A firm is considering purchasing a machine that costs $57,000. It will be used f

Question

A firm is considering purchasing a machine that costs $57,000. It will be used for six years, and the salvage value at that time is expected to be zero. The machine will save $35,000 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 17%. Should the machine be purchased?

The present worth of the project is ________

6172 37665544444444444444 5 % 0050 33^0 0 1 0 1 0 1 0 15 1-50 0557 9 2 9 9 9 9 9 9 9 9 9 9 0841976666 0% 9999, 93 92 93 46 728884 00 20 62 52 78 33 44 14 7. 0123456789 123456789

Explanation / Answer

Woking notes:

(1) MACRS Depreciation schedule as follows.

(2) Before tax cash flow (BTCF) ($) = Annual savings - Annual operating cost = 35,000 - 10,000 = 25,000

(3) Taxable income (TI) = BTCF - Annual depreciation

(4) Net income (NI) = TI x (1 - Tax rate) = TI x (1 - 0.35) = TI x 0.65

(5) After-tax cash flow (ATCF) = NI + Annual depreciation

Note that in year 0, ATCF = - $57,000

ATCF and Present Worth thereof are computed as follows.

Year Asset Cost ($) Depreciation Rate (%) Annual Depreciation ($) (A) (B) (C) = (A) x (B) 1 57,000 20 11,400 2 57,000 32 18,240 3 57,000 19.2 10,944 4 57,000 11.52 6,566 5 57,000 11.52 6,566 6 57,000 5.76 3,283

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