Chapter 10 CFIN6
Chapter 10 Solutions
10-1 a. 1 3
Operating income before depreciation $25,000 $25,000
Depreciation* (19,800) ( 9,000)
NOI 5,200 16,000
Taxes (0.40) ( 2,080) ( 6,400)
After-tax NOI $ 3,120 $ 9,600
*Depreciation, based on MACRS 3-year class:
Depreciation in Year 1 = $60,000(0.33) = $19,800
Depreciation in Year 3 = $60,000(0.15) = $ 9,000
10-2 a & b
1 2 3 4
Sales $92,000 $92,000 $92,000 $92,000
Operating costs (0,75 x Sales) (69,000) (69,000) (69,000) (69,000)
Depreciation (49,500) (67,500) (22,500) (10,500)
NOI (26,500) (44,500) 500 12,500
Annual Depreciation:
Depreciable basis $150,000
Depreciation rates 0.33 0.45 0.15 0.07
Depreciation amount $49,500 $67,500 $22,500 $10,500
Chapter 10 CFIN6
10-3 Purchase price $(350,000)
Shipping cost ( 20,000)
Installation cost ( 50,000)
Depreciable basis $420,000
Year Depreciation: MACRS 3-year class
10-4 Purchase price $(500,000)
Shipping & installation costs ( 75,000)
Depreciable basis $575,000
Year Depreciation: MACRS 3-year class
1 $115,000 = $575,000 x 0.20
10-5 a. Purchase price $(214,000)
Installation ( 26,000)
Depreciable basis $(240,000)
Year Depreciation: MACRS 3-year class
1 $48,000 = $240,000 x 0.20
b. Selling price at the end of four years = $80,000
Book value at the end of four years = $240,000 – $48,000 – $76,800 – $45,600 – $28,800
= $40,800
Alternative computation of BV: Because 83 percent of the depreciable basis has been depreciated, 17
percent remains (0.17 = 1.00 – 0.20 – 0.32 – 0.19 – 0.12). Thus, the depreciable basis is $40,800 =
$240,000(0.17).
Chapter 10 CFIN6
10-6 Because the depreciation expense is the same each year, the supplemental operating cash flow will be the
same for every year.
Operating savings $110,000
Depreciation ( 84,000) = ($840,000 – $0)/10
10-7 Depreciable basis = $120,000
1 2 3 4
Percent depreciated 0.33 0.45 0.15 0.07
Depreciation $39,600 $54,000 $18,000 $8,400
1 2 3 4
Savings $30,000 $30,000 $30,000 $30,000
Depreciation (39,600) (54,000) (18,000) ( 8,400)
NOI (9,600) (24,000) 12,000 21,600
10-8 a. Old Machine New Machine Difference
NOI, excluding depreciation $90,000 $90,000 $ 0
Depreciation (40,000) (35,000) 5,000
NOI 50,000 55,000 5,000
Chapter 10 CFIN6
b. Old Machine New Machine Difference
Net income $30,000 $33,000 $3,000
Depreciation 40,000 35,000 (5,000)
Supplemental operating CF $70,000 $68,000 $(2,000)
10-9 Selling price = $102,000
Book value = $90,000
10–10 Selling price = $4,000
Book value = $6,000
10–11 Initial investment outlay:
Purchase price $(432,000)
Installation ( 52,000)
Increase in net working capital ( 22,000)
Initial investment outlay $(506,000)
Chapter 10 CFIN6
Supplemental operating cash flows:
1 2 3
Savings $185,000 $185,000 $185,000
Depreciation (159,720) (217,800) ( 72,600)
NOI 25,280 ( 32,800) 112,400
Depreciation % 0.33 0.45 0.15
Depreciation = $484,000 x Deprec % $159,720 $217,800 $72,600
Alternative solution:
1 2 3
Savings $185,000 $185,000 $185,000
Taxes (0.40) ( 10,112) 13,120 ( 44,960)
Supplemental operating CF $174,888 $198,120 140,040
Terminal cash flow:
Selling price = $220,000
Cash flow timeline:
0 1 2 3
(506,000.00) 174,888 198,120 140,040
167,552
r = 14%
Chapter 10 CFIN6
Financial calculator solution:
CF0 = –506,000
CF1 = 174,888
NPV > 0, which means the setter should be purchased.
10–12 Initial investment outlay = Purchase price = $90,000
Supplemental operating cash flows:
1 2 3 4 5
Increase in operating income $29,800 $29,800 $29,800 $29,800 $29,800
Depreciation (29,700) (40,500) (13,500) ( 6,300) 0
NOI 100 (10,700) 16,300 23,500 29,800
Depreciable basis $90,000
Depreciation rates 0.33 0.45 0.15 0.07 0.00
Depreciation $29,700 $40,500 $13,500 $6,300 $0
Terminal cash flow:
Salvage value $8,000
Chapter 10 CFIN6
Financial calculator solution:
CF0 = -90,000
CF1 = 29,766
CF2 = 33,438
NPV > 0, which means the machine should be purchased.
10–13 Initial investment outlay:
Purchase price of new machine $(37,500)
Salvage of old machine 5,000
Tax on sale of old machine* 1,320
Initial investment outlay $(31,180)
*tax on sale of old machine = 0.4($5,000 – $8,300) = -$1.320, which represents a tax refund
Supplemental operating cash flows:
1 2 3
operating income $14,300 $14,300 $14,300
Cash Flow Timeline:
0 1 2 3 4 5
(90,000.00) 29,766 33,438 24,258 21,810 19,668
5,280
24,948
r = 15%
25,283.93
Chapter 10 CFIN6
Alternative solution:
Increase in operating income $14,300 $14,300 $14,300
Taxes ( 1,690) 110 ( 4,390)
Supplemental operating CF $12,610 $14,410 $ 9,910
Terminal cash flow:
Salvage value of new machine $6,000
Tax on sale of new machine (1,350) = 0.4($6,000 – $2,625)
Loss of sale of old machine (2,000)
Taxes on sale of old machine that are not paid 240 = 0.4($2,000 – $1,400)
Terminal cash flow $2,890
Cash Flow Timeline:
0 1 2 3
(31,180.00) 12,610 14,410 9,910
2,890
12,800
r = 11%
11,360.36
Chapter 10 CFIN6
Financial calculator solution:
CF0 = -31,180
CF1 = 12,610
CF2 = 14,410
10–14 Initial investment outlay:
Purchase price $(153,800)
Salvage value of old machine 10,860
Supplemental Operating Cash Flows:
1 2 3 4 5 6
operating income $40,000.0 $40,000.0 $40,000.0 $40,000.0 $40,000.0 $40,000.0
depreciation (22,760.0) (49,216.0) (29,222.0) (18,456.0) (16,918.0) ( 9,228.0)
Alternative solution:
Increase in operating income 40,000.0 40,000.0 40,000.0 40,000.0 40,000.0 40,000.0
Taxes ( 6,896.0) 3,686.4 ( 4,311.2) ( 8,617.6) ( 9,232.8) (12,308.8)
Supplemental operating CF 33,104.0 43,686.4 35,688.8 31,382.4 30,767.2 27,691.2
Depreciable basis—new machine: $153,800
Chapter 10 CFIN6
Financial calculator solution:
CF0 = -126,084.0
CF1 = 33,104.0
CF2 = 43,686.4
CF3 = 35,688.8
NPV > 0, which means the old machine should be replaced with the new machine
10–15 r = 4% + (11% – 4%)(0.8) = 9.6%
17
(1.096)
1
NPV $6,250 $29,500

