Corporate finance
Equivalent Annual Annuity (EAA) Calculator
Enter a project’s NPV, effective annual discount rate and life to calculate its equivalent annual annuity and annuity present-value factor.
Results
Start with your numbers
Review or adjust your inputs, then calculate to see your results and interpretation.
Understand this calculation
EAA is the equal year-end amount with the same present value as NPV, not the project’s actual annual cash flow.
See calculation method and assumptions
Formula
Equivalent Annual Annuity (EAA)
Nonzero discount rate (r ≠ 0)
Zero discount rate (r = 0)
Variables, rates and periods
- NPV
- Time-zero net present value; A/B use a common currency and valuation date.
- r
- Effective annual discount rate: input 10 for 10%; formulas use 0.10.
- n
- Whole years (1–1000), with equivalent payments at year end.
- AF
- Annuity present-value factor: EAA = NPV / AF; at zero rate AF = n.
Think of NPV as the value a whole project adds today
- Money paid today and money received five years from now are not directly interchangeable.
- Discount future cash flows to today, then subtract the investment to obtain NPV.
- For example, an outlay of 100,000 and discounted future net receipts of 110,000 give an NPV of 10,000.
- That is the whole project’s net value today, not annual income of 10,000 or a 10% return.
- EAA starts from this already-calculated NPV.
Why not simply divide by the number of years?
- Without discounting, 10,000 spread over five years is equivalent to 2,000 a year.
- At a 10% discount rate, however, five future payments of 2,000 add up to less than 10,000 today.
- An equivalent payment of about 2,637.97 is needed to preserve the same present value.
- Think of the annuity factor as the value today of receiving one unit at each year-end for n years.
- Divide NPV by that factor to find the annual equivalent.
- This is a change of scale, not a claim that the actual project pays the same amount every year.
Why not compare unequal lives using NPV alone?
- For one-off projects, compare complete cash flows over the relevant common decision horizon using NPV.
- If projects can repeat under the same terms, EAA helps compare annual equivalent net benefits.
- A longer project’s higher NPV need not imply greater annual value creation.
Convert NPV rather than reconstruct cash flows
- Use the annuity factor AF = [1 − (1+r)^(−n)] / r, then EAA = NPV / AF.
- Here r is the effective annual discount rate and n is a whole number of years, with equivalent payments at year end.
- At zero r, the factor equals n.
EAA, NPV and IRR
- NPV is a present-value amount;
- EAA is its annual equivalent;
- IRR is a discount rate that makes NPV zero.
- Their units differ, so EAA is not a percentage.
- Unconventional cash flows may lack a unique IRR, and EAA does not remove limitations in the underlying NPV assumptions.
Signed EAA and equivalent annual cost
- The annuity factor is positive within this tool’s domain, so EAA has the same sign as NPV.
- Negative EAA indicates negative annual equivalent net value.
- EAC usually states the annual equivalent of costs as a positive cost.
- If pure costs enter as a negative NPV, EAA is negative;
- the sign convention cannot be ignored.
Assumptions behind comparison
- When comparing projects A and B, use one common effective annual discount rate, currency and valuation date.
- Also assess feasible replacement, repeatable terms, comparable risk and the decision horizon.
- If useful lives, residual values, prices or replacement costs change, return to full cash flows and a common-horizon analysis.
Enter one project’s NPV, effective annual discount rate and life to calculate its equivalent year-end annuity and annuity present-value factor.
Worked example
- Use an NPV measured at time zero with the same effective annual discount rate.
- Find the five-year, 10% annuity present-value factor, about 3.7908.
- Divide 10,000 by the factor to obtain about 2,637.97 per year.
Frequently asked questions
What if the discount rate is zero?
Use EAA = NPV / n without dividing by zero. A stable numerical method also handles near-zero rates.
Can NPV or the discount rate be negative?
NPV can be positive, zero or negative. The effective annual rate must exceed −100%, and life must be an integer from 1 to 1000. Unrepresentable results produce an error, not infinity.
Must I choose the higher EAA?
No. Repeatability, funding limits, risk, other benefits and a comparable decision horizon also matter.