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 14 percent, and that the maximum allowable payback and discounted payback statistic for the project are 2 and 3 years, respectively.

Time	0	1	2	3	4	5	6
Cash Flow	-1,120	60	540	740	740	340	740

Use the payback decision rule to evaluate this project; should it be accepted or rejected?

Answer 1

Payback period is the period in which the initial investment is recovered.

Initial Investment = $1120

Amount recovered in Year 1 = $60

Amount recovered in Year 2 = $540

Amount left to be recovered = $1120 - ($60 + $540) = $520

Therefore, payback period = (2 + 520/740) years = 2.70 years

Because the maximum allowable payback statistic is 2 years, the project should not be accepted using the payback period rule.

Discounted payback period

Discount payback period is the period when the discounted values of cash flows is equal to the initial investment.

Initial Investment = $1120

Discounted value of Year 1 cash flow = $60/(1+14%) = 60/1.14 = $52.63

Discounted value of Year 2 cash flow = $540/(1+14%)² = 540/1.14² = $415.51

Discounted value of Year 3 cash flow = $740/(1+14%)³ = 740/1.14³ = $499.48

Discounted value of Year 4 cash flow =  $740/(1+14%)⁴ = 740/1.14⁴ = $438.14

Discounted payback period = (3 + ($1120-$52.63-$415.51-$499.48)/$438.14) years = 3.35 years

Because the maximum allowable discounted payback statistic is 3 years, the project should not be accepted using the discounted payback period rule.

So, the project should be rejected.