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

(a) A new operating system for an existing machine is expected to cost $260,000 and have a useful life of four years. The system yields an incremental after-tax income of $75,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000.

(b) A machine costs $170,000, has a $14,000 salvage value, is expected to last nine years, and will generate an after-tax income of $41,000 per year after straight-line depreciation.

1.89 years and 2.91 years

Explanation:

The formula to compute the payback period is shown below:

= Initial investment : Net cash flow

For first case

The initial investment is $260,000

And, the net cash flow is shown below:

= Depreciation + incremental after tax income

where,

Depreciation equals to

= (Original cost - residual value) : (useful life)

= ($260,000 - $10,000) : (4 years)

= ($20,000) : (4 years)

= $62,500

And the incremental after tax income is $75,000

So, the net cash flow would equal to

= $62,500 + $75,000

= $137,500

So, the payback period would be

= $260,000 : $137,500

= 1.89 years

For second case

The initial investment is $170,000

And, the net cash flow is shown below:

= Depreciation + incremental after tax income

where,

Depreciation equals to

= (Original cost - residual value) : (useful life)

= ($170,000 - $14,000) : (9 years)

= ($156,000) : (9 years)

= $17,333

And the incremental after tax income is $41,000

So, the net cash flow would equal to

= $17,333 + $41,000

= $58,333

So, the payback period would be

= $170,000 : $58,333

= 2.91 years