Net Present Value (NPV)

Net present value (NPV) is the sum of all the cash flows an investment is expected to generate, each converted into today's money, minus the cost of making the investment. If the result is positive, the project is expected to earn more than the return required on the money tied up in it; if negative, it is expected to destroy value. Companies use NPV to decide which factories, products or acquisitions to fund, governments use it in cost-benefit appraisal, and investors use it to value businesses and bonds.

NPV is a direct application of the time value of money: every future amount is discounted at a rate that reflects the opportunity cost of capital and the risk of the cash flows. It is usually compared with the Internal Rate of Return (IRR), which uses the same cash flows but reports a percentage rather than an amount. Finance textbooks treat NPV as the more reliable of the two for choosing between projects.

Think of buying a small coffee cart. You pay for it today, and over the next few years it hands you money back. The question is whether those future takings, once you allow for the fact that money later is worth less than money now, add up to more than the price of the cart.

NPV is the scorecard for that question. It translates every future payment into "today money", adds them up, and subtracts what you paid. A score above zero says the cart is worth more than it costs, even after allowing for the interest you could have earned by leaving the money in the bank. A score below zero says you would be better off doing that instead.

The standard calculation is:

• $C_t$ is the net cash flow in period $t$; the initial investment at $t = 0$ is negative.
• $r$ is the discount rate per period, written as a decimal.
• $n$ is the final period of the project.

Worked example: a machine costs 10,000 today and is expected to add 4,000 of cash in each of the next three years. At a 10% discount rate the inflows are worth $3{,}636 + 3{,}306 + 3{,}005 = 9{,}947$, so the NPV is $9{,}947 - 10{,}000 = -53$. The project narrowly fails. At an 8% rate the same inflows are worth 10,308 and the NPV becomes +308, which shows how much the answer depends on the rate.

For a company the usual rate is its weighted average cost of capital: the blended return demanded by lenders and shareholders, with the cost of equity often estimated using the Capital Asset Pricing Model (CAPM). Riskier projects should be discounted at a higher rate, which adds a risk premium above the risk-free rate. Many firms set a hurdle rate above their cost of capital to allow for optimistic forecasts.

Cash flows and rates must be consistent. Forecasts in nominal money need a nominal rate; forecasts in real terms need a real rate, or inflation is counted twice or not at all. Governments use a social discount rate for public projects: in September 2026 HM Treasury accepted a review recommendation to lower the standard rate in its Green Book guidance from 3.5% to 3.0% for the first 30 years of an appraisal, confirmed in its October 2026 response.

NPV is the core of cost-benefit analysis and of discounted cash-flow valuation in mergers and acquisitions, private equity and equity research. A widely cited survey of US chief financial officers by John Graham and Campbell Harvey, published in 2001, found that about three-quarters always or almost always used NPV, roughly the same share as used IRR. Banks apply the same logic when pricing a loan, and the price of a bond is effectively the NPV of its coupons and principal at the market yield.

The decision rules are simple:

• Single project. Accept if NPV is positive, reject if negative.
• Competing projects. Where only one can be chosen, pick the one with the highest NPV, not the highest IRR.
• Limited budget. When capital is rationed, rank projects by NPV per unit of capital (the profitability index) and fund down the list.

• Forecast risk. NPV converts guesses about distant cash flows into a precise-looking number. Small changes in growth or margin assumptions can flip the sign, so analysts run sensitivity and scenario tests.
• Rate sensitivity. Long projects are highly sensitive to the discount rate, which is why the rate for climate and infrastructure appraisal is hotly debated.
• Ignoring flexibility. Standard NPV assumes a fixed plan. The value of being able to expand, delay or abandon a project is captured by real-options analysis, which borrows from option pricing.
• Behaviour inside firms. Managers rewarded on short-run earnings may reject positive-NPV projects that hurt this year's profit, one form of short-termism, while past spending that cannot be recovered, a sunk cost, should be left out of the calculation but often is not.

• HM Treasury: The Green Book, appraisal and evaluation in central government
• Aswath Damodaran, NYU Stern School of Business: valuation data and teaching materials