Present value (PV)

Present value answers the opposite question to future value: how much would I have to have today for it to grow into that amount later? Money you receive only later is worth less to you today: you have to wait for it, and in the meantime it could have been earning elsewhere.

It is a view backwards in time. You know the future sum and are looking for its price today.

The formula

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

• $PV$: the present value, that is today's price
• $FV$: the sum you will receive in the future
• $r$: the annual interest rate as a decimal
• $t$: the number of years until payment

It is the same formula as for future value, only turned around. Where future value multiplies, present value divides. The calculation itself is called discounting.

Two views, one formula

• Future value: "How much will my money today be worth in the future?"
• Present value: "How much is a future sum worth today?"

The higher the rate and the more distant the payment, the smaller the present value. A million euro in fifty years is not worth much today.

What it means in practice

Present value is the foundation of almost every valuation. The price of a bond is the present value of its future payments. The value of a company is calculated as the present value of its future profits. Insurers use it to set their reserves.

For an ordinary person it is most useful in decisions of the kind "take less now, or more later?": severance, a prize, or being bought out of a stake. Present value tells you which option is genuinely better.

Try it yourself

In the discounting calculator you can work out a single future payment or a whole series. It also shows the discount factor: what one euro received in a few years' time is worth today.