6.4 Present Worth, Life-Cycle Cost, and Sustainability
Key Takeaways
- Present worth converts future costs, savings, replacements, and salvage values to a common time zero basis.
- Life-cycle cost comparisons must include capital, operation, maintenance, energy, replacement, residual value, and service-life assumptions.
- Use real discount rates with constant-dollar costs or nominal discount rates with inflated costs, but do not mix the two.
- For mutually exclusive WRE alternatives, the lowest first cost can lose when energy, maintenance, or replacement costs dominate.
- Sustainability analysis should support, not replace, the economic comparison by addressing resource use, resilience, emissions, and public impacts.
Put Alternatives on One Time Basis
The April 2024 WRE Project Planning area includes economic and sustainability analysis, including present worth, life-cycle costs, and comparison of alternatives. The exam will usually give the interest rate and cash flows, so the challenge is setting up the timeline correctly. Do not compare a low bid pump station to a high-efficiency pump station by first cost alone if one option uses much more energy for 20 years.
Present worth (PW) converts all costs and benefits to equivalent dollars at time zero. Typical factors are P = F(P/F,i,n) for a single future amount and P = A(P/A,i,n) for a uniform annual amount. Costs are usually positive in a cost comparison, while salvage value or residual value is subtracted because it offsets cost at the end of the study period.
| Cash flow | WRE example | Present-worth treatment |
|---|---|---|
| Initial capital | Basin excavation, pumps, controls | Already at year 0 |
| Annual operation | Pump energy, chemicals, operator time | Multiply by P/A factor |
| Periodic replacement | Pump overhaul, membrane replacement | Multiply by P/F at replacement year |
| Salvage or residual | Remaining equipment value | Subtract present value |
| Avoided cost | Reduced flooding damage or hauling | Treat consistently as benefit or negative cost |
| External factor | Emissions, water reuse, resilience | Quantify if data are given; otherwise discuss qualitatively |
Life-Cycle Cost Workflow
Use a repeatable setup:
- Confirm the study period and discount rate.
- Draw the cash-flow timeline for each alternative.
- Put all amounts in the same dollar basis: constant dollars with real rate, or inflated dollars with nominal rate.
- Discount each cost to present worth.
- Subtract salvage or residual value at the end of the period.
- Select the alternative with the lower equivalent cost if service and non-cost requirements are equal.
- State non-economic considerations separately when the question asks for sustainability.
Example: compare two pump alternatives for a 20 year planning period at i = 5 percent. Alternative A costs $600,000 initially, has annual energy and maintenance of $58,000, needs a $90,000 overhaul in year 10, and has $50,000 salvage in year 20. Alternative B costs $720,000 initially, has annual energy and maintenance of $41,000, needs a $70,000 overhaul in year 10, and has $70,000 salvage in year 20. Use factors (P/A,5%,20) = 12.462, (P/F,5%,10) = 0.6139, and (P/F,5%,20) = 0.3769.
For A, PW = 600,000 + 58,000(12.462) + 90,000(0.6139) - 50,000(0.3769) = $1,359,301. For B, PW = 720,000 + 41,000(12.462) + 70,000(0.6139) - 70,000(0.3769) = $1,247,546. Even though B costs $120,000 more initially, its present worth is about $111,800 lower because energy, maintenance, overhaul, and salvage improve the long-term economics.
Sustainability Interpretation
Sustainability is not a slogan in an exam calculation. It becomes meaningful when tied to measurable outcomes: lower energy use, fewer chemical deliveries, reduced sanitary sewer overflows, more reliable drought supply, smaller disturbed area, beneficial reuse, or improved flood resilience. If the alternatives have similar present worth, sustainability criteria may justify choosing the option with lower life-cycle emissions or better service continuity. If one alternative fails a permit, level of service, or public safety requirement, a lower present worth does not make it acceptable.
A pump alternative has a $90,000 overhaul in year 10. At a 5 percent discount rate, the given single-payment present-worth factor for year 10 is 0.6139. What present cost should be included for the overhaul?
Two stormwater retrofit alternatives meet the same hydraulic performance requirement. Alternative X has lower first cost but higher annual maintenance for 25 years. Alternative Y has higher first cost and lower annual maintenance. What is the best economic comparison method?