Question

A project that provides annual cash flows of $11,700 for 9 years costs $63,000 today.

a. What is the NPV for the project if the required return is 8%
b. What is the profitability index for this project when the required return is 8%?
c. What is the NPV for the project if the required return is 20%?
d. What is the profitability index for this project when the required return is 20%? e. At what discount rate would you be indifferent between accepting or rejecting the project?

Answer 1

The NPV for the project can be calculated by discounting the cash flows at the required return rate. The profitability index is the present value of cash inflows divided by the initial investment. The discount rate at which you would be indifferent between accepting or rejecting the project can be found by setting the NPV equation equal to zero and solving for the discount rate.

Step-by-step explanation:

a. To calculate the NPV, we need to discount the cash flows at the required return rate. For an 8% required return, the NPV can be calculated as follows:

NPV = (Cash Flow Year 1 / (1 + Required Return)^1) + (Cash Flow Year 2 / (1 + Required Return)^2) + ... + (Cash Flow Year 9 / (1 + Required Return)^9) - Initial Cost

Using the given information, the NPV for the project at an 8% required return is:

NPV = (11,700 / (1 + 0.08)^1) + (11,700 / (1 + 0.08)^2) + ... + (11,700 / (1 + 0.08)^9) - 63,000

b. The profitability index is calculated by dividing the present value of cash inflows by the initial investment. For an 8% required return, the profitability index can be calculated as follows:

Profitability Index = (Present Value of Cash Inflows / Initial Investment)

c. To calculate the NPV at a 20% required return, we use the same formula as in part a, but with a different required return rate. The NPV can be calculated as follows:

NPV = (11,700 / (1 + 0.20)^1) + (11,700 / (1 + 0.20)^2) + ... + (11,700 / (1 + 0.20)^9) - 63,000

d. To calculate the profitability index at a 20% required return, we use the same formula as in part b, but with a different required return rate. The profitability index can be calculated as follows:

Profitability Index = (Present Value of Cash Inflows / Initial Investment)

e. To find the discount rate at which you would be indifferent between accepting or rejecting the project, you need to find the discount rate that makes the NPV equal to zero. This can be done by setting up the NPV equation and solving for the discount rate. For example:

(11,700 / (1 + Discount Rate)^1) + (11,700 / (1 + Discount Rate)^2) + ... + (11,700 / (1 + Discount Rate)^9) - 63,000 = 0