Question

A machine can be purchased for $204,000 and used for five years, yielding the following net incomes. In projecting net incomes, double-declining depreciation is applied using a five-year life and a zero salvage value.

	Year 1				Year 2				Year 3				Year 4				Year 5
Net income		$	23,000			$	32,000			$	52,000			$	37,500			$	122,000

Compute the machine’s payback period (ignore taxes).

Answer 1

Depreciation under Double declining balance method = (Cost - Accumulated deprection) / Useful life * 2

	Depreciation expense
Year 1	$81,600 [($204,000-$0)/5*2]
Year 2	$48,960 [($204,000-$81,600)/5*2]
Year 3	$29,376 [($204,000-$81,600-$48,960)/5*2]
Year 4	$17,626 [($204,000-$81,600-$48,960-$29,376)/5*2]
Year 5	$10,576 [($204,000-$81,600-$48,960-$29,376-$10,576)/5*2]

Cash flow = Net income + Depreciation

Year	Cash flow	Cumulative cash flow
1	$104,600 ($23,000+$81,600)	$104,600
2	$80,960 ($32,000+$48,960)	$185,560
3	$81,376 ($52,000+$29,376)	$266,936

Pay back period = 2 + ($204,000 - $185,560) / $266,936

= 2 + $18,440 / $266,936

= 2 + 0.7

= 2.07 years