Cost-Volume-Profit Relationships

Solutions to Questions

6-1The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue. It can be used in a variety of ways. For example, the change in total contribution margin from a given change in total sales revenue can be estimated by multiplying the change in total sales revenue by the CM ratio. If fixed costs do not change, then a dollar increase in contribution margin will result in a dollar increase in net operating income. The CM ratio can also be used in break-even analysis. Therefore, knowledge of a product’s CM ratio is extremely helpful in forecasting contribution margin and net operating income.

6-2Incremental analysis focuses on the changes in revenues and costs that will result from a particular action.

6-3All other things equal, Company B, with its higher fixed costs and lower variable costs, will have a higher contribution margin ratio than Company A. Therefore, it will tend to realize a larger increase in contribution margin and in profits when sales increase.

6-4Operating leverage measures the impact on net operating income of a given percentage change in sales. The degree of operating leverage at a given level of sales is computed by dividing the contribution margin at that level of sales by the net operating income at that level of sales.

6-5The break-even point is the level of sales at which profits are zero. It can also be defined as the point where total revenue equals total cost or as the point where total contribution margin equals total fixed cost.

6-6Three approaches to break-even analysis are (a) the graphical method, (b) the equation method, and (c) the contribution margin method.

In the graphical method, total cost and total revenue data are plotted on a graph. The intersection of the total cost and the total revenue lines indicates the break-even point. The graph shows the break-even point in both units and dollars of sales.

The equation method uses some variation of the equation Sales = Variable expenses + Fixed expenses + Profits, where profits are zero at the break-even point. The equation is solved to determine the break-even point in units or dollar sales.

In the contribution margin method, total fixed cost is divided by the contribution margin per unit to obtain the break-even point in units. Alternatively, total fixed cost can be divided by the contribution margin ratio to obtain the break-even point in sales dollars.

6-7(a) If the selling price decreased, then the total revenue line would rise less steeply, and the break-even point would occur at a higher unit volume. (b) If the fixed cost increased, then both the fixed cost line and the total cost line would shift upward and the break-even point would occur at a higher unit volume. (c) If the variable cost increased, then the total cost line would rise more steeply and the break-even point would occur at a higher unit volume.

6-8The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. It states the amount by which sales can drop before losses begin to be incurred.

6-9The sales mix is the relative proportions in which a company’s products are sold. The usual assumption in cost-volume-profit analysis is that the sales mix will not change.

6-10A higher break-even point and a lower net operating income could result if the sales mix shifted from high contribution margin products to low contribution margin products. Such a shift would cause the average contribution margin ratio in the company to decline, resulting in less total contribution margin for a given amount of sales. Thus, net operating income would decline. With a lower contribution margin ratio, the break-even point would be higher because more sales would be required to cover the same amount of fixed costs.

Exercise 6-1 (20 minutes)

1.The new income statement would be:

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