Equivalent Annual Annuity (EAA)
Constant annual cash flow that, over the project's life and at the project's discount rate, would produce the same NPV. Standardizes NPV across projects of different lifespans for fair comparison.
When to use: Use when comparing projects with different durations — e.g., a 5-year project with NPV $100K vs a 10-year project with NPV $150K. Direct NPV comparison is misleading because the longer project has had more time to compound; EAA gives a yearly equivalent that lets you compare them on equal footing.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| EAA | Equivalent Annual Annuity | Annual cash flow that would yield the same NPV over the project life | $ |
| NPV | Net Present Value | Present value of all cash flows discounted at the required rate | $ |
| k | Discount Rate | Cost of capital or required rate of return as a decimal (e.g. 0.10 for 10%) | % |
| n | Project Life | Number of years over which to spread the NPV | years |
Real-Life Examples
Example 1: 4-Year Project EAA
NPV is $267.95, discount rate 10%, project life 4 years.
Given
Step-by-Step
$84.53/year — the project is equivalent in value to receiving $84.53 per year for the 4-year life. Compare directly against another project's EAA regardless of differing horizons.
Example 2: Longer Project Comparison
A 10-year project has NPV $500. Discount rate 8%.
Given
Step-by-Step
$74.51/year. Despite the higher absolute NPV, the 4-year project above ($84.53/year) creates more annualized value — useful insight when ranking under capital constraints.
Frequently Asked Questions
Because NPV scales with project length. A 20-year project will almost always have higher NPV than a 5-year project at the same scale, even if the 5-year project is more efficient. EAA strips away the duration effect and shows you the value-per-year equivalent.
Mathematically yes — it's the payment that, paid annually for n years and discounted at k, has present value equal to NPV. Conceptually different though: EAA describes the value of the project, not the payment on a loan or annuity.
When the assumption of "indefinite chained replication" doesn't hold — EAA implicitly assumes you could repeat the project. If the underlying opportunity is one-of-a-kind and won't recur, NPV is the more honest comparison.