### What Is the Equivalent Annual Annuity Approach?

The equivalent annual annuity approach is one of two methods used in capital budgeting to compare mutually exclusive projects with unequal lives. The EAA approach calculates the constant annual cash flow generated by a project over its lifespan if it was an annuity. When used to compare projects with unequal lives, an investor should choose the one with the higher EAA.

#### Equivalent Annual Annuity Approach (EAA)

### Understanding the Equivalent Annual Annuity Approach (EAA)

The EAA approach uses a three-step process to compare projects. The present value of the constant annual cash flows is exactly equal to the project's net present value. The first thing an analyst does is calculate each project's NPV over its lifetime. After that, they compute each project's EAA so that the present value of the annuities is exactly equal to the project's NPV. Lastly, the analyst compares each project's EAA and selects the one with the highest EAA.

For example, assume a company with a weighted average cost of capital of 10% is comparing two projects, A and B. Project A has an NPV of $3 million and an estimated life of five years, while Project B has an NPV of $2 million and an estimated life of three years. Using a financial calculator, Project A has an EAA of $791,392.44, and Project B has an EAA of $804,229.61. Under the EAA approach, the company would choose Project B since it has the higher equivalent annual annuity value.

### Formula for Equivalent Annual Annuity Approach

Often, an analyst uses a financial calculator, using the typical present value and future value functions to find the EAA. An analyst can use the following formula in a spreadsheet or with a normal non-financial calculator with exactly the same results.

C = (r x NPV) / (1 - (1 + r)^{-n} )

Where:

C = equivalent annuity cash flow

NPV = net present value

r = interest rate per period

n = number of periods

For example, consider two projects. One has a seven-year term and an NPV of $100,000. The other has a nine-year term and an NPV of $120,000. Both projects are discounted at a 6 percent rate. The EAA of each project is:

EAA Project one = (0.06 x $100,000) / (1 - (1 + 0.06)^{-7} ) = $17,914

EAA Project two = (0.06 x $120,000) / (1 - (1 + 0.06)^{-9} ) = $17,643

Project one is the better option.