58,320
13,992
16,871
25,307
39,299
4
122,504
62,986
9,992
19,810
29,716
39,708
5
131,080
68,024
7,144
22,365
33,547
40,691
6
140,255
73,466
7,136
23,861
35,792
42,928
7
150,073
79,344
7,144
25,434
38,151
45,295
8
160,578
85,691
3,568
28,528
42,791
46,359
9
171,819
92,547
0
31,709
47,563
47,563
10
183,846
99,950
0
33,558
50,338
50,338
c. NPV = -$80,000 + $34,573(.833) + $39,637(.694) + $39,299(.579)+ $39,708(.482) +
$40,691(.402)
+ $42,928(.335) + $45,295(.279) + $46,359(.233)
+ $47,563(.194) + $50,338(.162)
= $89,761
Yes, build the plant because NPV > 0.
d. Payback calculation:
Payback period is slightly more than two years because the sum of the first two years of
NCF is $74,210, compared to the NINV of $80,000.
e. The project has one internal rate of return because its cash flows have one sign change.
16. a
NPVA = -$30,000 + $10,000(3.433) = $4,330
NPVB = -$60,000 + $20,000(3.433) = $8,660
b. IRRA: $30,000 = $10,000(PVIFAr,5)
PVIFAr,5= 3.000
CHAPTER 9/CAPITAL BUDGETING  129
From Table IV, IRRA = 20% (19.86% by calculator)
IRRB: $60,000 = $20,000(PVIFAr,5)
PVIFAr,5= 3.000
From Table IV, IRRB = 20% (19.86% by calculator)
c. PIA = $34,330/$30,000 = 1.14
PIB = $68,660/$60,000 = 1.14
d. PBA = 3 years
PBB = 3 years
e. Monroe should accept project B because its NPV is positive and higher than the NPV of
project A.
17. $3,300,000,000 = $651,000,000(PVIFA0.19,n)
PVIFA0.19,n = 5.069
From Table IV, n __19
18. NINV = $31,400
Basis for MACRS depreciation: $32,000
NCF1 = (0 - (-$9,000) - $4,572.8)(1 - .40) + $4,572.8 = $7,229.12
NCF2 = (0 - (-$9,000) - $7,836.8)(1 - .40) + $7,836.8 = $8,534.72
NCF3 = (0 - (-$9,000) - $5,596.8)(1 - .40) + $5,596.8 = $7,638.72
NCF4 = (0 - (-$9,000) - $3,996.8)(1 - .40) + $3,996.8 = $6,998.72
NCF5 = (0 - (-$9,000) - $2,857.6)(1 - .40) + $2,857.6 = $6,543.04
NCF6 = (0 - (-$9,000) - $2,854.4)(1 - .40) + $2,854.4 = $6,541.76
NCF7 = (0 - (-$9,000) - $2,857.6)(1 - .40) + $2,857.6 = $6,543.04
NCF8 = (0 - (-$9,000) - $1,427.2)(1 - .40) + $1,427.2 = $5,970.88
NCF9-19 = (0 - (-$9,000) - 0)(1 - .40) + 0 = $5,400
NCF20 = $5,400 + $2,000(1 - .4) = $6,600
130  CHAPTER 9/CAPITAL BUDGETING
NPV = -$31,400+ $7,229.12(0.893) + $8,534.72(0.797)
+ $7,638.72(0.712) + $6,998.72(0.636) + $6,543.04(0.567)
+ $6,541.76(0.507) + $6,543.04 (0.452) + $5970.88(0.404)
+ $5,400(5.938)(.404) + $6,600(.104)
= $17,785
The NPV is higher with accelerated (MACRS) depreciation than with straight-line depreciation.
19. a. NPV = -$1,200,000 + $168,000(PVIFA0.12,10)
= -$1,200,000 + $168,000 (5.650)
= -$250,800
b. The project is unacceptable.
c. The project has one internal rate of return because its cash flows have only one sign change.
d. Internal rate of return calculation:
$1,200,000 = $168,000(PVIFAr,10)
PVIFAr,10 = 7.143
IRR = r = 6.64% (by calculator)
20. a
NPV = -$400,000 + $196,000(0.847) + $214,600(0.718)
+ $234,982(0.609) + $257,309(0.516) + $281,759(0.437)
$321,818(0.314) + $353,866(0.266)
+ $388,920(0.225) + $633,250(0.191)
= $830,970
b. Yes, the store has a positive net present value.
c. IRR = 57.1% (by calculator)
d. PI = 3.08, i.e., $1,230,970/$400,000.
