# Equivalent Annual Annuity (EAA)

Comparing projects with unequal lives

## What is the Equivalent Annual Annuity?

Equivalent Annual Annuity (or EAA) is a method of evaluating projects with different life durations. Traditional project profitability metrics such as NPV, IRR, or payback period provide a very valuable perspective on how financially viable projects are overall. EAA is a metric used to determine how financially efficient projects are.

### How to Calculate Equivalent Annual Annuity

Equivalent Annual Annuity essentially smoothes out all cash flows and generates a single average cash flow for all periods that (when discounted) equal the project’s NPV. EAA is calculated using the following formula:

Where:

r -Project discount rate (WACC)

NPV – Net present value of project cash flows

– Project life (in years)

### Equivalent Annual Annuity Example

Suppose that Sally’s Doughnut Shop is considering purchasing one of two machines. Machine A is a dough mixing machine that has a useful life of 6 years. During this time, the machine will enable Sally to realize significant cost savings and represents an NPV of \$4 million.

Machine B is an icing machine with a useful life of 4 years. During this time, the machine will allow Sally’s to reduce icing waste and represents an NPV of \$3 million. Sally’s Doughnut Shop has a cost of capital of 10%. Which machine should the company invest in?

Using the Equivalent Annual Annuity method:

This EAA number tells us what the average cash flow from each machine will be, given their NPVs and useful lives. Using the EAA method, we see that Machine B has a higher EAA. Thus, we would recommend that Sally’s invest in this machine. Another way to think of EAA is that it measures the financial efficiency of each project (i.e., the average annual cash flow that the business will see).

### Further Considerations

Using the traditional NPV approach, we see that Machine A has a higher NPV than Machine B. Thus, we would recommend that Sally’s invest in Machine A. However, which machine Sally’s decides to invest in depends on the business’ situation and goals.

For example, if the company is facing difficulties making interest payments on its debt, choosing a project with a lower NPV but higher average cash flows may be a better decision. In contrast, if the business is financially healthy, going with the highest NPV-project may be the way to go since this will provide the greatest financial benefit.