# Equivalent Annual Annuity (EAA) Approach: Overview and Formulas

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## What Is the Equivalent Annual Annuity (EAA) Approach?

The equivalent annual annuity (EAA) approach is one of two methods used in [capital budgeting](https://www.investopedia.com/terms/c/capitalbudgeting.asp) to compare [mutually exclusive](https://www.investopedia.com/terms/m/mutuallyexclusive.asp) projects with unequal lives. The EAA approach calculates the constant annual cash flow generated by a project over its lifespan if it were an annuity. When used to compare projects with unequal lives, an investor should choose the one with the higher EAA.

### Key Takeaways

*   When used to compare projects with unequal lives, an investor should choose the one with the higher equivalent annual annuity (EAA).
*   An analyst could use a financial calculator with the typical present value and future value functions to find the EAA.

## Understanding the Equivalent Annual Annuity (EAA) Approach

The EAA approach uses a three-step [process to compare projects](https://www.investopedia.com/terms/e/eac.asp). The present value of the constant annual cash flow is exactly equal to the project's [net present value](https://www.investopedia.com/terms/n/npv.asp) (NPV). 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, let's say a company with a [weighted average cost of capital](https://www.investopedia.com/terms/w/wacc.asp) 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.

## Calculating the Equivalent Annual Annuity (EAA)

Often, an analyst will use a financial calculator with the typical present value and [future value](https://www.investopedia.com/terms/f/futurevalue.asp) functions to find the EAA.

An analyst can use the following formula in a spreadsheet or with a non-financial calculator with exactly the same results.

*   C = (r x NPV) / (1 - (1 + r) )

Where:

*   C = equivalent annuity cash flow
*   NPV = net present value
*   r = interest rate per period
*   n = number of periods

For example, consider two projects. Project A has a seven-year term and an NPV of $100,000. Project B 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 A = (0.06 x $100,000) / (1 - (1 + 0.06) ) = $17,914
*   EAA Project B = (0.06 x $120,000) / (1 - (1 + 0.06) ) = $17,643

Project A is the better option.

## What Is an Annuity?

An annuity is a contract between an investor and an [insurance](https://www.investopedia.com/terms/i/insurance.asp) company. Typically used in retirement, an annuity guarantees that you won't outlive your savings. However, they may come with high fees. One fee is the [surrender charge](https://www.investopedia.com/terms/s/surrendercharge.asp), which you would need to pay if you withdrew a certain amount of funds from the annuity during the surrender period, which can last up to two decades or so. Details vary from contract to contract, so if you're considering an annuity, be sure to read the fine print.

## What Kinds of Annuities Are There?

There are a few types of annuities. [Fixed annuities](https://www.investopedia.com/terms/f/fixedannuity.asp) offer a guaranteed interest rate, which means a minimum amount of income on a periodic basis. [Variable annuities](https://www.investopedia.com/terms/v/variableannuity.asp) allow you to invest in the market. [Indexed annuities](https://www.investopedia.com/terms/i/indexedannuity.asp) track a particular [index](https://www.investopedia.com/terms/i/index.asp), such as the [S&P 500](https://www.investopedia.com/terms/s/sp500.asp).

Annuities' payouts can be immediate or deferred.

## What Is the Formula for the Equivalent Annual Annuity Approach?

The formula for the equivalent annual annuity is:

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

## The Bottom Line

The equivalent annual annuity approach is a method used to compare projects that will each last a specific amount of time. You can use a financial calculator to help you determine which project is best, or you can try your hand at these formulas.