Equivalent Annual Value

\[EAV=NPV\frac{i(1+i)^n}{(1+i)^n-1}\]

Variables

EAVequivalent annual value (currency/year)

NPVnet present value (currency)

idiscount rate per period (decimal)

nnumber of periods

Description

What is this formula?

Equivalent Annual Value (EAV) converts a project's Net Present Value into an equivalent constant annual amount over the project's life.

This allows projects with different lifespans to be compared on a common annual basis.

When to use it

Use this formula when comparing mutually exclusive projects that have different useful lives but require evaluation using a common annual measure.

Example

Suppose:

NPV = $50,000

i = 0.08

n = 10 years

Formula:

EAV=NPV(i(1+i)^n)/((1+i)^n−1)

Substitution:

EAV=50000(0.08×1.08^10)/(1.08^10−1)

EAV=7,451.47

Result:

Equivalent Annual Value = $7,451.47 per year

Applications

Capital budgeting

Equipment replacement analysis

Project comparison

Investment evaluation

Engineering economics

Financial planning

Note

EAV is derived from annuity mathematics and assumes a constant discount rate throughout the project life. It is especially useful when comparing projects of unequal duration. Real-world projects may involve varying discount rates, changing cash flows, or uncertainty that require more advanced evaluation methods.