+ $292,525(0.370) +
CHAPTER 9/CAPITAL BUDGETING  131
21. a
Net investment:
Installed cost
$15,000,000
Less: After-tax salvage (old)
-1,200,000
Less: Net working capital recovered from old asset
-1,000,000
Plus: Net working capital needed for new asset
Equals: Net investment
500,000
$13,300,000
b. Basis for MACRS depreciation = $15,000,000
Year
Revenues
Operating Costs
Depreciation
OEAT
NCF
1
$2,000,000
$-800,000
$2,143,500
$393,900
$2,537,400
2
2,000,000
-800,000
3,673,500
-524,100
3,149,400
3
2,000,000
-800,000
2,623,500
105,900
2,729,400
4
2,000,000
-800,000
1,873,500
555,900
2,429,400
5
2,000,000
-800,000
1,339,500
876,300
2,215,800
6
2,000,000
-800,000
1,338,000
877,200
2,215,200
7
2,000,000
-800,000
1,339,500
876,300
2,215,800
8
2,000,000
-800,000
669,000
1,278,600
1,947,600
9
2,000,000
-800,000
-
1,680,000
1,680,000
10
2,000,000
-800,000
-
1,680,000
2,180,000*
*Year 10 NCF includes impact of incremental net working capital change of -$500,000.
132  CHAPTER 9/CAPITAL BUDGETING
c. NPV = $-13,300,000 + $2,537,400 (0.870) + $3,149,400(0.756)
+ $2,729,400(0.658) + $2,429,400(0.572) + $2,215,800(0.497)
+ $2,215,200(0.432) + $2,215,800(0.376) + $1,947,600(0.327)
+ $1,680,000(0.284) + $2,180,000(0.247)
= $-982,149
22. IRRAlpha: $10,000 = $20,000 [1/(1 + r)1]
1+r=2
r = 1 (or 100%)
IRRBeta: $20,000 = $35,000 [1/(1 + r)1
1 + r = 1.75
r = 0.75 (or 75%)
NPVAlpha = - $10,000 + $20,000 (PVIF0.10,1)
= - $10,000 + $20,000 (0.909)
= $8,180
NPVBeta = - $20,000 + $35,000 (PVIF0.10,1)
= -$20,000 + $35,000 (0.909)
= $11,815
The company should accept project Beta because its NPV is positive and higher than the
NPV of project Alpha.
CHAPTER 9/CAPITAL BUDGETING  133
23. PVNCFf = SF5.0(4.833) = SF24.17 million
PVNCFh = SF24.17 x $0.16/SF = $3.87 million
NPV = $3.87 - $8.0 = $-4.13 million
The project is unacceptable.
24.
 Project evaluation is based on cash flows, not accounting earnings. The projects could have
deferred returns;
 Lack of profitability could be based on assets in place, not incremental investments;
 Risk projects that were not successful;
 The impact of competition; cost variations, etc.
 Possibly biased cash flow estimates.
25. No recommended solution.
SOLUTION TO INTEGRATIVE CASE PROBLEM:
CAPITAL BUDGETING
Net investment calculation:
Cost of equipment
Plus: Delivery and installation
Plus: Additional net working capital
Equals: Net investment
$1,000,000
100,000
50,000
$1,150,000
134  CHAPTER 9/CAPITAL BUDGETING
Net cash flow calculation:
Calculation of year 1 revenues:
Q = 20,000 - 200($14) = 17,200 units
Revenues = 17,200 units ($14 / unit)
= $240,800
Additional Working
Year
Revenues
Operating Costs*
Depreciation
Taxes
Capital
NCF
1
$240,800
$-100,000
157,190
$62,427
$25,000
$253,373
2
228,760
-93,700
269,390
18,044
-
304,416
3
217,322
-86,959
192,390
38,043
-
266,238
4
206,456
-79,746
137,390
50,596
-
235,606
5
196,133
-72,028
98,230
57,777
-
210,384
6
186,326
-63,770
98,120
51,672
-
198,424
7
177,010
-54,934
98,230
45,463
-
186,481
8
168,160
-45,480
49,060
55,957
-
157,683
9
159,752
-35,364
-
66,339
-
128,776
10
151,764
-24,539
-
59,943
-75,000
257,360**
* Operating costs reflect the $190,000 saving plus the annual operating costs (including costs
related to off-system sales) on the new system.
