What is Equivalent Annual Cost (EAC)?
– Equivalent Annual Cost (EAC) converts the total cost of owning and operating an asset over its useful life into an equal annual amount. It’s used in capital budgeting to compare alternatives that have different lifespans (for example, two machines with different useful lives) by putting their costs on a common annual basis.
– Source & background: This summary builds on the Investopedia treatment of EAC (see Mira Norian, Investopedia).
Why use EAC (key benefits)
– Makes apples-to-apples comparisons between assets with different useful lives.
– Helps decide whether to buy or lease, or whether to replace or keep existing equipment.
– Converts lifecycle costs (purchase, operating, maintenance, disposal, salvage) into a single annual figure that’s easy to compare.
– Useful for finding the optimal replacement period for equipment.
Core formulas
– Annuity factor (present value of $1 per year for n periods at rate r):
A(n,r) = (1 − (1 + r)^−n) / r
– Capital recovery factor (CRF), the annualized factor to convert a present value into an equivalent annual payment:
CRF = r / (1 − (1 + r)^−n)
– Two equivalent ways to compute EAC:
1) EAC = NPV of all costs over the asset’s life ÷ A(n,r)
– Here NPV of costs = PV(purchase + operating/maintenance costs − salvage proceeds), using discount rate r.
2) If you only have an upfront purchase price P and a constant annual operating cost O:
EAC = P × CRF + O
– If there is a salvage value S at the end, include PV(S) as a negative cost in the NPV, or subtract PV(S) from P before multiplying by CRF.
Step-by-step practical procedure to calculate EAC
1. Define the analysis parameters
– Choose the useful life n for each alternative.
– Choose the discount rate r (company’s cost of capital or required return). Decide whether to use nominal or real rates (consistent with cash flow estimates).
2. Forecast cash flows
– Initial purchase price (cash outflow at time 0).
– Annual operating and maintenance costs for each year (can be level or varying).
– Any tax effects, depreciation tax shields, or financing impacts if you want after‑tax EAC (recommended in corporate decisions).
– Expected salvage or disposal value at end of life.
3. Compute the present value (PV) of costs
– PV(costs) = Purchase price + PV(annual O&M costs) − PV(salvage).
– Use the discount rate r to obtain PV of future items.
4. Convert PV to an annual equivalent
– EAC = PV(costs) ÷ A(n,r) OR EAC = (Purchase price) × CRF + annual O&M (if O&M is constant and salvage is handled in PV).
5. Compare alternatives
– The asset with the lower EAC is the cheaper choice on an annualized basis.
6. Run sensitivity and scenario analysis
– Vary r, maintenance cost assumptions, salvage values, and useful life to see how robust the choice is.
7. Consider non-cost factors
– Capacity, reliability, product quality, safety, learning curves, and strategic fit can justify choosing a higher-cost option.
Worked example (machines A and B)
Assumptions:
– Cost of capital r = 5% (0.05)
– Machine A: purchase P_A = $105,000; life n_A = 3 years; annual maintenance O_A = $11,000; no salvage (for simplicity).
– Machine B: purchase P_B = $175,000; life n_B = 5 years; annual maintenance O_B = $8,500; no salvage.
Step A — compute annuity factors:
– A(3,0.05) = (1 − (1+0.05)^−3) / 0.05 ≈ 2.723
– A(5,0.05) = (1 − (1+0.05)^−5) / 0.05 ≈ 4.329
Step B — annualize purchase and add maintenance:
– EAC_A = P_A / A(3,0.05) + O_A ≈ 105,000 / 2.723 + 11,000 ≈ 38,564 + 11,000 ≈ $49,564
– EAC_B = P_B / A(5,0.05) + O_B ≈ 175,000 / 4.329 + 8,500 ≈ 40,420 + 8,500 ≈ $48,920
Decision: Machine B has the lower EAC (≈ $48,920 vs. $49,564), so it’s the cheaper choice per year by about $640 (rounded). Note: include taxes, salvage, and differing performance characteristics if relevant.
Practical variations and important adjustments
– Salvage value: include PV(salvage) as a reduction in PV(costs) before annuitizing. Equivalent approach: subtract PV(salvage) from purchase price when using CRF.
– Varying annual costs: if operating costs vary year to year, compute PV of those costs explicitly, then divide by A(n,r).
– Taxes & depreciation: calculate after-tax cash flows. Depreciation creates tax shields that affect the PV of costs.
– Inflation: use nominal discount rate with nominal cash flows or convert to real rates and real cash flows. Be consistent.
– Replacement cycles: to compare assets with different lives in perpetuity, compute EAC over their respective lives, or compare the cost per year over a common horizon (or use least-common-multiple approach). EAC is often interpreted as the annual cost if you were to repeatedly replace an asset indefinitely.
When to use EAC — and when not to
Use EAC when:
– You must compare mutually exclusive alternatives with different lifespans and costs are the principal decision factor.
– You want a simple, comparable annual metric for budget planning.
Don’t rely solely on EAC when:
– Alternatives have different production capacities, different revenue impacts, or qualitative differences (e.g., reliability, compliance, brand impact).
– There’s significant uncertainty in lives, costs, or discount rate — then supplement with scenario and sensitivity analysis.
– You need to evaluate one-off projects where timing of cash inflows matters more than smoothed annual costs.
Limitations and common pitfalls
– Choice of discount rate matters — small changes in r can change rankings.
– Estimates of maintenance, downtime costs, and salvage are uncertain.
– EAC focuses on costs; revenue or performance differences must be treated separately.
– If assets are used unequally (different annual usage or capacity), EAC per hour or per unit of output is a more appropriate comparison.
– Using nominal costs with a real discount rate (or vice versa) will produce wrong results — be consistent.
Quick checklist before making a decision using EAC
– Have you included all relevant cash flows (purchase, installation, operating, maintenance, disposal, salvage)?
– Are cash flows measured on an after-tax basis (if taxes are material)?
– Is your discount rate appropriate, and are you consistent about nominal vs. real?
– Did you do sensitivity tests on discount rate, useful life, and maintenance costs?
– Have you considered non-cost factors (capacity, reliability, regulatory risk)?
Bottom line
– EAC is a practical, widely used capital-budgeting tool for comparing the annual cost of assets with different lives. When applied correctly — using consistent discounting, including salvage and tax effects, and complemented by sensitivity analysis and qualitative considerations — it offers a clear way to make cost-focused equipment and replacement decisions.
Primary source
– Investopedia: “Equivalent Annual Cost (EAC)” — Mira Norian. https://www.investopedia.com/terms/e/eac.asp
If you’d like, I can:
– Recalculate the example including salvage values and taxes, or
– Build a small spreadsheet template (with formulas) you can paste into Excel/Google Sheets to compute EACs and run sensitivity analysis. Which would help you most?