The annual worth method converts a project’s cash flows into the equivalent uniform annual cash flow over its life. Instead of “this project has a present worth of $320k,” you say “this project is equivalent to an annual surplus of $45k for each year of its life.”
Formally:
— the present worth multiplied by the Capital recovery factor. Conceptually, you’re amortising the PW (positive or negative) over the project life at rate .
Decision rules are the same as for PW:
- : project benefits exceed costs on an annualised basis. Accept.
- : reject.
For projects whose cash flows are mostly costs (an existing asset under replacement analysis, or a public-works comparison), the convention is to flip signs and use annual cost (AC). Same calculation, just relabelled — minimise AC instead of maximising AW.
The big advantage of AW is for comparing alternatives with different lifespans. PW and FW require equal lifespans (or a least-common-multiple repetition trick, or a study-period truncation with salvage). AW sidesteps this entirely: each alternative is converted to its own annualised value over its own life, and the resulting per-year numbers are directly comparable. Year-for-year, the cheaper-AW alternative is the better deal — as long as you’d actually be willing to commit to either life length.
A worked example. Compare:
- Option A: 10-year life, PW = \50,000i = 8%50,000 \cdot (A/P, 8%, 10) = 50,000 \cdot 0.1490 = $7,452/\text{year}$.
- Option B: 15-year life, PW = \60,000i = 8%60,000 \cdot (A/P, 8%, 15) = 60,000 \cdot 0.1168 = $7,008/\text{year}$.
Option B has higher PW, but Option A has higher AW. Which to pick depends on whether you’d repeat A or live with B’s longer commitment. If the asset need is indefinite (and you assume similar future replacements), AW is the cleaner comparison.
A subtlety: AW comparison implicitly assumes that each alternative will be repeated with similar cash flows after its life ends. If the cash flows of repetitions would be very different, this assumption breaks. See Repeated lives approach and Study period approach for explicit handling of unequal lifespans.
For the present-worth analogue see Present worth method; for the future-worth analogue see Future worth method; for the related cost-side concept used in replacement analysis see Equivalent annual cost.