Exercises: Cost-benefit analysis

Explain what cost-benefit analysis is and what public authorities use it for before approving a project. Give an example of a project in your local municipality to which it could be applied.

A local council is considering building a cycle lane. Classify these items as costs or benefits of the project: the construction of the cycle lane, reduced congestion, annual maintenance, health improvements for cyclists, and lost parking spaces.

A project has estimated benefits of $\text{€}\ 90,000$ and costs of $\text{€}\ 60,000$.

1. a) Calculate the net benefit and decide whether the project is advisable according to the cost-benefit criterion.
2. b) What warning would you give before relying entirely on this calculation? Mention at least one.

Explain the difference between a company's profit and loss account (the revenue it receives minus the expenses it pays) and the cost-benefit analysis of a public project, which also values effects that nobody directly charges or pays for. Give an example of each type of effect.

A council is considering creating a park on a vacant plot. Classify these items as costs or benefits of the project: building the park, its annual maintenance, the shade and rest for neighbours, the increase in customers for nearby bars and the noise of any fairs held there.

A village switches all its street lighting to LED: the investment costs $\text{€}\ 50,000$ and saves $\text{€}\ 10,000$ a year on the electricity bill. Calculate the payback period of the investment and explain what that figure means.

A skate park project has estimated benefits of $\text{€}\ 120,000$ and costs of $\text{€}\ 95,000$.

1. a) Calculate the net benefit.
2. b) According to the cost-benefit criterion, is it advisable? What margin of error does that recommendation have if the estimates are uncertain? Discuss it.

A public library does not charge admission and yet it "produces" a great deal of value. Explain why the cost-benefit analysis of a library must count benefits that are not charged for (reading, study, internet access) and what would happen if we only looked at its revenue.

The school is considering installing solar panels: they cost $\text{€}\ 24,000$ and save $\text{€}\ 4,000$ a year on the electricity bill.

1. a) Calculate the payback period of the investment.
2. b) Name two non-monetary benefits that should also be counted in the analysis and explain how you would include them.

The figure shows the initial cost of a sports centre's solar installation and the cumulative savings year by year, in thousands of euros.

1. a) Read from the graph in which year cumulative savings equal the cost.
2. b) Explain what this point means and what happens from then on.

To assess a road improvement, the administration estimates the time drivers will save and assigns it a monetary value per hour.

1. a) Do you think it is reasonable to monetise time? Justify your answer.
2. b) What other effect that is difficult to monetise should be included in the analysis (noise, safety, environment)? Explain how you would address it.

A municipality can only afford one of these projects: a swimming pool (cost of $\text{€}\ 500,000$, estimated benefits of $\text{€}\ 650,000$) or a sports centre (cost of $\text{€}\ 400,000$, benefits of $\text{€}\ 560,000$).

1. a) Calculate the net benefit and the benefit-cost ratio of each one.
2. b) Which would you choose and on what criterion? Reason why net benefit and the ratio can recommend different projects.

Planting $10,000$ trees in a city costs $\text{€}\ 200,000$. Experts value the shade, the CO₂ absorbed and the health improvement at $\text{€}\ 15$ per tree per year.

1. a) Calculate the estimated annual benefit and the payback period of the investment (without discounting).
2. b) Discuss the reliability of putting a price on shade or clean air: what can go wrong in the estimate and how does it affect the decision?

A cycle lane costs $\text{€}\ 300,000$, has annual maintenance of $\text{€}\ 10,000$ and benefits (time, health, less congestion) are estimated at $\text{€}\ 60,000$ a year.

1. a) Calculate the net benefit over ten years (without discounting).
2. b) What key assumptions would you review before approving it (actual number of users, valuation of time)? Explain how the decision would change if users were half of those expected.

It is proposed to pedestrianise the high street: shopkeepers fear losing customers who come by car; residents will gain silence and space.

1. a) Explain how the effects on both groups enter a cost-benefit analysis: are they added with the same sign?
2. b) Propose two compensatory measures that improve the outcome of the project (park-and-ride car parks, aid for the shops) and explain what each one achieves.

Many grandiose projects end up costing twice the budget and receiving half the announced users (the "white elephant syndrome").

1. a) What biases and interests explain why they get approved (promoters' optimism, the political gain of a big project)?
2. b) Propose two improvements to the analysis process that reduce the problem (comparing with similar projects already built, review by independent experts) and explain how they work.

