Carlyle Inc. is considering two mutually exclusive projects. Both require an initial investment of $15,000 at t = 0. Project S has an expected life of 2 years with after-tax cash inflows of $7,000 and $12,000 at the end of Years 1 and 2, respectively. In addition, Project S can be repeated at the end of Year 2 with no changes in its cash flows. Project L has an expected life of 4 years with after-tax cash inflows of $5,200 at the end of each of the next 4 years. Each project has a WACC of 9.00%. What is the equivalent annual annuity of the most profitable project?

Question

Quizplus · Accepted Answer

To find the equivalent annual annuity (EAA), we need to calculate the annual cash flows of each project and then find the uniform series of payments that has the same present value as the project's cash flows.

For Project S, we can calculate the present value (PV) of the cash flows at the end of Year 2 and then use the perpetuity formula to find the equivalent annual annuity:

PV = $7,000 / (1 + 0.09)^1 + $12,000 / (1 + 0.09)^2 = $16,013.05
EAA = [$16,013.05 / ((1 - 1 / (1 + 0.09)^2) / 0.09)] / 2 = $8,301.46

Note that we divide by 2 at the end because Project S can be repeated at the end of Year 2 and the cash flows will be the same.

For Project L, we can calculate the present value of the 4-year cash flows and then use the annuity formula to find the equivalent annual annuity:

PV = $5,200 / (1 + 0.09)^1 + $5,200 / (1 + 0.09)^2 + $5,200 / (1 + 0.09)^3 + $5,200 / (1 + 0.09)^4 = $16,004.51
EAA = $16,004.51 / ((1 - 1 / (1 + 0.09)^4) / 0.09) = $4,698.20

Comparing the two projects, we can see that Project S has a higher EAA of $8,301.46 compared to Project L's EAA of $4,698.20. Therefore, the best choice is Project S.