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direct fixed expenses are those fixed costs that can be traced to each segment and would be avoided if the segment did not exist. The common fixed expenses are the fixed costs that are not traceable to the segments and would remain even if one of the segments was eliminated.Break-Even Point in UnitsThe owner of Whittier is a bit concerned about adding a new product line and wants to know how many units of each model must be sold to break even. If you were responsible for answering this question, how would you respond? One possibility is to use the equation developed earlier in which fixed costs were divided by the con-tribution margin. However, this equation was developed for single-product analysis. For two products, there are two prices and two variable costs per unit, calculated as follows:4O B J E C T I V EApply cost-volume-profit analysis in a multiple-product setting.NOT FOR SALE
96Chapter 4Cost-Volume-Profit Analysis: A Managerial Planning ToolEquation Mulching Mower Riding MowerTotal variable costs Variable cost per unit$390,000$325$480,000$600Price 1,200 800Contribution margin Total contribution margin$400 $325 $800 $600 Sales $75 = $200One possible solution is to apply the analysis separately to each product line. It is possible to obtain individual break-even points when income is defined as product margin. Breakeven for the mulching mower is as follows:Mulching mower break-even units Fixed cost Price Unit variable cost$30,000$75400 unitsBreakeven for the riding mower can be computed as well:Riding mower break-even units Fixed cost Price Unit variable cost$40,000$200200 unitsThus, 400 mulching mowers and 200 riding mowers must be sold to achieve a break-even product margin. But a break-even product margin covers only direct fixed costs; the common fixed costs remain to be covered. Selling these numbers of lawn mowers would result in a loss equal to the common fixed costs. This level of sales is not the break-even point for the firm as a whole; somehow the common fixed costs must be factored into the analysis.We could allocate the common fixed costs to each product line before computing a break-even point. However, the allocation of the common fixed costs is arbitrary. Thus, no meaningful break-even volume is readily apparent.Another possible solution is to convert the multiple-product problem into a single-product problem. If this can be done, then all of the single-product CVP methodology can be applied directly. The key to this conversion is to identify the expected sales mix, in units, of the products being marketed. Sales mixis the relative combination of products being sold by a firm.Determining the Sales Mix The sales mix is measured in units sold. For example, if Whittier plans on selling 1,200 mulching mowers and 800 riding mowers, then the sales mix in units is 1,200:800. Usually, the sales mix is reduced to the smallest possible whole numbers. Thus, the relative mix, 1,200:800, can be reduced to 12:8, and further reduced to 3:2. That is, Whittier expects that for every three mulching mowers sold, two riding mowers will be sold.