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Discounted-cash-flow engineering economics (consistent with IEEE 1013 practice)9 min read

Worked Example: Standard vs. Premium-Efficiency Equipment Over a 20-Year Discounted Life Cycle

A $18,000 higher upfront cost for premium-efficiency equipment, evaluated against its lower annual operating cost over 20 years at a 6% discount rate — with a clear payback point.

Scenario

Option A — Standard efficiencyInitial cost $50,000, annual operating cost $12,000 (3%/yr escalation)
Option B — Premium efficiencyInitial cost $68,000, annual operating cost $8,500 (3%/yr escalation)
Discount rate6% per year
Analysis period20 years
Salvage value (both options)$0

Step-by-step calculation

Step 1: Compute the present worth of Option A's escalating operating costs

PW = Σ [annualCost x (1+e)^(t-1)] / (1+r)^t, for t = 1 to 20
e = 3%, r = 6%, annualCost = $12,000
presentWorthOperating(A) = $174,738.39

Step 2: Compute Option A's total life-cycle cost

LCC = initialCost + presentWorthOperating - presentWorthSalvage
50,000 + 174,738.39 - 0
LCC(A) = $224,738.39

Step 3: Repeat for Option B's escalating operating costs and total LCC

PW = Σ [annualCost x (1+e)^(t-1)] / (1+r)^t LCC = initialCost + PW - salvage
annualCost = $8,500 68,000 + presentWorthOperating(B)
presentWorthOperating(B) = $123,773.03, LCC(B) = $191,773.03

Step 4: Compare the two options' life-cycle cost and find the lower-cost option

savings = LCC(A) - LCC(B)
224,738.39 - 191,773.03
lccSavingsBvsA = $32,965.36 — Option B (premium) has the lower life-cycle cost

Step 5: Compute simple payback on the extra upfront cost

payback = (initialCost_B - initialCost_A) / (annualCost_A - annualCost_B)
(68,000 - 50,000) / (12,000 - 8,500)
simplePaybackYears = 5.14 years

Step 6: Compute each option's Equivalent Annual Cost (EAC) for comparison on an annualized basis

EAC = LCC x CRF, where CRF = r(1+r)^N / ((1+r)^N - 1)
EAC(A) = $19,593.72/yr, EAC(B) = $16,719.65/yr — Option B is about $2,874/yr cheaper on an annualized basis too

Result summary

CheckRequirementActualStatus
Option A life-cycle costn/a (comparison basis)$224,738.39✓ PASS
Option B life-cycle costn/a (comparison basis)$191,773.03✓ PASS
Lower life-cycle cost optionn/a (this is the result)Option B (premium efficiency)✓ PASS
Simple payback on the extra $18,000 upfront costn/a (informational)5.14 years✓ PASS
Despite costing $18,000 more upfront, the premium-efficiency option has a $32,965 lower life-cycle cost over 20 years at a 6% discount rate — its extra upfront cost pays back in 5.14 years from the $3,500/year operating-cost saving, and it remains the cheaper option on both total LCC and equivalent-annual-cost bases.

Key insight: Simple payback period and life-cycle cost can agree (as they do here) or disagree depending on the analysis period and discount rate — payback only asks 'when does the extra cost break even', while LCC captures the entire remaining value of ongoing savings after that break-even point, discounted back to present value. A project could have an attractive payback but a poor LCC if the analysis period is short relative to the payback, so both figures are worth checking rather than relying on payback alone.

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Frequently asked questions

Why does the operating cost escalation rate matter separately from the discount rate?

The discount rate converts future dollars to present value regardless of what's driving them, while the escalation rate reflects that the operating cost itself is expected to grow year over year (e.g. from rising energy prices) — the calculation nets these two effects against each other every year, which is why a 3% escalation against a 6% discount rate still produces a declining (not flat) contribution to present worth from later years, not a simple 20x multiplication of the annual cost.

What does Equivalent Annual Cost (EAC) add that life-cycle cost alone doesn't show?

EAC converts a lump-sum life-cycle cost into a level annual figure using the capital recovery factor, which is useful for comparing options with different initial costs and cash-flow timing on a common 'cost per year' basis, or for comparing against an annual budget or lease-equivalent figure — it carries exactly the same ranking information as total LCC (the cheaper LCC option always has the cheaper EAC too) but expressed in a more budget-familiar unit.

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