Net Present Value

The sum of a stream of future cash flows, each discounted to its present-day value, minus the initial cost of the investment.

Source: Brealey, Myers & Allen 2019

Each future cash flow is divided by one plus the discount rate raised to the power of the number of periods until it occurs, which converts it to its present-day equivalent, and the discounted flows are summed with the initial outlay subtracted. A positive result indicates the investment produces more value than it consumes at the rate applied. The calculation requires the flows, their timing and the rate, and the last of these is frequently the assumption on which the result most depends. Where flows occur throughout a year rather than at a single point, a mid-year adjustment is sometimes applied, which makes little difference over short horizons and more over long ones.

Source: Brealey, Myers & Allen 2019

Because it measures the size of the gain rather than a rate or a period, so it can be compared directly across projects and summed across a portfolio. The internal rate of return expresses performance as a percentage, which says nothing about scale and can rank mutually exclusive projects incorrectly. The payback period ignores everything occurring after the threshold is reached. Net present value has neither defect and rests on assumptions that are stated rather than implied. It is also additive across projects, so the value of a portfolio is the sum of the values of its components, which no rate-based or period-based criterion permits.

Source: Brealey, Myers & Allen 2019

The discount rate above all, since its effect compounds with the horizon and a modest change can reverse the sign for a project whose returns arrive late. It depends on the projected flows, which for long-lived assets are estimates rather than observations. And it depends on the horizon assumed, since truncating the analysis removes flows that would otherwise contribute. Reporting the result across a range of rates is standard for this reason. Reporting the result across a range of rates, rather than at the single specified rate, is therefore standard practice for schemes with long horizons.

Source: Brealey, Myers & Allen 2019

In appraising capital schemes, where the initial outlay is large and the benefits accrue over decades, and in assessing invest-to-save proposals where spending now is expected to reduce spending later. Public sector appraisal guidance specifies the rate to be applied and requires costs and benefits to be expressed in constant prices, so that general inflation is excluded and a real rate is used. The criterion is the same one applied in economic evaluation, where net benefit is net present value expressed in health or money. The same criterion underlies incremental net benefit in economic evaluation, which is net present value with health substituted for the monetary return.

Source: HM Treasury, The Green Book 2022

It assumes the discount rate correctly reflects the alternative use of the resources, which is contested for public investment where no market rate applies. It treats projected flows as though they were known, so uncertainty must be handled separately through scenarios or simulation. It gives no weight to the distribution of gains and losses across parties. And a positive figure indicates a project is worthwhile without indicating whether a better use of the same resources exists. It also takes the projected flows as given, so optimism in the underlying estimates passes straight through to the result without the criterion signalling anything.

Source: Brealey, Myers & Allen 2019