An investment project provides cash inflows of $675 per year for eight years.

Problem 9-2 Calculating Payback [LO2]
An investment project provides cash inflows of $675 per year for eight years.
a.    What is the project payback period if the initial cost is $1,850? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)

b.    What is the project payback period if the initial cost is $3,600? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)
c.    What is the project payback period if the initial cost is $5,500? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)


Explanation
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

To calculate the payback period, we need to find the time that the project requires to recover its initial investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is $1,850, the payback period is:

Payback = 2 + ($500/$675) = 2.74 years
 
There is a shortcut to calculate the payback period when the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the $3,600 cost, the payback period is:

Payback = $3,600/$675 = 5.33 years
 
The payback period for an initial cost of $5,500 is a little trickier. Notice that the total cash inflows after eight years will be:

Total cash inflows = 8($675) = $5,400

If the initial cost is $5,500, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get:

Payback = $5,500/$675 = 8.15 years

This answer does not make sense since the cash flows stop after eight years, so again, we must conclude the payback period is never.