Time Value of Money

Three reasons. First, opportunity cost / earning power: a dollar today can be invested and earn a return, so it grows into more than a dollar by next year. Second, inflation: prices tend to rise, so a future dollar buys less. Third, risk and uncertainty: a promise of future money carries the risk it never arrives. Because of these forces, you can never compare cash flows from different points in time directly — you must first translate them all to a common point in time (usually today, via present value) before adding or comparing them.

Future value (FV) answers 'what will this money grow to?' — it compounds a present amount forward at an interest rate. Present value (PV) does the reverse: it discounts a future amount back to today. The two are mirror images. The discount rate is the engine: it's the assumed rate of return, and the higher it is, the more aggressively future cash gets shrunk. For a stream of multiple cash flows (like a DCF), you compute the present value of each individual cash flow and sum them — that sum is the value today of the whole stream.

Time value of money is everywhere in banking. A DCF discounts projected free cash flows and a terminal value back to today using a discount rate — pure TVM. IRR is the discount rate that sets a deal's net present value to zero, central to LBO and project analysis. Bond pricing discounts coupon and principal payments. Even the choice between a lump sum now versus payments over time — common in deal structuring, earn-outs, and settlements — reduces to TVM. Master it early because every valuation technique you'll touch is built on it.