A city council has a maximum budget of $\text{€}\ 800,000$ and must choose between two mutually exclusive projects:

• Project A (Underground car park with 100 spaces): construction cost of $\text{€}\ 600,000$ and expected direct revenue from fees of $\text{€}\ 900,000$ (in present value). A municipal report warns that the increase in road traffic towards the city centre will cause $\text{€}\ 150,000$ in external congestion and pollution costs, plus $\text{€}\ 50,000$ in maintenance.

• Project B (Library and study centre): construction cost of $\text{€}\ 800,000$ and direct revenue from membership cards and workshops of $\text{€}\ 200,000$. An external study values the social benefits (access to educational resources, study support, and reduction of school failure) at $\text{€}\ 800,000$.

1. a) Calculate the benefit-cost ratio ($B/C$) and the net benefit of both projects from the perspective of social cost-benefit analysis (integrating all costs and benefits, not just direct monetary ones).
2. b) The Councillor for Finance states: "The car park is the only reasonable option: it generates a surplus, leaves $\text{€}\ 200,000$ of the budget unspent to pay off debt, and its financial ratio is $1.5$, whereas the library runs a deficit." Technically refute their position by differentiating between financial (private) profitability and social profitability.
3. c) If the city council decided to carry out the car park, design a pricing policy or usage restriction proposal that helps correct the detected negative externality without eliminating revenue.

A feasibility report for building a toll motorway with an initial cost of $300$ million euros and a $20$-year horizon presents the following annual estimates:

• Toll revenue collected from drivers: $25$ million euros.

• Monetarily valued time savings for users: $10$ million euros.

• Road maintenance and management: $5$ million euros.

The report concludes that the annual net social benefit is $30$ million euros ($25 + 10 - 5$), accumulating $600$ million over $20$ years, thus recommending the project without hesitation.

1. a) Identify and justify the methodological error committed by the report when counting the $25$ million in tolls as a social benefit. Why is the toll in social cost-benefit analysis a mere transfer and not a net gain in welfare for society?
2. b) After opening the road, it is found that the toll price deters $50\ \%$ of potential drivers, who choose to drive along a free regional road that passes through three towns. Qualitatively model which unforeseen external costs now appear in the overall social cost-benefit analysis.
3. c) Considering that the marginal cost of one additional vehicle using an uncongested motorway is practically zero ($CMg \approx 0$), explain what toll price would maximise economic efficiency and what financial dilemma this would pose for the Public Administration.

The city council in plenary session debates whether to transform a centrally located public plot of land valued at $12$ million euros into a park with mature trees or sell it to a commercial developer who will create $80$ direct jobs. A neighbourhood spokesperson states: "A park, lung health, or quietness are priceless; trying to measure them in euros degrades politics and distorts reality." The Councillor for Urban Planning replies: "If economists do not try to put a monetary value on those intangible benefits, the tacit value assigned to them in the final decision will be exactly zero euros."

1. a) Interpret the councillor's warning: why can refusing in principle to monetise intangible goods paradoxically lead to decisions that go against environmental and social protection?
2. b) Design a methodological proposal to estimate the value of the park in euros by applying two different economic valuation methods for non-market goods (such as hedonic pricing in nearby housing, travel costs, or avoided health costs). Explain what each one would measure in this case.
3. c) Suppose that the estimated value of the park's benefits amounts to $14$ million euros, but $85\ \%$ of that gain is concentrated in the property appreciation of adjoining high-income homes. Reason why a favourable social cost-benefit analysis alone does not guarantee that the decision is equitable or fair.

A property developer requests the rezoning of a coastal wetland to build a hotel complex that would generate a net business profit of $18$ million euros over $20$ years. The environmental department quantifies the ecological services that the wetland currently provides for free:

1. Hydrological regulation: the wetland mitigates flash floods. If it disappears, it will be compulsory to build canalisations with an investment cost of $8$ million euros and an annual maintenance cost of $\text{€}\ 150,000$.

2. Natural purification: it filters $1.5$ million $\text{m}^3$ of wastewater per year; treating that same water in a conventional wastewater treatment plant would cost $\text{€}\ 0.40$ per $\text{m}^3$.

3. Storm buffering: reports estimate that without the wetland there will be flood damage to the urban centre with an average expected value of $\text{€}\ 500,000$ each year.

1. a) Calculate the total annual shadow price (imputed economic value) of the ecosystem services provided by the wetland and obtain its accumulated value over a $20$-year horizon (without applying discounting).
2. b) With the obtained data, evaluate whether the hotel rezoning is efficient from the point of view of social welfare.
3. c) The developer claims: "Those ecological costs are theoretical; nobody pays bills for the water the wetland cleans, whereas the hotels will generate real GDP." Technically refute this argument drawing on the concepts of market failure and opportunity cost.

