 # ANNUITIES LÀ GÌ

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## What is the Equivalent Annual Annuity?

Equivalent Annual Annuity (or EAA) is a method of evaluating projects with different life durations. Traditional project profitability metrics such as NPVNPV FormulaA guide to the NPV formula in Excel when performing financial analysis. It"s important to understand exactly how the NPV formula works in Excel and the math behind it. NPV = F / < (1 + r)^n > where, PV = Present Value, F = Future payment (cash flow), r = Discount rate, n = the number of periods in the future, IRRInternal Rate of Return (IRR)The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero. In other words, it is the expected compound annual rate of return that will be earned on a project or investment. or payback periodPayback PeriodThe payback period shows how long it takes for a business to recoup an investment. provide a very valuable perspective on how financially viable projects are overall. Equivalent annual annuity is a metric used to determine how financially efficient projects are.

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EAA essentially smoothes out all cash flows and generates a single average cash flow for all periods that (when discounted) equal the project’s NPV. EAA is calculated using the following formula: Where:

r –Project discount rate (WACC)

NPV– Net present valueNPV FormulaA guide to the NPV formula in Excel when performing financial analysis. It"s important to understand exactly how the NPV formula works in Excel and the math behind it. NPV = F / < (1 + r)^n > where, PV = Present Value, F = Future payment (cash flow), r = Discount rate, n = the number of periods in the future of project cash flows

n– project life (in years)

### Equivalent Annual Annuity Example

Suppose that Sally’s Doughnut Shop is considering purchasing one of two machines. Machine A is a dough mixing machine that has a useful life of 6 years. During this time, the machine will enable Sally to realize significant cost savings and represents an NPV of \$4 million. Machine B is an icing machine that has a useful life of 4 years.

During this time, the machine will allow Sally to reduce icing waste and represents an NPV of \$3 million. Sally’s doughnuts has a cost of capital of 10%. Which machine should Sally invest in?

Using the Equivalent Annual Annuity method: This EAA number tells us what the average cash flow from each machine will be, given their NPVs and useful lives. Using the EAA method, we see that Machine B has a higher EAA. Thus, we would recommend that Sally’s invest in this machine. Another way to think of EAA is that it measures the financial efficiency of each project (i.e., the average annual cash flowCash FlowCash Flow (CF) is the increase or decrease in the amount of money a business, institution, or individual has. In finance, the term is used to describe the amount of cash (currency) that is generated or consumed in a given time period. There are many types of CF that the business will see).

### Further Considerations

Using the traditional NPV approach, we see that Machine A has a higher NPV than Machine B. Thus, we would recommend that Sally’s invest in Machine A. However, which machine Sally’s decides to invest in depends on the business’ situation and goals. For instance, if the company is having trouble making interest payments on its debt, choosing a project with a lower NPV but higher average cash flows may be a better decision. In contrast, if the business is financially healthy, going with the highest NPV-project may be the way to go since this will provide the greatest financial benefit.

### More Resources

Thank you for reading CFI’s explanation of Equivalent Annual Annuity. CFI offers the Financial Modeling & Valuation Analyst (FMVA)™Become a Certified Financial Modeling & Valuation Analyst (FMVA)® certification program for those looking to take their careers to the next level. To learn more about related topics, check out the following CFI resources: