Calculate the proﬁtability index of a 20-year project with a cost of $400,000 and annual cash ﬂows of $50,000 in years 1-10 and $25,000 in years 11-20. The company's required rate of return is 10%.
A) 0.92
B) 0.98
C) 1.02
D) 1.08
E) 1.15

Question

Quizplus · Accepted Answer

The profitability index is calculated as the present value of the cash flows divided by the initial investment. The present value of the cash flows is calculated as the sum of the present values of each individual cash flow. The present value of a cash flow is calculated as the cash flow multiplied by the discount factor. The discount factor is calculated as 1 / (1 + r)^n, where r is the required rate of return and n is the number of years from the present.In this case, the present value of the cash flows is calculated as follows:PV = $50,000 * (1 / (1 + 0.1)^1) + $50,000 * (1 / (1 + 0.1)^2) + ... + $50,000 * (1 / (1 + 0.1)^10) + $25,000 * (1 / (1 + 0.1)^11) + $25,000 * (1 / (1 + 0.1)^12) + ... + $25,000 * (1 / (1 + 0.1)^20)= $50,000 * 6.14457 + $50,000 * 5.58234 + ... + $50,000 * 0.38554 + $25,000 * 0.34980 + $25,000 * 0.31863 + ... + $25,000 * 0.06355= $307,228.50 + $279,117.00 + ... + $19,277.00 + $8,745.00 + $7,965.75 + ... + $1,588.75= $623,922.00The profitability index is then calculated as follows:PI = PV / Initial Investment= $623,922.00 / $400,000= 1.56Therefore, the profitability index is 1.56, which is greater than 1. This indicates that the project is profitable and should be undertaken.

Calculate the Proﬁtability Index of a 20-Year Project with a Cost