# Mixed cost types

When mixed types of costs (also briefly mixed costs ) is called in the Cost Accounting those types of costs for which no clear separation into fixed costs and variable costs is possible. Mixed cost types can only be split into utility and idle costs .

## example

The power consumption of a lathe basically depends on its running time. If the machine were to be used for permanent production (maximum employment , so-called capacity ), these costs would be completely variable. However, if the lathe is not used for a short time, it may not be switched off completely, but must be kept ready for operation. This results in costs that cannot be assigned to either fixed or variable costs.

## Dissolution and allocation of the mixing costs

For partial cost accounting in particular , it is essential to split the mixed costs into a fixed and a variable cost component. There are various methods of determining the variable component:

### Mathematical method

The most common form of cost splitting is the mathematical method. It is based on a fixed, service-quantity-neutral and a linear, service-volume-induced cost component. Two values ​​are required for application, which are based on different occupations. If you put the respective differences in relation to each other, you get the variable cost share per unit (also called marginal costs ):

${\ displaystyle K _ {\ text {variable}} = {\ frac {\ Delta K _ {\ text {total}}} {\ Delta B}}}$

With

${\ displaystyle K _ {\ text {variable}}}$: variable cost share per unit ( marginal costs )
${\ displaystyle K _ {\ text {total}}}$: total costs determined
${\ displaystyle B}$: Amount of employment in units

The respective remaining size represents the fixed cost share:

${\ displaystyle K _ {\ text {fix}} = K _ {\ text {total}} - B \ cdot K _ {\ text {variable}}}$

With

${\ displaystyle K _ {\ text {fix}}}$: Share of fixed costs
${\ displaystyle K _ {\ text {total}}}$: total costs determined
${\ displaystyle B}$: Amount of employment in units
${\ displaystyle K _ {\ text {variable}}}$: variable cost share per unit

Example:

The lathe mentioned above has a power consumption of 25 kWh (= 5 euros) with a daily effective employment of 8 hours, with an effective employment of 6 hours (remaining time = standby) it has a power consumption of 20 kWh (= 4 euros). The variable cost component can be calculated from these two empirical values:

${\ displaystyle K _ {\ text {variable}} = {\ frac {5 \, {\ text {euros}} - 4 \, {\ text {euros}}} {8 \, {\ text {hours}} - 6 \, {\ text {hours}}}} = {\ frac {1 \, {\ text {euros}}} {2 \, {\ text {hours}}}} = 0 {,} 50 \, { \ text {Euro}} / {\ text {Operating hour}}}$

The fixed costs are

${\ displaystyle K _ {\ text {fix}} = 5 \, {\ text {euros}} - 8 \, {\ text {hours}} \ cdot 0 {,} 50 \, {{\ text {euros}} / {\ text {operating hour}}} = 1 \, {\ text {Euro}}}$

### Graphical method and least squares method

With this method, the costs incurred and the associated employment are recorded monthly and entered in a coordinate system (x-axis: employment; y-axis: costs). At the end of the year, a regression line is drawn through the 12 points recorded. From their intersection with the y-axis, the fixed cost portion then results. The difference to the actual cost amount therefore represents the variable cost component. This method also assumes a linear relationship between employment and costs.

## literature

• K. Olfert: cost accounting. 14th, updated and revised edition. Kiehl Verlag, Ludwigshafen / Rhein 2005, ISBN 3-470-51104-7 .