Equivalent Annual Cost

Equivalent annual cost (EAC) is the annual cost of owning and maintaining an asset determined by dividing the net present value of the asset purchase, operations and maintenance cost by the present value of annuity factor. It is a capital budgeting tool used by companies to compare assets with unequal useful lives. The same concept can be applied to analyse projects which have unequal useful lives.

Let’s say your company must decide between installing tube-lights or LED lights at its office. A tube light has a useful life of 2 years and an LED lights has useful life of 4 years. 200 tube-lights costs $1,000 and consume electricity of $18,000 per annum. 200 LED lights will cost $3,000 and consume electricity of $12,000 per annum.

You must be wondering how to approach it because each light has different useful life. The concept of equivalent annual cost is relevant in such situations.

Formula

We just need to find the net present value of both assets. There is no cash inflow here, so it will essentially be negative. Net present value can be calculated by discounting the future cash flows and subtracting the asset cost:

$$ NPV\\=\frac{{\rm CF}_1}{{(1+r)}^1}+\frac{{\rm CF}_2}{{(1+r)}^2}+\frac{{\rm CF}_3}{{(1+r)}^3}+\ldots+\ \frac{{\rm CF}_n}{\left(1+r\right)^n}-I $$

Now that we have the net present value, we must convert it to annual terms which we can do by treating the net present value obtained as the present value of an ordinary annuity of duration equal to the asset life.

$$ NPV\\=PV\ of\ Annuity\\=EAC\times\frac{1-{(1+\frac{r}{m})}^{-n\times m}}{\frac{r}{m}} $$

$$ Equivalent\ Annual\ Cost\\=\frac{NPV\times\frac{r}{m}}{1-{(1+\frac{r}{m})}^{-n\times m}} $$

Where r is the annual percentage rate, n is the number of years and m is the number of compounding periods per year.

Example

Assuming a discount rate of 10%, find out which type of lights your company must install.

Net present value of the tube-lights is −$26,976:

$$ NPV\\=-18,000\times\frac{1-{(1+10\%)}^{-2}}{10\%}-$1,000\\=-$33,240 $$

Net present value of the LED lights is -$33,491:

$$ NPV\\=-12,000\times\frac{1-{(1+10\%)}^{-4}}{10\%}−$3,000\\=-$40,538 $$

Now, we need to divide the net present value amount by the present value factor for annuity of 2 years and 4 years respectively at 10% interest rate compounded monthly:

$$ EAC\ (tube\ lights)\\=\frac{-$33,240\times10\%}{1-{(1+10\%)}^{-2}}\\=$19,152 $$

$$ EAC\ (LED\ lights)\\=\frac{-$40,538\times10\%}{1-{(1+10\%)}^{-4}}\\=$12,789 $$

Written by Obaidullah Jan