# Mutually Exclusive/ Equivalent annual annuities

The Company is considering two mutually exclusive projects. Both require an initial investment of $10,000 at t = 0.

Project X has an expected life of 2 years with after-tax cash inflows of $6,000 and $8,500 at the end of Years 1 and 2, respectively.

Project Y has an expected life of 4 years with after-tax cash inflows of $4,500 at the end of each of the next 4 years.

Each project has a WACC of 11%.

Set up the equation to find the equivalent annual annuity of the most profitable project.

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#### Solution Preview

For project X, the cash flows are -10,000, 600, and 8500 for year 0, 1 and 2

Then we use PVi= CFi/ (1+WACC)^i to compute the present value of each cash flow

In the same way, we can compute its NPV:

Year CF PV

0 -10,000 -10,000.00

1 6,000 ...

#### Solution Summary

The solution compares two projects to find the most profitable project.