A firm is reviewing a project that has an initial cost of $71,000. The project will produce annual cash inflows, starting with year 1, of $8,000, $13,400, $18,600, $33,100 and finally in year five, $37,900. What is the profitability index if the discount rate is 11 percent?
A) 0.92
B) 0.98
C) 1.02
D) 1.07
E) 1.12

Question

Quizplus · Accepted Answer

To calculate the profitability index, we need to divide the present value of the future cash inflows by the initial cost:
PV of Year 1 cash inflow = $8,000 / (1 + 0.11)^1 = $7,207.21
PV of Year 2 cash inflow = $13,400 / (1 + 0.11)^2 = $10,648.02
PV of Year 3 cash inflow = $18,600 / (1 + 0.11)^3 = $12,635.54
PV of Year 4 cash inflow = $33,100 / (1 + 0.11)^4 = $20,020.43
PV of Year 5 cash inflow = $37,900 / (1 + 0.11)^5 = $22,796.78

Total PV of cash inflows = $73,307.98

Profitability index = Total PV of cash inflows / Initial cost
= $73,307.98 / $71,000
= 1.07

Therefore, the profitability index is 1.07, which means that for every dollar invested, the project will return $1.07 in present value. Choice D is the best answer.

A Firm Is Reviewing a Project That Has an Initial