5 Cost-Volume-Profit Analysis

Special Cost-Volume-Profit Relationships

Cost-volume-profit analysis can also be used when a company sells several products with different costs and prices. In addition, operating leverage and the margin of safety are useful in analyzing cost-volume-profit relationships.

Graphic Approach to Cost-Volume-Profit Analysis

Cost-volume-profit analysis can be presented graphically as well as in equation form. Many managers prefer the graphic form because the operating profit or loss for different levels can be easily seen.

Assumptions of Cost-Volume-Profit Analysis

Cost-volume-profit analysis depends on several assumptions. The primary assumptions are as follows: ▪ Total sales and total costs can be represented by straight lines. ▪ Within the relevant range of operating activity, the efficiency of operations does not change. ▪ Costs can be divided into fixed and variable components. ▪ The sales mix is constant. ▪ There is no change in the inventory quantities during the period. These assumptions simplify cost-volume-profit analysis. Because they are often valid for the relevant range of operations, cost-volume-profit analysis is useful for decision making.

operating leverage

The relationship between a company's contribution margin and income from operations is measured by *operating leverage*. A company's operating leverage is computed as follows: Operating Leverage = Contribution Margin / Income from Operations. The difference between contribution margin and income from operations is fixed costs. Thus, companies with high fixed costs will normally have high operating leverage. Examples of such companies include airline and automotive companies, like Ford Motor Company. Low operating leverage is normal for companies that are labor intensive, such as professional service companies, which have low fixed costs... Operating leverage can be used to measure the impact of changes in sales on income from operations. Using operating leverage, the effect of changes in sales on income from operations is computed as follows: Percent Change in Income from Operations = Percent Change in Sales × Operating Leverage.

Cost behavior, activity bases, relevant range

*Cost behavior* is the manner in which a cost changes as a related activity changes. The behavior of costs is useful to managers for a variety of reasons. For example, knowing how costs behave allows managers to predict profits as sales and production volumes change. Knowing how costs behave is also useful for estimating costs, which affects a variety of decisions such as whether to replace a machine. Understanding the behavior of a cost depends on the following: ▪ Identifying the activities that cause the cost to change. These activities are called *activity bases* (or *activity drivers*). ▪ Specifying the range of activity over which the changes in the cost are of interest. This range of activity is called the *relevant range*. To illustrate, assume that a hospital is concerned about planning and controlling patient food costs. A good activity base is the number of patients who *stay* overnight in the hospital. The number of patients who are *treated* is not as good an activity base because some patients are outpatients and, thus, do not consume food. Once an activity base is identified, food costs can then be analyzed over the range of the number of patients who normally stay in the hospital (the relevant range).

Cost-volume-profit analysis

*Cost-volume-profit analysis* is the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits. Cost-volume-profit analysis is useful for managerial decision making. Some of the ways cost-volume-profit analysis may be used include the following: ▪ Analyzing the effects of changes in selling prices on profits ▪ Analyzing the effects of changes in costs on profits ▪ Analyzing the effects of changes in volume on profits ▪ Setting selling prices ▪ Selecting the mix of products to sell ▪ Choosing among marketing strategies

Fixed costs

*Fixed costs* are costs that remain the same in total dollar amount as the activity base changes. When the activity base is units produced, many factory overhead costs such as straight-line depreciation are classified as fixed costs... As shown, fixed costs have the following characteristics: ▪ *Cost per unit* decreases as the activity level increases and increases as the activity level decreases... ▪ *Total cost* remains the same regardless of changes in the activity base.

Mixed costs, high-low method

*Mixed costs* are costs that have characteristics of both a variable and a fixed cost. Mixed costs are sometimes called *semivariable* or *semifixed costs*... For purposes of analysis, mixed costs are usually separated into their fixed and variable components. The *high-low method* is a cost estimation method that may be used for this purpose.1 The high-low method uses the highest and lowest activity levels and their related costs to estimate the variable cost per unit and the fixed cost... Variable Cost per Unit = Difference in Total Cost / Difference in Units Produced... The fixed cost is estimated by subtracting the total variable costs from the total costs for the units produced, as follows: Fixed Cost = Total Costs - (Variable Cost per Unit × Units Produced)... Total Cost = (Variable Cost per Unit × Units Produced) + Fixed Costs... Fixed Cost per Unit = Total Fixed Costs / Units Produced... Note: A salesperson's compensation can be a mixed cost comprised of a salary (fixed portion) plus a commission as a percent of sales (variable portion)...

