The bar value (partially present value or from the English: present VALUE) is a term from mathematics of finance and corresponds to the value, which a payment in the present, resulting in the future, possesses. It is differently expressed the value of all payments at the beginning of the running time (at the time 0). Besides there is still the term of the statistical bar value, which represents a Verallgemeinerung of the financialmathematical bar value.

Bar value of only one payment

Explanation

By the bar value it is possible to determine with equal lasting interest rate and annual payments the height of the investment at the today's time. Thus different investments can be compared with different running times and interest rates with one another.

In order to compute a bar value (also present value), the following data must be given:

• The height of the payment Z flowing in the future (in the formula with Z_T designates).
• The number of periods, during which the payment is to be abgezinst (T).
• The interest rate r, with which the payment is abgezinst:
  • If it concerns here a plant interest rate, then the bar value corresponds to the value, which an investor in the present must put on, in order in the future from this plant a payment according to Z_T to get.
  • If r is an indebtedness interest rate, then the bar value corresponds the height of the credit, which an applicant for the credit with the Z_T-Einzahlungen can erase.

The simplest formula for the computation of the bar value reads: Test specification (Z_T) = \ frac {Z_T} {(1+r_T) ^T}

It applies to exactly one payment, which is appropriate for T years in the future. Besides from a remaining alike interest rate r one proceeds.

Example

A would like to buy in four years a new car, which will then cost 30,000 "€. He would like to know already today, how much money he must put on, if it can count on interest charges of 6% per annum.

Solution: Test specification (30000) = \ frac {30000} {(1+0,06) ^4} = 23762 {,} 81

Bar value with under-year old interest charges

With the formation of a bar value it can every now and then to occur that per period several payments take place, which to be abgezinst have. To it e.g. comes if interest due of the investor is half-yearly served.

With m interest payments in the year during one period of T years must the bar value of the amount Z_T flowing at the end read: Test specification (Z_T) = \ frac {Z_T} {\ left (1+ \ frac {r_T} {m} \ right) ^ {TM}}

Bar value of an annuity

Explanation

Annuity (or pension) one calls a remaining alike regular payment in mathematics of finance. If this payment is limited not to one period, but flows for an unlimited period for a long time, one speaks of an infinite pension (also "“perpetuity"”). For both cases the respective bar values can be computed, whereby at longer periods the bar values for finite and infinite payment stream can be nearly identical.

• Bar value of the amount Z, which flows m-times in the year on unrestricted duration (r = interest rate): Test specification (Z) = \ frac {Zm} {r}

The bar value is thus with a positive interest rate always finally, even with an eternal pension. See annuity bar value insurance.

• Bar value of the amount Z, which flows to N years m-times per year: Test specification (Z) = Z \ Bigg [\ frac {m} {r} - \ frac {1} {\ frac {r} {m} \ big (1 + \ frac {r} {m} \ big) ^ {Nm}} \ Bigg]

Example

Computation (life expectancy of the nut/mother: 80 years, see also statistical bar value):

Test specification (500) = 500 \ Bigg [\ frac {12} {0.05} - \ frac {1} {\ frac {0.05} {12} \ big (1 + \ frac {0.05} {12} \ big) ^ {20 \ cdot {} 12}} \ Bigg] = 75762 {,} 66

Statistical bar value

The statistical bar value is a Verallgemeinerung of the financialmathematical bar value. Where the latter the value, which payments in the present, resulting in the future, possess, (only) with consideration of the discounting represents, also still statistic and/or stochastic sizes flow as (probabilities of dying) and something similar at the statistical bar value.

The statistical bar value life annuities for example is the sum of all possible future pension payments (including possible survivor's pension payments after the death of the annuitant), in each case with the probability of their occurring weighted and on the computation time abgezinst.

See also

Gordon formula, value of a gold donkey, CBL, collection of formulae economics

Articles in category "Bar value"

We found here 4 articles.

Related Websites

We found here 3 related websites.

• Linotype.com - Menue Card Bar Value Pack
  Menue Card Bar Value Pack: Background Information + Purchase Options.


• Linotype.com - Menue Card Bar Value Pack
  Menue Card Bar Value Pack: Background Information + Purchase Options.


• Linotype.com - Menue Card Bar Value Pack
  Menue Card Bar Value Pack: Background Information + Purchase Options.