−

=−

IRR = 10.95%
Calculator solution: CF0 = –29,500, CF1 – CF7 = 6,250, I = 9.6; compute NPV = 1,332.53; IRR = 10.95%
Cash Flow Timeline:
IRR = 15.97%
0 1 2 3 4 5 6
(126,084.00) 33,104.0 43,686.4 35,688.8 31,382.4 30,767.2 27,691.2
( 3,000.0)
24,691.2
r = 12%
29,557.14
34,826.53
13,613.80 = NPV
Chapter 10 CFIN6
Alternative calculator solution using TVM keys: N = 7, PV = -29,500, PMT = 6,250, FV = 0; compute I/Y
= 10.95% = IRR
The new division should be added, because NPV > 0.
IRR = 10.75%
Calculator solution: CF0 = -405,000, CF1 – CF3 = 165,000, I = 10.8; compute NPV = -380.36; IRR =
10.75%
10–17 NPV Probability NPV x Probability
$31,500 0.20 $6,300
19,800 0.70 13,860
-20,100 0.10 -2,010
E(NPV) = $18,150
CV = 0.75 < 0.80, so the project should be purchased.
10–18 NPV Probability NPV x Probability
$185,400 0.25 $46,350
128,300 0.60 76,980
-77,600 0.15 -11,640
E(NPV) = $111,690
Chapter 10 CFIN6
2 = 0.25($185,400 – $111,690)2 + 0.60($128,300 – $111,690)2 +0.15(-$77,600 – $111,690)2
The project should not be purchased, because CV > 0.70.
10–19 Project IRR Risk Risk-Adjusted r Acceptable?
P 10.0% Low 9% = 11% – 2% Yes, IRR > r (risk-adjusted)
10–20 Project IRR Risk Risk-Adjusted r Acceptable?