Equivalent Annual Annuity (EAA)
Enter one project’s , effective annual and life to calculate its equivalent year-end annuity and annuity present-value factor.
Two machines, one valuation date, different useful lives
Does more value today always mean more value per year?
Think of NPV as the net value a whole project creates today. Suppose two machines can be replaced on the same terms and have comparable risk: A creates 10,000 over five years; B creates 13,000 over 8 years. Start by observing, without memorizing a formula.
Key points: EAA translates present value into an annual equivalent. Before comparing, check lives, discount rates, repeatability and sign conventions.
What did you just see?
measures value added today. EAA translates that same value into an annual equivalent, making differences in project life easier to examine.
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 . 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% , 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 . 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 . 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 = / AF. Here r is the effective annual 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
is a present-value amount; EAA is its annual equivalent; IRR is a 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 . 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 , 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.
Another 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.
Show formal definition and formula
Equivalent annual annuity expresses a project’s net present value as an equal year-end amount over its stated life.
- 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.
Common mistakes
EAA is not an actual cash flow, an annual return rate or guaranteed income. Comparing unequal lives requires repeatability and comparable risk and discount-rate assumptions; EAA alone cannot rank every project.
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.
You can now explore…
- Convert NPV into EAA
- Check assumptions before comparing lives
Term reference3 terms
Open a term when you need a reminder. Underlined words in the article work too.
Explore further
Understand a concept, or calculate it on its own.
- NPV
- IRR
- Annuity present value