Accounting: The Language of Business Vol. 1 (Part 126)

Accounting keeps you going in life as well as in work.
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 Cost Behavior and Cost-Volume-Profit Analysis (Part H)

by

Charles Lamson

Special Cost-Volume-Profit Relationships

Some additional relationships useful to managers can be developed from cost-volume-profit data. Two of these relationships are the operating leverage and the margin of safety.

Operating Leverage

The relevant mix of a business's variable costs and fixed costs is measured by the operating leverage. It is computed as follows:

Operating leverage = Contribution margin / Income from operations

Since the difference between contribution margin [selling price per unit, minus the variable cost (production cost for each unit produced that is affected by changes in a firm's output or activity level) per unit] and income from operations is fixed costs, companies with large amounts of fixed costs will generally have a high operating leverage. Thus, companies in capital-intensive industries, such as the airline and automotive industries, will generally have a high operating leverage. A low operating leverage is normal for companies in industries that are labor intensive, such as professional services.

Managers can use operating leverage to measure the impact of changes in sales on income from operations. A high operating leverage indicates that a small increase in sales will yield a large percentage increase in income from operations. In contrast, a low operating leverage indicates that a large increase in sales is necessary to significantly increase income from operations. To illustrate, assume the following operating data for Jones Inc. and Wilson Inc.:

Both companies have the same sales, the same variable costs, and the same contribution margin. Jones Inc. has larger fixed costs than Wilson Inc. and, as a result, a lower income from operations and a higher operating leverage. 

                                  Jones Inc.                                                                      Wilson Inc 

  Operating leverage = $100,000 / $20,000 = 5    Operating leverage = $100,000 / $50,000 = 2

Jones Inc.'s operating leverage indicates that, for each percentage point change in sales, income from operations will change five times that percentage. In contrast, for each percentage point change in sales, the income from operations of Wilson Inc. will change only two times that percentage. For example, if sales increased by 10% ($40,000) for each company, income from operations will increase by 50% (10% * 5), or $10,000 (50% * $20,000), for Jones Inc. The sales increase of $40,000 will increase income from operations by only 20% (10% * 2), or $10,000 (20% * $50,000), for Wilson Inc. The validity of this analysis is shown as follows:

                                         

For Jones Inc., even a small increase in sales will generate a large percentage increase in income from operations. Thus, Jones's managers may be motivated to think of ways to increase sales. In contrast, Wilson's managers might attempt to increase operating leverage by reducing variable costs and thereby change the cost structure.

Margin of Safety

The difference between the current sales revenue and the sales at the break-even point is called margin of safety. It indicates the possible decrease in sales that may occur before an operating loss results. For example, if the margin of safety is low, even a small decline in sales revenue may result in an operating loss.

If sales are $250,000, the unit selling price is $25 and sales at the break-even point are $200,000, the margin of safety is 20%, computed as follows:

Margin of safety = Sales - Sales at break-even point / Sales

Margin of Safety = $250,000 - $200,000 / $250,000 = 20%

The margin of safety may also be stated in terms of units. In this illustration, for example, the margin of safety of 20% is equivalent to $50,000 ($250,000 * 20%). In units, the margin of safety is 2,000 units ($50,000 / $25). Thus, the current sales of $250,000 may decline $50,000 or 2,000 units before an operating loss occurs.

Assumptions of Cost-Volume-Profit Analysis

The reliability of cost-volume-profit analysis depends upon the validity of several assumptions. The primaries assumptions are as follows:

1. Total sales and total costs can be represented by straight lines.

2. Within the relevant range of operating activity, the efficiency of operations does not change.

3. Costs can be accurately divided into fixed and variable components.

4. The sales mix is constant.

5. There is no change in the inventory quantities during the period.

These assumptions simplify cost-volume-profit analysis. Since they are often valid for the relevant range of operations, cost-volume-profit analysis is useful for decision making. 

*WARREN, REEVE, & FESS, 2005, ACCOUNTING, 21ST ED., PP. 844-846*

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