Discuss a concept, or problem in chapter 18 that you struggled with or could relate to on some level.? If your question relate

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.

,

Mixed Costs Analysis

LEARNING OBJECTIVE 2

Apply the high-low method to determine the components of mixed costs.

For purposes of cost-volume-profit analysis, mixed costs must be classified into their fixed and variable elements. How does management make the classification? One possibility is to determine the variable and fixed components each time a mixed cost is incurred. But because of time and cost constraints, this approach is rarely followed. Instead, the usual approach is to collect data on the behavior of the mixed costs at various levels of activity. Analysts then identify the fixed- and variable-cost components. Companies use various types of analysis. One type of analysis, called the high-low method, is discussed next.

High-Low Method

The high-low method uses the total costs incurred at the high and low levels of activity to classify mixed costs into fixed and variable components. The difference in costs between the high and low levels represents variable costs, since only the variable-cost element can change as activity levels change.

The steps in computing fixed and variable costs under this method are as follows.

1. Determine variable cost per unit from the formula shown in Illustration 18.6. This is the slope of the cost function.

Change in Total Costs at High versus Low Activity Level ÷ High minus Low Activity Level = Variable Cost per Unit

ILLUSTRATION 18.6 Formula for variable cost per unit using high-low method

To illustrate, assume that Metro Transit Company has the maintenance costs and mileage data for its fleet of buses over a 6-month period shown in Illustration 18.7.

Month

Miles

Driven

Total

Cost

January     

20,000

    

$30,000

February

40,000

  48,000

March

35,000

  49,000

April

50,000

63,000

May

30,000

  42,000

June

43,000

  61,000

ILLUSTRATION 18.7 Assumed maintenance costs and mileage data

The high and low levels of activity are 50,000 miles in April and 20,000 miles in January. The maintenance costs at these two levels are $63,000 and $30,000, respectively. The difference in maintenance costs is $33,000 ($63,000 − $30,000), and the difference in miles is 30,000 (50,000 − 20,000). Therefore, for Metro Transit, variable cost per unit is $1.10, computed as follows.

$

33,000

÷

30,000

=

$

1.10

2. Determine the total fixed costs by subtracting the total variable costs at either the high or the low activity level from the total cost at that activity level.

Illustration 18.8 shows the computations for Metro Transit.

ILLUSTRATION 18.8 High-low method computation of fixed costs

Maintenance costs are therefore $8,000 per month of fixed costs plus $1.10 per mile of variable costs. This is represented by the following formula, referred to as the total cost equation.

Maintenance costs

=

$

8,000

+

(

$

1.10

×

Miles driven

)

For example, at 45,000 miles, estimated maintenance costs would be $8,000 fixed and $49,500 variable ($1.10 × 45,000) for a total of $57,500.

The graph in Illustration 18.9 plots the 6-month data for Metro Transit Company. The red line drawn in the graph connects the high and low data points (in squares) and therefore represents the equation that we just solved using the high-low method. The red, “high-low” line intersects the y-axis at $8,000 (the fixed-cost level), and it rises by its slope of $1.10 per unit (the variable cost per unit). Note that a completely different line would result if we chose any two of the other data points. That is, by choosing any two other data points, we would end up with a different estimate of fixed costs and a different variable cost per unit. Thus, from this scatter plot, we can see that while the high-low method is simple, the result is rather arbitrary. A better approach, which uses information from all the data points to estimate fixed and variable costs, is called regression analysis. A discussion of regression analysis is provided in Appendix 18A as well as in the Excel video available in WileyPLUS.

ILLUSTRATION 18.9 Scatter plot for Metro Transit Company

Management Insight  Kroger Co.

Are Robotic Workers More Humane?

Warehouse distribution centers for large retailers and grocers employ more than 800,000 people in the United States. But many companies, such as grocer Kroger Co., have a hard time finding and retaining warehouse workers. One reason? Studies have shown that some warehouse workers walk up to 20 miles and lift 50,000 pounds during a single day. As a result, as the needs for storage increases and companies are faced with the proposition of building massive new warehouses, some are choosing instead to invest in robotic warehousing systems.

Robots can provide many advantages over their human counterparts. Robots need aisles that are less than 30 inches wide, as opposed to traditional warehouse aisles that are 10 to 12 feet wide. Moving at speeds of up to 25 miles per hour, robots can drop off and retrieve warehouse cases about five times as fast as a human. Robotic systems cut labor costs by about 80%, and they cut warehouse size anywhere from 25% to 40%. However, a fully automated system costs between $40 to $80 million, so the switch to robotic systems is not a trivial decision.

Source: Robbie Whelan, “Fully Autonomous Robots: The Warehouse Workers of the Near Future,” Wall Street Journal (September 20, 2016).