**Year 10 net cash flow includes recovery of $75,000 of net working capital and $66,000
recovery of after-tax salvage value.
NPV = $-1,150,000 + $253,373 (0.870) + $304,416(0.756)
+ $266,238(0.658) + $235,606(0.572) + $210,384(0.497)
+ $198,424(0.432) + $186,481(0.376) + $157,683(0.327)
+ $128,776(0.284) + $257,360(0.247)
= $22,624
Therefore the project is acceptable.
APPENDIX 9A
MUTUALLY EXCLUSIVE INVESTMENTS
HAVING UNEQUAL LIVES
SOLUTIONS TO PROBLEMS:
1. a.
NPVA = -$30,000 + $10,500(3.037) = $1,888.50
NPVB = -$30,000 + $6,500(4.968) = $2,292
b. NPVA(chain) = $1,888.50 - $30,000(PVIF.12,4 )
+ $10,500(PVIFA.12,4)(PVIF.12,4) = $3,089.59
c. Alternative A should be chosen because it has the higher positive net present value when the
two alternatives are compared for an equal period of time.
d. NPVA = $1,888.50 (from part a)
NPVB = $2,292 (from part a)
Equivalent annual annuity (A) = $1,888.5/3.037 = $621.83
Equivalent annual annuity (B) = $2,292/4.968 = $461.35
NPVA (infinite replacement) = $621.83/.12 = $5,181.92
NPVB (infinite replacement) = $461.35/.12 = $3,844.58
The equivalent annual annuity method also recommends project A.
2.
NPVP = - $100,000 + $22,000 (PVIFA0.12,10)
= - $100,000 + $22,000 (5.650)
= $24,300
NPVR = - $85,000 + $18,000 (PVIFA0.12,8)
= - $85,000 + $18,000 (4.968)
= $4,424
135
136  APPENDIX 9A/MUTUALLY EXCLUSIVE INVESTMENTS HAVING UNEQUAL LIVES
Equivalent annual annuity (P) = $24,300/(PVIFA0.12,10)
= $24,300/5.650
= $4,300.9
Equivalent annual annuity (R) = $4,424/(PVIFA0.12,8)
= $4,424/4.968
= $890.5
NPVP (assuming infinite replacement)
= $4,300.9/0.12 = $35,841
NPVR (assuming infinite replacement)
= $890.5/0.12 = $7,421
Investment P should be selected, because it has the higher net present value when evaluated over
an infinite replacement horizon.
3.
NPVA = - $50,000 + $25,000 (PVIFA0.19,3)
= - $50,000 + $25,000 (2.140)
= $3,500
NPVB = - $79,000 + $28,000 (PVIFA0.19,5)
= - $79,000 + $28,000 (3.058)
= $6,624
Equivalent annual annuity (A)
= $3,500/(PVIFA0.19,3)
= $3,500/2.140
= $1,636
Equivalent annual annuity (B)
= $6,624/3.058
= $2,166
= $6,624/(PVIFA0.19,5)
APPENDIX 9A/MUTUALLY EXCLUSIVE INVESTMENTS HAVING UNEQUAL LIVES  137
NPVA (assuming infinite replacement)
= $1,636/0.19 = $8,611
NPVB (assuming infinite replacement)
= $2,166/0.19 = $11,400
Investment B should be selected, because it has the higher net present value when evaluated over
an infinite replacement horizon.
4. a. NPVD = -$50,000 + $24,000(2.322) = $5,728
NPVE = -$50,000 + $15,000(3.889) = $8,335
b. NPVD (replacement chain)
= $5,728 - $50,000 (PVIF0.14, 3) + $24,000(PVIFA0.14, 3) (PVIF0.14, 3)
= $9,594
c. Investment D should be chosen because it has the higher positive net present value when the
two investments are compared for an equal period of time.
d. NPVD = $5,728 (from Part a)
NPVE = $8,335 (from Part a)
Equivalent annual annuity (D) = $5,728 / (PVIFA0.14, 3) = $2,467
Equivalent annual annuity (E) = $8,335 / (PVIFA0.14, 6) = $2,143
NPVD (assuming infinite replacement) = $2,467 / 0.14 = $17,621
NPVE (assuming infinite replacement) = $2,143 / 0.14 = $15,307
Investment D should be selected because it has the higher net present value when evaluated
over an infinite replacement horizon.