Cost Benefit Analysis Calculator

Cost-benefit analysis converts every consequence of a decision into money, places each in the year it occurs, and discounts it back to the present so that streams arriving at different times can be added. The decision rule is net present value: if the discounted benefits exceed the discounted costs the proposal passes. The benefit-cost ratio divides discounted benefits by discounted costs and gives the same accept or reject signal at 1.0, but it is scale-free, which makes it the more convenient screen when a fixed budget must be spread across competing proposals. Internal rate of return, solved here by bisection, is the discount rate at which net present value reaches zero; it is intuitive but unreliable when cash flows change sign more than once or when projects of different size are compared. The discount rate is the single most consequential input. US Office of Management and Budget Circular A-94 has directed federal agencies to present regulatory analyses at 7 percent, representing an estimate of the pre-tax return on private capital, with a 3 percent social rate of time preference as an alternative view; private firms usually substitute their weighted average cost of capital, commonly 8 to 15 percent. Higher rates penalise projects whose benefits arrive late, which is why the choice is contested for long-horizon environmental and infrastructure work. The main limitations are practical rather than mathematical: intangible effects have to be monetised by proxy, opportunity costs are easy to omit, benefits can be double counted, and appraisal optimism is well documented, so scenario ranges beat single point estimates.

The intellectual origin is usually traced to Jules Dupuit, a French civil engineer who in 1844 published a paper on the measurement of the utility of public works, introducing the notion that the value of a bridge or road to society is the surplus users gain over what they pay. Alfred Marshall gave the surplus concept its formal shape in the 1890s, and the welfare economics that underpins the accept-reject rule was supplied in 1939 by Nicholas Kaldor and John Hicks, whose compensation criterion holds that a change is an improvement if the gainers could in principle compensate the losers. The method became administrative practice in the United States rather than in academia. The Flood Control Act of 1936 authorised federal flood projects on the condition that benefits, to whomsoever they accrue, exceed estimated costs, and the interagency report of 1950 known as the Green Book set out consistent procedures for evaluating river basin projects. Formal discounting guidance followed with OMB Circular A-94, and Executive Order 12291 in 1981 required regulatory impact analyses for major federal rules, a requirement carried forward by Executive Order 12866 in 1993. Parallel development occurred in transport appraisal in the United Kingdom and at the World Bank, where economists including Ian Little and James Mirrlees developed shadow pricing for project appraisal in developing economies during the 1960s and 1970s.