Question

Suppose your firm is considering two mutually exclusive, required projects with the cash flows shown below. The required rate of return on projects of both of their risk class is 8 percent, and that the maximum allowable payback and discounted payback statistic for the projects are 2 and 3 years, respectively.

time	0	1	2	3
project A cash flow	-25,000	15,000	35,000	6,000
project B cash flow	-35,000	15,000	25,000	55,000

Time: 0 1 2 3 Project A Cash Flow -25,000 15,000 35,000 6,000 Project B Cash Flow -35,000 15,000 25,000 55,000

Use the PI decision rule to evaluate these projects; accept the project with the higher PI value.

A. accept A, reject

B. accept neither A nor B

C. reject A, accept B

D. accept both A and B

Answer 1

The profitability index of project A is computed as shown below:

= Present value of future cash flows / Initial investment

Present value is computed as follows:

= Future value / (1 + r)ⁿ

= 15,000 / 1.08 + 35,000 / 1.08² + 6,000 / 1.08³

= 48,658.74015

So, the profitability index will be computed as follows:

= 48,658.74015 / 25,000

= 1.9463 Approximately

The profitability index of project B is computed as shown below:

= Present value of future cash flows / Initial investment

Present value is computed as follows:

= Future value / (1 + r)ⁿ

= 15,000 / 1.08 + 25,000 / 1.08² + 55,000 / 1.08³

= 78,983.13265

So, the profitability index will be computed as follows:

= 78,983.13265 / 35,000

= 2.2567 Approximately

Since the PI of Project B is greater than the PI of Project A, Project B shall be accepted.

So, the correct answer is option C.

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