1. Cost Behavior: Analysis and Use
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Chapter 5
Cost Behavior: Analysis and Use
Chapter 5: Cost Behavior: Analysis and Use.
Managers who understand how costs behave are better able to predict costs and make decisions under various circumstances. This chapter explores the meaning of fixed, variable, and mixed costs (the relative proportions of which define an organization’s cost structure). It also introduces a new income statement format called the contribution approach.
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Types of Cost Behavior Patterns
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Types of Cost Behavior Patterns
Recall the summary of our cost behavior discussion from Chapter 1.
A variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level.

3. A measure of what causes the incurrence of a variable cost.
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The Activity Base
Units produced
Miles driven
Machine hours
Labor hours
A measure of what causes the incurrence of a variable cost.
An activity base (also called a cost driver) is a measure of what causes the incurrence of variable costs. As the level of the activity base increases, the variable cost increases proportionally. Units produced (or sold) is not the only activity base within companies. A cost can be considered variable if it varies with activity bases such as miles driven, machine hours, or labor hours.

4. True Variable Cost Example
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True Variable Cost Example
A variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level.
Your total long distance telephone bill is based on how many minutes you talk.
Total Long Distance Telephone Bill
As an example of an activity base, consider your total long distance telephone bill. The activity base is the number of minutes that you talk.
Minutes Talked

5. Types of Cost Behavior Patterns
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Types of Cost Behavior Patterns
Recall the summary of our cost behavior discussion from Chapter 1.
Variable costs remain constant if expressed on a per unit basis.

6. Variable Cost Per Unit Example
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Variable Cost Per Unit Example
A variable cost remains constant if expressed on a per unit basis.
The per minute cost of long distance calls is constant, for example, 10¢ per minute.
Per Minute Telephone Charge
Referring to the telephone example, the cost per minute talked is constant (e.g., 10 cents per minute)
Minutes Talked

7. Extent of Variable Costs
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Extent of Variable Costs
The proportion of variable costs differs across organizations. For example . . .
A public utility with large investments in equipment will tend to have fewer variable costs.
A manufacturing company will often have many variable costs.
The proportion of variable costs differs across organizations. For example:
A public utility like Florida Power and Light, with large investments in equipment, will tend to have fewer variable costs.
A manufacturing company like Black and Decker will often have many variable costs associated with the manufacture and distribution of its products to customers.
A merchandising company like Wal-Mart will usually have a high proportion of variable costs such as the cost of merchandise purchased for resale.
Some service companies, such as restaurants, have a high proportion of variable costs due to their raw material costs. Other service companies, such as an architectural firm, have a high proportion of fixed costs in the form of highly trained salaried employees.
A merchandising company usually will have a high
proportion of variable costs
like cost of sales.
A service company will normally have a high
proportion of variable costs.

8. Examples of Variable Costs
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Examples of Variable Costs
Merchandising companies – cost of goods sold.
Manufacturing companies – direct materials, direct labor, and variable overhead.
Merchandising and manufacturing companies – commissions, shipping costs, and clerical costs such as invoicing.
Service companies – supplies, travel, and clerical.
Common examples of variable costs are: 
1.  Merchandising companies  cost of goods sold.
Manufacturing companies  direct materials, direct labor, and variable overhead.
Merchandising and manufacturing companies  commissions, shipping costs, and clerical costs such as invoicing.
Service companies  supplies, travel, and clerical.

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True Variable Cost
Direct materials is a true or proportionately variable cost because the amount used during a period will vary in direct proportion to the level of production activity.
 A true variable cost is an amount used during the period that varies in direct proportion to the activity level. The long distance phone bill was one example of a true variable cost. Direct material is another example of a cost that behaves in a true variable pattern. Direct materials purchased but not used can be stored and carried forward to the next period as inventory.
Cost
Volume

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Step-Variable Costs
A resource that is obtainable only in large chunks (such as maintenance workers) and whose costs increase or decrease only in response to fairly wide changes in activity.
Volume
Cost
A step variable cost is a resource that is obtainable only in large chunks and whose costs change only in response to fairly wide changes in activity. For example, maintenance workers are often considered to be a variable cost, but this labor cost does not behave as a true variable cost.

