Chapman Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine for $390,000 is estimated to result in $135,000 in annual pretax cost savings. The press falls in the MACRS five-year class, and it will have a pretax salvage value at the end of the project of $198,000. The MACRS rates are .2, .32, .192, .1152, .1152, and .0576 for Years 1 to 6, respectively. Ignore bonus depreciation. The press also requires an initial investment in inventory of $8,000, along with an additional $1,500 in inventory for each succeeding year of the project. The inventory will return to its original level when the project ends. The shop's tax rate is 21 percent and its discount rate is 16 percent. Should the firm buy and install the machine? Why or why not?
A) Yes; The net present value is $47,048.86.
B) No; The net present value is −$36,329.09.
C) No; The net present value is $56,652.88.
D) Yes; The net present value is $44,319.97.
E) Yes; The net present value is $56,329.09.

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV), we need to find the present value of the cost savings and salvage value, as well as the present value of the initial investment and the annual inventory costs. We can use MACRS to calculate the depreciation expense each year, and we need to adjust for taxes. With a discount rate of 16%, we get:

Year 1:
Depreciation = $390,000 x 0.2 = $78,000
Taxable income = $135,000 - $78,000 = $57,000
Taxes = $57,000 x 0.21 = $11,970
Cash flow = $135,000 - $11,970 = $123,030
PV factor = 1 / (1 + 0.16)^1 = 0.8621
PV = $123,030 x 0.8621 = $106,055.67
Inventory = -$8,000

Year 2:
Depreciation = $390,000 x 0.32 = $124,800
Taxable income = $135,000 - $124,800 = $10,200
Taxes = $10,200 x 0.21 = $2,142
Cash flow = $135,000 - $124,800 - $2,142 + $8,500 = $16,558
PV factor = 1 / (1 + 0.16)^2 = 0.7432
PV = $16,558 x 0.7432 = $12,299.09
Inventory = -$9,500

Year 3:
Depreciation = $390,000 x 0.192 = $74,880
Taxable income = $135,000 - $74,880 = $60,120
Taxes = $60,120 x 0.21 = $12,625.20
Cash flow = $135,000 - $74,880 - $12,625.20 + $11,000 = $58,594.80
PV factor = 1 / (1 + 0.16)^3 = 0.6412
PV = $58,594.80 x 0.6412 = $37,569.92
Inventory = -$11,000

Year 4:
Depreciation = $390,000 x 0.1152 = $44,928
Taxable income = $135,000 - $44,928 = $90,072
Taxes = $90,072 x 0.21 = $18,914.32
Cash flow = $135,000 - $44,928 - $18,914.32 + $12,500 = $83,657.68
PV factor = 1 / (1 + 0.16)^4 = 0.5523
PV = $83,657.68 x 0.5523 = $46,171.25
Inventory = -$12,500

Year 5:
Depreciation = $390,000 x 0.1152 = $44,928
Taxable income = $135,000 - $44,928 = $90,072
Taxes = $90,072 x 0.21 = $18,914.32
Cash flow = $135,000 - $44,928 - $18,914.32 + $15,000 = $86,157.68
PV factor = 1 / (1 + 0.16)^5 = 0.4810
PV = $86,157.68 x 0.4810 = $41,463.58
Inventory = -$14,000

Year 6:
Depreciation = $390,000 x 0.0576 = $22,176
Taxable income = $135,000 - $22,176 = $112,824
Taxes = $112,824 x 0.21 = $23,693.04
Cash flow = $135,000 - $22,176 - $23,693.04 + $213,000 = $302,950.96
PV factor = 1 / (1 + 0.16)^6 = 0.4122
PV = $302,950.96 x 0.4122 = $124,863.06
Inventory = -$15,500

NPV = PV(cost savings) + PV(salvage value) + PV(initial investment) + PV(inventory costs)
NPV = $106,055.67 + $124,863.06 - $390,000 - $12,720.86 - $37,569.92 - $46,171.25 - $41,463.58 - $124,863.06 - $15,500
NPV = $47,048.86

Since the NPV is positive, the project is expected to earn a return greater than the required rate of return (the cost of capital), so the firm should buy and install the machine.

Chapman Machine Shop Is Considering a Four-Year Project to Improve