Benefit-Cost Ratio

The benefit-cost ratio (BCR) is a measure used to judge whether a project, investment or policy is worthwhile. It divides the present value of all expected benefits by the present value of all expected costs. A ratio greater than 1 means the benefits outweigh the costs, a ratio of exactly 1 means they balance, and a ratio below 1 means the project would destroy value on the assumptions used.

The ratio is a summary output of cost-benefit analysis, the wider process of listing, valuing and comparing a project's effects. Governments use it to rank transport, health and environmental schemes, development banks use it to screen loans, and companies use it alongside measures such as net present value and the internal rate of return in capital budgeting. It is also called the benefit-cost ratio or cost-benefit ratio, though the latter sometimes means the inverse.

Imagine deciding whether to insulate your loft. It costs money now, but it will cut your heating bills every winter for years. To compare the two fairly, you add up all the future savings, remembering that money saved years from now is worth a little less than money in your pocket today, and divide by the cost of the work.

If the answer is 1.5, you expect to get back $1.50 in savings for every $1 spent, which looks like a good deal. If the answer is 0.8, you would get back only 80 cents for each dollar, so the project does not pay for itself. The ratio turns a complicated set of costs and gains into one easy-to-compare number.

The standard calculation is:

• $B_t$ is the benefit expected in year $t$.
• $C_t$ is the cost incurred in year $t$.
• $r$ is the discount rate, written as a decimal.
• $n$ is the number of years in the appraisal period.

Suppose a town considers a $1,000,000 flood barrier built today, with maintenance of $20,000 a year, and expected avoided flood damage of $150,000 a year, for 10 years, at a discount rate of 5%. The present value factor for a 10-year annuity at 5% is about 7.722. Benefits are worth $150{,}000 \times 7.722 = 1{,}158{,}300$. Costs are $1{,}000{,}000 + 20{,}000 \times 7.722 = 1{,}154{,}440$. The ratio is $1{,}158{,}300 \div 1{,}154{,}440 \approx 1.003$, only just above 1, suggesting the project barely breaks even and that the result is sensitive to the assumptions.

Analysts read the ratio together with other measures:

• Above 1. Benefits exceed costs in present value terms, so the project adds value on the stated assumptions.
• Below 1. Costs exceed benefits, and the project would normally be rejected unless there are important effects that could not be valued.
• Ranking projects. When a budget is limited, projects with higher ratios deliver more benefit per dollar, which helps allocate scarce funds.
• Scale. A high ratio on a small project may add less total value than a lower ratio on a large one, which is why net present value is checked as well.

The UK Treasury's Green Book and its Department for Transport use value-for-money categories based on the ratio, and US federal agencies apply benefit-cost analysis to major regulations under guidance from the Office of Management and Budget.

The result depends heavily on the discount rate. A higher rate shrinks the value of benefits that arrive far in the future, so long-lived projects such as flood defences, schools or climate measures look worse. Public bodies set official social discount rates, such as the UK's 3.5% for the first 30 years, while companies usually use their cost of capital or a hurdle rate. Small changes in the rate can push a ratio from above 1 to below it, so good practice includes sensitivity analysis showing results under several rates and benefit estimates. Reflecting the time value of money correctly is what separates the ratio from a simple comparison of totals.

The ratio inherits all the difficulties of valuing benefits and costs in money. Effects such as lives saved, time saved, pollution or social cohesion must be given monetary values, which can be contested. Results are sensitive to how items are classified: treating a cost saving as a benefit or as a reduced cost changes the ratio even when net present value is unchanged. The ratio says nothing about who gains and who pays, so a project with a high ratio may still be unfair to some groups. Optimism bias, the tendency to underestimate costs and overestimate benefits, has been documented in many large projects, and official guidance often requires adjustments for it. Ratios are best treated as one input to a decision, alongside break-even analysis, opportunity cost and judgement about wider effects.

• HM Treasury: The Green Book