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Step-Variable Costs
Small changes in the level of production are not likely to have any effect on the number of maintenance workers employed.
Volume
Cost
Small changes in the level of production are not likely to have any effect on the number of maintenance workers employed.

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Step-Variable Costs
Only fairly wide changes in the activity level will cause a change in the number of maintenance workers employed.
Volume
Cost
Only fairly wide changes in the activity level will cause a change in the number of maintenance workers employed. Maintenance workers are obtainable only in large chunks of a whole person who is capable of working approximately 2,000 hours a year.

13. The Linearity Assumption and the Relevant Range
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The Linearity Assumption and the Relevant Range
Relevant Range
A straight line closely approximates a curvilinear variable cost line within the relevant range.
Economist’s Curvilinear Cost Function
Total Cost
Part I Economists correctly point out that many costs that accountants classify as variable costs actually behave in a curvilinear fashion.
Part II Nonetheless, within a narrow band of activity known as the relevant range, a curvilinear cost can be satisfactorily approximated by a straight line.
Part III The relevant range is the range of activity within which the assumptions made about cost behavior are valid.
Accountant’s Straight-Line Approximation (constant unit variable cost)
Activity

14. Types of Cost Behavior Patterns
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Types of Cost Behavior Patterns
Let’s turn our attention to fixed cost behavior.
A fixed cost is a cost whose total dollar amount remains constant as the activity level changes.

15. Total Fixed Cost Example
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Total Fixed Cost Example
A fixed cost is a cost whose total dollar amount remains constant as the activity level changes.
Your monthly basic telephone bill is probably fixed and does not change when you make more local calls.
Monthly Basic Telephone Bill
For example, your monthly basic telephone bill is probably fixed and does not change when you make more local calls.
Number of Local Calls

16. Types of Cost Behavior Patterns
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Types of Cost Behavior Patterns
Recall the summary of our cost behavior discussion from Chapter 1.
Average fixed costs per unit decrease as the activity level increases.

17. Fixed Cost Per Unit Example
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Fixed Cost Per Unit Example
Average fixed costs per unit decrease as the activity level increases.
The fixed cost per local call decreases as more local calls are made.
Monthly Basic Telephone Bill per Local Call
For example, the fixed cost per local call decreases as more local calls are made.
Number of Local Calls

18. Types of Fixed Costs Committed Discretionary Examples Examples
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Types of Fixed Costs
Committed
Long-term, cannot be significantly reduced in the short-term.
Discretionary
May be altered in the short-term by current managerial decisions
Examples
Depreciation on Buildings and Equipment and Real Estate Taxes
Examples
Advertising and Research and Development
Part I
Committed costs are long-term in nature (i.e., greater than one year). These costs cannot be significantly reduced even for short periods of time without seriously impairing the long-run goals of the organization. Examples of committed-fixed costs include depreciation on buildings and equipment and real estate taxes.
Part II
Discretionary costs usually arise from annual decisions by management to spend in certain fixed cost areas. These costs can be cut for short periods of time with minimal damage to the long-term goals of the organization. Examples of discretionary fixed costs include advertising and research and development.
A cost may be discretionary or committed depending on management’s strategy. For example, some construction companies may layoff workers during months with minimal customer demand. However, other construction companies may opt to retain their workers all year.

19. The Trend Toward Fixed Costs
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The Trend Toward Fixed Costs
The trend in many industries is toward greater fixed costs relative to variable costs.
As machines take over many mundane tasks previously performed by humans, “knowledge workers” are demanded for their minds rather than their muscles.
Knowledge workers tend to be salaried, highly-trained, and difficult to replace. The cost to compensate these valued employees is relatively fixed rather than variable.
Part I
The trend in many industries is toward greater fixed costs relative to variable costs. For example: H&R Block employees used to fill out tax returns for customers by hand. Now, computer software is used to complete tax returns. Safeway and Kroger employees used to key-in prices by hand on cash registers. Now, barcode readers enter price and other product information automatically.
Part II
As machines take over many mundane tasks previously performed by humans, “knowledge workers” are demanded for their minds rather than their muscles. Knowledge workers tend to be salaried, highly-trained, and difficult to replace; consequently, the cost of compensating these valued employees is relatively fixed rather than variable.

