Question

A company is deciding whether to lease or purchase an asset. In this question we will evaluate the NPV of the purchase decision. The capital cost required to purchase the asset is $1,000,000 (at time zero) with a salvage value of $500,000 at the end of the 5th year. The purchased asset can be depreciated based on MACRS 5-year life depreciation with the half year convention (table A-1 at IRS (Links to an external site.)Links to an external site.) over six years (from year 0 to year 5). The asset would yield annual revenue of $350,000 for five years (from year 1 to year 5) and operating cost of $60,000 for year 1 to 5. If the income tax is 40% and the annual discount rate is 16%, calculate the NPV for the purchase decision

Answer 1

Working notes:

(a) First cost ($) = 1,000,000

(b) MACRS-GDS depreciation schedule for initial 5 years as follows. This method does not consider salvage value.

Year	First cost ($)	Depreciation rate (%)	Annual depreciation ($)
1	10,00,000	14.29	1,42,900
2	10,00,000	24.49	2,44,900
3	10,00,000	17.49	1,74,900
4	10,00,000	12.49	1,24,900
5	10,00,000	8.93	89,300

(c) Taxable income (TI), years 1-4 = Annual revenue - Operating Cost - Depreciation

(d) Taxable income (TI), year 5 = Annual savings - Operating cost - Depreciation + Salvage value

(e) Post-tax (Net) income (NI) = TI x (1 - Tax rate) = TI x (1 - 0.4) = TI x 0.6

(f) After-tax cash flow (ATCF) = NI + Depreciation

(g) ATCF, year 0 = - First Cost

(h) After-tax NPV is computed below. Note that PV Factor in year N = (1.16)^-N.

Year	Revenue ($)	Cost ($)	Depreciation ($)	TI ($)	NI ($)	ATCF ($)	PV Factor @16%	Discounted ATCF ($)
0						-10,00,000	1.0000	-10,00,000
1	3,50,000	60,000	1,42,900	1,47,100	88,260	2,31,160	0.8621	1,99,275.86
2	3,50,000	60,000	2,44,900	45,100	27,060	2,71,960	0.7432	2,02,110.58
3	3,50,000	60,000	1,74,900	1,15,100	69,060	2,43,960	0.6407	1,56,294.85
4	3,50,000	60,000	1,24,900	1,65,100	99,060	2,23,960	0.5523	1,23,691.11
5	8,50,000	60,000	89,300	7,00,700	4,20,420	5,09,720	0.4761	2,42,684.33
							NPV ($) =	-75,943.27