Equivalent annual cost

Equivalent annual cost is the uniform annual amount whose present value over an asset's life equals its total NPV of costs, used to compare assets with different useful lives. The lower figure identifies the cheaper long-run option.

ByHoang TruongUpdated July 3, 2026

FrameworkDCF investment appraisal

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Machine A has a total NPV of costs of €90,000 over three years, giving an equivalent annual cost of €34,924. Machine B costs €110,000 in NPV terms over five years, but its EAC is only €27,549. Despite its higher total cost, Machine B is cheaper per year and is the better choice under the replacement-chain assumption.

Where it fits

TopicCapital Budgeting & Investment AppraisalAdvancedSubjectCorporate FinanceAdvanced

The formula

LaTeX

EAC = \frac{NPV_{\text{costs}} \times r}{1-(1+r)^{-n}}

Variables

$E A C$: equivalent annual cost: the level annual charge equating to the project's total NPV of costs
$N P V_{c} os t s$: present value of all costs over the asset's useful life, discounted at r
$r$: discount rate per period (decimal)
$n$: asset useful life in periods

Under the replacement-chain assumption, prefer the asset with the lower EAC when comparing options with different useful lives. The denominator is the standard annuity factor A_{r,n}.

Check yourself

PracticeCORE

Machine A has a total NPV of costs of €60,000 over a 3-year life. Machine B has a total NPV of costs of €85,000 over a 5-year life. At a 10 per cent discount rate the annuity factors are 2.487 (3 years) and 3.791 (5 years). Under the replacement-chain assumption, which machine is cheaper to operate in the long run?

Select an answer to check your understanding.