Chapter 12 Solutions
E12.1 Owners’ equity = $2,690,000 - $1,600,000 = $1,090,000. Weighted average cost of capital = ($1,600,000/$2,690,000 * 0.09) + ($1,090,000/$2,690,000 * 0.14) =
11.03%
E12.2 ($1,600,000/$2,690,000 * 0.11) + ($1,090,000/$2,690,000 * 0.14) = 12.22%
E12.3 ANN = $8,857, n = 10, c = 1, r = 12, FV = 0, PV = $50,044.03
NPV = $50,044.03 - $46,200 = $3,844.03. The company should buy the machine.
E12.4 ANN = $2,850, n = 5, c = 1, r = 14, FV = 0, PV = $9,784.28. The maximum amount the United Way should pay is $9,784.28.
NPV = $9,784.28 - $9,000 = $784.28. Since the NPV is positive, they should acquire the machine
E12.5 ANN = $192,850, n = 8, c = 1, r = 14, FV = 0, PV = $894,604.90
NPV = $894,604.90 - $958,000 = ($63,395.10). They should not buy the machine.
E12.6 c = 1, r = 15, ANN = 0, FV = $14,000, n = 1, PV = $12,173.91 c = 1, r = 15, ANN = 0, FV = $12,000, n = 2, PV = 9,073.72 c = 1, r = 15, ANN = 0, FV = $10,000, n = 3, PV = 6,575.16 c = 1, r = 15, ANN = 0, FV = $8,000, n = 4, PV = 4,574.03 c = 1, r = 15, ANN = 0, FV = $6,000, n = 5, PV = 2,983.06 c = 1, r = 15, ANN = 0, FV = $4,000, n =6, PV = 1,729.31
Total present value
Initial investment
NPV
E12.11
Murdock should not purchase the copier.
$37,109.19
(42,600.00)
$(5,490.81)
Year
1
After-tax
Cash Inflow
$7,490
After-tax Cash
Outflow
$1,890
Tax Shield After-tax
Cash Flows
$2,800 $8,400
2
3
7,490
7,490
2,275
2,800
3,734
1,244
8,949
5,934
4 7,490 3,150 623 4963
E12.12 Book value = $155,000 - $50,700 = $104,300
Proceeds
Less BV
Gain
$116,000 Gain $11,700 Proceeds $116,000
(104,300) Tax 0.30 Tax paid
$ 11,700 Tax paid $ 3,510
3,510
Cash inflows $112,490
Proceeds
Less BV
Loss
$ 94,000
(104,300)
$ 10,300
Loss $10,300
Tax 0.30
Tax saved $ 3,090
Proceeds
Tax saved
$94,000
3,090
Cash inflows $97,090

E12.13 After-tax cash flows:
2008 $42,000 * 0.7 = $29,400 c = 1, r = 12, ANN = 0, FV = $29,400, n = 1, PV = $ 26,250.00
2009 $48,000 * 0.7 = $33,600 c = 1, r= 12, ANN = 0, FV = $33,600, n = 2, PV = 26,785.71
2010 $50,000 * 0.7 = $35,000 c = 1, r = 12, ANN = 0, FV = $35,000, n = 3, PV = 24,912.31
2011 $46,000 * 0.7 = $32,200 c = 1, r = 12, ANN = 0, FV = $32,200, n = 4, PV = 20,463.68
2012 $32,000 * 0.7 = $22,400 c = 1, r = 12, ANN = 0, FV = $22,400, n = 5, PV = 12,710.36
2013 $51,000 * 0.7 = $35,700 c = 1, r = 12, ANN = 0, FV = $35,700, n = 6, PV = 18,086.73
2014 $34,000 * 0.7 = $23,800 c = 1, r = 12, ANN = 0, FV = $23,800, n = 7, PV = 10,765.91
Tax shield:
$196,000/7 = $28,000 depreciation * 0.3 = $8,400 tax shield c = 1, r = 12, FV = 0, ANN = $8,400 , n = 7, PV = 38,335.55
Total present value
Initial investment
NPV
Alvarado should not investment in this machine.
$178,310.25
(196,000.00)
$(17,689.75)
E12.17 Investment A:
Tax shield:
$26,000 * 0.3 = $7,800 c = 1, r = 12, FV = 0, ANN = $7,800, n = 4, PV =
After-tax cash flows:
2006 $38,000 * 0.7 = $26,600 c = 1, r = 12, ANN = 0, FV = $26,600, n = 1, PV =
2007 $42,000 * 0.7 = $29,400 c = 1, r = 12, ANN = 0, FV = $29,400, n = 2, PV =
2008 $34,000 * 0.7 = $23,800 c = 1, r = 12, ANN = 0, FV = $23,800, n = 3, PV =
2009 $36,000 * 0.7 = $25,200 c = 1, r = 12, ANN = 0, FV = $25,200, n = 4, PV =
Total present value of cash flows
Initial investment
NPV
Investment B:
Tax shield:
$25,000 * 0.3 = $7,500 c = 1, r = 12, FV = 0, ANN = $7,500, n = 6, PV =
After-tax cash flows:
2006 $48,000 * 0.7 = $33,600
$ 23,691.32
23,750.00
23,437.50
16,940.37
16,015.06
$103,834.25
(104,000.00)
$ (165.75)
$ 30,835.55