How would a company's variable and fixed costs change if it adopts a robotic system? (Go to WileyPLUS for this answer and additional questions).

Importance of Identifying Variable and Fixed Costs

Why is it important to segregate mixed costs into variable and fixed elements? The answer may become apparent if we look at the following four business decisions.

1. If American Airlines is to make a profit when it reduces all domestic fares by 30%, what reduction in costs or increase in passengers will be required?

Answer: To make a profit when it cuts domestic fares by 30%, American Airlines will have to increase the number of passengers or cut its variable costs for those flights. Its fixed costs will not change.

2. If Ford Motor Company meets workers' demands for higher wages, what increase in sales revenue will be needed to maintain current profit levels?

Answer: Higher wages at Ford Motor Company will increase the variable costs of manufacturing automobiles. To maintain present profit levels, Ford will have to cut other variable or fixed costs, sell more automobiles, or increase the price of its automobiles.

3. If United States Steel Corp.'s program to modernize plant facilities through significant equipment purchases reduces the work force by 50%, what will be the effect on the cost of producing one ton of steel?

Answer: The modernizing of plant facilities at United States Steel Corp. changes the proportion of fixed and variable costs of producing one ton of steel. Fixed costs increase because of higher depreciation charges, whereas variable costs decrease due to the reduction in the number of steelworkers.

4. What happens if Kellogg's increases its advertising expenses but cannot increase prices because of competitive pressure?

Answer: Sales volume must be increased to cover the increase in fixed advertising costs.

  

DO IT! 2 | High-Low Method

Byrnes Company accumulates the following data concerning a mixed cost, using units produced as the activity level.

Units Produced

Total Cost

March     

9,800

    

$14,740

April

8,500

  13,250

May

7,000

  11,100

June

7,600

  12,000

July

8,100

  12,460

a. Compute the variable-cost and fixed-cost elements using the high-low method.

b. Using the information from your answer to part (a), write the cost formula.

c. Estimate the total cost if the company produces 8,000 units.

ACTION PLAN

Determine the highest and lowest levels of activity.

Compute variable cost per unit as Change in total costs ÷ (High − low activity level) = Variable cost per unit.

Compute fixed cost as Total cost − (Variable cost per unit × Units produced) = Total fixed cost.

Solution

a. Variable cost: ($14,740 − $11,100) ÷ (9,800 − 7,000) = $1.30 per unit

  Fixed cost: $14,740 − ($1.30 × 9,800 units) = $2,000 or $11,100 − ($1.30 × 7,000 units) = $2,000

b. Cost = $2,000 + ($1.30 × units produced)

c. Total cost to produce 8,000 units: $2,000 + $10,400 ($1.30 × 8,000 units) = $12,400

Related exercise material: BE18.4, BE18.5, DO IT! 18.2, E18.3, and E18.5.

Cost-Volume-Profit Analysis

LEARNING OBJECTIVE 3

Prepare a CVP income statement to determine contribution margin.

Cost-volume-profit (CVP) analysis is the study of the effects of changes in costs and volume on a company's profits. CVP analysis is important in profit planning. It also is a critical factor in such management decisions as setting selling prices, determining product mix, and maximizing use of production facilities.

Basic Components

CVP analysis considers the interrelationships among the components shown in Illustration 18.10.

ILLUSTRATION 18.10 Components of CVP analysis

The following assumptions underlie each CVP analysis.

1. The behavior of both costs and revenues is linear throughout the relevant range of the activity index.

2. Costs can be classified accurately as either variable or fixed.

3. Changes in activity are the only factors that affect costs.

4. All units produced are sold.

5. When more than one type of product is sold, the sales mix will remain constant. That is, the percentage that each product represents of total sales will stay the same. Sales mix complicates CVP analysis because different products will have different cost relationships. In this chapter, we assume a single product. In Chapter 19, however, we examine the sales mix more closely.

When these assumptions are not valid, the CVP analysis may be inaccurate.

CVP Income Statement

Because CVP is so important for decision-making, management often wants this information reported in a cost-volume-profit (CVP) income statement format for internal use. The CVP income statement classifies costs as variable or fixed and computes a contribution margin. Contribution margin (CM) is the amount of revenue remaining after deducting variable costs. It is often stated both as a total amount and on a per unit basis.

We use Vargo Electronics Company to illustrate a CVP income statement. Vargo Electronics produces cell phones. Illustration 18.11 presents relevant data for the cell phones sold by this company in June 2022.

Unit selling price of cell phone      $500

Unit variable costs* $300

Total monthly fixed costs** $200,000

Units sold 1,600

*Includes variable manufacturing costs and variable selling and administrative expenses.

