Compute the payback period for each of these two separate investments: A new operating system for an existing machine is expected to cost $290,000 and have a useful life of six 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. A machine costs $190,000, has a $15,000 salvage value, is expected to last eight years, and will generate an after-tax income of $46,000 per year after straight-line depreciation.

Payback period is the number of years it takes a project's expected future cashflows to fully recover the initial outlay.

a.) New Operating system;

Year CF Net CF

0 - 290,000 - 290,000

1 83,653 - 206,347

2 83,653 - 122,694

3 83,653 - 39,041

4 83,653 44,612

Payback period = last year with negative net CF + (absolute value of Net CF that year / Total CF the following year)

Payback = 3 + (39,041 / 83,653)

= 3 + 0.4667

= 3.47 years

b.) Machine

Year CF Net CF

0 - 190,000 - 190,000

1 46,000 - 144,000

2 46,000 - 98,000

3 46,000 - 52,000

4 46,000 - 6,000

5 46,000 40,000

Payback period = 4 + (6,000/46,000)

= 4+0.1304

= 4.13 years