Discounting

Discounting (also discounting, discounting engl; . Often wrongly known as discounting ) is an arithmetic operation of mathematics of finance, in which the value of a future payment for a time that the payment is before, is calculated. Frequently, but not necessarily, the present value ( NPV) is calculated by discounting the future cash.

Accordingly, the accrued interest (also Askontierung ) is the inverse arithmetic operation. In it, the value that has a payment at a later time is determined.

Due to the existence of interest, the same amount of money has to be all the higher value, the sooner you get it. This relationship is represented by the arithmetic operations of discounting and compounding.

The value of V, the current flowing at time t2 has a payment of the amount C at time t1, calculated as the product of C and the discount rate or discount rate in the DF, which is a function of time points t1 and t2 as well as the relevant interest rate z.

Since it is a discounting, the time t1 is before time t2 (t1 < t2).

The compounding factor is simply the inverse of the discount factor for the same period. It is used eg to determine a final value.

Assuming positive interest rate, the discount factor DF is always less than 1 and greater than 0 According to the compounding factor is always greater than 1, the exact shape of the Aufzinsungs and the discount factor depends on the chosen interest rate convention.

The interest may be either actual interest rates ( market rates) as well as fictitious, about imputed or act Alternatively, interest (such as in business valuation ).

Determination of the discount rate and the Aufzinsfaktors

In the following, the shape of the discount factor DF is first for discounting to the present ( ie t1 = 0) given. The discount rate then depends only on the timing of future payments t2 = t and the interest rate used z from. The Aufzinsfaktor AF applies for the compounding of a present payment to a later time t2 = t.

Linear interest

The linear rate of interest is usually applied for periods that are less than a year. The factors DF and AF are calculated as follows

Where n is the number of interest days to t2 and m is the number of interest days per year according to the chosen method of calculating interest.

• Example

Exponential rate of return

The exponential rate of return is usually used for periods that are longer than one year. They implicitly takes into account compound interest effects. If the interest rate at z and payment is made in t2 years, so is the discount factor

• Example

Continuous compounding

The constant interest rate is a special case of the exponential rate of interest and is often used in theoretical mathematical problems. It takes into account compound interest effects. The discount factor for a payment in years t2 is here

E here is the Euler number

• Example

Discounting at a future date

If the time should be discounted to, in the future, the calculation is the same. The interest rate to be used is then an interest rate for a period that starts in the future and thus corresponds to a forward interest rate. Assuming an interest rate of z, the time of payment t2 is 9 months and it should be discounted to a time t1 in 3 months, so is the discount factor

If a linear interest rate and in turn the German interest rate method is adopted. It is about 9 - discounted 3 = 6 months because the time is discounted to the, is 6 months before the date of payment.