11-8 a. Sales = 1,000($138) $138,000
Cost = 1,000($105) 105,000
Net before tax $ 33,000
Taxes (34%) 11,220
(1 + rr)(1.06) = 1.15
Thus, the NPV considering inflation is calculated as
780,21$
should be accepted. This demonstrates the bias that inflation can induce into the
capital budgeting process: Inflation is already reflected in the denominator (the cost
of capital), so it must also be reflected in the numerator.
so the NPV = 256,520 – 150,000 = 106,520, which is the same answer we’d have
gotten above if in calculating the real required rate of return we had used enough
decimal places.
website, in whole or in part.
b. If part of the costs were fixed, and hence did not rise with inflation, then sales
revenues would rise faster than total costs. However, when the plant wears out and
solution to (a), or better, split the cash flows into two parts: a growing part that grows
at 6% and a non-growing part. Use the constant growth formula on the growing part
with g = 6%, and use the constant growth formula on the non-growing part with g =
0%.
11-9 First determine the net cash flow at t = 0:
Purchase price ($12,000)
Sale of old machine 4,150
a The market value is $4,150 – $3,550 = $600 above the book value. Thus, there is a $600 recapture of
depreciation, and Taylor would have to pay 0.40($600) = $240 in taxes.
b The change in net working capital is a $2,900 increase in current assets minus a $700 increase in current
liabilities, which totals to $2,200.
Now, examine the annual cash inflows:
After-tax revenue increase:
Depreciation:
Year 1 2 3 4 5 6
Newa $2,400 $8,840 $2,304 $1,382 $1,382 $691
b Depreciation tax savings = T(Depreciation) = 0.4(Depreciation).
Now recognize that at the end of Year 6 Taylor would recover its net working capital
investment of $2,200, and it would also receive $1,500 from the sale of the replacement
Finally, place all the cash flows on a time line:
0 1 2 3 4 5 6
| | | | | | |
Net investment (10290)
Opportunity cost of
old machine (480)
Project cash flows (10,290) 3,040 3,616 3,002 2,633 2,633 5,106
15%
11–10 1. Net investment at t = 0:
Cost of new machine $182,500
Net investment outlay (CF0) $182,500
2. After-tax
6 28,200 4,205 32,405
7 28,200 0 28,200
8 28,200 0 28,200
Notes:
2 0.3200 182,500 58,400
3 0.1920 182,500 35,040
4 0.1152 182,500 21,024
5 0.1152 182,500 21,024
-182,500 42,800 51,560 42,216 36,610 36,610 32,405 28,200 28,200
With a financial calculator, input the appropriate cash flows into the cash flow register,
input I/YR = 12, and then solve for NPV = $11,468.48. The NPV of the investment is
positive; therefore, the new machine should be bought.
$23.622
Answers and Solutions: 11 – 16
11-12 a.
0
1
2
3
4
5
Machine cost
(350,000)
Net working
capital
(35,000)
Cost savings
110,000
110,000
110,000
110,000
110,000
Depreciation
116,655
155,575
51,835
25,935
–
Op. Inc. before
taxes
(6,655)
(45,575)
58,165
84,065
110,000
Taxes
(2,662)
(18,230)
23,266
33,626
44,000
A-T operating
income
(3,993)
(27,345)
34,899
50,439
66,000
Add depreciation
116,655
155,575
51,835
25,935
–
Operating CF
112,662
128,230
86,734
76,374
66,000
Return of NWC
35,000
Sale of machine
33,000
Tax on sale
(13,200)
Total CF
(385,000)
112,662
128,230
86,734
76,374
120,800
NPV
15,732
IRR
11.64%
MIRR
10.88%
Cumulative CF
(385,000)
(272,338)
(144,108)
(57,374)
19,000
139,800
Payback
3.75
Notes:
a Depreciation Schedule, Basis = $250,000
MACRS Rate
Basis =
Year Beg. Bk. Value MACRS Rate Depreciation Ending BV
1 $350,000 0.3333 $ 116,665 $233,345
Answers and Solutions: 11 – 17
© 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.
b. If savings increase by 20%, then savings will be (1.2)($110,000) = $132,000.
If savings decrease by 20%, then savings will be (0.8)($110,000) = $88,000.
