How to Calculate Equivalent Annual Cost (EAC)

A straightforward breakdown of the formula for EAC and how to use it

Equivalent annual cost (EAC) is the cost per year for owning or maintaining an asset over its lifetime. Calculating EAC is useful in budgeting decision-making by converting the price of an asset to an equivalent annual amount. EAC helps to compare the cost effectiveness of two or more assets with different lifespans. The formula for EAC is:

${\text{Asset Price}}*{\frac {\text{Discount Rate}}{1-(1+{\text{Discount Rate}})^{\text{-Periods}}}}+{\text{Annual Maintenance Costs}}$ .

Let's see how this equation is applied.

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^{[1]XResearch source} For example, suppose you are comparing two analyzers, A and B, costing $100,000 and $130,000, respectively. These are the Asset Prices.
^{[2]XResearch source} Suppose Analyzer A is expected to last 5 years, while Analyzer B is expected to last 7 years. These are the number of Periods.
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Determine your discount rate.^{[3]XResearch source} Discount rate is the cost of capital, or how much return your capital is required to generate each year. Say your organization uses a Discount Rate of 10%.
- Determine the annual maintenance costs for the asset.^{[4]XResearch source} Suppose Analyzer A has an annual maintenance expense of $11,000, while Analyzer B has annual maintenance expense of $8,000.
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Plug the numbers into the equation Asset Price x Discount rate / (1-(1+Discount Rate)^-Periods) + Annual Maintenance Costs.^{[5]XResearch source} It should be apparent that Analyzer B is the more cost effective option, with a net savings of $2,677.03 a year, compared to Analyzer A.
- For Analyzer A, ${\text{EAC}}=\$100,000*{\frac {0.10}{(1-(1+0.10)^{-5})}}+\$11,000=\$37,379.75$
- For Analyzer B, ${\text{EAC}}=\$130,000*{\frac {0.10}{(1-(1+0.10)^{-7})}}+\$8,000=\$34,702.72$

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A precision lathe costs $10,000 and will cost $20,000 a year to operate and maintain. If the discount rate is 10% and the lathe will last for 5 years, what is the equivalent annual cost of the tool?
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Using the formula above: EAC = $10,000 * (10% / (1 - (1 + 10%)^-5) + $20,000 = $22,637.97
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This part of the formula, ${\frac {\text{Discount Rate}}{1-(1+{\text{Discount Rate}})^{\text{-Periods}}}}$ $How.com.vn English: {\frac {{\text{Discount Rate}}}{1-(1+{\text{Discount Rate}})^{{\text{-Periods}}}}}$ is the inverse of the annuity factor (AF). ${\text{AF}}={\frac {1-(1+{\text{Discount Rate}})^{\text{-Periods}}}{\text{Discount Rate}}}$ $How.com.vn English: {\text{AF}}={\frac {1-(1+{\text{Discount Rate}})^{{{\text{-Periods}}}}}{{\text{Discount Rate}}}}$ , is used to calculate present values of annuities.
- It is often abbreviated as $AF(n,r)$ , which can be readily computed by financial calculators plugging in values for n (periods) and r (discount rate). AF can also be looked up from an annuity factor table. The EAC formula may be simplified as ${\frac {\text{Asset Price}}{\text{Annuity Factor}}}+{\text{Annual Maintenance Cost}}$ .
- From an annuity factor table, AF(5,10%) = 3.7908 for Analyzer A and AF(7,10%) = 4.8684 for Analyzer B, so EAC = $100,000/3.7908 + $11,000 = $37,379.65 for Analyzer A and $130,000/4.8684 + $8,000 = $34,702.81 for Analyzer B.
- Note that these figures are very close to the actual figures as calculated above. The minuscule differences arise from rounding errors attributed to AF having only 5 significant figures from the AF table.
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