Compute the payback period for each of these two separate investments: a. A new operating system for an existing machine is expected to cost $290,000 and have a useful life of four years. The system yields an incremental after-tax income of $83,653 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $11,000.
b. A machine costs $200,000, has a $15,000 salvage value, is expected to last eleven years, and will generate an after-tax income of $46,000 per year after straight-line depreciation.

1.89 years

3.18 years

Explanation:

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

Payback period = Amount invested / cash flow

Cash flow = net income + depreciation

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

(290,000 -11,000) / 4 = 69,750

Cash flow = $83,653 + 69,750 = 153,403

Payback = $290,000 / 153,403 = 1.89

(200,000 - 15,000) / 11 = 16,818.18

Cash flow = $46,000 +  16,818.18 = 62,818.18

Payback = 200,000 / 62,818.18 = 3.18

1.57

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