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These two approaches result in the same general formula for computing the break-even point (in units). Under the equation approach, the profit equation is specified as follows: Sales revenue - Variable expenses - Fixed expenses = Profit. When this equation is manipulated, the contribution-margin approach to the break-even point results, as follows: Break-even point (in units) = Fixed expenses divided by Unit contribution margin.
Break-even analysis in a multiproduct firm is accomplished by computing a weighted-average contribution margin, which is based on the expected sales mix. The same break-even formulas are used as in a single-product analysis, except that the unit contribution margin is replaced by the weighted-average contribution margin. This analysis is limited by the assumption of a constant sales mix across the range of total sales volume.
CVP analysis involves several key assumptions, which follow: (1) Total revenue is linear (i.e., a straight line) with respect to changes in the volume of activity. (2) Total expense is linear (i.e., a straight line) with respect to changes in the volume of activity. An implication of this assumption is that the efficiency and productivity of the production process remains constant. (3) The sales mix remains constant over the relevant range. (4) The beginning and ending inventory levels are the same in a manufacturing firm.
Cost-volume-profit relationships are important enough to operating managers that some firms prepare a contribution income statement. This income-statement format separates fixed and variable expenses and computes the aggregate contribution margin. This statement format helps managers discern the effects on profit from changes in volume. The contribution income statement also discloses an organization's cost structure, which is the relative proportion of its fixed and variable costs.
Activity-based costing (ABC) provides a richer description of an organization's cost behavior and CVP relationships than is provided by a traditional costing system. An ABC cost-volume-profit analysis recognizes that some costs that are fixed with respect to sales volume may not be fixed with respect to other important cost drivers. In many cases, management can benefit substantially from such an improved understanding of cost behavior and CVP relationships.
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