# Equivalent Annual Cost (EAC)

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## Definition of 'Equivalent Annual Cost (EAC)'

The equivalent annual cost (EAC) is a method of comparing different capital investment projects by converting all future cash flows into a single equivalent annual cash flow. This allows for easier comparison between projects with different lifespans and/or different cash flow patterns.

The EAC is calculated by taking the present value of all future cash flows and dividing by the number of years in the project's lifespan. The present value is calculated using a discount rate, which is the rate of return that the investor requires on their investment.

The EAC can be used to compare projects with different cash flow patterns and/or different lifespans. For example, a project with a shorter lifespan but higher cash flows may have a lower EAC than a project with a longer lifespan but lower cash flows. This is because the shorter project will have a lower present value of its future cash flows, which will result in a lower EAC.

The EAC can also be used to compare projects with different levels of risk. A project with a higher risk will have a higher discount rate, which will result in a higher EAC. This is because the investor will require a higher return on their investment to compensate for the higher risk.

The EAC is a useful tool for comparing different capital investment projects. It allows for easier comparison between projects with different cash flow patterns and/or different lifespans. The EAC can also be used to compare projects with different levels of risk.

Here is a more mathematical explanation of the EAC:

The EAC is calculated as follows:

$$EAC = \frac{\sum_{t=0}^{n} C_t(1+r)^{-t}}{n}$$

where:

* $C_t$ is the cash flow in year $t$
* $r$ is the discount rate
* $n$ is the number of years in the project's lifespan

The EAC can be used to compare projects with different cash flow patterns and/or different lifespans. For example, a project with a shorter lifespan but higher cash flows may have a lower EAC than a project with a longer lifespan but lower cash flows. This is because the shorter project will have a lower present value of its future cash flows, which will result in a lower EAC.

The EAC can also be used to compare projects with different levels of risk. A project with a higher risk will have a higher discount rate, which will result in a higher EAC. This is because the investor will require a higher return on their investment to compensate for the higher risk.

The EAC is a useful tool for comparing different capital investment projects. It allows for easier comparison between projects with different cash flow patterns and/or different lifespans. The EAC can also be used to compare projects with different levels of risk.

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