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

a. 3.53 years, reject

b. 3.35 years, reject

c. 2.57 years, accept

d. 2.65 years, accept

Answer 1

The discounted payback period is computed as shown below:

Cumulative discounted cash flows from year 1 to year 3 is computed as follows:

= 60 / 1.14¹ + 540 / 1.14² + 740 / 1.14³

= 967.6229663

Cumulative discounted cash flows from year 1 to year 4 is computed as follows:

= 60 / 1.14¹ + 540 / 1.14² + 740 / 1.14³ + 740 / 1.14⁴

= 1,405.762372

It means that the discounted payback period lies between year 3 and year 4, since the initial investment of $ 1,120 is recovered between them. So, the discounted payback period will be computed as follows:

= 3 years + Balance investment to be recovered / Year 4 discounted cash flow

= 3 years + [ (1,120 - 967.6229663) / ( 720/ 1.14⁴) ]

= 3 years + 152.3770337 / 426.2977997

= 3.35 years Approximately

Since the discounted payback period is greater than the maximum allowable discounted payback period of 3 years, hence the project shall be rejected.

Hence the correct answer is option b.

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