Discounting

Money you will only receive in a few years' time is worth less to you today than the same amount right now. You have to wait for it, and meanwhile it could have been working elsewhere. Discounting is the calculation that converts a future sum into its value today.

Why money is worth more today

There are three reasons, and together they make up what is called the discount rate:

• The chance to earn. Money you hold today can be invested. Money promised for later earns you nothing in the meantime.
• Inflation. Prices rise, so the same sum buys less in a year.
• Uncertainty. A promise may not be kept. Money in hand carries no such risk.

The greater the opportunity, the inflation or the risk, the higher the discount rate, and the less a future payment is worth today.

The formula

Discounting is compound interest run backwards. Where compounding moves value forward, discounting pulls it back:

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

• $PV$: the present value
• $FV$: the future amount
• $r$: the discount rate as a decimal
• $t$: the number of years until it falls due

The ratio $1 / (1+r)^t$ is called the discount factor. It says what one euro received in the future is worth today, and it is always less than or equal to one.

A worked example

A friend promises to pay you €10,000 in 5 years. Your money would earn 6% a year elsewhere.

The discount factor is 0.7473, so the present value of the promise is €7,472.58. That is the most it is worth paying today: the difference of €2,527 is the price of waiting.

What to watch out for

The discount rate is not the same thing as the interest rate on a deposit, even though the formulas are related. The discount rate expresses the return you require, including the risk of the particular project.

Consistency matters too: either work with nominal amounts and a nominal rate, or with real amounts and a real rate. Mixing the two counts inflation twice.

Where you will use it

Discounting underpins almost every valuation in finance: bond prices, company valuations by DCF, retirement calculations and insurance reserves. With several payments the step repeats for each and the results are added up, that is the principle of an annuity.

Try it in the discounting calculator, which handles a single payment or a whole series of cash flows.