Question

You’ve been asked to calculate the equivalent annual benefit (EUAB) of a new machine.The initial cost is $100,000; use full life is 10 years; and salvage value is $10,000. The new machine is expected to reduce operating costs by $24,000 per year. Assume MARR of 10% and 40% tax bracket.You a real ways thorough and you plan make three calculations. PartA:NPV that does NOT include tax or depreciation.PartB:NPV includes the 40% tax,but NOT any depreciation. PartC:NPV that includes 40% tax after straight-line depreciation.

Answer 1

(Part A)

NPV computed as follows. Note that PV factor in year N = (1.10)-N.

Year	Cash Flow ($)	PV Factor @10%	Discounted cash flow ($)
0	-1,00,000	1.0000	-1,00,000
1	24,000	0.9091	21,818
2	24,000	0.8264	19,835
3	24,000	0.7513	18,032
4	24,000	0.6830	16,392
5	24,000	0.6209	14,902
6	24,000	0.5645	13,547
7	24,000	0.5132	12,316
8	24,000	0.4665	11,196
9	24,000	0.4241	10,178
10	34,000	0.3855	13,108
		NPV ($) =	51,325

EUAB = NPV / P/A(10%, 10) = 51,325 / 6.1446 = 8,352.86

(Part B)

After-tax income = Annual saving x (1 - Tax rate) = Annual saving x (1 - 0.4) = Annual saving x 0.6

NPV computed as follows. Note that PV factor in year N = (1.10)-N.

Year	Pre-tax Cash Flow ($)	After-Tax Cash Flow ($)	PV Factor @10%	Discounted After-tax cash flow ($)
0	-1,00,000	-1,00,000	1.0000	-1,00,000
1	24,000	14,400	0.9091	13,091
2	24,000	14,400	0.8264	11,901
3	24,000	14,400	0.7513	10,819
4	24,000	14,400	0.6830	9,835
5	24,000	14,400	0.6209	8,941
6	24,000	14,400	0.5645	8,128
7	24,000	14,400	0.5132	7,389
8	24,000	14,400	0.4665	6,718
9	24,000	14,400	0.4241	6,107
10	34,000	20,400	0.3855	7,865
			NPV ($) =	-9,205

EUAB = NPV / P/A(10%, 10) = - 9,205 / 6.1446 = - 1,498.06

(Part C)

(I) Annual depreciation = (Cost - salvage value)/Life = (100,000 - 10,000)/10 = 90,000/10 = 9,000

(II) Taxable income (TI) = Annual saving - Depreciation

(III) After-tax income = TI x (1 - Tax rate) = TI x (1 - 0.4) = TI x 0.6

(IV) After-tax cash flow (ATCF) = After-tax income + Depreciation

NPV computed as follows. Note that PV factor in year N = (1.10)-N.

Year	Savings ($)	Depreciation ($)	TI ($)	ATCF ($)	PV Factor @10%	Discounted ATCF ($)
0	-1,00,000			-1,00,000	1.0000	-1,00,000
1	24,000	9,000	15,000	18,000	0.9091	16,364
2	24,000	9,000	15,000	18,000	0.8264	14,876
3	24,000	9,000	15,000	18,000	0.7513	13,524
4	24,000	9,000	15,000	18,000	0.6830	12,294
5	24,000	9,000	15,000	18,000	0.6209	11,177
6	24,000	9,000	15,000	18,000	0.5645	10,161
7	24,000	9,000	15,000	18,000	0.5132	9,237
8	24,000	9,000	15,000	18,000	0.4665	8,397
9	24,000	9,000	15,000	18,000	0.4241	7,634
10	34,000	9,000	25,000	24,000	0.3855	9,253
					NPV ($) =	12,915

EUAB = NPV / P/A(10%, 10) = 12,915 / 6.1446 = 2,101.85