Question

A manufacturer of printed circuit boards is considering purchasing a new surface mount technology component placement system. Two machines are under consideration and the following information is prepared for the economic evaluation. If the company's after-tax MARR of 12% per year and MACRS with a 7-year recovery period is used, compute the after-tax cash flow(ATCF) at the end of year 8 for the Machine Q. Assume an effective tax of 35% per year.

Machine	Q	R
First costs	$392,248	$395,000
Net annual revenue	$150,000 in year 1, increasing by $500 per year thereafter	$152,500
Market value at the end of the useful life	$4000	0
Life, years	8	10

Correct answer is 108,497.9

Please show all work to get answer, also please don't just use excel

Answer 1

First find the depreciation schedule for  MACRS with a 7-year recovery period

Year	Depreciation rate	Depreciation	Depreciation cumulative	Book value
1	14.29%	56052.24	56052.24	336195.8
2	24.49%	96061.54	152113.8	240134.2
3	17.49%	68604.18	220717.9	171530.1
4	12.49%	48991.78	269709.7	122538.3
5	8.93%	35027.75	304737.5	87510.53
6	8.92%	34988.52	339726	52522.01
7	8.93%	35027.75	374753.7	17494.26
8	4.46%	17494.26	392248	0

Below is the cash flow statement for 8 years. Revenue is increased at $500 per year. Taxable income is Revenue - depreciation. Then taxes are charged at 35% so that net income is 65% of taxable income

Depreciation is added back to the net income to get the required after tax cash flows. In year 8, book value is 0, so capital gain is entire salvage value which is 4000. Capital gain tax is 35% or 1400 so the same is subtracted in year 8. This gives the ATCF for 8th year

Year		0	1	2	3	4	5	6	7	8
Income statement
Revenues			150000	150500	151000	151500	152000	152500	153000	153500
Expenses
Depreciation			56052.24	96061.54	68604.18	48991.78	35027.75	34988.52	35027.75	17494.26
Taxable income			93947.76	54438.46	82395.82	102508.2	116972.3	117511.5	117972.3	136005.7
Income tax			32882	19053	28839	35878	40940	41129	41290	47602
Net income			61066	35385	53557	66630	76032	76382	76682	88404
Cash flow statement
Operating activities
Net income			61066	35385	53557	66630	76032	76382	76682	88404
Depreciation			56052.24	96061.54	68604.18	48991.78	35027.75	34988.52	35027.75	17494.26
Investment activities
Investment		-392248
Salvage										4000
Gains tax										-1400
Net cash flow		-392248	117118	131447	122161	115622	111060	111371	111710	108498