c = 1, r = 12, ANN = 0, FV = $33,600, n = 1, PV =
2007 $46,000 * 0.70 = $32,200 c = 1, r = 12, ANN = 0, FV = $32,200, n = 2, PV =
2008 $60,000 * 0.7 = $42,000 c = 1, r = 12, ANN = 0. FV = $42,000, n = 3, PV =
2009 $51,000 * 0.7 = $35,700 c = 1, r = 12, ANN = 0, FV = $35,700, n = 4, PV =
2010 $53,000 * 0.7 = $37,100
30,000.00
25,669.64
29,894.77
22,688.00 c = 1, r = 12, ANN = 0, FV = $37,100, n = 5, PV =
2011 $52,000 * 0.7 = $36,400 c = 1, r = 12, ANN = 0, FV = $36,400, n = 6, PV =
Total present value of cash flows
Initial investment
NPV
21,051.54
18,441.37
$178,580.87
(150,000.00)
$ 28,580.87
Chin Imports should invest in Investment B. However since Investment A is only slightly negative, Chin should consider whether other balanced scorecard goals would make this investment desirable.
E12.18 2007 c = 1, ANN = 0, r = 12, FV = $240,000, n = 1, PV =
2008 c = 1, ANN = 0, r = 12, FV = $260,000, n = 2, PV =
2009 c = 1, ANN = 0, r = 12, FV = $253,000, n = 3, PV =
2010 c = 1, ANN = 0, r = 14, FV = $290,000, n = 4, PV =
$ 214,285.71
207,270.41
180,080.40
171,703.28
161,004.29
101,140.21
90,224.89
71,918.39
$1,197,627.58
(1,040,000.00)
$ 157,627.58
2011 c = 1, ANN = 0, r = 14, FV = $310,000, n = 5, PV =
2012 c = 1, ANN = 0, r = 14, FV = $222,000, n = 6, PV =
2013 c = 1, ANN = 0, r = 15, FV = $240,000, n = 7, PV =
2014 c = 1, ANN = 0, r = 15, FV = $220,000, n = 8, PV =
Total present value of cash flows
Initial investment
NPV
Sprague should invest in the diagnostic machine.
P12.4 a. 2006: $21,500 * 0.7 = $15,050
$80,000 * 0.1429 * .3 = $3,429.60 c = 1, r = 14, ANN = 0, FV = $18,479.60, n = 1, PV =
2007: $25,000 * 0.7 =$17,500
$80,000 * 0 .2449 * .3 = $5,877.60 c = 1, r =14, ANN = 0, FV = $23,377.60, n = 2, PV =
2008: $22,000 * 0.7 = $15,400
$80,000 * 0.1749 * 0.3 = $4,197.60 c = 1, r = 14, ANN = 0, FV = $19,597.60, n = 3, PV =
2009: $20,000 * 0.7 = $14,000
$80,000 * 0.1249 * 0.3 = $2,997.60 c = 1, r = 14, ANN = 0, FV = $16,997.60, n = 4, PV =
2010: $19,000 * 0.7 = $13,300
$80,000 * 0.0893 * 0.3 = $2,143.20
$ 16,210.18
17,988.30
13,227.82
10,063.94

