# Equivalent annual cost

In finance, the **equivalent annual cost** (**EAC**) is the cost per year of owning and operating an asset over its entire lifespan. It is calculated by dividing the NPV of a project by the “present value of annuity factor”:

${displaystyle EAC={frac {NPV}{A_{t,r}}}}$

, where

${displaystyle {A_{t,r}}={frac {1-{frac {1}{(1+r)^{t}}}}{r}}}$where r is the annual interest rate and

t is the number of years.

Alternatively, EAC can be obtained by multiplying the NPV of the project by the “loan repayment factor”.

EAC is often used as a decision making tool in capital budgeting when comparing investment projects of unequal lifespans. However, the projects being compared must have equal risk: otherwise, EAC must not be used.[1]

The technique was first discussed in 1923 in engineering literature,[2] and, as a consequence, EAC appears to be a favoured technique employed by engineers, while accountants tend to prefer net present value (NPV) analysis.[3] Such preference has been described as being a matter of professional education, as opposed to an assessment of the actual merits of either method.[4] In the latter group, however, the Society of Management Accountants of Canada endorses EAC, having discussed it as early as 1959 in a published monograph[5] (which was a year before the first mention of NPV in accounting textbooks).[6]

## . . . Equivalent annual cost . . .

EAC can be used in the following scenarios:

- Assessing alternative projects of unequal lives (where only the costs are relevant) in order to address any built-in bias favouring the longer-term investment.[7]
- Determining the optimum economic life of an asset, through charting the change in EAC that may occur due to the fluctuation of operating costs and salvage values over time.[8]
- Assessing whether leasing an asset would be more economical than purchasing it.[9]
- Assessing whether increased maintenance costs will economically change the useful life of an asset.[10]
- Calculating how much should be invested in an asset in order to achieve a desired result (i.e., purchasing a storage tank with a 20-year life, as opposed to one with a 5-year life, in order to achieve a similar EAC).[11]
- Comparing to estimated annual cost savings, in order to determine whether it makes economic sense to invest.[12]
- Estimating the cost savings required to justify the purchase of new equipment.[13]
- Determining the cost of continuing with existing equipment.[14]
- Where an asset undergoes a major overhaul, and the cost is not fully reflected in salvage values, to calculate the optimum life (i.e., lowest EAC) of holding on to the asset.[15]

## . . . Equivalent annual cost . . .

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