Question

Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 8 percent, and that the maximum allowable payback and discounted payback statistics for the project are 3.5 and 4.5 years, respectively.

Time:	0	1	2	3	4	5	6
Cash flow:	−$5,000	$1,200	$2,400	$1,600	$1,600	$1,400	$1,200

Use the payback decision rule to evaluate this project. (Round your answer to 2 decimal places.)

Payback _______ years

Should it be accepted or rejected?

Answer 1

To calculate the payback period, we need to calculate the cumulative cash flows

Payback period is the period when the cumulative cash flow becomes positive

Time	Cash Flow	Cumulative Cash Flow
0	-5000	-5000
1	1200	-3800
2	2400	-1400
3	1600	200
4	1600	1800
5	1400	3200
6	1200	4400

Hence, Payback period = 2 + 1400/1600 = 2.875 years

To calculate the discounted payback period, we need to find the discounted cumulative cash flow

Discounted cash flow = Cash Flow / (1 + discount Rate)^year

Time	Cash Flow	Discounted Cash Flow	Cumulative Cash Flow
0	-5000	-5000	-5000
1	1200	1111.111111	-3888.8889
2	2400	2057.613169	-1831.2757
3	1600	1270.131586	-561.14413
4	1600	1176.047764	614.90363
5	1400	952.8164758	1567.72011
6	1200	756.2035523	2323.92366

Discounted Payback period = 3 + 561.14/1176.05 = 3.477 years

Since, both the payback period and discounted payback period is within the maximum allowable threshold, the project should be accepted