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Chapter 6

Cost-Volume-Profit Relationships

Solutions to Questions

6-1 The 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 ...view middle of the document...

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 breakeven 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 breakeven 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 breakeven point would occur at a higher unit volume. 6-8 The 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. 6-9 The 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. 255

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6-10 A 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.

© The McGraw-Hill Companies, Inc., 2008. All rights reserved. 256 Managerial Accounting, 12th Edition

Exercise 6-1 (20 minutes) 1. The new income statement would be: Sales (8,050 units) ..... Variable expenses ...... Contribution margin ... Fixed expenses .......... Net operating income . $209,300 144,900 64,400 56,000 $ 8,400

Total

Per Unit

$26.00 18.00 $ 8.00

You can get the same net operating income using the following approach. Original net operating income .. Change in contribution margin (50 units × $8.00 per unit).... New net operating income ....... $8,000 400 $8,400

2. The new income statement would be: Sales (7,950 units) ............ Variable expenses ............. Contribution margin .......... Fixed expenses ................. Net operating income ........ $206,700 143,100 63,600 56,000 $ 7,600

Total

Per Unit

$26.00 18.00 $ 8.00

You can get the same net operating income using the following approach. Original net...

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