nuvärde

Nuvärde, in finance, denotes the present value of a future amount of money or a stream of future cash flows, discounted at a given rate. It reflects the time value of money: money available now can be invested to earn a return, so a future sum is worth less today.

For a single payment FV to be received after t years, nuvärde is PV = FV / (1 + i)^t, where i is the discount rate. For a series of cash flows CF_t at times t = 1 to n, PV = sum CF_t / (1 + i)^t. Special cases include the annuity, when payments are constant: PV = PMT * [1 − (1 + i)^−n] / i. A perpetuity, with payments continuing forever, has PV = PMT / i. The discount rate i captures the opportunity cost of capital, risk, and expectations for inflation or returns.

Nuvärde is used to compare alternatives by converting future cash flows to their value today. It is a building block in more comprehensive measures such as net present value (NPV), where NPV = nuvärde − initial investment. If NPV is positive, the project may be considered financially attractive, assuming the cash flows and rate are reliable.

Limitations include sensitivity to the estimated cash flows and the chosen discount rate. Small changes can substantially alter the present value, and nuvärde does not guarantee future results. Related concepts include the time value of money, discount rate, annuities, perpetuities, and NPV.