Equivalent Annual Annuity (EAA) Approach

The Equivalent Annual Annuity (EAA) approach converts the net present value (NPV) of a project into a constant annual cash flow—an “annuity”—that yields the same present value over the project’s life. EAA is commonly used in capital budgeting to compare mutually exclusive projects that have unequal lives. When comparing such projects, the one with the higher EAA is preferred.

When to use EAA

• Comparing mutually exclusive projects with different durations (unequal lives).
• Choosing between projects when you want a per-year economic comparison rather than a one-time NPV number.
• Useful when projects are repeatable and can be thought of as perpetually replaced.

How it works (three steps)

1. Calculate each project’s NPV using the appropriate discount rate.
2. Convert each NPV into an equivalent annual cash flow (the EAA).
3. Compare the EAAs and select the project with the higher EAA.

Formula

C = (r × NPV) / (1 − (1 + r)^−n)

Where:
* C = equivalent annual annuity (annual cash flow)
* NPV = net present value of the project
* r = discount rate (interest rate per period)
* n = number of periods (project life in years)

You can compute C using:
* A financial calculator (use PMT function with PV = −NPV), or
* A spreadsheet: =PMT(r, n, -NPV)

Examples

Example 1 — choose between two projects with different lives:
* Company WACC = 10%
* Project A: NPV = $3,000,000, n = 5 → EAA = $791,392.44
* Project B: NPV = $2,000,000, n = 3 → EAA = $804,229.61
Result: Choose Project B (higher EAA).

Example 2 — numeric illustration with formula:
* Project A: NPV = $100,000, n = 7, r = 6%
* EAA = (0.06 × 100,000) / (1 − (1.06)^−7) ≈ $17,914
* Project B: NPV = $120,000, n = 9, r = 6%
* EAA = (0.06 × 120,000) / (1 − (1.06)^−9) ≈ $17,643
Result: Choose Project A (higher EAA).

Quick note on annuities

An annuity is a stream of equal payments made at regular intervals. EAA treats a project’s NPV as if it were the present value of an annuity to derive an equivalent annual payment.

Advantages

• Makes projects with different time horizons directly comparable on an annualized basis.
• Simple to compute using standard financial functions.

Limitations and cautions

• EAA assumes projects can be repeated or replaced at the same economics; if not, interpretation is less clear.
• It ignores differences in project scale—NPV still shows absolute value added, while EAA shows annualized return.
• Does not account for differing risk profiles unless discount rates are adjusted appropriately.
• For projects with significant non-periodic cash flows or varying cash-flow patterns, EAA is only an approximation.

Key takeaways

• EAA converts NPV into an equivalent annual cash flow to compare projects with unequal lives.
• Compute NPV first, then apply the EAA formula or a PMT function to get the annualized value.
• Choose the project with the higher EAA, keeping in mind assumptions about repeatability, scale, and risk.