Compounding and Discounting

Compounding and discounting

Compounding is the way to determine the future value of a sum of money invested

now, for example in a bank account, where interest is left in the account after it has

been paid. Since interest received is left in the account, interest is earned on interest

in future years. The future value depends on the rate of interest paid, the initial sum

invested and the number of years the sum is invested for:

where: FV
future value

C0
sum deposited now

i
interest rate

n
number of years until the cash flow occurs

For example, £20 deposited for five years at an annual interest rate of 6 per cent

will have a future value of:

In corporate finance, we can take account of the time value of money through the

technique of discounting. Discounting is the opposite of compounding. While compounding

takes us forward from the current value of an investment to its future

value, discounting takes us backward from the future value of a cash flow to its present

value. Cash flows occurring at different points in time cannot be compared

directly because they have different time values; discounting allows us to compare

these cash flows by comparing their present values.

Consider an investor who has the choice between receiving £1000 now and £1200

in one year’s time. The investor can compare the two options by changing the future

value of £1200 into a present value, and comparing this present value with the offer

of £1000 now (note that the £1000 offered now is already in present value terms).

The present value can be found by applying an appropriate discount rate, one which

reflects the three factors discussed earlier: time, inflation and risk. If the best investment

the investor can make offers an annual interest rate of 10 per cent, we can use

this as the discount rate. Reversing the compounding illustrated above, the present

value can be found from the future value by using the following formula:

where: PV
present value

FV
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