Equivalent Annual Annuity Approach (EAA)
The equivalent annual annuity approach is one of two methods used in capital budgeting to compare mutually exclusive projects with unequal lives. The EAA of each project is: EAA Project one = (0.06 x $100,000) / (1 - (1 + 0.06)\-7 ) = $17,914 EAA Project two = (0.06 x $120,000) / (1 - (1 + 0.06)\-9 ) = $17,643 Project one is the better option. For example, assume a company with a weighted average cost of capital of 10% is comparing two projects, A and B. Project A has an NPV of $3 million and an estimated life of five years, while Project B has an NPV of $2 million and an estimated life of three years. Under the EAA approach, the company would choose Project B since it has the higher equivalent annual annuity value. Often, an analyst will use a financial calculator, using the typical present value and future value functions to find the EAA.
What Is the Equivalent Annual Annuity Approach?
The equivalent annual annuity approach is one of two methods used in capital budgeting to compare mutually exclusive projects with unequal lives. The EAA approach calculates the constant annual cash flow generated by a project over its lifespan if it was an annuity. When used to compare projects with unequal lives, an investor should choose the one with the higher EAA.
Understanding the Equivalent Annual Annuity Approach (EAA)
The EAA approach uses a three-step process to compare projects. The present value of the constant annual cash flows is exactly equal to the project's net present value. The first thing an analyst does is calculate each project's NPV over its lifetime. After that, they compute each project's EAA so that the present value of the annuities is exactly equal to the project's NPV. Lastly, the analyst compares each project's EAA and selects the one with the highest EAA.
For example, assume a company with a weighted average cost of capital of 10% is comparing two projects, A and B. Project A has an NPV of $3 million and an estimated life of five years, while Project B has an NPV of $2 million and an estimated life of three years. Using a financial calculator, Project A has an EAA of $791,392.44, and Project B has an EAA of $804,229.61. Under the EAA approach, the company would choose Project B since it has the higher equivalent annual annuity value.
Special Considerations
Calculating the Equivalent Annual Annuity Approach
Often, an analyst will use a financial calculator, using the typical present value and future value functions to find the EAA. An analyst can use the following formula in a spreadsheet or with a normal non-financial calculator with exactly the same results.
For example, consider two projects. One has a seven-year term and an NPV of $100,000. The other has a nine-year term and an NPV of $120,000. Both projects are discounted at a 6 percent rate. The EAA of each project is:
Project one is the better option.
Related terms:
Average Annual Growth Rate (AAGR)
Average annual growth rate (AAGR) is the average increase in the value of an investment, portfolio, asset, or cash stream over the period of a year. read more
Annuity Method of Depreciation
The annuity method of depreciation, also known as the compound interest method, looks at an asset's depreciation be determining its rate of return. read more
Annuities: Insurance for Retirement
An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income stream for retirees. read more
Capital Budgeting
Capital budgeting is a process a business uses to evaluate potential major projects or investments. It allows a comparison of estimated costs versus rewards. read more
Discounted Cash Flow (DCF)
Discounted cash flow (DCF) is a valuation method used to estimate the attractiveness of an investment opportunity. read more
Future Value (FV)
Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth over time. read more
Internal Rate of Return (IRR) & Formula
The internal rate of return (IRR) is a metric used in capital budgeting to estimate the return of potential investments. read more
Mutually Exclusive
Mutually exclusive is a statistical term describing two or more events that cannot occur simultaneously. read more
Net Present Value (NPV)
Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. read more
Replacement Chain Method
The replacement chain method is a decision model for evaluating projects with unequal lives. read more