Economics
Present Value
Quick fact
The concept of present value was formalized by English mathematician Richard Witt in 1613, though the idea of discounting future sums dates back to medieval interest tables.
Why this is interesting
Would you rather have $100 today or $100 a year from now? The answer reveals the surprising power of time over money.
Read the full explanation
Understanding Present Value
Present value is based on the simple insight that money available now can be invested to grow. If you have $100 today and can earn 5% per year, you’ll have $105 in one year. So receiving $100 in a year is less valuable than receiving $100 today. To find the present value of a future amount, we reverse the growth process: we ‘discount’ it by the expected rate of return. For instance, if you are promised $105 in one year and your required return is 5%, the present value is $100. This logic extends to multiple periods and irregular cash flows.
A deeper explanation
The mathematical mechanism is exponential discounting: PV = FV / (1 + r)^n, where r is the discount rate and n is the number of periods. The discount rate reflects the opportunity cost of capital and risk. Higher rates or longer time horizons dramatically shrink present value. This principle forces decision-makers to weigh the timing of cash flows, not just their size. Present value is fundamental to evaluating investments (e.g., net present value), pricing bonds and stocks, and comparing financial alternatives. It underscores that a dollar today is not equal to a dollar tomorrow—time transforms value.