11-13 a. Old depreciation = $5,500 per year.
Book value = $55,000 – 5($5,500) = $27,500.
Gain = $35,000 – $27,500 = $7,500.
Tax on book gain = $7,500(0.35) = $2,625.
Price ($55,000)
b.
1
2
3
4
5
Old depreciation
5,500
5,500
5,500
5,500
5,500
Old tax shield
1,925
1,925
1,925
1,925
1,925
Basis
120,000
New depreciation
39,996
53,340
17,772
8,892
–
New tax shield
13,999
18,669
6,220
3,112
–
0
1
2
3
4
5
After tax savings
19,500
19,500
19,500
19,500
19,500
Depreciation tax shield new
13,999
18,669
6,220
3,112
–
Depreciation tax shield old
(1,925)
(1,925)
(1,925)
(1,925)
(1,925)
Opportunity cost of not selling old machine (after-tax)*
(13,000)
Total CF
(87,625)
31,574
36,244
23,795
20,687
4,575
c. NPV
(4,623)
The NPV is negative therefore, the firm should not replace the old machine.
*After-tax opportunity cost of not being able to sell old machine at end of its useful life.
11-14 a. Cost of new machine ($775,000)
Salvage value, old 135,000
Savings due to loss on sale ($450,000 – $135,000) 0.35 110,250
Cash outlay for new machine ($ 529,750)
MACRS Rate
33.33%
44.45%
14.81%
7.41%
0.00%
Answers and Solutions: 11 – 22
b. Recovery Depreciable Depreciation Depreciation Change in
1
2
3
4
5
Old depreciation
90,000
90,000
90,000
90,000
90,000
Old tax shield
31,500
31,500
31,500
31,500
31,500
Basis
775,000
MACRS depreciation rate
20.00%
32.00%
19.20%
11.52%
11.52%
New depreciation
155,000
248,000
148,800
89,280
89,280
New tax shield
54,250
86,800
52,080
31,248
31,248
Incremental depreciation
65,000
158,000
58,800
(720)
(720)
Incremental depreciation tax
shield
22,750
55,300
20,580
(252)
(252)
c. CFt = (Operating expenses)(1 – T) + (Depreciation)(T).
0
1
2
3
4
5
After tax cost savings
120,250
120,250
120,250
120,250
120,250
Incremental Depreciation tax
shield
22,750
55,300
20,580
(252)
(252)
Salvage value
83,874
Total CF
(529,750)
143,000
175,550
140,830
119,998
203,872
NPV
30,059
*The salvage value of the new machine is calculated as: Book value = 7.41%(775,000) =
NPV = $30,059
Since the NPV is positive, the project should be accepted. To buy the new machine
would increase the value of the firm by $30,059.
2. The higher capital cost should be used in the analysis.
Answers and Solutions: 11 – 23
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
11-15 a. Expected annual cash flows:
Project A: Probable
Probability Cash Flow = Cash Flow
Project B: Probable
Probability Cash Flow = Cash Flow
Coefficient of variation:
CV =
CVB = $5,797.84/$7,650 = 0.7579.
NPV Expected
=
valueExpected
deviation Standard NPV
b. Project B is the riskier project because it has the greater variability in its probable
cash flows, whether measured by the standard deviation or the coefficient of
variation. Hence, Project B is evaluated at the 12 percent cost of capital, while
Project A requires only a 10 percent cost of capital.
Project A: With a financial calculator, input the appropriate cash flows into the cash
flow register, input I/YR = 10, and then solve for NPV = $10,036.25.
Project B: With a financial calculator, input the appropriate cash flows into the cash
11-16 a. First, note that with symmetric probability distributions, the middle value of each
distribution is the expected value. Therefore,
Expected Values
Sales (units) 200
Sales price $13,500
Answers and Solutions: 11 – 25
c. (1) a. Calculate developmental costs. The 44 random number value, coming
between 30 and 70, indicates that the costs for this run should be taken to be
$4 million.
b. Calculate the project life. The 17, being less than 20, indicates that a 3–year
(3) Repeat the process for Year 2. Sales will be 200 with a random number of 79;
the price will be $13,500 with a random number of 83; and the cost will be
$7,000 with a random number of 86:
[200($13,500) – 200($7,000)](0.6) = $780,000 = CF2.
(5) a. 0 = – $4,000,000
IRR = -31.55%.
321 )IRR1(
000,510$
)IRR1(
000,780$
)IRR1(
000,510$
website, in whole or in part.
4000000, CF1 = 510000, CF2 = 780000, CF3 = 510000, and solve for IRR =
-31.55%.
b. NPV = – $4,000,000.
have been about $1 million.
321 )15.1(
000,510$
)15.1(
000,780$
)15.1(
000,510$
(6) & (7) The computer would store NPVs and IRRs for the different trials, then
of occurrence
X
XX
XXXX
X
XX
XXXX
the input and output distributions are badly skewed. The frequency
values would also be used to calculate σNPV and IRR; these values would
be printed out and available for analysis.
website, in whole or in part.
11-17 a. The resulting decision tree is:
NPV
t = 0 t = 1 t = 2 t = 3 P NPV Product
$3,000,000 0.24 $881,718 $211,612
($1,000,000) P = 0.5
($500,000) P = 0.5
P = 0.60
100,000 0.12 (376,709) (45,205)
($10,000) P = 0.20
The NPV of the top path is:
– – – $10,000 = $881,718.
3
)12.1(
000,000,3$
2
)12.1(
000,000,1$
1
)12.1(
000,500$
b. σ2NPV = 0.24($881,718 – $117,779)2 + 0.24(-$185,952 – $117,779)2
+ 0.12(-$376,709 – $117,779)2 + 0.4(-$10,000 – $117,779)2
= 198,078,470,853.
σNPV = $445,060.
CVNPV = = 3.78.
Since the CV is 3.78 for this project, while the firm’s average project has a CV of 1.0 to
779,117$
060,445$
website, in whole or in part.
SOLUTION TO SPREADSHEET PROBLEM
11-18 The detailed solution for the problem is available in the file Ch 11 P18 Build a Model