Question

You are deciding between two mutually exclusive investment opportunities.

Project A requires an investment of $1,000 at t = 0 and generates a perpetual cash flow of $150 starting at t = 1.

Project B requires an investment of $1,000 at t = 0 and generates a cash flow of $60 at t = 1. After t = 1 the cash flow grows at the rate of 4% in perpetuity (so the cash flow at t = 2 is 4% higher than the cash flow at t = 1, the cash flow at t = 3 is 4% higher than the cash flow at t = 2 and so on).

a. Which investment has the higher IRR?

b. Which investment has the higher NPV when the cost of capital is 6%?

c. Which investment should you pick (if any) if the cost of capital is 6%? d. For what range of values for the opportunity cost of capital would you make the opposite decision, compared to part c?

Answer 1

a.

We can calculate the IRR of the two projects using the Goal seek function in excel.

Firstly, we need to calculate the NPV of the two projects. Using the Goal seek function, we need to set the NPV as zero by changing the cell where cost of capital is mentioned. IRR is the cost of capital at which the NPV is zero.

IRR of project A

Formulas:

So, IRR of project A is 15%

IRR of project B

Formulas:

So, IRR of project B is 10.24%

b.

NPV when the cost of capital is 6%

Formulas:

So, NPV of project B is higher than project A.

c.

Project B should be picked as it has a higher NPV and the projects are mutually exclusive which means that only only one of them could be chosen.

d.

Firstly, we need to calculate the cost of capital at which both the projects have the same NPV.

We can calculate this using the goal seek function.

Formulas:

So, if the cost of capital is more than 6.85% and below or equal to the IRR of project A, i.e. 15%, Project A should be chosen over project B.

So, the range is 6.85%-15%.