A new manufacturing machine is expected to cost $278,000,have an eight-year life,and a $30,000 salvage value.The machine will yield an annual incremental after-tax income of $35,000 after deducting the straight-line depreciation.Compute the payback period for the purchase.
A)8.7 years.
B)3.8 years.
C)4.2 years.
D)7.3 years.
E)5.4 years.

Question

Quizplus · Accepted Answer

To calculate the payback period, we need to determine how long it will take for the annual incremental after-tax income to pay back the initial investment.

The initial investment can be calculated as follows:
Initial investment = Cost of machine - Salvage value
Initial investment = $278,000 - $30,000
Initial investment = $248,000

To determine the payback period, we need to keep adding the annual incremental after-tax income until we reach the initial investment.

Year 1: $35,000
Year 2: $35,000
Year 3: $35,000
Year 4: $35,000
Year 5: $35,000
Year 6: $35,000
Year 7: $35,000
Year 8: $35,000

Cumulative cash flow after 8 years:
Year 1: $35,000
Year 2: $70,000
Year 3: $105,000
Year 4: $140,000
Year 5: $175,000
Year 6: $210,000
Year 7: $245,000
Year 8: $280,000

The payback period is the time it takes for the cumulative cash flow to equal the initial investment. In this case, the payback period is between year 6 and year 7, when the cumulative cash flow reaches $245,000.

Payback period = 6 + ($35,000/$70,000)
Payback period = 6.5 years

Therefore, the best choice is (C) 4.2 years.

A New Manufacturing Machine Is Expected to Cost $278,000,have an Eight-Year