Equivalent Annual Annuity (EAA)

Comparing projects with unequal lives

What is the Equivalent Annual Annuity?

Equivalent Annual Annuity (or EAA) is a method of evaluating projects with different life durations. While traditional project profitability metrics such as NPV, IRR or payback period provide a very valuable perspective on how financially viable projects are overall, they don’t take into account how financially efficient the projects are.

 

Equivalent Annual Annuity

 

How can we calculate EAA?

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:

 

Equivalent Annual Annuity

 

Where:

r – Project discount rate (WACC)

NPV – Net present value of project cash flows

– project life (in years)

 

EAA 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 have a cost of capital of 10%. Which machine should Sally invest in?

Using the EAA method:

 

Equivalent Annual Annuity

 

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 would be that it measures the “efficiency” of each project (i.e., the average annual cash flow 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. By contrast, if the business is financially healthy, going with the highest NPV-project may be the way to go since this will provide the most financial benefit.

 

More Resources

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