The equivalent uniform annual cost (EUAC) formula converts upfront costs into an equivalent annual expense to enable accurate comparisons between similar expense terms. As an example, you might have the option to rent a piece of equipment for $700 per year or buy it outright for $5,000. Assuming you know the equipment's useful life, you can convert its purchase price using the EUAC formula to see how it stacks up against the rental fee. In this comparison, the lowest annual cost would be the best deal.

To make this formula work, however, you must have a comparative interest rate, such as an alternative investment that you miss out on when you choose to spend the investment capital on the equipment.

## Raise 1 + Interest Rate to the Power of n

Add 1 to the interest rate and raise the result to the power of n, where "n" is the useful life of the purchase measured in years. In the aforementioned example, assume the equipment had a useful life of nine years and you could alternatively place the purchase price in a savings bond that yielded 7 percent per year. In that scenario, add 1 to 0.07 and then raise the result to the power of 9 to get 1.84. Remember this number, because you'll need it later on.

## Subtract 1 from the Result

Subtract 1 from the result. In the example, 1.84 minus 1 gives you 0.84. Remember this number as well, because you'll need it to later factor in any salvage value the purchased equipment may have.

## Divide the Result

Divide the result into the figure you achieved from the Step 1. In the example, 1.84 divided by 0.84 gives you 2.19.

## Multiply the Result by the Interest Rate

Multiply the result by the interest rate. In the example, 2.19 divided by 0.07 gives you 0.15.

## Calculate the EUAC

Multiply the result by the purchase price to calculate the EUAC of the purchase. In the example, 0.15 times $5,000 calculates the EUAC of $750. Compared to the annual rental cost of $700, you're better off renting in this scenario. However, if the purchased equipment had a salvage value at the end of its useful life, continue the calculation to see how it changes the evaluation.

## Calculate Annualized Salvage Value

Multiply the salvage value by the figure you acquired in Step 2 and then divide the result into the interest rate. To continue the example, if the equipment could be sold for $1,000 after nine years, multiply 0.84 times $1,000 and then divide the result into 0.07 to get a annualized salvage value of $83.33.

## Calculate Updated EUAC

Subtract the salvage value from the previously calculated EUAC to update it with respect to the gain you receive at the end of the equipment's useful life. In the example, $750 minus $83.33 gives you an updated EUAC of $666.67. Therefore, when you factor in the salvage value, you'll see purchasing the equipment is a better value than renting for $700 per year.

#### Tips

If the upfront purchase also had an associated annual cost, such as a maintenance fee that wasn't charged in the alternative rental fee, simply add this already annualized figure to the EUAC figure. Continuing with the example, if the purchased equipment also costs $50 per year in maintenance, add $50 to $666.67 to get a total of $716.67. With that added fee, renting again looks more attractive.

You can also calculate and compare the EUAC for different purchases that have varying useful lives. In the example, if another machine costs $7,000 and has a useful life of 20 years with no salvage value, its EUAC would be $660.75, making it the best choice.

References

Tips

- If the upfront purchase also had an associated annual cost, such as a maintenance fee that wasn't charged in the alternative rental fee, simply add this already annualized figure to the EUAC figure. Continuing with the example, if the purchased equipment also costs $50 per year in maintenance, add $50 to $666.67 to get a total of $716.67. With that added fee, renting again looks more attractive.
- You can also calculate and compare the EUAC for different purchases that have varying useful lives. In the example, if another machine costs $7,000 and has a useful life of 20 years with no salvage value, its EUAC would be $660.75, making it the best choice.