Cost-Benefit Analysis Calculator

The systematic decision framework

Cost-Benefit Analysis (CBA) is a methodology for comparing the total expected costs and benefits of a project, policy, or investment. It originated in 19th-century French civil engineering (Jules Dupuit, 1844) and was formalized in the US Flood Control Act of 1936, which required federal projects to demonstrate that “the benefits to whomsoever they may accrue are in excess of the estimated costs.” It remains the standard framework for evaluating public infrastructure, environmental regulation, and major business investments.

The core idea: convert all costs and benefits to monetary terms, discount future flows to present value, and decide whether the project is worth doing. Three principal metrics fall out of this.

The three main metrics

Net Present Value (NPV): the simplest and most theoretically defensible measure.

NPV = Σ [B(t) − C(t)] ÷ (1 + r)^t

Where B(t) and C(t) are benefits and costs in year t, and r is the discount rate. If NPV > 0, the project creates net value (worth doing). If NPV < 0, it destroys value.

Benefit-Cost Ratio (BCR): useful for ranking projects under a budget constraint.

BCR = PV(Benefits) ÷ PV(Costs)

BCR > 1 means benefits exceed costs. A BCR of 1.5 means each dollar of cost generates $1.50 of benefits. Use BCR for ranking but never use it alone for accept/reject decisions — it can favor small high-ratio projects over larger ones that create more total value.

Payback Period: how long until cumulative benefits cover cumulative costs. Easy to communicate but loses information about post-payback value. A 5-year payback project that runs another 25 years generates dramatically different value than one that ends at year 5.

The discount rate — the most important and contested variable

The discount rate captures the time value of money: future dollars are worth less than present dollars because (a) money can earn interest, (b) future events are uncertain, and (c) people prefer present consumption.

Recommended rates by context:

The discount rate matters enormously over long horizons. A 50-year project’s value computed at 3% is roughly 4x larger than at 7%. Climate change CBA is particularly sensitive — most damages occur 50-200 years out, so the choice of discount rate effectively decides the answer.

The ethical question: is a benefit to people 100 years from now worth less than a benefit to you today? Most economists say yes, slightly. Some philosophers say no — Frank Ramsey argued in 1928 that the only valid time-preference is mortality risk, which gives a 0.1-0.5% rate.

Practical CBA workflow

For a well-conducted CBA:

1. Define alternatives including the do-nothing baseline
2. Identify all costs and benefits including indirect and external effects
3. Quantify in physical units (lives saved, tons of CO2 reduced, hours commuted)
4. Convert to monetary terms (this is the hard part)
5. Discount to present value at an appropriate rate
6. Compute NPV, BCR, and payback
7. Sensitivity analysis — how do results change if assumptions change?
8. Distributional analysis — who wins and who loses?

Valuing the unvaluable

The hardest part of CBA is putting dollar values on non-market goods:

• Statistical value of a life (VSL): US EPA uses ~$11.5 million (2024), based on willingness-to-pay for small risk reductions
• Carbon dioxide damage: US Social Cost of Carbon $51-$190/ton CO2 (Biden EPA 2023)
• Time savings (commute): typically 50% of after-tax hourly wage
• Recreational value of a park visit: $30-$100/day from travel cost or contingent valuation studies
• Endangered species: $10-$200/year per household from willingness-to-pay surveys
• Health (QALY): $50,000-$150,000 per quality-adjusted life year

These numbers are real, but they vary across studies and ethical frameworks. Different agencies use different VSL values, and the choice affects which projects pass.

Common CBA mistakes

The literature documents typical errors:

1. Optimism bias: project sponsors overestimate benefits and underestimate costs. UK Treasury data found average cost overruns of 20-86% across infrastructure projects.
2. Failing to count opportunity costs: spending $1B on Project A means $1B not available for Project B. The opportunity cost is the next-best foregone use.
3. Double counting: counting both job creation AND increased tax revenue, when the jobs are how the taxes come.
4. Wrong discount rate: using a corporate rate (10%) for a public project that should use 3%, or vice versa.
5. Ignoring distributional effects: a project that creates $1B in benefits but takes $500M from poor communities and gives $1.5B to rich ones may “pencil” but be politically unworkable.
6. Confusing financial vs economic analysis: financial analysis looks at the project sponsor’s cash flow; economic analysis looks at society’s total welfare. They’re different.

