Cost Behavior Analysis
LEARNING OBJECTIVE 1
Explain variable, fixed, and mixed costs and the relevant range.
Cost behavior analysis is the study of how specific costs respond to changes in the level of business activity. As you might expect, some costs change when activity changes and others remain the same. For example, for an airline company such as Southwest or United, the longer the flight, the higher the fuel costs. On the other hand, Massachusetts General Hospital‘s costs to staff the emergency room on any given night are relatively constant regardless of the number of patients treated. A knowledge of cost behavior helps management plan operations and decide between alternative courses of action. Cost behavior analysis applies to all types of entities.
The starting point in cost behavior analysis is measuring the key business activities. Activity levels may be expressed in terms of sales dollars (in a retail company), miles driven (in a trucking company), room occupancy (in a hotel), or dance classes taught (by a dance studio). Many companies use more than one measurement base. A manufacturer, for example, may use direct labor hours or units of output for manufacturing costs, and sales revenue or units sold for selling expenses.
For an activity level to be useful in cost behavior analysis, changes in the level or volume of activity should be correlated with changes in costs. The activity level selected is referred to as the activity index or driver. The activity index identifies the activity that causes changes in the behavior of costs. With an appropriate activity index, companies can classify the behavior of costs in response to changes in activity levels into three categories: variable, fixed, or mixed.
Variable Costs
Variable costs are costs that vary in total directly and proportionately with changes in the activity level. If the level increases 10%, total variable costs will increase 10%. If the level of activity decreases by 25%, variable costs will decrease 25%. Examples of variable costs include direct materials and direct labor for a manufacturer; cost of goods sold, sales commissions, and freight-out for a merchandiser; and gasoline in airline and trucking companies. A variable cost may also be defined as a cost that remains the same per unit at every level of activity.
To illustrate the behavior of a variable cost, assume that Damon Company manufactures tablet computers that contain cameras that cost $10. The activity index is the number of tablet computers produced. As Damon manufactures each tablet, the total cost of cameras installed in tablets increases by $10. As part (a) of Illustration 18.1 shows, total cost of the cameras will be $20,000 (2,000 × $10) if Damon produces 2,000 tablets, and $100,000 when it produces 10,000 tablets. We also can see that a variable cost remains the same per unit as the level of activity changes. As part (b) of Illustration 18.1 shows, the unit cost of $10 for the cameras is the same whether Damon produces 2,000 or 10,000 tablets.
ILLUSTRATION 18.1 Behavior of total and unit variable costs; variable costs per unit remain constant
Companies that rely heavily on labor either to manufacture a product or perform a service, such as Hilton or Marriott, are likely to have a high percentage of variable costs. In contrast, companies that use a high proportion of machinery and equipment in producing revenue, such as AT&T or Duke Energy Co., may have a lower percentage of variable costs.
Fixed Costs
Fixed costs are costs that remain the same in total regardless of changes in the activity level. Examples include property taxes, insurance, rent, supervisory salaries, and depreciation on buildings and equipment. Because total fixed costs remain constant as activity changes, it follows that fixed costs per unit vary inversely with activity: As volume increases, unit cost declines, and vice versa.
To illustrate the behavior of fixed costs, assume that Damon Company leases its productive facilities at a cost of $10,000 per month. Total fixed costs of the facilities remain a constant $10,000 at every level of activity, as part (a) of Illustration 18.2 shows. But, on a per unit basis, the cost of rent declines as activity increases, as part (b) of Illustration 18.2 shows. At 2,000 units, the unit cost per tablet computer is $5 ($10,000 ÷ 2,000). When Damon produces 10,000 tablets, the unit cost of the rent is only $1 per tablet ($10,000 ÷ 10,000).
ILLUSTRATION 18.2 Behavior of total and unit fixed costs
The trend for many manufacturers is to have more fixed costs and fewer variable costs. This trend is the result of increased use of automation and less use of employee labor. As a result, depreciation and lease charges (fixed costs) increase, whereas direct labor costs (variable costs) decrease.
People, Planet, and Profit Insight BrightFarms
Gardens in the Sky
Because of population increases, the United Nations’ Food and Agriculture Organization estimates that food production will need to increase by 70% by 2050. Also, by 2050, roughly 70% of people will live in cities, which means more food needs to be hauled further to get it to the consumer. To address the lack of farmable land and reduce the cost of transporting produce, some companies, such as New York-based BrightFarms, are building urban greenhouses.
This sounds great, but do the numbers work? Some variable costs would be reduced. For example, the use of pesticides, herbicides, fuel costs for shipping, and water would all drop. Soil erosion would be a non-issue since plants would be grown hydroponically (in a solution of water and minerals), and land requirements would be reduced because of vertical structures. But, other costs would be higher. First, there is the cost of the building. Also, any multistory building would require artificial lighting for plants on lower floors.
