# Equivalent Annual Cost - EAC

## What is the 'Equivalent Annual Cost - EAC'

The equivalent annual cost (EAC) is the annual cost of owning, operating and maintaining an asset over its entire life. EAC is often used by firms for capital budgeting decisions. The equivalent annual cost methodology allows a company to compare the cost effectiveness of various assets that have unequal lifespans.

## BREAKING DOWN 'Equivalent Annual Cost - EAC'

In capital budgeting, EAC is used for a variety of purposes. Most often, EAC is used to analyze two or more possible projects with different lifespans and where costs are the most relevant variable. Other typical uses of EAC include calculating the optimal life of an asset, determining if leasing or purchasing an asset is the better option, determining the magnitude of which maintenance costs will impact an asset, determining the necessary cost savings to support purchasing a new asset, or to determine the cost of keeping existing equipment.

## Calculating the Equivalent Annual Cost and Example

The formula for calculating the EAC is straightforward. It is equal to net present value (NPV) divided by A(t,r), which is the present value annuity factor, taking into account r, the cost of capital, and t, the number of years in question. The resulting EAC allows managers to compare NPVs of differing projects over different periods, to accurately determine the best option.

The annuity factor A(t,r) is calculated as follows:

A(t,r) = (1 - (1 / (1 + r) ^ t)) / r

As an example, consider two alternative investments in machinery equipment. Machine A has an initial capital outlay of \$105,000. It has an expected lifespan of three years and an annual maintenance expense of \$11,000. Machine B has an initial capital outlay of \$175,000, an expected lifespan of five years, and an annual maintenance expense of \$8,500. The cost of capital for the firm making the decision is 5%.

First, the A(t,r) of each project must be calculated. These calculations would be as follows:

Machine A A(t,r) = (1 - (1 / (1 + 5%) ^ 3)) / 5% = 2.72

Machine B A(t,r) = (1 - (1 / (1 + 5%) ^ 5)) / 5% = 4.33

Next, the initial costs must be divided by the A(t,r) and the annual maintenance cost added in. The resulting calculation is the EAC.

EAC Machine A = \$105,000 / 2.72 + \$11,000 = \$49,557

EAC Machine B = \$175,000 / 4.33 + \$8,500 = \$48,921

By standardizing the annual cost, a manager in charge of a capital budgeting decision where cost is the only issue would select Machine B, because it has an EAC that is \$636 lower than Machine A.