Equivalent Annual Cost
Comparing projects with different lifespans by raw NPV is unfair, because a longer project has more years to accumulate value. The equivalent annual cost (EAC), or its mirror the equivalent annual annuity, fixes this by converting each project’s present value into a level annual cash flow spread over its own life. The conversion divides the present value by the annuity factor for that life at the discount rate. The project with the lower equivalent annual cost (or the higher equivalent annual benefit) wins, because the comparison is now on a like-for-like per-year basis. EAC works on discounted cash flows, not accounting depreciation schedules.
Why it matters
A machine that lasts ten years and one that lasts five cannot be judged by total cost alone, since the cheap short-lived one will need replacing sooner. EAC re-expresses each option as a flat yearly rental, the level annual amount whose present value matches the project. Once both are quoted as a cost per year, they line up on equal terms regardless of how long each lasts. It is the same trick a lease uses, turning a lumpy upfront price into a smooth annual figure you can compare directly.
Formulas
Worked examples
Machine A costs US$900 today and lasts 3 years. Machine B costs US$1,300 today and lasts 5 years. Both do the same job and the discount rate is 10 percent. Which is cheaper on an equivalent annual basis?
For Machine A, the 3-year annuity factor at 10 percent is (1 minus 1.10 to the power minus 3) divided by 0.10, about 2.487. EAC is 900 divided by 2.487, which is about US$362 a year. For Machine B, the 5-year annuity factor is (1 minus 1.10 to the power minus 5) divided by 0.10, about 3.791. EAC is 1,300 divided by 3.791, which is about US$343 a year. Machine B has the lower equivalent annual cost, about US$343 against US$362, so it is the better choice even though its upfront price is higher, because its cost spreads over more years.
Common mistakes
- ✗The project with the lower total cost is always better. Total cost ignores differing lives. A cheaper short-lived asset needs replacing sooner, so the fair comparison is the equivalent annual cost.
- ✗EAC can compare projects of any length without adjustment. EAC is precisely the adjustment for different lengths. It rescales each present value to a per-year figure so unequal lives become comparable.
- ✗EAC uses accounting depreciation to spread the cost. EAC spreads the discounted present value using the annuity factor, a time-value calculation, not a depreciation schedule.
- ✗A higher equivalent annual cost is preferred. For costs, lower is better. The rule flips for benefits, where the higher equivalent annual annuity wins.
Revision bullets
- •Raw NPV unfairly favours longer projects with more years to accrue value
- •EAC converts a present value into a level annual cash flow over the project’s life
- •Divide the present value of costs by the annuity factor for that life
- •Choose the option with the lowest equivalent annual cost
- •For benefits, choose the highest equivalent annual annuity instead
- •EAC uses discounted cash flows, not accounting depreciation
Quick check
The equivalent annual cost method is most useful for
Connected topics
Sources
- Titman & Martin, Ch. 2Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.Covers comparing mutually exclusive projects, including those with unequal lives.