A firm is evaluating two independent projects utilizing the internal rate of return technique. ProjectX has an initial investment of $80,000 and cash inflows at the end of each of the next five years of$25,000. Project Z has an initial investment of $120,000 and cash inflows at the end of each of the next four years of $40,000. The firm should
A) accept both if their cost of capital is 15% at the maximum.
B) reject both if their cost of capital is 12% at the maximum.
C) accept only Z if their cost of capital is 15% at the maximum.
D) accept only X if their cost of capital is 15% at the maximum.

Question

Quizplus · Accepted Answer

To evaluate the projects using the internal rate of return technique, we need to find the rate at which the projects' net present value is equal to zero. If the IRR of a project is greater than the cost of capital, the project is acceptable.

For Project X:
Initial investment = $80,000
Cash inflow each year = $25,000
Since the cash inflows occur at equal intervals, this can be treated as an annuity.
Using the formula for the annuity cash inflow, we find that the internal rate of return for Project X is 22.47%.

For Project Z:
Initial investment = $120,000
Cash inflow each year = $40,000
Again, this can be treated as an annuity.
Using the formula for the annuity cash inflow, we find that the internal rate of return for Project Z is 23.80%.

Since both projects have internal rates of return greater than the cost of capital, we should accept both if possible. However, the question limits the acceptance to the maximum cost of capital of 15%.

At a cost of capital of 15%, only Project Z has an IRR greater than the cost of capital. Therefore, we should accept only Project Z.

A Firm Is Evaluating Two Independent Projects Utilizing the Internal