To protect an agricultural and urban plain from the projected rise in sea level, a sea wall barrier is planned with an immediate construction cost of $200$ million euros ($I_0 = 200$). Hydrological models predict that the project will prevent a flood catastrophe estimated at $1,000$ million euros in damage exactly $40$ years from now ($t = 40$).

1. a) Calculate the social Net Present Value (NPV) of the project by applying a social discount rate standard in infrastructure works of $r = 5\ \%$ (where the discount factor is $(1 + 0.05)^{40} \approx 7.04$). Determine whether the project would be carried out under this criterion.
2. b) Recalculate the social NPV using the rate proposed by economist Nicholas Stern for intergenerational climate risks of $r = 1.4\ \%$ (where $(1 + 0.014)^{40} \approx 1.74$). How does the technical investment decision change?
3. c) A critic argues: "Using a positive discount rate in environmental problems implies treating future generations as second-class citizens." Justify the ethical argument of this criticism and present what financial argument supports the use of positive discount rates.

A large conference and sports arena built for an international event cost public funds $25$ million euros. The ex ante feasibility study forecasted $100$ days of use per year with a local economic impact of $2.5$ million euros annually. Five years later, the ex post reality shows that the venue is only used $10$ days a year, generating gross revenue of $\text{€}\ 120,000$ against a fixed maintenance and security cost of $\text{€}\ 600,000$ per year.

1. a) Identify and explain two common causes or methodological biases in public project evaluation that led to the huge discrepancy between forecast and reality.
2. b) A private corporation proposes leasing the building for $10$ years, taking on all maintenance and paying an annual municipal fee of $\text{€}\ 40,000$ to turn it into a logistics centre closed to the public. The councillor in charge rejects the offer: "We cannot hand over a building that cost $25$ million for peanuts; we must keep managing it as a public space until the investment is amortised." Show what economic fallacy the councillor is committing and quantitatively compare the annual budgetary impact of keeping the arena open versus accepting the lease.
3. c) Design two mechanisms or safeguards that public procurement legislation should impose before approving similar projects to discourage oversized works.

A single-track regional train line runs an annual operating deficit of $2$ million euros (operating cost: $2.8$ million; ticket sales revenue: $\text{€}\ 800,000$). The operator records $500$ daily users on weekdays ($250$ days a year, taking $2$ trips per day per user). The Ministry proposes closing the train line and replacing it with a bus network supported by a public subsidy of $\text{€}\ 400,000$ per year. The mobility study reveals two additional pieces of data:

1. The bus will take $20$ minutes longer per trip than the train. Commuters' average value of time is estimated at $\text{€}\ 6$ per hour.

2. It is projected that $150$ of the $500$ daily users will choose private vehicles instead of the bus, which will generate negative externalities estimated at $\text{€}\ 420,000$ per year due to increased accident rates, polluting emissions, and congestion on regional roads.

1. a) Quantify the annual social cost of the additional time users will lose as a result of switching to the bus.
2. b) Conduct the social cost-benefit balance of the decision: compare the direct budgetary savings for the State with the sum of the value of lost time and the environmental and accident externalities. Is closing the railway efficient from the perspective of social welfare?
3. c) Argue what territorial equity and social cohesion issues this decision creates for groups with reduced mobility or low incomes, justifying whether the closure could accelerate depopulation in the region.

The Directorate-General for Traffic is assessing resurfacing and signage improvements on a high-accident road section at a total cost of $6$ million euros. Road engineering models forecast that the intervention will prevent a statistically proven $3$ deaths over the next five years. To evaluate whether the project is a priority through a cost-benefit analysis, the technical team applies the official "Value of a Statistical Life" (VSL) of $1.8$ million euros per person (obtained from willingness-to-pay surveys for marginal risk reductions).

1. a) Calculate the net social benefit of the project and determine what the formal technical recommendation derived from the cost-benefit analysis would be.
2. b) Upon learning that the work is being rejected based on the technical calculation, a citizens' group protests: "Human life is priceless; setting a monetary figure to decide whether to save people on the road is immoral." Justify why in the real management of public spending it is inevitable to implicitly or explicitly assign a monetary limit to road safety measures, and what would happen to the health and education budgets if we acted under the premise that a life has infinite economic value.
3. c) Based on this case, refute the idea that "cost-benefit analysis is a neutral and objective mathematical technique." Identify two ethical-political value judgements that completely determine the final outcome of this type of study.