Question

A firm is considering purchasing a machine that costs ​$69,000. It will be used for six​ years, and the salvage value at that time is expected to be zero. The machine will save

​$42,000 per year in​ labor, but it will incur ​$10,000 in operating and maintenance costs each year. The machine will be depreciated according to​ five-year MACRS. The​ firm's tax rate is

35​%, and its​ after-tax MARR is 11​%. What is the present worth of the project?

Answer 1

Working notes:

(a) First cost = 29,000 + 137,000 = 166,000

(b) MACRS depreciation schedule as follows.

Year	Equipment cost ($)	Depreciation Rate	Annual Depreciation ($)
1	69,000	0.2000	13,800
2	69,000	0.3200	22,080
3	69,000	0.1920	13,248
4	69,000	0.1152	7,949
5	69,000	0.1152	7,949
6	69,000	0.0576	3,974

(c)

Taxable income (TI) = Revenue - Operating expense - Depreciation

= (42,000 - 10,000) - Depreciation

= 32,000 - Depreciation

**Revenue - Operating expense = Net savings

(d)

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

= TI x (1 - 0.35)

= TI x 0.65

(e)

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

(f)

PV Factor in year N = (1.11)-N.

Present worth (PW) of ATCF is as follows.

Year	Net Savings ($)	Depreciation ($)	TI ($)	After-tax Income ($)	ATCF ($)	PV Factor @11%	Discounted ATCF ($)
0					-69,000	1.0000	-69,000.00
1	32,000	13,800	18,200	11,830	25,630	0.9009	23,090.09
2	32,000	22,080	9,920	6,448	28,528	0.8116	23,153.96
3	32,000	13,248	18,752	12,189	25,437	0.7312	18,599.17
4	32,000	7,949	24,051	15,633	23,582	0.6587	15,534.25
5	32,000	7,949	24,051	15,633	23,582	0.5935	13,994.82
6	32,000	3,974	28,026	18,217	22,191	0.5346	11,864.24
						PW of ATCF ($) =	37,236.52