Question

PLEASE DO PROBLEM

A machine can be purchased for $60,000 and used for five years, yielding the following net incomes. In projecting net incomes, straight-line 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		$	3,900			$	9,900			$	32,000			$	14,700			$	39,600

Compute the machine’s payback period (ignore taxes). (Round your intermediate calculations to 3 decimal places and round payback period answer to 3 decimal places.)

	Year Net Income Depreciation Net Cash Flow Cumulative Cash Flow 0 (60,000) $(60,000) 1 $3,900 2 9,900 3 32,000 4 14,700 5 39,600 Payback period =

Answer 1

• All working forms part of the answer
• Payback period is the period in which the amount initially invested is recovered.
• In our question , $ 60,000 is invested and Payback period will be calculated to see when that $60,000 is recovered back as Cash Inflow.
• Cash Inflow = Net Income + Depreciation, because Depreciation is a non-cash item that reduces the net income, hence it is to be added back.
• Straight Line Depreciation = Cost / Life = $60,000 / 5 year = $ 12,000 per year
• Working

Year	Net Income	Depreciation	Net Cash Flow	Cumulative Cash Flow
[Period]	[A]	[B]	[C=A + B]	[D = D + C]
0			$                             (60,000.00)	$                         (60,000.00)
1	$                   3,900.00	$                        12,000.00	$                               15,900.00	$                         (44,100.00)
2	$                   9,900.00	$                        12,000.00	$                               21,900.00	$                         (22,200.00)
3	$                 32,000.00	$                        12,000.00	$                               44,000.00	$                            21,800.00
4	$                 14,700.00	$                        12,000.00	$                               26,700.00	$                            48,500.00
5	$                 39,600.00	$                        12,000.00	$                               51,600.00	$                        1,00,100.00

• From above working it is clear that out of $60,000, $ 48,500 is recovered in 4 years. Remaining $ 11,500 is recovered during the year 5.

Time taken to recover $ 11,500 in year 5 = $11,500 / $ 51,600 = 0.223

• Hence, total payback period = 4 years + 0.223 = 4.223 years