Question

A firm is considering investing $42,000 in equipment that is expected to have a useful life of four years and is expected to reduce (save) the firm’s labor costs by $8,900 per year. The equipment can be sold for $18,000 at the end of the period. Assume the firm pays a 40% income tax rate on its taxable income and uses the declining balance (200%) depreciation method. The firm’s after tax MARR is 5% per year.

What are the after-tax cash flow amounts for years 1 through 4? Is this investment profitable or not?

Answer 1

depreciation rate = 2 / 4 = 0.5

Depreciation in any year m = P *(1-d)^(m-1) * d

Depreciation in year 1 = 42000 *(1-0.5)^(1-1) * 0.5 = 21000

Depreciation in year 2 = 42000 *(1-0.5)^(2-1) * 0.5 = 10500

Depreciation in year 3 = 42000 *(1-0.5)^(3-1) * 0.5 = 5250

Depreciation in year 4 = 42000 *(1-0.5)^(4-1) * 0.5 = 2625

Tax rate = 40%

Taxable income = Net cash flow - Depreciation

Tax = Tax rate * Taxable income

ATCF = Taxable income - Tax + Depreciation

Year	Untaxed BTCF	Taxed BTCF	DDB Dep	Recaptured Dep	Tax income	Tax	ATCF
0	-42000						-42000
1		8900	21000.00		-12100.00	-4840.00	13740.00
2		8900	10500.00		-1600.00	-640.00	9540.00
3		8900	5250.00		3650.00	1460.00	7440.00
4	18000	8900	2625.00	15375.00	21650.00	8660.00	18240.00
						NPW	1,171.82

NPW = 1171.82 ~ 1172

As NPW is positive, project should be selected

Showing formula in excel

Year	Untaxed BTCF	Taxed BTCF	DDB Dep	Recaptured Dep	Tax income	Tax	ATCF
0	-42000						=B12
1		8900	21000		=C13-D13	=F13*0.4	=C13-G13
2		8900	10500		=C14-D14	=F14*0.4	=C14-G14
3		8900	5250		=C15-D15	=F15*0.4	=C15-G15
4	18000	8900	2625	=B16-(42000-SUM(D13:D16))	=C16-D16+E16	=F16*0.4	=B16+C16-G16
						NPW	=NPV(5%,H13:H16)+H12