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Formal multi-product break-even-analysis: Unterschied zwischen den Versionen
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Formal multi-product break-even-analysis (Quelltext anzeigen)
Version vom 26. Januar 2012, 20:55 Uhr
, 26. Januar 2012→The case of two products with joint fixed costs
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: K<sup>f</sup> = (p<sub>1</sub>-k<sup>v</sup><sub>1</sub>) · x<sub>1</sub> + (p<sub>2</sub>-k<sup>v</sup><sub>2</sub>) · x<sub>2</sub> = d<sub>1</sub> · x<sub>1</sub> + d<sub>2</sub> · x<sub>2</sub><br> | : K<sup>f</sup> = (p<sub>1</sub>-k<sup>v</sup><sub>1</sub>) · x<sub>1</sub> + (p<sub>2</sub>-k<sup>v</sup><sub>2</sub>) · x<sub>2</sub> = d<sub>1</sub> · x<sub>1</sub> + d<sub>2</sub> · x<sub>2</sub><br> | ||
It is obvious that the contribution to be achieved with one product depends on the contribution provided by the other product. In extreme cases, we concentrate on one of the products and set the volume of the other equal to zero. This leads to the individual break-even-points (or '''break-even-corner-points'''):<br> | It is obvious that the contribution to be achieved with one product depends on the contribution provided by the other product. In extreme cases, we concentrate on one of the products and set the volume of the other equal to zero. This leads to the individual break-even-points (or '''break-even-corner-points'''):<br> | ||
: | |||
: | : [[Datei:x_hat_1.png]] = K<sup>f</sup>/d<sub>1</sub> (if x<sub>2</sub> = 0)<br> | ||
: [[Datei:x_hat_2.png]] = K<sup>f</sup>/d<sub>2</sub> (if x<sub>1</sub> = 0)<br> | |||
Since we assumed '''linear cost-volume-profit-relations''' (due to the constant unit prices and variable costs), a 50/50-combination of x<sub>1</sub>* and x<sub>2</sub>* will cover the fixed costs too. This can be easily seen for x<sub>1</sub> = 0.5· x<sub>1</sub>* and x<sub>2</sub> = 0.5 · x<sub>2</sub>*: <br> | Since we assumed '''linear cost-volume-profit-relations''' (due to the constant unit prices and variable costs), a 50/50-combination of x<sub>1</sub>* and x<sub>2</sub>* will cover the fixed costs too. This can be easily seen for x<sub>1</sub> = 0.5· x<sub>1</sub>* and x<sub>2</sub> = 0.5 · x<sub>2</sub>*: <br> | ||
: d<sub>1</sub> · x<sub>1</sub> + d<sub>2</sub> · x<sub>2</sub> = d<sub>1</sub> · 0.5 · x<sub>1</sub>* + d<sub>2</sub> · 0.5 · x<sub>2</sub>* = d<sub>1</sub> · 0.5 · K<sup>f</sup>/d<sub>1</sub> + d<sub>2</sub> · 0.5 * K<sup>f</sup>/d<sub>2</sub> = K<sup>f</sup>.<br> | : d<sub>1</sub> · x<sub>1</sub> + d<sub>2</sub> · x<sub>2</sub> = d<sub>1</sub> · 0.5 · x<sub>1</sub>* + d<sub>2</sub> · 0.5 · x<sub>2</sub>* = d<sub>1</sub> · 0.5 · K<sup>f</sup>/d<sub>1</sub> + d<sub>2</sub> · 0.5 * K<sup>f</sup>/d<sub>2</sub> = K<sup>f</sup>.<br> | ||
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: [[Datei:break-even-line-set.png]] | : [[Datei:break-even-line-set.png]] | ||
==The case of two products with individual and joint fixed costs== | ==The case of two products with individual and joint fixed costs== | ||