Replacement Analysis The Gilbert Instrument Corporation is considering replacing
ID: 2738250 • Letter: R
Question
Replacement Analysis The Gilbert Instrument Corporation is considering replacing the wood steamer it currently uses to shape guitar sides. The steamer, purchased just 2 years ago, is being depreciated on a straight-line basis and has 6 years of remaining life. Its current book value is $2,400, and it can be sold on an Internet auction site for $4,500 at this time. Thus, the annual depreciation expense is $2,400/6=$400 per year. If the old steamer is not replaced, it can be sold for $800 at the end of its useful life. Gilbert is considering purchasing the Side Steamer 3000, a higher-end steamer, which costs $7,800, and has an estimated useful life of 6 years with an estimated salvage value of $780. This steamer falls into the MACRS 5-years class, so the applicable depreciation rates are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. The new steamer is faster and would allow for an output expansion, so sales would rise by $2,000 per year; even so, the new machine's much greater efficiency would reduce operating expenses by $1,400 per year. To support the greater sales, the new machine would require that inventories increase by $2,900, but accounts payable would simultaneously increase by $700. Gilbert's marginal federal-plus-state tax rate is 40%, and its WACC is 14%. What is the NPV of the project? Round your answer to the nearest dollar.
Explanation / Answer
Year
1
2
3
4
5
6
Rate of depreciation for new steamer
20%
32%
19.20%
11.52%
11.52%
5.76%
Depreciation of new steamer
$ 1,560.00
$ 2,496.00
$ 1,497.60
$ 898.56
$ 898.56
$ 449.28
Depreciation of old steamer
$ 400.00
$ 400.00
$ 400.00
$ 400.00
$ 400.00
$ 400.00
Incremental depreciation
$ 1,160.00
$ 2,096.00
$ 1,097.60
$ 498.56
$ 498.56
$ 49.28
Tax savings on depreciation
$ 464.00
$ 838.40
$ 439.04
$ 199.42
$ 199.42
$ 19.71
Present value factor @ 14%
0.8772
0.7695
0.6750
0.5921
0.5194
0.4556
Present value of tax savings on depreciation
$ 407.02
$ 645.12
$ 296.34
$ 118.08
$ 103.57
$ 8.98
Present value of tax savings on depreciation = $1,579.11
Increase in net income due to new steamer = $2,000 + $1,400 = $3,400
Incremental net income after tax = $3,400*0.6 = $2,040
Present value of annual after tax net income = $2,040 * {1-1.14-6}/0.14 = $7,932.88
Present value of free cash flows = present value of post tax income + Present value of tax savings on depreciation = $1,579.11 + $7,932.88 = $9,512
Gain on sale of old machine today = $4,500 - $2,500 = $2,000
Tax on gain on sale of old machine = $2,000 * 0.40 = $800
Cash flow from sale of old steamer today = $4,500 - $800 = $3,700
Net cash outflow at year 0 = - $7,800 + $3,700 – ($2,900-$700) = -$6,300
After tax proceeds from sale of new steamer = $780 * 0.6 = $468
Release of working capital investment = $2,200
Net terminal cash inflows at year 6 = $468 + $2,200 = $2,668
Present value of sale proceeds of new steamer = $2,668/1.146 = $1,215.51
Net present value = -$6,300 + $9,512 + $1,215.51 = $4,427.51
Year
1
2
3
4
5
6
Rate of depreciation for new steamer
20%
32%
19.20%
11.52%
11.52%
5.76%
Depreciation of new steamer
$ 1,560.00
$ 2,496.00
$ 1,497.60
$ 898.56
$ 898.56
$ 449.28
Depreciation of old steamer
$ 400.00
$ 400.00
$ 400.00
$ 400.00
$ 400.00
$ 400.00
Incremental depreciation
$ 1,160.00
$ 2,096.00
$ 1,097.60
$ 498.56
$ 498.56
$ 49.28
Tax savings on depreciation
$ 464.00
$ 838.40
$ 439.04
$ 199.42
$ 199.42
$ 19.71
Present value factor @ 14%
0.8772
0.7695
0.6750
0.5921
0.5194
0.4556
Present value of tax savings on depreciation
$ 407.02
$ 645.12
$ 296.34
$ 118.08
$ 103.57
$ 8.98