A machine can be purchased for $150,000 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 10,000 25,000 50,000 37,500 100,000
Compute the machine’s payback period (ignore taxes). (Round payback period to 3 decimal places.)

2.69 years

Explanation:

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

To derive cash flows from net income, add depreciation to the net income.

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

$150,000 / 5 = $30,000

The depreciation expense each year would be $30,000.

Cash flow in year 1 = $30,000 + $10,000 = $40,000

Cash flow in year 2 = $30,000 + $25,000 = $55,000

Cash flow in year 3 = $30,000 + $50,000 = $80,000

Cash flow in year 4 = $30,000 + $37,500 = $67,500

Cash flow in year 5 = $30,000 + $100,000 = $130,000

In the first year, -150,000 + $40,000 = $-110,000 is recovered

In the second year, $-110,000 + $55,000 = $-55,000 is recovered

In the third year, $-55,000 + $80,000 = $25,000 is recovered.

The cash payback period is 2 years + $-55,000 / $80,000 = 2.69 years

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