Question

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

1. A new operating system for an existing machine is expected to cost $520,000 and have a useful life of six years. The system yields an incremental after-tax income of $150,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000.
2. A machine costs $380,000, has a $20,000 salvage value, is expected to last eight years, and will generate an after-tax income of $60,000 per year after straight-ine depreciation. Assume the company requires a 10% rateo return on its vestments.

Answer 1

The payback period is the time that a project needs to recover its initial investment.

1) initial investment = -$520,000

salvage value = $10,000

depreciation per year = $510,000 / 6 years = $85,000

incremental cash flow = $150,000 + $85,000 = $235,000

payback period = $520,000 / $235,000 = 2.212 years or 2 years, 2 months and 17 days.

2) initial investment = -$380,000

salvage value = $20,000

depreciation per year = $320,000 / 8 years = $40,000

incremental cash flow = $60,000 + $40,000 = $100,000

payback period = $380,000 / $100,000 = 3.8 years or 3 years, 9 months and 18 days.

Answer 2

1.

2.2 years

2.

3.6 years

Step-by-step explanation:

Payback period is the time in which a project returns back the initial investment in the form of net cash flow. For this purpose we use the net cash flows to calculate the payback.

1.

to calculate the net cash flow we need to adjust the depreciation in incremental after tax income.

Depreciation = ( $520,000 - $10,000 ) / 6 = $85,000

Add this depreciation in the depreciation in incremental after tax income.

Net Cash flow = $150,000 + $85,000 = $235,000

Payback Period = Initial Investment / Incremental net cash flow each year

Payback Period = $520,000 / $235,000 = 2.2 years

2.

to calculate the net cash flow we need to adjust the depreciation in incremental after tax income.

Depreciation = ( $380,000 - $20,000 ) / 8 = $45,000

Add this depreciation in the depreciation in incremental after tax income.

Net Cash flow = $60,000 + $45,000 = $105,000

Payback Period = Initial Investment / Incremental net cash flow each year

Payback Period = $380,000 / $105,000 = 3.6 years