20. Is Labor a Variable or a Fixed Cost?
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Is Labor a Variable or a Fixed Cost?
The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom.
In France, Germany, China, and Japan, management has little flexibility in adjusting the size of the labor force. Labor costs are more fixed in nature.
The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom. For example: In France, Germany, China, and Japan management has little flexibility in adjusting the size of the labor force; hence, labor costs are more fixed in nature.
Within countries managers can view labor costs differently depending on their strategy. Nonetheless, most companies in the United States continue to view direct labor as a variable cost.
Most companies in the United States continue to view direct labor as a variable cost.

21. Fixed Costs and Relevant Range
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Fixed Costs and Relevant Range 90
Total cost doesn’t change for a wide range of activity, and then jumps to a new higher cost for the next higher range of activity.
Relevant Range 60
Rent Cost in Thousands of Dollars
The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat. 30
, , , Rented Area (Square Feet)

22. Fixed Costs and Relevant Range
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Fixed Costs and Relevant Range
The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat.
Example: Office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows, more space is rented, increasing the total cost.
For example, assume office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. Fixed costs would increase in a step fashion at a rate of $30,000 for each additional 1,000 square feet.

23. Fixed Costs and Relevant Range
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Fixed Costs and Relevant Range
Step-variable costs can be adjusted more quickly and . . .
The width of the activity steps is much wider for the fixed cost.
How does this type of fixed cost differ from a step-variable cost?
While this step-function pattern appears similar to the idea of step-variable costs, there are two important differences between step-variable costs and fixed costs:
Step-variable costs can often be adjusted quickly as conditions change, whereas fixed costs cannot be changed easily.
The width of the steps for fixed costs is wider than the width of the steps for step-variable costs. For example, a step-variable cost such as maintenance workers may have steps with a width of 40 hours a week. However, fixed costs may have steps that have a width of thousands or tens of thousands of hours of activity.

24. Which of the following statements about cost behavior are true?
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Quick Check 
Which of the following statements about cost behavior are true?
Fixed costs per unit vary with the level of activity.
Variable costs per unit are constant within the relevant range.
Total fixed costs are constant within the relevant range.
Total variable costs are constant within the relevant range.
Take a minute to answer this question before we move on. There can be more than one correct answer. Be careful and take your time.

25. Fixed Monthly Utility Charge
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Mixed Costs
A mixed cost has both fixed and variable components. Consider your utility costs. X Y
Total mixed cost
Total Utility Cost
A mixed cost contains both variable and fixed cost elements. For example, utility bills often contain fixed and variable cost components. The fixed portion of the utility bill is constant regardless of kilowatt hours consumed. This cost represents the minimum cost that is incurred to have the service ready and available for use. The variable portion of the bill varies in direct proportion to the consumption of kilowatt hours.
Variable Cost per KW
Fixed Monthly Utility Charge
Activity (Kilowatt Hours)

26. Fixed Monthly Utility Charge
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Mixed Costs X Y
Total mixed cost
Total Utility Cost
An equation can be used to express the relationship between mixed costs and the level of the activity. This equation can be used to calculate what the total mixed cost would be for any level of activity.
The equation is Y = a + bX
Y = The total mixed cost.
a = The total fixed cost (the vertical intercept of the line).
b = The variable cost per unit of activity (the slope of the line).
X = The level of activity.
Variable Cost per KW
Fixed Monthly Utility Charge
Activity (Kilowatt Hours)

27. Mixed Costs Example Y = a + bX Y = $40 + ($0.03 × 2,000) Y = $100
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Mixed Costs Example
If your fixed monthly utility charge is $40, your variable cost is $0.03 per kilowatt hour, and your monthly activity level is 2,000 kilowatt hours, the amount of your utility bill is:
Y = a + bX
Y = $40 + ($0.03 × 2,000)
Y =
$100
For example, if your fixed monthly utility charge is $40, your variable cost is 3 cents per kilowatt hour, and your monthly activity level was 2,000 kilowatt hours, this equation can be used to calculate your total utility cost of $100.

