How To Calculate Equivalent Annual Annuity

Equivalent Annual Annuity Formula:

\[ EAA = \frac{NPV}{Annuity\ Factor} \] \[ Annuity\ Factor = \frac{1 - (1 + r)^{-n}}{r} \]

Equivalent Annual Annuity (EAA):

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1. What is Equivalent Annual Annuity?

Equivalent Annual Annuity (EAA) is a financial metric used to compare projects with different lifespans by converting their net present values into equivalent annual cash flows. It helps in making apples-to-apples comparisons between investment alternatives.

2. How Does the Calculator Work?

The calculator uses the EAA formula:

\[ EAA = \frac{NPV}{Annuity\ Factor} \] \[ Annuity\ Factor = \frac{1 - (1 + r)^{-n}}{r} \]

Where:

$ EAA $ — Equivalent Annual Annuity (currency per year)
$ NPV $ — Net Present Value (currency)
$ r $ — Discount rate (decimal)
$ n $ — Number of years

Explanation: The annuity factor represents the present value of $1 received annually for n years at discount rate r. Dividing NPV by this factor converts the lump-sum present value into an equivalent annual amount.

3. Importance of EAA Calculation

Details: EAA is crucial for capital budgeting decisions when comparing projects with different durations. It allows for fair comparison by annualizing the NPV, making it easier to select the most economically viable investment.

4. Using the Calculator

Tips: Enter NPV in currency units, discount rate as a decimal (e.g., 0.08 for 8%), and the project duration in years. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: When should I use EAA instead of NPV?
A: Use EAA when comparing projects with different lifespans. For projects with equal durations, NPV alone is sufficient for comparison.

Q2: What discount rate should I use?
A: Typically use the company's cost of capital or the required rate of return for similar investments.

Q3: Can EAA be negative?
A: Yes, if the NPV is negative, the EAA will also be negative, indicating the project destroys value annually.

Q4: How does EAA differ from annual cash flow?
A: EAA represents the constant annual cash flow that would give the same NPV as the actual cash flow pattern, while annual cash flow is the actual periodic cash inflow/outflow.

Q5: What are the limitations of EAA?
A: EAA assumes cash flows are constant and the discount rate remains unchanged over time. It may not capture complex cash flow patterns accurately.