Capital budgeting
Projects with unequal lives
Compare mutually exclusive projects that last different lengths of time with equivalent annual annuities.
Learning objectives
- Explain why NPV alone can mislead when lives differ
- Calculate an equivalent annual annuity (EAA) and an equivalent annual cost (EAC)
- Choose between machines with different lives and running costs
When two projects are mutually exclusive and will be repeated (a machine that will be replaced when it wears out, a fleet renewed on a cycle), comparing their NPVs directly is unfair. A three-year machine's NPV covers three years of service; a five-year machine's covers five. The longer-lived option looks better simply because it counts more years.
The fix is to put both on a per-year basis: convert each NPV into the level annual amount over its own life that has the same present value. That is the equivalent annual annuity (EAA). For cost-only choices, the same calculation on the PV of costs gives the equivalent annual cost (EAC): pick the lowest.
EAA = NPV × r ÷ [1 − (1 + r)⁻ⁿ] · worksheet: =PMT(r, n, −NPV)
- NPV
- the project's NPV over one life (or the PV of its costs, for an EAC)
- r
- discount rate
- n
- the project's life in years
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