Question

An injection molding machine can be purchased and installed for $120000. It is in the seven-year GDS property class and is expected to be kept in service for 8 years. It is believed that $10000 can be obtained when the machine is disposed of at the end of year 8. The net annual value added (i.e., revenues less expenses) that can be attributed to this machine is constant each year and amounts to $37000. An effective income tax rate of 35% is used by the company, and the after-tax MARR equals 18% per year. What is the AW of the after-tax cash flow? (Please round your answer to nearest Integer)

Answer 1

To find the annual worth of the after tax cash flows, we first calculate the present worth of the after tax cash flow.

Year	Seven year GDS property Depreciation rate	Depreciation expense	Net value added	Before tax cash flow = Net value added - depreciation expense	Taxes@35%	After tax cash flow = Before tax cash flow - taxes + depreciation
1	14.29%	17148	37000	19852	6948.2	30051.8
2	24.49%	29388	37000	7612	2664.2	34335.8
3	17.49%	20988	37000	16012	5604.2	31395.8
4	12.49%	14988	37000	22012	7704.2	29295.8
5	8.93%	10716	37000	26284	9199.4	27800.6
6	8.92%	10704	37000	26296	9203.6	27796.4
7	8.93%	10716	37000	26284	9199.4	27800.6
8	4.46%	5352	37000	31648	11076.8	25923.2

The present worth of the after tax cash flow at a MARR = 18% is calculated as follows

30051.8 (1+0.18) 34335. 8 31395. 8 29295. 8 (1+0.18)' (1+0.18) s' (1+0.18)+ 27800. 6 (1+0.18) 27796.4 . (1+0.18) 27800.6 . (1+0.18) _ Present worth = 25923.2 10,000 (1+0.18)$*(1+0.18) 0.28)

Present worth of the After tax cash flow = $ 122,418.39

Annual worth of the after tax cash flow = Present worth x ( A/P, 18% , 8 years)

Where ( A/P, 18% , 8 years) = Capital recovery factor

Annual worth of the after tax cash flow = $ 122,418.39 x 0.2452

Annual worth of the after tax cash flow = $ 30,017