Compare payments at different dates, with the assumptions made visible.
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The idea
The time value of money starts with a simple observation: money today can be used, saved, or invested today. Money promised later cannot do those things yet.
That does not mean every investment will grow. It means time has a price. If someone asks you to wait for money, the wait matters because you give up other uses of that money and accept uncertainty.
Inflation is part of the reason future money may feel smaller: if prices rise, the same cash buys less. Risk is another part: a promised future payment may not arrive on time or in full.
Future value asks what money today could become if it grows at an assumed rate. Present value works in the other direction: it translates a future amount back into today’s terms.
Compounding moves an amount forward through time; discounting moves it back to a common date. The calculation only becomes meaningful when the payment date and rate refer to the same period. An annual effective rate already includes the year's compounding. It cannot be inserted unchanged into a formula whose periods are months.
Present value is a comparison under stated assumptions. It does not tell us that a promised payment will arrive, or that a particular investment will earn the rate used.
Worked Example
Putting a future amount into today’s terms
Suppose you expect to receive 1,200 pounds in three years. If the relevant annual discount rate is 4%, the present value is not 1,200 pounds.
Using the standard present-value formula, the calculation is 1,200 divided by 1.04 raised to the third power. That gives 1,066.80 pounds, rounded to the nearest penny.
Read this as a translation, not a prediction. Under a 4% annual discount rate, 1,066.80 pounds today and 1,200 pounds in three years are equivalent in the model.
For this hypothetical payment, the 4% rate is an annual effective discount rate and the £1,200 arrives once, exactly three years from today. Divide £1,200 by 1.04 three times: the denominator is 1.124864, giving £1,066.80 when rounded to the nearest penny. Keep the unrounded figure when checking the calculation in reverse.
At a 6% annual effective rate, the same payment has a present value of £1,007.54. Nothing happened to the future £1,200: the comparison rate changed. These are illustrative assumptions, not available savings rates or forecasts of investment returns.
Formula
Present value equals future value divided by one plus the discount rate raised to the number of periods.
Present value: what the future amount is worth today in the model.
Future value: the amount expected later.
Discount rate per period, stated on the same time basis as n.
Number of periods until the cash flow arrives.
The rate is an assumption about time, opportunity cost, inflation, and risk. Changing it changes the answer.
Future amount
1,200 pounds
Discount rate
4% per year
Time
3 years
Present value
1,066.80 pounds
Reading the result
What the discount changes
The gap between future and present value represents the effect of time at the chosen rate. A higher positive discount rate gives a lower present value for a fixed positive payment. A later payment is also worth less under that assumption because it is discounted over more periods.
Discounting can therefore make two differently timed offers comparable, but it cannot settle every difference between them. A payment from a reliable payer and an uncertain business forecast are different claims. Their timing may be identical while their risk is not. The arithmetic should make the assumptions visible instead of disguising them as a precise answer.
Limits and assumptions
Purchasing power and uncertainty
Nominal amounts are measured in future currency units. Real amounts describe purchasing power after allowing for inflation. Pair nominal cash flows with a nominal rate, and real cash flows with a real rate; mixing the two can count inflation twice or omit it.
The single-payment formula leaves out taxes, fees, changing rates and the possibility of non-payment. Several payments require discounting each one from its own date before adding them. A negative discount rate can reverse the familiar relationship between time and present value. These limits explain why a tidy spreadsheet is only as useful as its inputs.
Common Mistake
Treating the rate as a fact
The most common mistake is to treat the discount rate as if it were a fact about the world. It is an assumption that should fit the timing, risk, and inflation context of the cash flow.
A higher rate makes future money worth less today. A lower rate makes future money worth more today. In valuation work, a large part of the debate is really a debate about the cash flows and the rate applied to them.
Writing “4% annually, one payment after three years” beside the example prevents an apparently small convention change from becoming a large modelling error. The final number should always travel with that explanation.
Self-check
Check your understanding
Why is £1,200 in three years discounted rather than simply compared with cash today?
The payments occur at different dates. Discounting puts them on a common date using a stated rate; it does not establish that the future payment is certain.
What happens if the assumed rate rises from 4% to 6%?
The present value falls from about £1,066.80 to £1,007.54, because the fixed payment is divided by a larger compounding factor. The payment itself is unchanged.
Can an annual rate be used unchanged with twelve monthly periods?
No. The rate and period must match. An annual effective rate needs conversion to its equivalent monthly rate before a monthly-period formula is used.
Further application
Make the timing visible
A cash-flow worksheet can put each payment beside its date, currency and discount-rate convention. This makes a present-value comparison reproducible and shows which assumption explains a change.
Disclaimer
Educational Use Only
This article is for informational and educational purposes only. It does not provide personalised investment advice, tax advice, or a recommendation to buy or sell any security.
