Benefit-Cost, Replacement & Inflation Analysis

Replacement Analysis

and Replacement

Past irrecoverable spending is excluded. Compare defender vs challenger on incremental future cash flows.

Inflation

Use consistent nominal or real dollars: ( i_{real} \approx i_{nom} - \text{inflation} ).

Environmental Applications

UV vs chlorine LCC, landfill closure sinking funds, remediation schedule PW comparisons.

Exam trap: Arithmetic payback ignores time value — use PW/AW when discounting is required.

Benefit-Cost Ratio Rules

For independent projects: accept if B/C ≥ 1 when benefits and costs are in PW terms at MARR. For mutually exclusive alternatives, use incremental B/C on differences between pairs — not standalone B/C ranking alone.

Worked example: Alt A: PW cost $1M, PW benefit $1.3M → B/C = 1.3. Alt B: PW cost $1.5M, PW benefit $1.7M → B/C = 1.13. Incremental B vs A: Δcost $500k, Δbenefit $400k → incremental B/C = 0.8 < 1 → prefer A.

Equivalent Uniform Annual Cost (EUAC)

[ EUAC = P \times (A/P, i, n) + \text{annual O&M} ]

Defender old pump: remaining life 3 yr, market value (salvage now) $5k ignored as sunk; needs $8k/yr O&M; replace costs $40k new with 10 yr life, $3k/yr O&M, MARR 8%. Compare EUAC of keeping defender for its remaining life vs challenger — exclude sunk $5k purchase.

Inflation and Constant Dollars

If costs escalate at f = 3%/yr and MARR nominal i = 8%, real rate approximately:

[ i' \approx \frac{1+i}{1+f} - 1 = \frac{1.08}{1.03} - 1 \approx 4.85% ]

Use either all then-current dollars with nominal i, or all constant dollars with i' — never mix.

Life-Cycle Costing Environmental Assets

Include capital, O&M, energy, residual/salvage, and decommissioning. Solar panel project: subtract salvage PW at end of life. Carbon price may appear as added cost per ton CO₂ in advanced stems.

Payback vs. Discounted Payback

Simple payback = initial investment / annual savings — ignores time value. Discounted payback counts years until cumulative discounted savings recover investment — longer, more defensible. Exam stems stating "ignore time value" authorize simple payback.

Replacement Timing

Replace when cost to keep defender exceeds minimum EUAC of challenger over the comparison horizon, accounting for remaining useful life and technology change.

B–C, Replacement, and Inflation

Worked Incremental B–C

Alt A: cost 100, benefit 140. Alt B: cost 180, benefit 250. MARR given.

BCR_A = 1.40; BCR_B = 1.39. Incremental B→A: ΔC=80, ΔB=110 → BCR_inc=1.375 ≥ 1 → prefer B if budget allows the larger investment.

On the Exam: For defender/challenger, ignore original purchase price already spent; use remaining life and current salvage.

B–C, Replacement, and Inflation

Worked Incremental B–C

Alt A: cost 100, benefit 140. Alt B: cost 180, benefit 250. MARR given.

BCR_A = 1.40; BCR_B = 1.39. Incremental B→A: ΔC=80, ΔB=110 → BCR_inc=1.375 ≥ 1 → prefer B if budget allows the larger investment.

On the Exam: For defender/challenger, ignore original purchase price already spent; use remaining life and current salvage.

B–C, Replacement, and Inflation

Worked Incremental B–C

Alt A: cost 100, benefit 140. Alt B: cost 180, benefit 250. MARR given.

BCR_A = 1.40; BCR_B = 1.39. Incremental B→A: ΔC=80, ΔB=110 → BCR_inc=1.375 ≥ 1 → prefer B if budget allows the larger investment.

On the Exam: For defender/challenger, ignore original purchase price already spent; use remaining life and current salvage.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Incremental Benefit-Cost

Compare Alt B vs Alt A: incremental B/C = ΔBenefits/ΔCosts in PW terms. Accept B over A if incremental B/C ≥ 1.

EUAC Replacement

Defender: EUAC = O&M + capital recovery on remaining life. Challenger: EUAC on full life. Lower EUAC wins (cost minimization).

Inflation Example

Nominal MARR 9%, inflation 3%: real rate (i' \approx (1.09/1.03)-1 = 5.83%). Use real cash flows with i'.

Environmental LCC Items

Include energy, chemicals, residual disposal, carbon fees (if stem includes), salvage. Exclude sunk pilot study costs from forward-looking comparison.

Payback Trap

Simple payback 4 years ignores time value — a 4-year payback at year 10 end-of-life differs from infinite horizon.