b. c = 1, r = 14, ANN = 0, FV = $15,443.20, n = 5, PV =
2011: $17,500 * 0.7 = $12,250
$80,000 * 0.0892 * 0.3 = $2,140.80 c = 1, r = 14, ANN = 0, FV = $14,390.80, n = 6, PV =
2012: $16,000 * 0.7 = $11,200
$80,000 * 0.0893 * 0.3 = $2,143.20 c = 1, r = 14, ANN = 0, FV = $13,343.20, n = 7, PV =
2013: $14,000 * 0.7 = $9,800
8,020.71
6,556.25
5,332.44
$80,000 * 0.0446 * 0.3 = $1,070.40 c = 1, r = 14, ANN = 0, FV = $10,870.40, n = 8, PV =
Total present value of cash flows
Initial investment
NPV
3,810.72
$ 81,210.36
(80,000.00)
$ 1,210.36
Yes, because the NPV is positive indicating that the expected return on the investment is greater than the cost of capital.
P12.5 a. Sale of old boat:
Proceeds $32,000 Gain on sale $4,000 Proceeds $32,000
- BV 28,000 Tax rate 0.3 Tax paid (1,200)
Gain on sale $ 4,000 Tax paid $1,200 Cash inflow $30,800
Present value of cash flows from sale of old boat c = 1, r = 15, ANN = 0, FV = $14,000, n = 6, PV =
$ 30,800.00
Sale of new boat:
Proceeds $20,000 Gain on sale $20,000 Proceeds $20,000
- BV -0- Tax rate 0.3 Tax paid 6,000
Gain on sale $20,000 Tax paid $ 6,000 Cash inflow $14,000
6,052.59
2006 $67,500 - $30,000 = $37,500 * 0.7 = $26,250
$100,000 * 0.2 * 0.3 = $6,000 c = 1, r = 15, ANN = 0, FV = $32,250, n = 1, PV =
2007 $84,000 - $45,000 = $39,000 * 0.7 = $27,300
$100,000 * 0.32 * 0.3 = $9,600 c = 1, r = 15, ANN = 0, FV = $36,900, n = 2, PV =
2008 $73,500 - $37,500 = $36,000 * 0.7 = $25,200
$100,000 * 0.192 * 0.3 = $5,760 c = 1, r = 15, ANN = 0, FV = $30,960, n = 3, PV =
2009 $67,500 - $34,500 = $33,000 * 0.7 = $23,100
28,043.48
27,901.70
20,356.70
$100,000 * 0.1152 * 0.3 = $3,456 c = 1, r = 15, ANN = 0, FV = $26,556, n = 4, PV = 17,461.00
2010 $62,000 - $30,000 = $32,000 * 0.7 = $22,400
$100,000 * 0.1152 * 0.3 = $3,456 c = 1, r = 15, ANN = 0, FV = $25,856, n = 5, PV = 12,855.00

b.
2011 $59,000 - $32,000 = $27,000 * 0.7 = $18,900
$100,000 * 0.0576 * 0.3 = $1,728 c = 1, r = 15, ANN = 0, FV = $20,628, n = 6, PV =
Total present value of cash flows
Initial investment
NPV
8,918.05
$152,388.52
(100,000.00)
$ 52,388.52
Yes, because the positive NPV indicates that the expected return on the investment exceeds the cost of capital. a.
P12.10
Investment A:
Tax shield: $172,000 * 0.3 = $51,600 c = 1, r = 16, FV = 0, ANN = $51,600, n = 5, PV = $ 168,953.55
After-tax cash flows:
2007 $296,200 * 0.7 = $207,340 c = 1, r = 16, ANN = 0, FV = $207,340, n = 1, PV =
2008 $326,200 * .7 = $228,340 c = 1, r = 16, ANN = 0, FV = $228,340, n = 2, PV =
2009 $383,400 * 0.7 = $268,380 c = 1, r = 16, ANN = 0, FV = $268,380, n = 3, PV =
2010 $440,800 * 0.7 = $308,560 c = 1, r = 16, ANN = 0, FV = $308,560, n = 4, PV =
2011 $496,000 * 0.7 = $347,200 c = 1, r = 16, ANN = 0, FV = $347,200, n = 5, PV =
Total present value of cash flows
Initial investment
NPV
178,741.38
169,693.82
171,939.71
170,414.94
165,306.44
$1,025,049.84
(860,000.00)
$ 165,049.84
Investment B:
Tax shield: $172,000 * 0.3 = $51,600 c = 1, r = 16, FV = 0, ANN = $51,600, n = 5, PV =
After-tax cash flows:
2007 $254,000 * 0.7 = $177,800 c = 1, r = 16, ANN = 0, FV = $177,800, n = 1, PV =
2008 $283,400 * .7 = $198,380 c = 1, r = 16, ANN = 0, FV = $198,380, n = 2, PV =
2009 $312,000 * 0.7 = $218,400
$ 168,953.55
153,275.86
147,428.66 c = 1, r= 16, ANN = 0, FV = $218,400, n = 3, PV =
2010 $340,400 * 0.7 = $238,280 c = 1, r = 16, ANN = 0, FV = $238,280, n = 4, PV =
2011 $368,600 * 0.7 = $258,020 c = 1, r = 16, ANN = 0, FV = $258,020, n = 5, PV =
Total present value of cash flows
Initial investment
NPV
139,919.64
131,599.92
122,846.68
$ 864,024.31
(860,000.00)
$ 4,024.31

b. Both projects are acceptable since their NPVs are positive. However, the second project is riskier since its NPV is smaller meaning that fluctuations in projected cash flows could more easily turn it into an undesirable project.