Annual equivalent cost is the level yearly amount that is worth exactly the same, at a stated discount rate, as everything an asset will cost across its whole life. It is reached by discounting every cost of buying, running and disposing of the asset to one present value, then spreading that present value evenly over the years the asset serves. Because the answer comes out per year rather than per project, two assets with different useful lives, or the same asset kept for different lengths of time, can be set side by side. The method is also written as equivalent annual cost, and shortened to EAC.
Why a Present Value On Its Own Will Not Answer the Question
Discounting alone gives the wrong ranking whenever the options run for different lengths of time. Compare a machine bought and kept for two years against the same machine kept for three, and the longer cycle will nearly always show the larger cost, for a reason that has nothing to do with which is the better decision: the two NPVs calculated should not be compared as quite obviously buying and keeping an asset for a longer period is likely to cost more than buying and keeping it for a shorter period as there is less benefit to the owner (ACCA, Equivalent annual costs and benefits). The present value totals are measuring different amounts of service. How the underlying figure is built, and what may enter it, is set out in net present value.
Dividing that total by the number of years the asset serves does not fix it either, because a dollar in year three is not the same dollar as one in year one. The division has to be done at the same discount rate that produced the present value.
How Annual Equivalent Cost Is Calculated
The method runs in two steps and ends in a comparison. Step one is to calculate the net present value of cost for each potential replacement cycle, and step two is that for each potential replacement cycle an equivalent annual cost is calculated, after which the replacement cycle with the lowest equivalent annual cost may then be chosen, although other factors may also have to be considered (ACCA, Equivalent annual costs and benefits).
The second step is one division.
present value of all costs over the cycle
EAC = ---------------------------------------------------
annuity factor for the cycle length, at that rateThe logic behind the division is worth holding onto. If you have equal annual cash flows for a number of years and want to calculate a present value you must multiply the annual cash flow by an annuity factor, so to calculate the equivalent annual cost from a present value of cost you must divide by the relevant annuity factor (ACCA, Equivalent annual costs and benefits). The annuity factor is simply the discount factors for the years in the cycle, added together.
Federal life-cycle costing states the same operation as a multiplication rather than a division. The annual value formula is used to determine an equal payment per time period, usually years, which is equivalent to a one-time cost or a stream of costs incurred during the same time period, given the time value of money as reflected in the discount rate, and the uniform capital recovery factor can be used to calculate this annual value from the present value of a cost or of a stream of costs computed using the same discount rate (NIST Handbook 135, Life-Cycle Costing Manual for the Federal Energy Management Program, 2020, section 17.4).
d (1 + d)^n
A = P x -------------
(1 + d)^n - 1The two routes give the same answer, because the uniform capital recovery factor is the inverse of the uniform present value factor for the same number of years and the same discount rate (NIST Handbook 135, 2020). Dividing by an annuity factor and multiplying by its reciprocal are one step written two ways.
A Worked Example
ACCA’s own example prices a machine at $3,500 with forecast maintenance of $900 in the first year, $1,000 in the second and $1,200 in the third, an expected residual value of $2,100 after two years and $1,600 after three, and a cost of capital of 11% per year (ACCA, Equivalent annual costs and benefits). Only two cycles can be tested, because no residual value is given for a one-year cycle.
Two-year cycle
present value of cost 3,418
two-year annuity factor at 11% 1.713
EAC = 3,418 / 1.713 = 1,995 per year
Three-year cycle
present value of cost 4,831
three-year annuity factor at 11% 2.444
EAC = 4,831 / 2.444 = 1,977 per yearThe three-year cycle costs $4,831 against the two-year cycle’s $3,418, so on present value alone it looks worse. Stated per year it is the cheaper of the two, at $1,977 against $1,995, and the three-year replacement cycle is said to be the optimal replacement cycle (ACCA, Equivalent annual costs and benefits). The ranking reversed when the horizon was equalized, which is the entire reason the step exists.
One trap sits inside step one. The residual value belongs only at the end of the cycle being tested, since if you buy the asset once you can only sell it once (ACCA, Equivalent annual costs and benefits), so a two-year sale proceed has no place in a three-year column.
What the Method Assumes Away
Three assumptions sit under the arithmetic, and each of them can be wrong in a live decision.
The basic version ignores tax. Both buying an asset and incurring a maintenance cost will cause tax cash flows, and while these cash flows could be included they would add to the complexity of the calculation (ACCA, Equivalent annual costs and benefits). For a US taxpayer that omission is rarely trivial, because the cost recovery schedule described in MACRS fixes which year each deduction lands in, and a discounted calculation is sensitive to exactly that.
It also assumes replacement in perpetuity with an identical asset, which the source itself calls out twice: the analysis assumes that the asset can be replaced by exactly the same asset in perpetuity, and separately that a company will want to replace like with like, when in reality business needs develop (ACCA, Equivalent annual costs and benefits).
And it assumes one inflation rate. Different cash flows may suffer from different specific inflation rates, and where they do the plain method may not be correct, though if all the cash flows inflate at one rate then the method can be used with real cash flows and a real cost of capital (ACCA, Equivalent annual costs and benefits). Purchase prices and labor-heavy maintenance costs rarely move together, so this is the assumption that fails quietly.
The Same Method Applied to Benefits
Turn the sign around and the technique ranks projects rather than costs. Where mutually exclusive projects with different lives could each be repeated for the foreseeable future, the equivalent annual benefit approach divides each project’s NPV by the annuity factor for its own life. On ACCA’s second example, a project with an NPV of $47m over three years and one with an NPV of $58m over four years, at a cost of capital of 13% per year, come out at $47m divided by 2.361, or $19.9m per year, against $58m divided by 2.974, or $19.5m per year, so the shorter project wins despite the smaller NPV, because that NPV will be obtained more frequently (ACCA, Equivalent annual costs and benefits).
Where a Firm Meets the Number
No closing process produces this figure. It is an advisory calculation built on top of closed records: the purchase price off the fixed asset register, the running costs off the general ledger, the expected proceeds off a judgment about resale, and a discount rate taken from the client’s cost of capital. Because it is not a reported balance, nothing reconciles it, and the quality of the answer is entirely the quality of the estimates fed in.
Two habits keep it honest. State the discount rate beside the answer, since a different rate can flip the ranking the way the horizon did above. And keep the cycles genuinely comparable, which means the same cost categories in each column and residual value only where a sale actually happens.
Common Questions
Present value of the cycle’s costs, divided by the annuity factor for that cycle’s length at the same discount rate. Written the other way, it is the present value multiplied by the uniform capital recovery factor, which is that annuity factor’s inverse (NIST Handbook 135, 2020). There is no separate closed-form shortcut that skips the present value step, because uneven costs have to be discounted before they can be leveled out.
It is the same annuity-factor division applied to a project’s net present value rather than to a cost total, and it answers which repeatable project is worth more per year rather than which is worth more in total. ACCA’s technical article calls that measure the equivalent annual benefit and calculates it using annuity factors in exactly the same way as an equivalent annual cost is calculated (ACCA, Equivalent annual costs and benefits). The three-year against four-year project comparison is that calculation.
Accountably places trained offshore accountants and tax preparers inside US CPA and EA firms, and a firm can put a block of its own recurring close and reporting work through a trial task so its reviewers stay on the judgment calls.