Variable costs

*Variable costs* are costs that vary in proportion to changes in the activity base. When the activity base is units produced, direct materials and direct labor costs are normally classified as variable costs... As shown, variable costs have the following characteristics: ▪ *Cost per unit* remains the same regardless of changes in the activity base... ▪ *Total cost* changes in proportion to changes in the activity base.

cost-volume-profit chart

A *cost-volume-profit chart*, sometimes called a *break-even chart*, graphically shows sales, costs, and the related profit or loss for various levels of units sold. It assists in understanding the relationship among sales, costs, and operating profit or loss... The cost-volume-profit chart in Exhibit 14 is constructed using the following steps: ▪ Step 1. Volume in units of sales is indicated along the horizontal axis. The range of volume shown is the relevant range in which the company expects to operate. Dollar amounts of total sales and total costs are indicated along the vertical axis. ▪ Step 2. A total sales line is plotted by connecting the point at zero on the left corner of the graph to a second point on the chart. The second point is determined by multiplying the maximum number of units in the relevant range, which is found on the far right of the horizontal axis, by the unit sales price. A line is then drawn through both of these points. This is the total sales line... ▪ Step 3. A total cost line is plotted by beginning with total fixed costs on the vertical axis. A second point is determined by multiplying the maximum number of units in the relevant range, which is found on the far right of the horizontal axis, by the unit variable costs and adding the total fixed costs. A line is then drawn through both of these points. This is the total cost line... ▪ Step 4. The break-even point is the intersection point of the total sales and total cost lines. A vertical dotted line drawn downward at the intersection point indicates the units of sales at the break-even point. A horizontal dotted line drawn to the left at the intersection point indicates the sales dollars and costs at the break-even point... Operating profits will be earned when sales levels are to the right of the breakeven point (*operating profit area*). Operating losses will be incurred when sales levels are to the left of the break-even point (*operating loss area*).

profit-volume chart

Another graphic approach to cost-volume-profit analysis is the profit-volume chart. The *profit-volume chart* plots only the difference between total sales and total costs (or profits). In this way, the profit-volume chart allows managers to determine the operating profit (or loss) for various levels of units sold... The profit-volume chart in Exhibit 16 is constructed using the following steps: ▪ Step 1. Volume in units of sales is indicated along the horizontal axis. The range of volume shown is the relevant range in which the company expects to operate... ▪ Step 2. A point representing the maximum operating loss is plotted on the vertical axis at the left. This loss is equal to the total fixed costs at the zero level of sales... ▪ Step 3. A point representing the maximum operating profit within the relevant range is plotted on the right... ▪ Step 4. A diagonal profit line is drawn connecting the maximum operating loss point with the maximum operating profit point. ▪ Step 5. The profit line intersects the horizontal zero operating profit line at the break-even point in units of sales. The area indicating an operating profit is identified to the right of the intersection, and the area indicating an operating loss is identified to the left of the intersection... Operating profit will be earned when sales levels are to the right of the break-even point (*operating profit area*). Operating losses will be incurred when sales levels are to the left of the break-even point (*operating loss area*).

Target Profit

At the break-even point, sales and costs are exactly equal. However, the goal of most companies is to make a profit. By modifying the break-even equation, the sales required to earn a target or desired amount of profit may be computed. For this purpose, target profit is added to the break-even equation, as follows: Sales (units) = (Fixed Costs + Target Profit) / Unit Contribution Margin... Sales (dollars) = (Fixed Costs + Target Profit) / Contribution Margin Ratio.

Effect of Changes in Unit Selling Price

Changes in the unit selling price affect the unit contribution margin and, thus, the break-even point. Specifically, changes in the unit selling price affect the break-even point as follows: ▪ Increases in the unit selling price decrease the break-even point. ▪ Decreases in the unit selling price increase the break-even point.

contribution margin ratio

Contribution margin can also be expressed as a percentage. The *contribution margin ratio*, sometimes called the *profit-volume ratio*, indicates the percentage of each sales dollar available to cover fixed costs and to provide income from operations. The contribution margin ratio is computed as follows: Contribution Margin Ratio = Contribution Margin / Sales... The contribution margin ratio is most useful when the increase or decrease in sales volume is measured in sales *dollars*. In this case, the change in sales dollars multiplied by the contribution margin ratio equals the change in income from operations, computed as follows: Change in Income from Operations = Change in Sales Dollars × Contribution Margin Ratio.