Real-world CBA examples

US Army Corps of Engineers projects must demonstrate BCR > 1.0 to proceed. Famous examples:

• Tennessee-Tombigbee Waterway (Mississippi): BCR projected at 1.08; ultimate cost-benefit deeply negative. A textbook example of optimism bias.
• California High-Speed Rail: original BCR 1.7, revised down repeatedly as costs ballooned.
• EPA Mercury Regulations (2011): BCR of 9-90:1, depending on assumptions. Highly favorable.
• HOV Lane Construction: typically BCR 0.5-2.5; mixed results.
• National Highway System (1956): estimated BCR ~6:1; widely considered one of the highest-return public investments in US history.

The British Treasury Green Book — the global standard

The UK Treasury’s Green Book is one of the most rigorous CBA guides. It introduced the declining discount rate concept — instead of 3.5% forever, the rate declines to 3.0% after 30 years, 2.5% after 75, 2.0% after 125 years. This addresses long-term uncertainty and gives more weight to far-future generations.

Many EU governments and the World Bank have adopted similar declining-rate frameworks for climate and infrastructure decisions.

When CBA fails

CBA is best for projects with measurable, monetary costs and benefits. It struggles with:

• Distributional fairness — pure CBA is “Kaldor-Hicks efficient” but ignores who wins and loses
• Irreversible decisions — once a species goes extinct or a forest is logged, it’s gone. Standard discounting may justify destruction
• Catastrophic risks — climate tipping points or pandemic risks can’t be averaged with normal probabilities
• Moral and ethical concerns — slavery would have “passed” a CBA in some historical contexts; today we recognize it’s wrong regardless of cost-benefit
• Public goods with strong network effects — hard to estimate non-marginal changes

For these, supplement CBA with multi-criteria analysis, regulatory impact analysis, and ethical review.

Sensitivity analysis — required, not optional

Best practice in CBA includes:

1. Base case with central estimates
2. Low case (pessimistic on benefits, optimistic on costs)
3. High case (vice versa)
4. Break-even analysis — what assumption value makes NPV = 0?
5. Probabilistic Monte Carlo for sophisticated analyses

If a project’s NPV is positive only at the most optimistic assumptions, it’s a fragile recommendation. Robust projects pass under most scenarios.

Worked example — bus rapid transit line

A city is considering a BRT line:

• Capital cost: $200M (year 0)
• Annual operating costs: $15M
• Annual benefits: $45M (time savings, accident reduction, emissions reduction)
• Project life: 30 years
• Discount rate: 4% (typical for city infrastructure)

NPV = −$200M + Σ(t=1 to 30) [($45M − $15M) ÷ 1.04^t] NPV = −$200M + $30M × 17.292 (annuity factor for 30 years at 4%) NPV = −$200M + $518.8M = $318.8M positive NPV

BCR = $518.8M / ($200M + $15M × 17.292) = $518.8M / $459.4M = 1.13

Payback period: ~7-8 years from operations

Project is justified, though the BCR is modest. If costs come in 30% over budget (common), BCR drops to 0.90 — project becomes negative. This is a fragile-positive project that needs careful cost control.

Bottom line

CBA is the workhorse decision framework for public and large private investments. NPV is the best single metric; BCR ranks projects under budget constraints; payback is simplest to communicate. The discount rate is critical and often controversial — a 7% rate gives wildly different answers than 3%. Build sensitivity analysis into every CBA. CBA is necessary but not sufficient for major decisions; distributional, ethical, and irreversibility concerns require additional frameworks.