4229 WordsJun 10, 201417 Pages

Break-even Analysis
An enterprise, whether or not a profit maximizer, often finds it useful to know what price (or output level) must be for total revenue just equal total cost. This can be done with a breakeven analysis. Strictly speaking, this analysis is to determine the minimum level of output that allows the firm to break even, but it could be used for some other tasks. In this Appendix, we introduce: - The algebra of break-even analysis - Break-even diagram - Operating leverage
I. THE ALGEBRA OF BREAK-EVEN ANALYSIS
Let QBE denote the break-even output level. By definition TR (at QBE) = TC (at QBE) or TR (at QBE) = TFC + TVC (at QBE) The break-even condition (1) holds true for any cost and demand functions. Hence, in general, when costs and demand are complex, the analysis of this condition might not be any simpler than the analysis of profit maximization. Yet, what is widely known in business as break-even analysis is indeed much easier than profit analysis, although it also starts with the above identity, because it makes a very important assumption: that price and average variable cost do not change with output level. Thus, if we assume that price and AVC are constant, (1) can be rewritten as follows P.QBE = TFC + AVC.QBE which yields: (1)
Q BE =
TFC P − AVC
(2)
K The difference “P ! AVC” is often called the average contribution margin1 (ACM) because it represents the portion of selling price that "contributes" to paying the fixed costs. ! Formula (2) can be generalized to deal with the situation where the firm has determined in advance a target profit. The output quantity Q* that will yield this profit is implicitly given
1
The total contribution margin is simply (P ! AVC)Q = TR ! TVC.
BREAK-EVEN ANALYSIS -
2
by2 P.Q* = Target profit + TFC + AVC.Q* hence
Q BE = TFC + Target Profit P − AVC
TABLE 1 Effects of TFC, AVC, and P on break-even output

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