Value additivity

In business administration, value additivity is a special property in connection with payment flows : If the value of a payment flow combined from two payment flows corresponds to the sum of the values ​​of the individual payment flows, value additivity is present. Value additivity is a special form of additivity .

One of the secondary conditions of value additivity is that the law of the unit price applies, that is, a perfect market exists. Since the perfect market is a purely theoretical concept, value additivity is also of purely theoretical interest.

Mathematical definition

Let z ₁ and z _{2 be} payment flows and V ( z ₁ ), V ( z ₂ ) the values ​​of these payment flows. Let V ( z ₁ + z ₂ ) be the value of the cash flow combined from z ₁ and z ₂ .

The law of unit price applies as well

${\displaystyle V(z_{1}+z_{2})=V(z_{1})+V(z_{2})\,,}$

so there is value additivity.

properties

Obviously, value additivity is a monoid homomorphism property of the function

${\displaystyle V:\mathrm {Zahlungsstr{\ddot {o}}me} \rightarrow {\text{Werte}}}$

(e.g. market valuation function ) with regard to the monoid

${\displaystyle \left(\mathrm {Zahlungsstr{\ddot {o}}me} ,\Box +\Box \right)}$

and the monoid

${\displaystyle \left({\text{Werte}},\Box +\Box \right)}$.

Since homomorphism refers to two addition monoids, a function that has value additivity as a property is essentially a linear mapping .