Key takeaways
– Equivalent Annual Annuity (EAA) converts a project’s net present value (NPV) into an equal, constant annual cash flow over the project’s life so projects with unequal lives can be compared.
– Compute each project’s NPV using the same discount rate, convert each NPV into an annual payment (EAA), then choose the project with the higher EAA.
– EAA assumes projects are repeatable or will be replaced indefinitely under the same economics; if that assumption fails (or other differences exist), interpret results cautiously.
What is the Equivalent Annual Annuity (EAA) approach?
The EAA approach is a capital‑budgeting technique for comparing mutually exclusive projects that have different lifespans. Instead of comparing raw NPVs (which may favor longer projects simply because they last longer), EAA asks: “If I turned each project’s NPV into a level annuity payment over its life, what annual amount would each project produce?” The project with the larger annual equivalent is preferred.
Why use EAA?
– It makes NPVs for projects of unequal lengths directly comparable on a per‑year basis.
– It is especially useful when projects are repeatable (you would replace them when they end) and when you want to compare projects on an annual cash‑flow basis rather than total lifetime value.
Basic idea and derivation
If a project has NPV (present value) = NPV, discount rate r per period, and life n periods, then the present value of a level annuity C paid each period for n periods is:
NPV = C × [1 − (1 + r)^(−n)] / r
Solve for C (the EAA):
C = (r × NPV) / [1 − (1 + r)^(−n)]
Alternatively, define the annuity factor (PVIFA): PVIFA(r,n) = [1 − (1 + r)^(−n)] / r, and then C = NPV / PVIFA.
Step‑by‑step practical procedure
1. Choose the discount rate that reflects project risk (often WACC for corporate projects) and use the same rate for all projects being compared.
2. For each candidate project, estimate its cash flows and compute NPV (including initial investment and salvage, tax effects, working capital, etc.).
3. For each project, compute EAA using the formula:
C = (r × NPV) / [1 − (1 + r)^(−n)]
or equivalently: C = NPV / PVIFA(r,n).
4. Compare EAAs. The project with the highest EAA produces the greatest equivalent annual value and is preferred (if projects are mutually exclusive).
5. Check assumptions: ensure projects are comparable on risk, and consider capital constraints, replacement timing, and any non‑repeatable features (salvage, learning effects, etc.).
Worked examples
Example 1 (from Investopedia-style numbers)
– WACC r = 10%
– Project A: NPV = $3,000,000; n = 5 years
C_A = 0.10×3,000,000 / [1 − (1.10)^−5] ≈ $791,392.44 per year
– Project B: NPV = $2,000,000; n = 3 years
C_B = 0.10×2,000,000 / [1 − (1.10)^−3] ≈ $804,229.61 per year
Decision: Project B is preferred because its EAA is larger, even though A has a larger total NPV.
Example 2
– r = 6%
– Project A: NPV = $100,000; n = 7 → C_A ≈ $17,927 per year
– Project B: NPV = $120,000; n = 9 → C_B ≈ $17,643 per year
Decision: Project A is slightly better on an annual equivalent basis.
How to compute in a spreadsheet or calculator
– Excel / Google Sheets:
– Use the formula directly: = (r * NPV_value) / (1 – (1 + r)^(-n))
– Or use PMT to get the periodic payment: =PMT(r, n, -NPV_value)
(PMT returns the fixed payment equivalent to a present value, so sign conventions matter.)
– Financial calculator: input PV = NPV (as a negative number if required), i = r, n = periods, then compute the payment (PMT).
– Manual: compute PVIFA(r,n) = [1 − (1 + r)^−n] / r, then EAA = NPV / PVIFA.
When EAA is appropriate—and when it isn’t
Appropriate when:
– Projects are repeatable or will be replaced under similar conditions.
– You want to compare per‑year economic contribution between alternatives.
– Projects are mutually exclusive and you can choose only one.
Not appropriate / use with caution when:
– Projects are one‑off, nonrepeatable, or have different risk profiles.
– Projects have different salvage values, timing of cash flows, or important nonmonetary differences.
– Capital is rationed and you care about total value created rather than annualized value.
– You need to consider option value, strategic fit, or other qualitative factors.
Assumptions and limitations
– Same discount rate for all projects (assumes equal risk).
– Implicit assumption that the project can be replicated or “restarted” when it ends; comparing projects of unequal lives without that assumption may be misleading.
– EAA compares scale on a per‑period basis; if total wealth maximization is the objective and projects are not repeatable, raw NPV may be more relevant.
– Taxes, inflation, and timing conventions must be handled consistently across projects.
Bottom line
EAA is a simple, practical way to convert NPVs into comparable annual streams when comparing projects of unequal lives. Perform consistent NPVs, convert to EAAs (or use PMT), and choose the project with the higher EAA—but always check the underlying assumptions (repeatability, risk, salvage value, capital constraints) before making a final decision.
Source
Concept and formulas adapted from Investopedia: “Equivalent Annual Annuity (EAA) Approach” (see https://www.investopedia.com/terms/e/equivalent-annual-annuity-approach.asp).