NPVs

Net present value (NPV) is a financial metric used to evaluate the profitability of an investment or project. It represents the difference between the present value of expected cash inflows and the present value of expected cash outflows over the project’s life. For independent projects, NPVs can be added; for mutually exclusive choices, the project with the higher positive NPV is preferred.

Calculation is NPV = -C0 + Σ_{t=1}^n CF_t / (1 + r)^t, where C0 is the initial investment, CF_t are net cash inflows in period t, and r is the discount rate (the required rate of return or cost of capital). The discount rate reflects opportunity cost and risk; higher r lowers NPV.

Interpretation: a positive NPV indicates value creation above the required return, while a negative NPV suggests destruction of value. A zero NPV implies the project earns exactly the required return.

Usage and considerations: NPV is a core tool in capital budgeting because it accounts for the time value of money and all expected cash flows. It is, however, sensitive to the estimated cash flows and the chosen discount rate. Small changes in these inputs can change the decision. NPVs do not capture strategic value, option value, or non-financial considerations without adjustments; risks can be addressed via risk-adjusted discount rates or scenario analysis.