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Formal multi-product break-even-analysis (Quelltext anzeigen)
Version vom 26. Januar 2012, 22:00 Uhr
, 26. Januar 2012→The case of two products with individual and joint fixed costs
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==The case of two products with individual and joint fixed costs== | ==The case of two products with individual and joint fixed costs== | ||
Sometimes, cost-volume-profit analysis has to cope both with individual and joint fixed costs. Typical examples are '''multi-stage production processes''': Computers are often manufactured for global customers in a single plant (with joint fixed costs) and customized to local specifications (power plugs, manuals, packaging, …) in local facilities. Movie production requires a large joint cost block to get the director’s cut, but finishing, translating, synchronization, subtitles and marketing are done separately for different countries or languages and cause individual fixed costs. <br> | Sometimes, cost-volume-profit analysis has to cope both with individual and joint fixed costs. Typical examples are '''multi-stage production processes''': Computers are often manufactured for global customers in a single plant (with joint fixed costs) and customized to local specifications (power plugs, manuals, packaging, …) in local facilities. Movie production requires a large joint cost block to get the director’s cut, but finishing, translating, synchronization, subtitles and marketing are done separately for different countries or languages and cause individual fixed costs. <br> | ||
In our two-product case, we introduce K<sup>f</sup><sub>1</sub> and K<sup>f</sup><sub>2</sub> to capture the individual fixed costs of products 1 and 2 and get the following break-even-form:<br> | In our two-product case, we introduce K<sup>f</sup><sub>1</sub> and K<sup>f</sup><sub>2</sub> to capture the individual (or direct) fixed costs of products 1 and 2 and get the following break-even-form:<br> | ||
: (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> ≥ K<sup>f</sup> + K<sup>f</sup><sub>1</sub> + K<sup>f</sup><sub>2</sub><br> | : (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> ≥ K<sup>f</sup> + K<sup>f</sup><sub>1</sub> + K<sup>f</sup><sub>2</sub><br> | ||
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: x<sub>2</sub> ≥ x<sub>1</sub> = K<sup>f</sup>/d<sub>2</sub> <br> | : x<sub>2</sub> ≥ x<sub>1</sub> = K<sup>f</sup>/d<sub>2</sub> <br> | ||
The solution of the two individual conditions results in two break-even-points | The solution of the two individual conditions results in two break-even-points [[Datei:x_circle_1.png]] and [[Datei:x_circle_2.png]]. Considering too for the joint fixed cost leads to two break-even-corner-points [[Datei:x_tilde_1.png]] and [[Datei:x_tilde_1.png]]. The possible break-even-points lie on the line between these corner-points. The graphical presentation of this case is similar to the previous case without individual fixed costs. However, we adjust the horizontal axes (x<sub>1</sub> and x<sub>2</sub>) for the units that are necessary to cover the individual fixed costs.<br> | ||
[[Datei:break-even-line-both.png|thumb|left]]<br> | [[Datei:break-even-line-both.png|thumb|left]]<br> | ||
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: [[Datei:break-even-line-joint-set.png]] | : [[Datei:break-even-line-joint-set.png]] | ||
Note, that different to the previous case without individual fixed costs (and different to the formula proposed in Schweitzer/Troßmann (1998, p. 177), in this case the set of break-even-points is not just a linear combination of the two break-even-corner-points | Note, that different to the previous case without individual fixed costs (and different to the formula proposed in Schweitzer/Troßmann (1998, p. 177), in this case the set of break-even-points is not just a linear combination of the two break-even-corner-points[[Datei:x_tilde_1.png]] and [[Datei:x_tilde_2.png]]. Instead, it still is a linear combination of the break-even-points [[Datei:x_hat_1.png]] and [[Datei:x_hat_1.png]], corresponding to the joint fixed costs, plus the units [[Datei:x_circle_1.png]] and [[Datei:x_circle_2.png]] necessary to cover the individual fixed costs. | ||
== Analysis of the two-product case with restrictions== | == Analysis of the two-product case with restrictions== | ||