Question

A contractor purchased a piece of heavy equipment of $60,000 with an estimated life of 10 years and a salvage value of $5,000. The company's effective tax rate for state and federal taxes is 40% and its minimum attractive rate of return is 10%. The gross income generated by the equipment before depreciation and taxes was estimated to be $8000 per year.

Determine the after-tax cash flow for each year. Compare the present worths for the following methods of depreciation.

a) The straight-line method

b) The double-declining-balance method

c) Which depreciation method appears to be more desirable?

Answer 1

a)

Straight line method

Depreciation expense under straight line method for tax purposes

= (Cost of the equipment/ useful life) = ($60000/10 years) = $6000

Under straight line method depreciation will be same for all years.

Relevant cash flows;

1-9th year

After tax operating cash flow= $8000-40%= $4800

Depreciation tax shield= Depreciation expense* Tax percentage

                           = $6000*40%= $2400

Total = $4800+$2400= $7200

For 10th year;

After tax operating cash flow= $8000-40%= $4800

Depreciation tax shield= Depreciation expense* Tax percentage

                           = $6000*40%= $2400

Cash flow from disposal of the asset = Salvage value- tax percentage

= $5000 -40%= $3000

Total= $4800+$2400+$3000= $10200

Present value of cash inflows

= (annual cash inflow* Present value annuity factor for 9 years at 10% discounting rate) + (Cash flow for 10th year* Present value factor at 10% for 10th year)

= ($7200* 5.7590) +($10200* 0.3855)= $45396.9

Present value= Present value of cash inflows – Present value of cash outflows

= $45396.9 - $60000= $14603.1

b)

Double declining balance method

Year	Operating cash flow	Depreciation tax shield	Cash flow from disposal of the asset	Total cash flow	Present value factor @ 10%	Present value of cash inflow
1	8000-40%= $4800	(60000*20%) *40%= $4800		$9600	0.9053	$8,690.88
2	$4800	(48000*20%) *40%= $3840		$8640	0.8203	$7,087.39
3	$4800	(38400*20%) *40%= $3072		$7872	0.7441	$5,857.56
4	$4800	(30720*20%) *40%= $2457.6		$7257.6	0.6756	$4,903.23
5	$4800	(24576*20%) *40%= $3932.16		$8732.16	0.6139	$5,360.67
6	$4800	(19660.8*20%) *40%= $1572.86		$6372.86	0.5584	$3,558.61
7	$4800	(15728.64*20%) *40%= $1258.29		$6058.29	0.5083	$3,079.43
8	$4800	(12582.91*20%) *40%= $1006.63		$5806.63	0.4632	$2,689.63
9	$4800	(10066.33*20%) *40%= $805.31		$5605.31	0.4224	$2,367.68
10	$4800	(8053.06*20%) *40%= $644.25	$5823.02	$11267.27	0.3855	$4,343.53
Present value of cash inflows=$47,938.62

Double declining percentage= (100%/ Useful life) *2= (100/10) *2= 20%

Cash flow from disposal of the asset= Sale proceeds- Tax effect on gain

= 6000- ((6000-6442.45) *40%) = $5823.02

Present value= Present value of cash inflows – Present value of cash outflows

47938.62- 60000 = ($12061.38)

c)

Present value of cash inflows under straight line depreciation method= $45396.9

Present value of cash inflows under double declining balance method= 47938.62

Present value of cash inflows that is present worth under double declining balance method of depreciation is higher compared to straight line method. So double declining balance method appears to be more desirable.