Until these cost challenges can be overcome, it appears that these urban greenhouses may not break even. On the other hand, rooftop greenhouses on existing city structures already appear financially viable. For example, a 15,000 square-foot rooftop greenhouse in Brooklyn already produces roughly 30 tons of vegetables per year for local residents.
Sources: “Vertical Farming: Does It Really Stack Up?” The Economist (December 9, 2010); and Jane Black, “BrightFarms Idea: Greenhouses That Cut Short the Path from Plant to Grocery Shelf,” The Washington Post (May 7, 2013).
What are some of the variable and fixed costs that are impacted by hydroponic farming? (Go to WileyPLUS for this answer and additional questions.)
Relevant Range
In Illustration 18.1 part (a), a straight line is drawn throughout the entire range of the activity index for total variable costs. In essence, the assumption is that the costs are linear. If a relationship is linear (that is, straight-line), then changes in the activity index will result in a direct, proportional change in the total variable cost. For example, if the activity level doubles, the cost doubles.
It is now necessary to ask: Is the straight-line relationship realistic? In most business situations, a straight-line relationship does not exist for variable costs throughout the entire range of possible activity. At abnormally low levels of activity, it may be impossible to be cost-efficient. Small-scale operations may not allow the company to obtain quantity discounts for raw materials or to use specialized labor. In contrast, at abnormally high levels of activity, labor costs may increase sharply because of overtime pay. Also, at high activity levels, materials costs may jump significantly because of excess spoilage caused by worker fatigue.
As a result, in the real world, the relationship between the behavior of a variable cost and changes in the activity level is often curvilinear, as shown in part (a) of Illustration 18.3. In the curved sections of the line, a change in the activity index will not result in a direct, proportional change in the variable cost. That is, a doubling of the activity index will not result in an exact doubling of the variable cost. The variable cost may more than double, or it may be less than double.
ILLUSTRATION 18.3 Nonlinear behavior of variable and fixed costs
Total fixed costs also do not have a straight-line relationship over the entire range of activity. Some fixed costs will not change. But it is possible for management to change other fixed costs (see Helpful Hint). For example, in some instances, salaried employees (fixed) are replaced with freelance workers (variable). Some costs are step costs. For example, once a company exceeds certain levels of activity, it may have to add an additional warehouse. Illustration 18.3, part (b), shows an example of step-cost behavior of total fixed costs through all potential levels of activity.
HELPFUL HINT
Fixed costs that may be changed by managers include research, such as new product development, and management training programs.
For most companies, operating at almost zero or at 100% capacity is the exception rather than the rule. Instead, companies often operate over a somewhat narrower range, such as 40–80% of capacity. The range over which a company expects to operate during a year is called the relevant range of the activity index (see Alternative Terminology). Within the relevant range, as both diagrams in Illustration 18.4 show, a straight-line relationship generally exists for both variable and fixed costs between 40 and 80% of capacity.
ALTERNATIVE TERMINOLOGY
The relevant range is also called the normal or practical range.
ILLUSTRATION 18.4 Linear behavior within relevant range
As you can see, although the linear (straight-line) relationship may not be completely realistic, the linear assumption produces useful data for CVP analysis as long as the level of activity remains within the relevant range.
Mixed Costs
Mixed costs are costs that contain both a variable- and a fixed-cost element. Mixed costs, therefore, change in total but not proportionately with changes in the activity level.
The rental of a U-Haul truck is a good example of a mixed cost. Assume that local rental terms for a 17-foot truck, including insurance, are $50 per day plus 50 cents per mile. When determining the cost of a one-day rental, the per day charge is a fixed cost (with respect to miles driven), whereas the mileage charge is a variable cost. The graphic presentation of the rental cost for a one-day rental is shown in Illustration 18.5.
ILLUSTRATION 18.5 Behavior of a mixed cost
In this case, the fixed-cost element is the cost of having the service available. The variable-cost element is the cost of actually using the service (miles driven). Utility costs such as electricity are another example of a mixed cost. Each month the electric bill includes a flat service fee plus a usage charge.
DO IT! 1 | Types of Costs
Helena Company reports the following total costs at two levels of production.
10,000 Units
20,000 Units
Direct materials
$20,000
$40,000
Maintenance
8,000
10,000
Direct labor
17,000
34,000
Indirect materials
1,000
2,000
Depreciation
4,000
4,000
Utilities
3,000
5,000
Rent
6,000
6,000
Classify each cost as variable, fixed, or mixed.
ACTION PLAN
Recall that a variable cost varies in total directly and proportionately with each change in activity level.
Recall that a fixed cost remains the same in total with each change in activity level.
Recall that a mixed cost changes in total but not proportionately with each change in activity level.
Solution
Direct materials, direct labor, and indirect materials are variable costs because the total cost doubles with the doubling in activity.
Depreciation and rent are fixed costs because the total cost does not vary with the change in activity.
Maintenance and utilities are mixed costs because the total cost changes, but the change is not proportional to the change in activity.
Related exercise material: BE18.1, BE18.2, DO IT! 18.1, E18.1, E18.2, E18.4, and E18.6.