**Includes fixed manufacturing costs and fixed selling and administrative expenses.

ILLUSTRATION 18.11 Assumed selling and cost data for Vargo Electronics

Note that in Illustration 18.11, as well as in the applications and assignment material of CVP analysis that follow, we assume that the term “cost” includes all costs and expenses related to production and sale of the product. That is, cost includes manufacturing costs plus selling and administrative expenses.

The CVP income statement for Vargo would therefore be reported as shown in Illustration 18.12.

Vargo Electronics Company

CVP Income Statement

For the Month Ended June 30, 2022

    

Total

Sales (1,600 × $500) $800,000

Variable costs (1,600 × $300)   480,000

Contribution margin   320,000

Fixed costs   200,000

Net income $120,000

ILLUSTRATION 18.12 CVP income statement, with net income

A traditional income statement and a CVP income statement both report the same net income of $120,000. However, a traditional income statement does not classify costs as variable or fixed, and therefore it does not report a contribution margin. In addition, sometimes per unit amounts and percentage of sales amounts are shown in separate columns on a CVP income statement to facilitate CVP analysis. Homework assignments specify which columns to present.

Unit Contribution Margin

Illustration 18.13 shows the formula for unit contribution margin margin and the computation for Vargo Electronics.

Unit Selling Price − Unit Variable Costs = Unit Contribution Margin $500 − $300 = $200

ILLUSTRATION 18.13 Formula for unit contribution margin

Unit contribution margin indicates that for every cell phone sold, the selling price exceeds the variable costs by $200 (see Decision Tools). Vargo generates $200 per unit sold to cover fixed costs and contribute to net income. Because Vargo has fixed costs of $200,000, it must sell 1,000 cell phones ($200,000 ÷ $200) to cover its fixed costs.

Decision Tools

The unit contribution margin indicates the increase in income that results from every additional unit sold after the break-even point.

At the point where total contribution margin exactly equals fixed costs, Vargo will report net income of zero. At this point, referred to as the break-even point, total costs (variable plus fixed) exactly equal total revenue. Illustration 18.14 shows Vargo's CVP income statement at the point where net income equals zero. It shows a contribution margin of $200,000, and a unit contribution margin of $200 ($500 − $300).

Vargo Electronics Company

CVP Income Statement

For the Month Ended June 30, 2022

Total

Per Unit

Sales (1,000 × $500)     

$500,000

    

$500

Variable costs (1,000 × $300)

  300,000

  300

Contribution margin

200,000

$200

Fixed costs

  200,000

Net income

$  –0–    

ILLUSTRATION 18.14 CVP income statement, with zero net income

It follows that for every cell phone sold above the break-even point of 1,000 units, net income increases by the amount of the unit contribution margin, $200. For example, assume that Vargo sold one more cell phone, for a total of 1,001 cell phones sold. In this case, Vargo reports net income of $200, as shown in Illustration 18.15.

Vargo Electronics Company

CVP Income Statement

For the Month Ended June 30, 2022

Total

Per Unit

Sales (1,001 × $500)     

$500,500

    

$500

Variable costs (1,001 × $300)

  300,300

  300

Contribution margin

  200,200

$200

Fixed costs   200,000

Net income $        200

ILLUSTRATION 18.15 CVP income statement, with net income and per unit data

Contribution Margin Ratio

Some managers prefer to use a contribution margin ratio in CVP analysis. The contribution margin ratio is the contribution margin expressed as a percentage of sales. Vargo Electronics has a contribution margin ratio of 40% (contribution margin of $200,200 divided by sales of $500,500), as shown in the percent of sales column in Illustration 18.16.

Vargo Electronics Company

CVP Income Statement

For the Month Ended June 30, 2022

Total

Percent of Sales

Sales (1,001 × $500)     

$500,500

    

100%

Variable costs (1,001 × $300)   300,300

    60    

Contribution margin   200,200

  40%

Fixed costs   200,000

Net income $        200

ILLUSTRATION 18.16 CVP income statement, with net income and percent of sales data</p

Collepals.com Plagiarism Free Papers

Are you looking for custom essay writing service or even dissertation writing services? Just request for our write my paper service, and we'll match you with the best essay writer in your subject! With an exceptional team of professional academic experts in a wide range of subjects, we can guarantee you an unrivaled quality of custom-written papers.

Get ZERO PLAGIARISM, HUMAN WRITTEN ESSAYS

Why Hire Collepals.com writers to do your paper?

Quality- We are experienced and have access to ample research materials.

We write plagiarism Free Content

Confidential- We never share or sell your personal information to third parties.

Support-Chat with us today! We are always waiting to answer all your questions.