28. Analysis of Mixed Costs
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Analysis of Mixed Costs
Account analysis
Each account is classified as either variable or fixed based on the analyst’s knowledge of how the account behaves.
Engineering Approach
Cost estimates are based on an evaluation of production methods, and material, labor and overhead requirements.
In account analysis, each account under consideration is classified as variable or fixed based on the analyst’s prior knowledge about how costs behave. This approach is limited in value in the sense that it glosses over the fact that some accounts may have both fixed and variable components.
The engineering approach classifies costs based on an industrial engineer’s evaluation of production methods, material specifications, labor requirements, equipment usage, power consumption, and so on. This approach is particularly useful when no past experience is available concerning activity and costs.

29. The Scattergraph Method
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The Scattergraph Method
Plot the data points on a graph (total cost vs. activity). *
Maintenance Cost 1,000’s of Dollars 10 20
Patient-days in 1,000’s X Y
The scattergraph plot is also called the quick-and-dirty method.
The first step when using this method to analyze a mixed cost is to plot the data on a scattergraph. The cost, which is known as the dependent variable, is plotted on the Y axis. The activity, which is known as the independent variable, is plotted on the X axis.
The second step is to examine the dots on the scattergraph to see if they are linear, such that a straight line can be drawn that approximates the relation between cost and activity. If the dots are not linear, do not analyze the data any further. Instead, search for another independent variable that bears a stronger linear relationship with the dependent variable.

30. The Scattergraph Method
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The Scattergraph Method
Draw a line through the data points with about an equal number of points above and below the line. *
Maintenance Cost 1,000’s of Dollars 10 20
Patient-days in 1,000’s X Y
The third step is to draw a straight line where, roughly speaking, an equal number of points reside above and below the line. Make sure that the straight line goes through at least one data point on the scattergraph.

31. The Scattergraph Method
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The Scattergraph Method
Use one data point to estimate the total level of activity and the total cost. *
Maintenance Cost 1,000’s of Dollars 10 20
Patient-days in 1,000’s X Y
Total maintenance cost = $11,000
Patient days = 800
Intercept = Fixed cost: $10,000
Part I
The fourth step is to identify the Y intercept. This intercept represents the estimated fixed cost portion of the mixed cost ($10,000 in this example).
Part II
The fifth step is to estimate the variable cost per unit of the activity by first selecting one point on the scattergraph that intersects the straight line and then determining the total cost and the total activity level at the chosen point.

32. The Scattergraph Method
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The Scattergraph Method
Make a quick estimate of variable cost per unit and determine the cost equation.
Variable cost per unit =
$1,
= $1.25 per patient-day
Step 5 (continued)
Part I
Subtract the fixed costs from the total costs to arrive at the total variable costs for the chosen activity level.
Part II Divide the total variable costs by the activity level at the chosen point. This is the variable cost per unit of activity.
Part III Construct an equation that can be used to estimate total costs at any activity level.
Y = $10,000 + $1.25X
Number of patient days
Total maintenance cost

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The High-Low Method
Assume the following hours of maintenance work and the total maintenance costs for six months.
This method can be used to analyze mixed costs if a scattergraph plot reveals a linear relationship between the X and Y variables. For illustrative purposes, assume the information as shown.

