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A '''break-even-point''' (or break-even-volume) is a point at which the positive effects of a decision (typically sales revenues) cover the negative effects (typically costs). This critical point is interesting if both the positive and the negative effects depend in different ways on a common factor (e. g. production volume or activity) whose value is unknown. In this case it is not possible to calculate the profit of the decision. Instead, the break-even-point answers the question above which value of the common factor the decision will lead to higher positive than negative effects, or (to put it simple) above which value we will make profit. | A '''break-even-point''' (or break-even-volume) is a point at which the positive effects of a decision (typically sales revenues) cover the negative effects (typically costs). This critical point is interesting if both the positive and the negative effects depend in different ways on a common factor (e. g. production volume or activity) whose value is unknown. In this case it is not possible to calculate the profit of the decision. Instead, the break-even-point answers the question above which value of the common factor the decision will lead to higher positive than negative effects, or (to put it simple) above which value we will make profit. | ||
The relations between costs, sales revenues, profits and the unknown or uncertain common factor are the objects of break-even-analyses or '''cost-volume-profit-(CVP)-analyses.''' <br> | The relations between costs, sales revenues, profits and the unknown or uncertain common factor are the objects of break-even-analyses or '''cost-volume-profit-(CVP)-analyses.''' <br> | ||
Given the broad variety of decisions with positive and negative effects in business and daily life, and the uncertainty we often face with respect to important factors, break-even-analyses have a long tradition. Apart from earlier anecdotic evidence, we find first formal approaches in the 19th century. Schweitzer/Troßmann (1986, 1998) provide an excellent overview and detailed descriptions of numerous specific variants and extensions of break-even-analyses for very different situations. In the following, we present the basic model and an extension to the [[Multi-product break-even-analysis|multi-product case]].<br> | Given the broad variety of decisions with positive and negative effects in business and daily life, and the uncertainty we often face with respect to important factors, break-even-analyses have a long tradition in [[controlling]] and management. Apart from earlier anecdotic evidence, we find first formal approaches in the 19th century. Schweitzer/Troßmann (1986, 1998) provide an excellent overview and detailed descriptions of numerous specific variants and extensions of break-even-analyses for very different situations. In the following, we present the basic model and an extension to the [[Multi-product break-even-analysis|multi-product case]].<br> | ||
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: x* = K<sup>f</sup>/(p – k<sup>v</sup>). <br> | : x* = K<sup>f</sup>/(p – k<sup>v</sup>). <br> | ||
=== Standard break-even-analysis using contribution margins === | === Standard break-even-analysis using contribution margins === | ||
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The break-even point corresponds to the condition D(x) = K<sup>f</sup>:<br> | The break-even point corresponds to the condition D(x) = K<sup>f</sup>:<br> | ||
: x* = K<sup>f</sup>/d.<br> | : x* = K<sup>f</sup>/d.<br> | ||
=== Graphical break-even-analysis === | |||
An important appeal of break-even-analyses comes from its intuitive graphical presentation. The following graph shows the standard model of break-even-analysis.<br> | |||
[[Datei:Break-even-standard.PNG|thumb|left]]<br> | |||
<br style="clear:left;"/> | |||
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== Benefits of break-even-analyses == | == Benefits of break-even-analyses == | ||
Starting from the quite intuitive standard break-even-model, numerous variants and extensions have been suggested. Sometimes a more sophisticated approach might be seen as a “methodological overkill” and a simpler approach may be sufficient. This trade-off depends largely on the situation. However, the broad acceptance of break-even-analyses in everyday business situations goes beyond the calculation of break-even-points. It is due to the fact that even simple approaches require an analysis of the critical factors that influence sales, cost and profits, and of the way they do it – exactly the information every manager would like to have. | Starting from the quite intuitive standard break-even-model, numerous variants and extensions have been suggested. Sometimes a more sophisticated approach might be seen as a “methodological overkill” and a simpler approach may be sufficient. This trade-off depends largely on the situation and, properly used, break-even-analyses are among of the most important tools of [[controlling]] and [[managerial accounting]].<br> | ||
However, the broad acceptance of break-even-analyses in everyday business situations goes beyond the calculation of break-even-points. It is due to the fact that even simple approaches require an analysis of the critical factors that influence sales, cost and profits, and of the way they do it – exactly the information every manager would like to have. | |||