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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, 22:37 Uhr
, 26. Januar 2012→The case of two products with joint fixed costs
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: [[Datei:x_hat_2.png]] = K<sup>f</sup>/d<sub>2</sub> (if x<sub>1</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 | Since we assumed '''linear cost-volume-profit-relations''' (due to the constant unit prices and variable costs), a 50/50-combination of [[Datei:x_hat_1.png]] and [[Datei:x_hat_2.png]] will cover the fixed costs too. This can be easily seen for x<sub>1</sub> = 0.5 · [[Datei:x_hat_1.png]] and x<sub>2</sub> = 0.5 · [[Datei:x_hat_2.png]]: <br> | ||
: d<sub>1</sub> · x<sub>1</sub> + d<sub>2</sub> · x<sub>2</sub> = d<sub>1</sub> · 0.5 · | : d<sub>1</sub> · x<sub>1</sub> + d<sub>2</sub> · x<sub>2</sub> = d<sub>1</sub> · 0.5 ·[[Datei:x_hat_1.png]] + d<sub>2</sub> · 0.5 · [[Datei:x_hat_2.png]] = 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> | ||
Other linear combinations enable fixed-cost-coverage in a similar way. Together, the corresponding break-even-points build a straight line between the break-even-corner-points, the '''break-even-line,''' as can be seen in the following three-dimensional graph (with x<sub>1</sub> and x<sub>2</sub> as horizontal axes and the profit, contribution and costs at the vertical axis.<br> | Other linear combinations enable fixed-cost-coverage in a similar way. Together, the corresponding break-even-points build a straight line between the break-even-corner-points, the '''break-even-line,''' as can be seen in the following three-dimensional graph (with x<sub>1</sub> and x<sub>2</sub> as horizontal axes and the profit, contribution and costs at the vertical axis.<br> | ||
| Zeile 39: | Zeile 39: | ||
: [[Datei:break-even-line-set.png]]<br> | : [[Datei:break-even-line-set.png]]<br> | ||
==The case of two products with individual and joint fixed costs== | ==The case of two products with individual and joint fixed costs== | ||