presentvalue

Present value is the current worth of money or cash flows that are to be received in the future, discounted to reflect the time value of money, opportunity cost, and risk. In other words, a dollar today is worth more than a dollar in the future because it can be invested to earn a return.

For a single future sum FV received t periods from now, the present value is PV = FV / (1 + r)^t, where r is the per-period discount rate. For a stream of cash flows CF_t occurring at each period t, PV = sum over t of CF_t / (1 + r)^t. If the discounting uses continuous compounding, PV = FV * e^{-rt}. Perpetuities have PV = CF / r, where CF is the periodic cash flow.

Choosing the discount rate r reflects the opportunity cost, inflation, risk, and liquidity of the investment. Higher risk or inflation generally implies a higher r and a lower present value for the same future cash flow.

Applications of present value include capital budgeting (assessing projects via net present value), bond pricing, lease and loan calculations, and retirement planning. It is a foundational concept in finance and economics, often used to compare alternatives with different timing and risk profiles.

Limitations arise from sensitivity to the discount rate and cash-flow estimates. Small changes in r or in expected cash flows can produce large changes in PV. Real-world applications may incorporate risk adjustments, scenario analysis, and multiple discount rates. Related concepts include net present value, internal rate of return, and discounting methods for irregular cash flows.