Question

Thanks!

Problem 10-05 Payback A project has an initial cost of $50,050, expected net cash inflows of $12,000 per year for 8 years, and a cost of capital of 12%. What is the project's payback period? Round your answer to two decimal places. years

Answer 1

Payback period is the time required for the operating cash inflows to recover the initial investment in a project.

Here, initial investment = $50050

Cumulative cash flows after year 1 = $12000

Cumulative cash flows after year 2 = $12000 + $12000 = $24000

Cumulative cash flows after year 3 = $12000 + $12000 + $12000 = $36000

Cumulative cash flows after year 4 = $12000 + $12000 + $12000 + $12000 = $48000

Cumulative cash flows after year 5 = $12000 + $12000 + $12000 + $12000 + $12000 = $60000

The cumulative cash flows reach the initial investment amount of $50050 sometime in year 5.

Therefore the payback period would be more than 4 years and less than 5 years. Steps in the calculation of payback period are given below:

a. Amount of cash flow in year 5 needed to reach $50050 cumulative cash flows:

$50050 - $48000 (year 4's cumulative cash flow amount) = $2050

b. Percentage of year 5 until cumulative amount of $50050 is reached:

$2050 / $12000 = 0.171

c. Payback period = 4 + 0.171 = 4.171 years