Question

Compute the payback period for each of these two separate investments:

a. A new operating system for an existing machine is expected to cost $250,000 and have a useful life of four years. The system yields an incremental after-tax income of $72,115 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000.

b. A machine costs $200,000, has a $13,000 salvage value, is expected to last eight years, and will generate an after-tax income of $39,000 per year after straight-line depreciation.

Answer 1

A. 1.89 years

B. 2.33 years

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

(A) After-tax income = $72,115

Expected cost = $250,000

Useful life = 4 years

Salvage value = $10,000

Depreciation Value = ($250,000 - $10,000) ÷ 4 = $60,000

Annual net cashflow = After tax income + Depreciation

= $72,115 + $60,000 = $132,115

Payback Period = Machine expected cost ÷ Annual net cash flow

= $250,000 ÷ $132,115

= 1.89 years

(B) After-tax income = $39,000

Machine cost = $200,000

Useful life = 8 years

Salvage value = $13,000

Depreciation value = ($200,000 - $13,000) ÷ 4 = $46,750

Annual net cashflow = After tax income + Depreciation

= $39,000 + $46,750 = $85,750

Payback Period = Machine expected cost ÷ Annual net cash flow

= $200,000 ÷ $85,750

= 2.33 years