Benefit–Cost Ratio

The benefit–cost ratio is the public-sector counterpart of return on investment: discount everything a project will give back, discount everything it will cost, and divide. Above 1.0 the project is justified on this measure; below 1.0 it is not, however impressive the raw benefits look. Worked example: a culvert upgrade whose avoided flood damage has a present worth of $1.4 million against a present worth of costs of $1.0 million scores 1.4 — $1.40 of benefit for every $1 spent. Ranking projects by the ratio rather than by size is what lets a small scheme with a ratio of 3 beat a large one with a ratio of 1.1 when the budget is fixed.

The method is a creature of American flood-control policy: the Flood Control Act of 1936 required that a project's benefits, "to whomsoever they may accrue", exceed its costs, and the analytical machinery grew up around that sentence. Two cautions matter more than the arithmetic. First, the convention. The conventional ratio puts every cost in the denominator; the modified ratio subtracts annual operating and maintenance costs from the benefits instead, leaving only the capital cost below the line. The same project can land either side of 1.0 depending on which was used, so state the convention alongside the number. Second, both figures are present worths at an assumed discount rate over an assumed horizon, and a project heavy on distant benefits is extremely sensitive to that rate — which is why a serious analysis reports the ratio across a range of rates rather than as one figure.