# Discount

In finance, discounting is the process of finding the current value of an amount of cash at some future date, and along with compounding cash form the basis of time value of money calculations. The discounted value of a cash flow is determined by reducing its value by the appropriate discount rate for each unit of time between the time when the cashflow is to be valued to the time of the cash flow. Most often the discount rate is expressed as an annual rate.

To calculate the net present value of a single cash flow, it is divided by one plus the interest rate for each period of time that will pass. This is expressed mathematically as raising the divisor to the power of the number of units of time.

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## Example

For example: You want to find the net present value of $100 that will be received in five years time. What is it worth now? What amount of money, if you let it grow at the discount rate, would equal$100 in five years?

We will assume a 12% per year discount rate.

NPV = 100 dollars divided by 1 plus 12% (0.12) divided by 1 plus 12% (0.12), etc.

[itex]{\rm NPV}=\frac{100}{(1+0.12)^5}.[itex]

Since 1.125 is about 1.762, the net present value is about \$56.74.

## Discount rate

The discount rate used in financial calculations is usually chosen to be equal to the cost of capital. Some adjustment may be made to the discount rate to take account of risks associated with uncertain cashflows, with other developments.

## Discount factor

The discount factor', P(T), is the number by which a future cash flow to be received at time T must be multiplied in order to obtain the current present value. Thus for a fixed annually compounded discount rate r we have

[itex] P(T) = \frac{1}{(1+r)^T} [itex]

For a fixed continuously compounded discount rate r we have

[itex] P(T) = e^{-rT} [itex]

## Other discounts

For discounts in marketing, see discounts and allowances, sales promotion, and pricing.

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