( n ) Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% 1 .96154 .95238 .94340 .93458 .9
ID: 2599208 • Letter: #
Question
(n)
Periods
4%
5%
6%
7%
8%
9%
10%
11%
12%
15%
1
.96154
.95238
.94340
.93458
.92593
.91743
.90909
.90090
.89286
.86957
2
.92456
.90703
.89000
.87344
.85734
.84168
.82645
.81162
.79719
.75614
3
.88900
.86384
.83962
.81630
.79383
.77218
.75132
.73119
.71178
.65752
4
.85480
.82270
.79209
.76290
.73503
.70843
.68301
.65873
.63552
.57175
5
.82193
.78353
.74726
.71299
.68058
.64993
.62092
.59345
.56743
.49718
6
.79031
.74622
.70496
.66634
.63017
.59627
.56447
.53464
.50663
.43233
7
.75992
.71068
.66506
.62275
.58349
.54703
.51316
.48166
.45235
.37594
8
.73069
.67684
.62741
.58201
.54027
.50187
.46651
.43393
.40388
.32690
9
.70259
.64461
.59190
.54393
.50025
.46043
.42410
.39092
.36061
.28426
10
.67556
.61391
.55839
.50835
.46319
.42241
.38554
.35218
.32197
.24719
11
.64958
.58468
.52679
.47509
.42888
.38753
.35049
.31728
.28748
.21494
12
.62460
.55684
.49697
.44401
.39711
.35554
.31863
.28584
.25668
.18691
13
.60057
.53032
.46884
.41496
.36770
.32618
.28966
.25751
.22917
.16253
14
.57748
.50507
.44230
.38782
.34046
.29925
.26333
.23199
.20462
.14133
15
.55526
.48102
.41727
.36245
.31524
.27454
.23939
.20900
.18270
.12289
16
.53391
.45811
.39365
.33873
.29189
.25187
.21763
.18829
.16312
.10687
17
.51337
.43630
.37136
.31657
.27027
.23107
.19785
.16963
.14564
.09293
18
.49363
.41552
.35034
.29586
.25025
.21199
.17986
.15282
.13004
.08081
19
.47464
.39573
.33051
.27615
.23171
.19449
.16351
.13768
.11611
.07027
20
.45639
.37689
.31180
.25842
.21455
.17843
.14864
.12403
.10367
.06110
(a)
(b)
Jane’s Auto Care is considering the purchase of a new tow truck. The garage doesn’t currently have a tow truck, and the $60,020 price tag for a new truck would represent a major expenditure. Jane Austen, owner of the garage, has compiled the estimates shown below in trying to determine whether the tow truck should be purchased.Initial cost $60,020 Estimated useful life 8 years Net annual cash flows from towing $7,950 Overhaul costs (end of year 4) $5,950 Salvage value $12,010
Jane’s good friend, Rick Ryan, stopped by. He is trying to convince Jane that the tow truck will have other benefits that Jane hasn’t even considered. First, he says, cars that need towing need to be fixed. Thus, when Jane tows them to her facility, her repair revenues will increase. Second, he notes that the tow truck could have a plow mounted on it, thus saving Jane the cost of plowing her parking lot. (Rick will give her a used plow blade for free if Jane will plow Rick's driveway.) Third, he notes that the truck will generate goodwill; people who are rescued by Jane’s tow truck will feel grateful and might be more inclined to use her service station in the future or buy gas there. Fourth, the tow truck will have “Jane’s Auto Care” on its doors, hood, and back tailgate—a form of free advertising wherever the tow truck goes. Rick estimates that, at a minimum, these benefits would be worth the following.
Additional annual net cash flows from repair work $2,990 Annual savings from plowing 740 Additional annual net cash flows from customer “goodwill” 950 Additional annual net cash flows resulting from free advertising 760
The company’s cost of capital is 9%.
Table3Present Value of 1
(n)
Periods
4%
5%
6%
7%
8%
9%
10%
11%
12%
15%
1
.96154
.95238
.94340
.93458
.92593
.91743
.90909
.90090
.89286
.86957
2
.92456
.90703
.89000
.87344
.85734
.84168
.82645
.81162
.79719
.75614
3
.88900
.86384
.83962
.81630
.79383
.77218
.75132
.73119
.71178
.65752
4
.85480
.82270
.79209
.76290
.73503
.70843
.68301
.65873
.63552
.57175
5
.82193
.78353
.74726
.71299
.68058
.64993
.62092
.59345
.56743
.49718
6
.79031
.74622
.70496
.66634
.63017
.59627
.56447
.53464
.50663
.43233
7
.75992
.71068
.66506
.62275
.58349
.54703
.51316
.48166
.45235
.37594
8
.73069
.67684
.62741
.58201
.54027
.50187
.46651
.43393
.40388
.32690
9
.70259
.64461
.59190
.54393
.50025
.46043
.42410
.39092
.36061
.28426
10
.67556
.61391
.55839
.50835
.46319
.42241
.38554
.35218
.32197
.24719
11
.64958
.58468
.52679
.47509
.42888
.38753
.35049
.31728
.28748
.21494
12
.62460
.55684
.49697
.44401
.39711
.35554
.31863
.28584
.25668
.18691
13
.60057
.53032
.46884
.41496
.36770
.32618
.28966
.25751
.22917
.16253
14
.57748
.50507
.44230
.38782
.34046
.29925
.26333
.23199
.20462
.14133
15
.55526
.48102
.41727
.36245
.31524
.27454
.23939
.20900
.18270
.12289
16
.53391
.45811
.39365
.33873
.29189
.25187
.21763
.18829
.16312
.10687
17
.51337
.43630
.37136
.31657
.27027
.23107
.19785
.16963
.14564
.09293
18
.49363
.41552
.35034
.29586
.25025
.21199
.17986
.15282
.13004
.08081
19
.47464
.39573
.33051
.27615
.23171
.19449
.16351
.13768
.11611
.07027
20
.45639
.37689
.31180
.25842
.21455
.17843
.14864
.12403
.10367
.06110
Explanation / Answer
(a)
NO.
The tow truck should not be purchased since it has a negative net present value.
(b)
Additional annual net cash flows = 2990 + 740 + 950 + 760 = 5440
YES
The tow truck should be purcahsed since it has a positive net present value with the additional benefits.
Note: The calculations can also be done using the PVA of $1 for i = 9% and n=8 years for the annual net cash flows however, since the PV of $1 table only is provided with the question, the same has been used.
Cash Flow Year 0 1 2 3 4 5 6 7 8 Initial investment -60020 Net annual cash flows from towing 7950 7950 7950 7950 7950 7950 7950 7950 Overhaul costs -5950 Salvage value 12010 Net cash flows -60020 7950 7950 7950 2000 7950 7950 7950 19960 Discount factor 9% 1.00000 0.91743 0.84168 0.77218 0.70843 0.64993 0.59627 0.54703 0.50187 Present value -60020 7293.569 6691.356 6138.831 1416.86 5166.944 4740.347 4348.889 10017.33 Net present value -14206Related Questions
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