Contribution margin

Contribution margin is especially useful because it provides insight into the profit potential of a company. *Contribution margin* is the excess of sales over variable costs, computed as follows: Contribution Margin = Sales - Variable Costs.

variable costing

Exhibit 7 provides some examples of variable, fixed, and mixed costs for the activity base of *units produced*... One method of reporting variable and fixed costs is called *variable costing* or *direct costing*. Under variable costing, only the variable manufacturing costs (direct materials, direct labor, and variable factory overhead) are included in the product cost. The fixed factory overhead is treated as an expense of the period in which it is incurred. Variable costing is described and illustrated in the appendix to this chapter.

Effects of Changes in Fixed Costs

Fixed costs do not change in total with changes in the level of activity. However, fixed costs may change because of other factors such as advertising campaigns, changes in property tax rates, or changes in factory supervisors' salaries. Changes in fixed costs affect the break-even point as follows: ▪ Increases in fixed costs increase the break-even point. ▪ Decreases in fixed costs decrease the break-even point.

sales mix

Many companies sell more than one product at different selling prices. In addition, the products normally have different unit variable costs and, thus, different unit contribution margins. In such cases, break-even analysis can still be performed by considering the sales mix. The *sales mix* is the relative distribution of sales among the products sold by a company.

break-even point

The *break-even point* is the level of operations at which a company's revenues and expenses are equal, as shown in Exhibit 9. At break-even, a company reports neither income nor a loss from operations. The break-even point in *sales units* is computed as follows: Break-Even Sales (units) = Fixed Costs / Unit Contribution Margin... The break-even point in *sales dollars* can be determined directly as follows: Break-Even Sales (dollars) = Fixed Costs / Contribution Margin Ratio. The contribution margin ratio can be computed using the unit contribution margin and unit selling price as follows: Contribution Margin Ratio = Unit Contribution Margin / Unit Selling Price.

margin of safety

The *margin of safety* indicates the possible decrease in sales that may occur before an operating loss results. Thus, if the margin of safety is low, even a small decline in sales revenue may result in an operating loss. The margin of safety may be expressed in the following ways: ▪ Dollars of sales ▪ Units of sales ▪ Percent of current sales... Margin of Safety = (Sales - Sales at Break-Even Point) / Sales.

Summary of Effects of Changes on Break-Even Point

The break-even point in sales changes in the same direction as changes in the variable cost per unit and fixed costs. In contrast, the break-even point in sales changes in the opposite direction as changes in the unit selling price. These changes on the break-even point in sales are summarized in Exhibit 13.

Mathematical Approach to Cost-Volume-Profit Analysis

The mathematical approach to cost-volume-profit analysis uses equations to determine the following: ▪ Sales necessary to break even ▪ Sales necessary to make a target or desired profit.

unit contribution margin

The unit contribution margin is also useful for analyzing the profit potential of proposed decisions. The *unit contribution margin* is computed as follows: Unit Contribution Margin = Sales Price per Unit - Variable Cost per Unit... The unit contribution margin is most useful when the increase or decrease in sales volume is measured in sales *units* (quantities). In this case, the change in sales volume (units) multiplied by the unit contribution margin equals the change in income from operations, computed as follows: Change in Income from Operations = Change in Sales Units × Unit Contribution Margin.

Effect of Changes in Unit Variable Costs

Unit variable costs do not change with changes in the level of activity. However, unit variable costs may be affected by other factors such as changes in the cost per unit of direct materials, changes in the wage rate for direct labor, or changes in the sales commission paid to salespeople. Changes in unit variable costs affect the break-even point as follows: ▪ Increases in unit variable costs increase the break-even point. ▪ Decreases in unit variable costs decrease the break-even point.

Use of Computers in Cost-Volume-Profit Analysis

With computers, the graphic approach and the mathematical approach to cost-volume-profit analysis are easy to use. Managers can vary assumptions regarding selling prices, costs, and volume and can observe the effects of each change on the break-even point and profit. Such an analysis is called a "*what if*" analysis or *sensitivity* analysis.