The payback period on the new machine is closest to:
A) 1.4 years.
B) 2.7 years.
C) 3.6 years.
D) 5.0 years.

Question

Quizplus · Accepted Answer

To calculate the payback period, we need to find out how long it takes for the investment to generate an amount of cash flows equal to the initial investment.

Payback period = Initial Investment / Annual Cash Inflows

For the new machine, the initial investment is $20,000 and the annual cash inflows are:

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

Using the formula above, we can calculate the payback period as follows:

Payback period = $20,000 / $5,000 = 4 years

Since the payback period falls between Year 3 and Year 4, we need to use linear interpolation to find a more precise estimate.

Payback period = Year 3 + (Amount left to recover / Cash flow in Year 4)

Amount left to recover = $20,000 - ($5,000 + $8,000 + $7,000) = $20,000 - $20,000 = $0

Payback period = 3 + ($0 / $4,000) = 3 years

Therefore, the payback period on the new machine is closest to 2.7 years, which is Choice B.

The Payback Period on the New Machine Is Closest To