Question

A machine can be purchased for $283,000 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		$	21,000			$	30,000			$	73,000			$	41,000			$	122,000

Compute the machine’s payback period (ignore taxes). (Round payback period answer to 3 decimal places.)
  

Answer 1

Solution

Computation of Annual Depreciation

Cost of Machine = $ 283,000
Useful Life = 5 Years
Salvage Life = NIL
Normal Rate of Depreciation = (1 / Useful Life) X 100 = (1 / 5) X 100 = 20%
Rate of Depreciation under Double-Declining Depreciation method = 2 X Normal Rate of Depreciation = 2 X 20% = 40%

Now, the depreciation calculation chart has been provided below,

Year	Opening Balance	Rate of Depreciation	Depreciation	Closing Balance
	$	%	$	$
	(A)	(B)	(C = A x B)	(D = A - C)
1	2,83,000.00	40	1,13,200.00	1,69,800.00
2	1,69,800.00	40	67,920.00	1,01,880.00
3	1,01,880.00	40	40,752.00	61,128.00
4	61,128.00	40	24,451.00	36,677.00
5	36,677.00	40	14,671.00	22,006.00

Calculation of Payback Period

For computing Payback Period, following table should be used

Year	Net Income	Depreciation	Cash Flow After Tax (CFAT)	Cumulative CFAT
1	$          21,000.00	$       1,13,200.00	$        1,34,200.00	$      1,34,200.00
2	$          30,000.00	$          67,920.00	$           97,920.00	$      2,32,120.00
3	$          73,000.00	$          40,752.00	$        1,13,752.00	$      3,45,872.00
4	$          41,000.00	$          24,451.00	$           65,451.00	$      4,11,323.00
5	$      1,22,000.00	$          14,671.00	$        1,36,671.00	$      5,47,994.00

Payback Period is the minimum period to recover the initial investment. Here it can be seen from the chart that $ 283,000 can be recovered within 2 to 3 Years. So, assuming the payback period as X, using Interpolation we get,

(X - 2) / (3 - 2) = (283000 - 232120) / (345872 - 232120)

Or, X - 2 = 50880 / 113752

Or, X - 2 = 0.45 (Approx)

Or, X = 2.45

Therefore, Payback Period for the machine will be 2.45 Years.