Present Value and Cost-Benefit Analysis: Windmill Project
This paper applies two core public finance tools to practical scenarios. First, it calculates the present value of a $1,000,000 recycling program benefit at discount rates of 5%, 6%, and 7% over two years, demonstrating how rising rates erode present value. Second, it conducts a detailed cost-benefit analysis of a fictional community windmill energy project in Swobodaville, tallying capital, labor, maintenance, and social costs against quality-of-life and pollution-reduction benefits. The discussion critically examines ambiguous items — lost coal-worker wages, increased life expectancy, and unquantified climate harms — drawing on Mikesell's fiscal administration framework and the contingent-valuation method to highlight the fundamental limits of econometric decision-making tools.
- Introduction to Present Value Calculations: Scenario setup: recycling center benefit and discount rates
- Present Value at Three Discount Rates: PV calculated at 5%, 6%, and 7% rates
- Cost-Benefit Analysis: Framework and Setup: CBA definition, rules, and decision criteria
- Swobodaville Windmill Project: Costs and Benefits: Itemized costs and benefits for windmill project
- Discussion of Ambiguous and Excluded Items: Lost wages, life expectancy, and coal harm omissions
- Limits of Cost-Benefit Analysis and Conclusions: CVM method, environmental limits, and policy conclusions
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What makes this paper effective
- The paper moves logically from a straightforward quantitative exercise (present value) to a more complex and contested analytical tool (cost-benefit analysis), building the reader's understanding incrementally.
- It goes beyond mechanical calculation to critically interrogate ambiguous line items — such as lost wages and increased life expectancy — demonstrating analytical depth rather than simple arithmetic compliance.
- The discussion draws on credible academic sources (Mikesell, Hanley and Spash) to situate the scenario within broader debates about the limits of econometric methods, giving the paper intellectual grounding.
Key academic technique demonstrated
The paper exemplifies critical application of a quantitative tool: it performs the required calculations correctly but then questions their assumptions and omissions. By noting what the cost-benefit framework cannot capture — climate harm, life expectancy value, macroeconomic wage effects — the author shows that understanding a method's limits is as important as executing it correctly. This move from calculation to critique is a hallmark of strong applied policy analysis.
Structure breakdown
The paper opens with a two-part scenario structure. Section one addresses present value mechanics across three discount rates. Sections two through four set up, itemize, and total the windmill project's costs and benefits. The final two sections form the analytical core, interrogating excluded items and invoking the contingent-valuation literature to argue that cost-benefit analysis must always be understood as one input among many — not a definitive verdict.
Introduction to Present Value Calculations
Consider the following scenario: a city wants to open a recycling center aimed at reducing waste. The total benefits of the program are valued at $1,000,000. Three different discount rates are estimated at 5%, 6%, and 7%. The time period for receiving the benefits of the program is two years. The task is to calculate the present value at each interest rate and to discuss what happens to present value as the discount rate changes.
Present Value at Three Discount Rates
Using the standard present value formula PV = FV / (1 + r)n, the calculations for each discount rate are as follows:
5% discount rate: 1,000 / (1 + 0.05)2 = 1,000 / 1.1025 = $907.03
6% discount rate: 1,000 / (1 + 0.06)2 = 1,000 / 1.1236 = $890.00
7% discount rate: 1,000 / (1 + 0.07)2 = 1,000 / 1.1449 = $873.44
As the interest rate increases, the net present value decreases. This inverse relationship is a fundamental principle of time-value-of-money analysis: a higher discount rate assigns less value to future benefits, reflecting the greater opportunity cost of waiting.
It is also worth noting that Morgan Friedman's inflation calculator calculates a substantially higher rate of inflation over a comparable two-year period. Using Friedman's tool to calculate the inflation rate for $1,000 between 2013 and 2015, "what cost $1,000 in 2013 would cost $1,041.70 in 2015" (Friedman, n.d.). This is a useful reference point when considering how inflation affects net present value over a two-year period.
Cost-Benefit Analysis: Framework and Setup
Cost-benefit analysis is a technique that assumes all costs and benefits can have a dollar value attached to them. It is a tool and should not be used as the sole basis for decision-making. The result of a calculation is a ratio between costs and benefits. After all calculations have been made, the analysis concludes with that ratio. If costs exceed benefits — that is, if the ratio B/C is less than 1 — the advice is to reject the project. If benefits exceed costs, the project may be accepted.
Swobodaville Windmill Project: Costs and Benefits
The following example is drawn from the fictitious city of Swobodaville's efforts to build a Community Windmill Renewable Energy Project. The following conditions have been agreed upon for the analysis.
Costs:
Land is already owned. The price of a new windmill is $150,000, and a minimum of 50 windmills are needed to achieve the desired efficiency compared to the current coal-burning method.
150,000 × 50 = $7,500,000 (windmill capital cost)
Staff training costs over three years — including direct costs and the loss of productive hours while in training — will be $55,000 for each of the 10 specialists to be hired.
55,000 × 10 = $550,000 (training cost)
The annual operating and maintenance costs per windmill over the three-year period will be $35,000.
35,000 × 50 × 3 = $5,250,000 (operating and maintenance cost)
The cost of shutting down the relevant portion of the coal plant to achieve the same energy production as the windmills is $1,000,000.
Total Costs = $14,300,000
Benefits:
As a widely supported community project, reductions in pollution are expected to improve quality of life. The quality of life of 5,000 residents is expected to improve by an average of $1,500 per person (including men, women, and children) over the three-year period.
5,000 × 1,500 = $7,500,000 (quality-of-life benefit)
The three-year savings on pollution damage to buildings and grounds, as calculated by the Sierra Club, amount to $7,000,000.
Total Benefits = $14,500,000
Additionally, the medical center that conducted an analysis concluded that the value of increased life expectancy should be included as a benefit to the community, though no specific dollar amount was assigned to this item.
Three full-time coal workers will lose their jobs as a result of the transition. Their hourly wage is $35 per hour, and they work 2,080 hours annually.
3 × 35 × 2,080 × 3 = $655,200 (discussed further below)
References
Friedman, M. (n.d.). The inflation calculator. Retrieved from http://www.westegg.com/inflation/
Hanley, N., & Spash, C. L. (1993). Cost-benefit analysis and the environment. Northampton, MA: Elgar.
Mikesell, J. L. (2014). Fiscal administration: Analysis and applications for the public sector (9th ed.). Boston, MA: Wadsworth.
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