# What is an Equivalent Annual Annuity?

An equivalent annual annuity (EAA) calculation is used to evaluate investment projects that have unequal lives. If an investment analyst or portfolio manager compares two different investments with two different maturity dates, this calculation can help to determine the better investment opportunity. In general, investments are assessed by comparing risk and return. Longer dated investments have a higher degree of risk since they take longer to pay back the investor. As such, it is important to take the length of the investment into consideration before making a final purchase decision.

If there are two different terms to maturity for investments, it makes it difficult to compare return values since longer term securities are usually riskier. The equivalent annual annuity compares multiple opportunities with different terms to maturity by setting them all to one year. That is, the calculation translates return into an equivalent annual rate so that all investments can be compared and assessed on equal terms.

For example, if an investor has to choose between two investments that both cost $100,000 US Dollars (USD), he needs to know how long the two investments will provide value before making a final determination. The first investment has a maturity of five years and the second investment has a maturity of two years. Since the second investment has a shorter maturity, it is less risky and will therefore provide a lower rate of return. This determination is obvious for investments with the same initial investment value, but it becomes more challenging when the two amounts are not equal.

The EAA calculation provides an analyst with a way to compare different investment values with different time horizons by comparing total costs. The investment with the lowest cost is the better deal. For instance, if one investment has a measure of $5,000 USD and another investment has a measure of $2,500 USD, the second investment is the better deal since it has the lowest annual cost.

The actual calculation is complex. The two variables are the present value of cash flows (PV) and the annuity factor. Specifically, the EAA is calculated by dividing the PV by the annuity factor. The annuity factor is determined with the following formula: [1/r - 1/r(1+r)^t], where r is the rate of return or discount factor, and t is the time period. The investment with the larger present value and/or the lowest annuity factor will have the lowest cost.

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