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 negative NPV of a project by the "present value of annuity factor":
, where 
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. Such preference has been described as being a matter of professional education, as opposed to an assessment of the actual merits of either method. 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).
Such analysis can also be carried out on an after-tax basis, and extensive work has been undertaken in Canada for investment appraisal of assets subject to its capital cost allowance regime for computing depreciation for income tax purposes. It is subject to a three-part calculation:
- Determination of the after-tax NPV of the investment
- Calculation of the after-tax NPV of the operating cost stream
- Applying a sinking fund amortization factor to the after-tax amount of any salvage value.
In mathematical notation, for assets subject to the general half-year rule of CCA calculation, this is expressed as:
![{\displaystyle EAC={\frac {I\left[1-\left({\frac {td}{i+d}}\right)\left({\frac {1+{\frac {1}{2}}i}{1+i}}\right)\right]}{A_{{\overline {n|}}i}}}+{\frac {\sum _{n=0}^{N}{\frac {{R_{n}}\left(1-t\right)}{(1+i)^{n}}}}{A_{{\overline {n|}}i}}}-{\frac {S\left[1-\left({\frac {td}{i+d}}\right)\left({\frac {1+{\frac {1}{2}}i}{1+i}}\right)\right]}{F_{{\overline {n|}}i}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/de2f7c83741404d1aa7fafb6bff94fc53e3a241c)
where:
- A = Capital recovery (amortization) factor
- F = Sinking fund amortization factor
- I = Investment
- S = Estimated salvage value
= Operating expense stream- d = CCA rate per year for tax purposes
- t = rate of taxation
- n = number of years
- i = cost of capital, rate of interest, or minimum rate of return (whichever is most relevant)
and where
, 
...![{\displaystyle EAC={\frac {I\left[1-\left({\frac {td}{i+d}}\right)\left({\frac {1+{\frac {1}{2}}i}{1+i}}\right)\right]}{A_{{\overline {n|}}i}}}+{\frac {\sum _{n=0}^{N}{\frac {{R_{n}}\left(1-t\right)}{(1+i)^{n}}}}{A_{{\overline {n|}}i}}}-{\frac {S\left[1-\left({\frac {td}{i+d}}\right)\left({\frac {1+{\frac {1}{2}}i}{1+i}}\right)\right]}{F_{{\overline {n|}}i}}}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/de2f7c83741404d1aa7fafb6bff94fc53e3a241c)