(1) Savings increase by 20%:
0
1
2
3
4
5
Machine cost
(350,000)
Net working capital
(35,000)
Cost savings
132,000
132,000
132,000
132,000
132,000
Depreciation
116,655
155,575
51,835
25,935
–
Op. Inc. before taxes
15,345
(23,575)
80,165
106,065
132,000
Taxes
6,138
(9,430)
32,066
42,426
52,800
A-T operating income
9,207
(14,145)
48,099
63,639
79,200
Add depreciation
116,655
155,575
51,835
25,935
–
Operating CF
125,862
141,430
99,934
89,574
79,200
Return of NWC
35,000
Sale of machine
33,000
Tax on sale
(13,200)
Total CF
(385,000)
125,862
141,430
99,934
89,574
134,000
NPV
65,770
IRR
16.67%
MIRR
13.53%
Cumulative CF
(385,000)
(259,138)
(117,708)
(17,774)
71,800
205,800
Payback
3.20
Answers and Solutions: 11 – 18
(2) Savings decrease by 20%:
0
1
2
3
4
5
Machine cost
(350,000)
Net working capital
(35,000)
Cost savings
88,000
88,000
88,000
88,000
88,000
Depreciation
116,655
155,575
51,835
25,935
–
Op. Inc. before taxes
(28,655)
(67,575)
36,165
62,065
88,000
Taxes
(11,462)
(27,030)
14,466
24,826
35,200
A-T operating
income
(17,193)
(40,545)
21,699
37,239
52,800
Add depreciation
116,655
155,575
51,835
25,935
–
Operating CF
99,462
115,030
73,534
63,174
52,800
Return of NWC
35,000
Sale of machine
33,000
Tax on sale
(13,200)
Total CF
(385,000)
99,462
115,030
73,534
63,174
107,600
NPV
(34,307)
IRR
6.33%
MIRR
7.97%
Cumulative CF
(385,000)
(285,538)
(170,508)
(96,974)
(33,800)
73,800
Payback
4.31
website, in whole or in part.
c. Worst-case scenario:
0
1
2
3
4
5
Machine cost
(350,000)
Net working capital
(40,000)
Cost savings
88,000
88,000
88,000
88,000
88,000
Depreciation
116,655
155,575
51,835
25,935
–
Op. Inc. before taxes
(28,655)
(67,575)
36,165
62,065
88,000
Taxes
(11,462)
(27,030)
14,466
24,826
35,200
A-T operating
income
(17,193)
(40,545)
21,699
37,239
52,800
Add depreciation
116,655
155,575
51,835
25,935
–
Operating CF
99,462
115,030
73,534
63,174
52,800
Return of NWC
40,000
Sale of machine
28,000
Tax on sale
(11,200)
Total CF
(390,000)
99,462
115,030
73,534
63,174
109,600
NPV
(38,065)
IRR
5.99%
MIRR
7.76%
Cumulative CF
(390,000)
(290,538)
(175,508)
(101,974)
(38,800)
70,800
Payback
4.35
Base-case scenario:
This was worked out in Part a. NPV = $37,035.13.
website, in whole or in part.
Best-case scenario:
0
1
2
3
4
5
Machine cost
(350,000)
Net working capital
(30,000)
Cost savings
132,000
132,000
132,000
132,000
132,000
Depreciation
116,655
155,575
51,835
25,935
–
Op. Inc. before
taxes
15,345
(23,575)
80,165
106,065
132,000
Taxes
6,138
(9,430)
32,066
42,426
52,800
A-T operating
income
9,207
(14,145)
48,099
63,639
79,200
Add depreciation
116,655
155,575
51,835
25,935
–
Operating CF
125,862
141,430
99,934
89,574
79,200
Return of NWC
30,000
Sale of machine
38,000
Tax on sale
(15,200)
Total CF
(380,000)
125,862
141,430
99,934
89,574
132,000
NPV
69,528
IRR
17.15%
MIRR
13.76%
Cumulative CF
(380,000)
(254,138)
(112,708)
(12,774)
76,800
208,800
Payback
3.14
Worst-case 0.35 ($ 38,065) ($ 13,323)
Base-case 0.35 15,732 5,506
Best-case 0.30 69,528 20,858
E(NPV) $13,041
CV = $43,289/13,041 = 3.32.