A machine can be purchased for $140,000 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 $ 9,500 $ 23,500 $ 64,000 $ 35,500 $ 94,000
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 $ (140,000) $ (140,000)
1 $ 9,500
2 23,500
3 64,000
4 35,500 0
5 94,000 0
Payback period =

2.554 years

Explanation:

Payback period calculates the amount of time it takes to recover the amount invested in a project from its cumulative cash flows.

to derive cash flow from net income, add depreciation back

Straight line depreciation expense = (Cost of asset - Salvage value) / useful life

$140,000 / 5 = $28,000

depreciation expense each year would be $28,000

cash flow in year 1 = $9500 +  $28,000 = $37,500

cash flow in year 2= $23,500 + $28,000 =$51,500

cash flow in year 3 =$64,000 + $28,000 = $92,000

cash flow in year 4 =$35,500 + $28,000 = $63,500

cash flow in year 5 =$94,000 + $28,000 = $122,000

in year 1, the amount recovered = $-140,000 + $37,500 = $-102,500

in year 2, the amount recovered = $-102,500 + $51,500 = $-51,000

in year 3, the amount recovered =  $-51,000 + $92,000 = $41,000

the amount invested is recovered in 2 years + 51,000 / 92,000 = 2.554 years

the answer should be a)