EAA

Equivalent Annual Annuity

Short definition

Equivalent annual annuity converts NPVs of mutually exclusive projects with different lives into a common annual cash slice. It answers “which machine do we replace forever?” under a repeatable chain.

Detailed explanation

A five-year line and an eight-year line cannot be ranked on raw NPV. EAA turns each NPV into an annuity at r and n; the higher EAA wins. Equivalent annual cost (EAC) is the same formula on a cost PV.

The assumption is that the job can be repeated at the same risk and price. If technology, demand or replacement cost breaks, the chain fails; then a common-horizon scenario or a real option is needed.

Why it matters for the CFO

In replace-versus-repair and fleet decisions, “longer life, higher NPV” can eliminate a short-lived, efficient asset.

How it is calculated

EAA = NPV × r / [1 − (1+r)^(−n)]

NPV is turned into an annual slice by the inverse n-period annuity factor. Each project uses its own n.

Variables in the formula

• NPV: project net present value
• r: discount rate
• n: economic life in years

How to read it

EAA is a ranking rule only if infinite replacement is plausible. A one-off licence or campaign should stay on raw NPV.

Numerical example

A: NPV 3 mn TL, n = 3, r = 20% → EAA ≈ 3 × 0.20 / [1 − 1.20⁻³] ≈ 1.42 mn TL/year. B: NPV 4 mn TL, n = 6 → EAA ≈ 1.20 mn TL/year; A ranks first under replacement.

Definitions are educational. They are not investment, credit or tax advice.