SuperdayReps
DCF

Time value of money

By SuperdayReps · Michigan Ross Undergrad | Wharton MBA · ex-Citi | ex-Greenhill · Former Head Mentor at a Leading IB Prep Service

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.

FV=PV×(1+r)n\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. rr is the rate of return you earn each period, written as a decimal, so 10% becomes 0.10. And nn is the number of periods, usually years. You multiply by (1+r)(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:

PV=FV(1+r)n\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(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.

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Frequently asked

What is the time value of money?
The time value of money is the idea that a dollar today is worth more than a dollar a year from now, because you can invest today's dollar and earn a return on it. Run that logic backwards and a future dollar must be worth less than a dollar today. It is the engine under every valuation.
How do you calculate present value?
Present value equals the future cash flow divided by one plus the rate, raised to the number of periods. That division by one plus r to the power n is called discounting, which is just compounding run in reverse. At a 10 percent rate, 100 dollars arriving in five years is worth only about 62 dollars today.
Why do valuations fall when interest rates rise?
Because the rate sits in the denominator of the present value formula. A higher discount rate means investors demand more return, so they are willing to pay less today, and present value goes down. Push the denominator up and the value comes down. That is the mechanism behind rising rates lowering valuations.
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