DCF

Time value of money

6 min read · updated July 8, 2026

A dollar today is worth more than a dollar a year from now. That is the whole idea, and it is the engine under every valuation you will ever build: a DCF, a bond price, an LBO return. If you are fuzzy on this, every number downstream is fuzzy too.

Why is today's dollar worth more? Because you can put it to work. Invest it and it earns a return, so by next year it is worth more than a dollar. Run that logic backwards and a dollar you will not receive until next year has to be worth less than a dollar today. The time value of money is just that gap, made precise.

Compounding forward, discounting back

Put $100 in an account that earns 10% a year. After one year you have $110. Leave it another year and you earn 10% on the whole $110, so you have $121. That is compounding: you earn a return on the returns.

$\text{FV} = \text{PV}\times(1+r)^n$

Future value (FV) is what today's money grows into. Three letters carry the whole formula. PV is the amount you have today. $r$ is the rate of return you earn each period, written as a decimal, so 10% becomes 0.10. And $n$ is the number of periods, usually years. You multiply by $(1+r)$ once for every year that passes. Now flip it. If $100 today becomes $121 in two years at 10%, then $121 received in two years must be worth exactly $100 today. Solving the same equation for the present amount:

$\text{PV} = \frac{\text{FV}}{(1+r)^n}$

Present value (PV) is what a future cash flow is worth right now. Turning a future number into a present one by dividing by $(1+r)^n$ is called discounting, and it is simply compounding run in reverse.

Key insight

Compounding and discounting are the same machine pointed in opposite directions. Compounding pushes a value forward in time and it grows. Discounting pulls a value backward in time and it shrinks. A valuation is almost always the second one: you have future cash flows and you want their worth today.

The discount factor

The piece that does the shrinking is the discount factor: $1/(1+r)^n$ . Multiply any future dollar by it and you get that dollar's present value. At a 10% discount rate, the factor falls a little further out each year. The table shows each year's factor and the present value, in dollars, of a 100 payment arriving that year:

Year	Discount factor (10% rate)	Present value of a 100 payment
1	0.909	90.90
2	0.826	82.60
3	0.751	75.10
4	0.683	68.30
5	0.621	62.10

Read the bottom row: $100 you will not see for five years is worth only about $62 today. The further out the cash, the less it is worth now, and the higher the rate, the faster it decays.

The rate is a required return, not a fact of nature

The discount rate is not handed to you. It is the return an investor requires to part with their money, and it bundles three things: the pure time value (you could earn the risk-free rate doing nothing risky), the risk that the cash never shows up, and the loss of purchasing power to inflation. Riskier cash flows demand a higher rate.

Key insight

That first piece, the risk-free rate, is the anchor for every rate in finance. It is the return you can earn with essentially no risk, in practice the yield on a short-term government bond like a US Treasury bill, since the government is treated as certain to pay you back. It sets the floor. No one rationally accepts a lower return on something risky than they could earn risk-free doing nothing, so every discount rate starts at the risk-free rate and adds a premium on top for the extra risk being taken.

That is why the discount rate you pick depends on whose cash it is. Cash for everyone who funded the business gets discounted at the WACC; cash for shareholders alone gets discounted at the cost of equity. Those are the subjects of the next articles. For now, hold onto the direction of the effect:

Common mistake

Thinking a higher discount rate makes something worth more. It is the opposite. A higher rate means you demand more return, so you are willing to pay less today, and present value goes down. This is the mechanism behind a headline you have seen a hundred times: when interest rates rise, valuations fall. Rates are in the denominator. Push the denominator up and the value comes down.

Perpetuities: valuing "forever" in one line

You cannot discount an infinite stream of cash flows one year at a time. You do not have to. A perpetuity is a level cash flow that arrives every year forever, and its present value collapses to one clean expression:

$\text{PV} = \frac{\text{CF}}{r}$

Here CF is the cash flow you collect each year and $r$ is the same discount rate from before. A $50 cash flow every year forever, discounted at 10%, is worth $500 today ( $50 / 0.10 = 500$ ). That is it. If the cash flow instead grows at a steady rate $g$ each year (say 2% a year), you subtract that growth rate from the discount rate:

$\text{PV} = \frac{\text{CF}}{r-g}$

In that version CF is next year's cash flow, $r$ is the discount rate, and $g$ is the annual growth rate. The rate has to be larger than the growth, or the math breaks.

That second formula should look familiar the moment you meet it again: it is exactly the Gordon-growth terminal value, which is nothing more than the present value of the business cash flows continuing forever past your forecast. The whole intimidating idea of a terminal value is just a growing perpetuity wearing a suit.

Why this is the whole DCF

Stack these pieces up and you have already built a DCF without calling it one. Project a company unlevered free cash flow for a few years, multiply each year by its discount factor, capitalize the tail with a perpetuity, and add everything up. That sum is what the business is worth today.

Key insight

A DCF is not a new concept. It is time value of money applied to a stream of cash flows instead of a single one. Every valuation number you will ever defend traces back to two moves: a future cash flow, and a rate that pulls it back to today.

Interview tip

Interviewers rarely ask you to define the time value of money. They test it constantly anyway, buried inside a present-value question, a discount factor, a perpetuity, or "what happens to the valuation if rates rise." Do the arithmetic with clean round numbers and no calculator, and say the direction out loud without being asked: higher rate, lower value. Being fluent in the machinery here is what makes the rest of the DCF section feel easy instead of memorized.

Glossary

New to the lingo? Every term used above, in plain English.

Time value of money: The idea that a dollar today is worth more than a dollar in the future, because today’s dollar can be invested to earn a return. Every valuation method rests on it.
Present value (PV): What a future cash flow is worth today after discounting it back at a required rate of return. PV = future value divided by (1 + r) raised to the number of periods.
Future value (FV): What an amount invested today grows to after earning a return for some number of periods. FV = present value times (1 + r) raised to the number of periods.
Discount rate: The required rate of return used to translate future cash flows into today’s dollars. A higher discount rate makes future cash worth less now.
Discounting: Converting a future cash flow into its present value by dividing by (1 + r) for each period. It is the reverse of compounding.
Discount factor: The multiplier that turns one dollar received in a future period into its present value: 1 divided by (1 + r) raised to the number of periods.
Compounding: Earning a return on both the original amount and the returns already accumulated, so value grows faster over time. Discounting runs it in reverse.
Perpetuity: A stream of cash flows that continues forever. Its value is the cash flow divided by the discount rate, and a growing perpetuity is the basis of the Gordon growth terminal value.
WACC (Weighted Average Cost of Capital): The blended rate a company pays to fund itself with both debt and equity. In a DCF it is the discount rate used to bring future cash back to today.
Cost of equity: The return shareholders require to own a company stock, given its risk. Usually estimated with CAPM, and it is always higher than the cost of debt.
Risk-free rate: The return on an investment with essentially no risk, usually the yield on a long-term government bond. It is the starting point for the cost of equity.
Terminal Value: In a DCF, the estimated value of all the cash flows that come after the years you forecast explicitly. It often makes up most of the total value.
Unlevered free cash flow: The cash a business generates before any debt payments, so it belongs to all investors, both lenders and shareholders. This is the cash flow used in a DCF.

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