Question

Problem 10-05 Payback A project has an initial cost of $54,075, expected net cash inflows of $11,000 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.

Answer 1

1. Discount the cash flows back to their present value:

Year 0: -54,075/(1+.12)^0 = -54,075

Year 1 : 11,000/(1+.12)^1 = 9,821.43

Year 2: 11,000/(1+.12)^2 = 8,769.13

Year 3: 11,000/(1+.12)^3 = 7,829.58

Year 4: 11,000/(1+.12)^4 = 6,990.70

Year 5: 11,000/(1+.12)^5 = 6,241.70

Year 6: 11,000/(1+.12)^6 = 5,572.94

Year 7: 11,000/(1+.12)^7 = 4,975.84

Year 8: 11,000/(1+.12)^8 = 4,442.72

2. Calculate the cumulative discounted cash flows:

Year 0: -54,075

Year 1: -44,253.57

Year 2: -35,484.44

Year 3: -27,654.86

Year 4: -20,664.16

Year 5: -14,422.46

Year 6: -8,849.52

Year 7: -3,873.68

Year 8: 569.04

Payback period occurs when the negative cumulative discounted cash flows turn into positive cash flows which, in this case, is between the seventh and eighth year.

Payback Period = Year Before Payback Period Occurs + Cumulative Cash Flow in Year Before Recovery ÷ Discounted Cash Flow in Year After Recovery

So,

Payback Period in this case = 7 + 3873.68/4,442.72

= 7.87 years