NPV — Net Present Value

Net Present Value (NPV) is a single-figure financial valuation metric obtained by discounting each future cash flow of a project to the present at an appropriate discount rate r, summing those discounted flows and subtracting the initial investment. The formula is NPV = sum_{t=1..T} CF_t / (1+r)^t - I_0; a positive NPV signals that the project creates value above the cost of capital, zero is break-even, and a negative NPV destroys value. The decision rule is simple: accept any standalone project with positive NPV; among mutually exclusive projects, choose the one with the highest NPV. The theoretical basis is the time value of money — one TRY today is worth more than one TRY tomorrow because it can be invested, is eroded by inflation and bears risk. The discount rate is typically the firm's Weighted Average Cost of Capital (WACC) or a hurdle rate adjusted to the project's risk profile. An SMB finance manager uses NPV for machinery investments, plant expansion, product launches and long-term contract decisions. The bridge to operations research is #070 knapsack-style multi-project selection — maximizing portfolio NPV under capital constraints is a 0-1 integer program. Historically, Irving Fisher 1907 ('The Rate of Interest') laid the foundation of interest theory, and John Burr Williams 1938 ('The Theory of Investment Value') formally established the discounted-cash-flow valuation model.