How to Use Equivalent Annual Cost (EAC) in Capital Budgeting

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Equivalent annual cost (EAC) is the annual cost of owning, operating and maintaining an asset over its useful life, expressed as a level yearly amount whose present value equals the present value of all the asset’s costs. In capital budgeting, it puts assets with different lifespans on the same footing. A three-year machine and a five-year machine cannot be ranked fairly by total cost or by net present value of costs, because one delivers service for longer. Converting each to a cost per year removes that mismatch.

How the EAC formula works

For an asset with only an upfront price, the equivalent annual cost formula is:

EAC = Asset Price × r / [1 − (1 + r)^−n]

where r is the discount rate per period and n is the number of periods.

The fraction r / [1 − (1 + r)^−n] is the capital recovery factor. It is the reciprocal of the present value annuity factor:

Annuity Factor A(n, r) = [1 − 1/(1 + r)^n] / r

So the same result can be written as EAC = Asset Price / A(n, r). When the asset also has level annual operating or maintenance costs, those are added on top, because they already occur every year:

EAC = Asset Price / A(n, r) + Annual Operating Cost

The general version works for any cost pattern: compute the net present value of all costs over the asset’s life, then divide by the annuity factor. This handles costs that rise over time, overhauls in particular years and salvage value at the end.

The discount rate is the required return that makes a project worthwhile. Companies often use their weighted average cost of capital, which blends the cost of debt and the cost of equity. In engineering economics the same calculation is often called annual worth, and the rate used is the minimum acceptable rate of return (MARR).

Step-by-step: how to do an equalized annual cost analysis

1. List the alternatives that do the same job, since EAC compares costs only.
2. Gather each option’s cash flows: purchase price, installation, annual operating and maintenance costs, major repairs and expected salvage value.
3. Choose one discount rate for every option, unless their risk differs materially.
4. Convert costs to an annual figure using each option’s own life: divide the upfront cost (or the present value of uneven costs) by the annuity factor.
5. Add level annual costs such as maintenance, then compare. The lowest EAC is the cheapest option per year of service.

Spreadsheet functions can do step 4 directly: in Excel or Google Sheets, =PMT(rate, nper, −pv) returns the level annual payment for a given present value.

EAC example: comparing two machines

Hypothetical example. A company needs a packaging machine and uses an 8% discount rate. Annual costs are assumed to be paid at year end.

• Machine X: costs $60,000, lasts 4 years, $6,000 a year in operating and maintenance costs.
• Machine Y: costs $95,000, lasts 7 years, $4,500 a year in operating and maintenance costs.

Annuity factors

• Machine X: [1 − 1/1.08^4] / 0.08 = [1 − 0.7350] / 0.08 = 3.3121
• Machine Y: [1 − 1/1.08^7] / 0.08 = [1 − 0.5835] / 0.08 = 5.2064

Equivalent annual cost

• Machine X: $60,000 / 3.3121 + $6,000 = $18,115 + $6,000 = $24,115 per year
• Machine Y: $95,000 / 5.2064 + $4,500 = $18,247 + $4,500 = $22,747 per year

Machine Y costs about $1,368 less per year, even though its purchase price is $35,000 higher. Judging by upfront price, or by undiscounted totals that ignore the time value of money and Machine Y’s extra three years of service, would point to the wrong choice.

Adding salvage value. Suppose Machine Y can be sold for $15,000 at the end of year 7. The present value of that sale is $15,000 / 1.08^7 = $8,752. The net upfront cost becomes $95,000 − $8,752 = $86,248, and the EAC falls to $86,248 / 5.2064 + $4,500 = $21,066 per year. A salvage value shifts the comparison only if you include it for every option that has one.

How EAC is used in capital budgeting

EAC is most useful when two or more projects have different lifespans and costs are the main variable. Typical applications include:

• Choosing between competing assets, as in the example above.
• Lease versus buy decisions, by comparing the EAC of ownership with the annual lease payment on an equivalent basis.
• Finding the optimal replacement life. Calculating EAC for keeping an asset 3, 4, 5 or more years shows the life at which annual cost is lowest, since rising maintenance eventually outweighs spreading the purchase price over more years.
• Assessing maintenance costs, such as whether a service contract or overhaul lowers the annual figure.
• Keep or replace decisions for existing equipment, comparing the EAC of continuing with the old asset against a new one.
• Setting a savings target. The EAC of a new asset shows the annual cost savings it must generate to justify the purchase.

EAC vs. related terms

Whole-life cost. Whole-life (or life-cycle) cost is the total expense of an asset from acquisition to disposal, including purchase, operation, maintenance, financing and disposal. EAC expresses a discounted version of that lifetime cost as a yearly amount. Whole-life cost answers “how much in total?”; EAC answers “how much per year of service?”

NPV. NPV gives a single present value for a project. For cost-only alternatives with unequal lives, a lower NPV of costs can simply reflect a shorter life. EAC divides that NPV by the annuity factor so the lives no longer distort the ranking. It belongs to the same family of discounted cash flow methods.

Equivalent annual annuity (EAA). EAA applies the same conversion to a project’s NPV including revenues, so the higher figure wins. EAC focuses on costs, so the lower figure wins.

EAC in project management. In earned value management, EAC stands for “estimate at completion,” the forecast total cost of a project once finished. It shares the abbreviation but is a different measure.

Limitations

• The discount rate is an estimate. It must be set for each project, and a higher rate favors options with lower upfront costs. Rates can also change over an asset’s life.
• Cost forecasts can be wrong. Maintenance, energy use and salvage values are projections, and errors carry straight into the annual figure.
• It assumes repeated replacement. Comparing a 4-year and a 7-year asset by EAC implicitly assumes each can be replaced with a like-for-like asset at similar cost indefinitely. Technological change or a fixed project horizon can break that assumption.
• Inflation and taxes need consistent treatment. Use nominal cash flows with a nominal rate, or real cash flows with a real rate; mixing them skews results. Tax effects such as depreciation shields are excluded unless you add them to the cash flows.
• It ignores differences in output or quality. If one option produces more or better output, a cost-only comparison is incomplete, and measures such as NPV or IRR on full cash flows are more appropriate.

FAQs

The Bottom Line

EAC helps anyone choosing between assets that do the same job but last different lengths of time, including lease versus buy and replacement timing decisions. Use one discount rate, include salvage value for every option that has one, and treat inflation consistently. When options differ in output or quality, a cost-only comparison falls short, and NPV or IRR on full cash flows fits better.