Compute the payback period for each of these two separate investments: 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. 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-line depreciation.

The payback period for each of these two separate investments is 2.21 years and 3.62 years respectively.

Explanation:

Pay back period: The pay back period denotes that period in which the borrower is pay back the loan amount.

It shows a relationship between initial investment and annual cash inflows.

Mathematically,

Payback period = Initial Investment : Annual cash inflows

where,

initial investment is the purchase amount

and, annual cash flows = incremental income + depreciation

1. For one investment, the depreciation amount is

= (Purchase amount - salvage value) : useful life

= ($520,000 - $10,000) : 6

= $85,000

So annual cash flows = $150,000 + $85,000

= $235,000

Hence, the payback period = $520,000 : $235,000

= 2.21 years

2. For second investment, the depreciation amount is

= (Purchase amount - salvage value) : useful life

= ($380,000 - $20,000) : 8

= $45,000

So annual cash flows = $60,000 + $45,000

= $105,000

Hence, the payback period = $380,000 : $105,000

= 3.62 years

Thus, the payback period for each of these two separate investments is 2.21 years and 3.62 years respectively.