Time Value of Money

Time value of money (TVM) is the principle that a dollar today is worth more than a dollar tomorrow. You can invest today's dollar and earn a return; a dollar promised later cannot earn until you have it. So future cash flows must be discounted to be comparable to today's cash. The discount rate is the opportunity cost of capital — what you could earn elsewhere with the same risk. Present value (PV) of a future sum is that sum divided by (1 + r)^t, where r is the discount rate and t is time in years. Net present value (NPV) of a project is the sum of discounted cash flows minus initial investment; if NPV > 0, the project creates value.

The implication is that timing of cash flows matters as much as size. $100 in one year is worth less than $100 today; $100 in ten years is worth much less at any reasonable rate. Delaying receipt destroys value unless the delay is compensated by a higher payment. Conversely, delaying payment preserves value for the payer — which is why "pay later" terms can be attractive. The same project can be good or bad depending on how fast it generates cash: fast payback is worth more than slow payback at the same nominal total.

The mental model extends beyond finance. Any decision where outcomes occur at different times — hiring (pay now for future productivity), R&D (spend now for future product), or personal savings (spend now vs save for retirement) — involves TVM. The discipline is to express future outcomes in present terms so you can compare apples to apples.