A 25- year project has a cost of $1,500,000 and has annual cash ﬂows of $400,000 in years 1-15, and $200,000 in years 16-25. The company's required rate is 14%. Given this information, calculate
The proﬁtability index of the project.

Question

Quizplus · Accepted Answer

To calculate the profitability index, we need to find the present value of the cash flows and divide it by the initial investment.

PV of cash flows in years 1-15 = $400,000 x [(1 - 1/(1 + 0.14)^15)/0.14] = $2,440,570
PV of cash flows in years 16-25 = $200,000 x [(1 - 1/(1 + 0.14)^10)/0.14] = $1,096,643
PV of all cash flows = $2,440,570 + $1,096,643 = $3,537,213

Profitability index = PV of cash flows / Initial investment = $3,537,213 / $1,500,000 = 1.74

Therefore, the best choice is A, with a profitability index of 1.74, indicating that the project is profitable and should be undertaken.

A 25- Year Project Has a Cost of $1,500,000 and Has