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The High-Low Method
The variable cost per hour of maintenance is equal to the change in cost divided by the change in hours.
Part I
The first step is to choose the data points pertaining to the highest and lowest activity levels (high = 800 units; low = 500 units). Notice, this method relies on two data points to estimate the fixed and variable portions of a mixed cost, as opposed to one data point with the scattergraph method. The second step is to determine the total costs associated with the two chosen points (high = $9,800; low = $7,400).
Part II
The third step is to calculate the change in cost between the two data points ($2,400) and divide it by the change in activity level between the two data points (300 units). The quotient represents an estimate of variable cost per unit of activity ($8.00 per unit).
= $8.00/hour
$2, hours

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The High-Low Method
Total Fixed Cost = Total Cost – Total Variable Cost
The fourth step is to take the total cost at either activity level (in this case, $9,800) and deduct the variable cost component ($6,400). The residual represents the estimate of total fixed costs ($3,400).
The variable cost component ($6,400) is determined by multiplying the level of activity (800 units) by the estimated variable cost per unit of the activity ($8.00 per unit).
Total Fixed Cost = $9,800 – ($8/hour × 800 hours)
Total Fixed Cost = $9,800 – $6,400
Total Fixed Cost = $3,400

36. The Cost Equation for Maintenance
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The High-Low Method
The fifth step is to construct an equation that can be used to estimate the total cost at any activity level (Y = $3,400 + $8.00X).
Y = $3,400 + $8.00X
The Cost Equation for Maintenance

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Quick Check 
Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission?
a. $0.08 per unit
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
Now, let’s apply what we have just discussed to determine the variable portion of sales salaries and commissions for this company.

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Quick Check 
Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
Using the same data, calculate the total fixed cost portion of sales salaries and commissions.

39. Least-Squares Regression Method
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Least-Squares Regression Method
A method used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables.
This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost.
The least-squares regression method can be used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables.
This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost. Because it uses all of the data points, least-squares regression is superior to the scattergraph plot method that relies on only one data point and the high-low method that uses only two data points to estimate the fixed and variable cost components of a mixed cost.
The basic goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors. The regression errors are the vertical deviations from the data points to the regression line.
The goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors.

40. Least-Squares Regression Method
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Least-Squares Regression Method
Software can be used to fit a regression line through the data points.
The cost analysis objective is the same: Y = a + bX
The formulas that are used for least-squares regression are complex. Fortunately, computers can perform the calculations quickly. The observed values of the X and Y variables are entered into the computer and the software does the rest. The output from the regression analysis can be used to create an equation that enables you to estimate total costs at any activity level.
The output from the regression analysis can be used to create an equation that enables you to estimate total costs at any activity level.

41. Comparing Results From the Three Methods
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Comparing Results From the Three Methods
The three methods just discussed provide slightly different estimates of the fixed and variable cost components of the mixed cost.
This is to be expected because each method uses different amounts of the data points to provide estimates.
Least-squares regression provides the most accurate estimate because it uses all of the data points.
The three methods just discussed provide slightly different estimates of the fixed and variable cost components of the mixed cost.
This is to be expected because each method uses differing amounts of the data points to provide estimates.
Least-squares regression provides the most accurate estimates because it uses all of the data points.

42. The Contribution Format Income Statement
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The Contribution Format Income Statement
Let’s put our knowledge of cost behavior to work by preparing a contribution format income statement.
The contribution approach provides an income statement format geared directly to cost behavior, which has been the focus of discussion in this chapter.

43. The Contribution Format
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The Contribution Format
The contribution margin format emphasizes cost behavior, by separating costs into fixed and variable categories. Contribution margin covers fixed costs and provides for income.
This approach separates costs into fixed and variable categories. Sales minus variable costs equals contribution margin. The contribution margin minus fixed costs equals net operating income.

44. Uses of the Contribution Format
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Uses of the Contribution Format
The contribution income statement format is used as an internal planning and decision making tool. We will use this approach for:
Cost-volume-profit analysis (chapter 6).
Budgeting (chapter 7).
Special decisions such as pricing and make-or-buy analysis (chapter 11).
This approach is used as an internal planning and decision making tool. For example, this approach is useful for: 
1.    Cost-volume-profit analysis (chapter 6).
2.    Budgeting (chapter 7).
3.    Special decisions such as pricing and make-or-buy analysis (chapter 11).

45. The Contribution Format
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The Contribution Format
The contribution approach differs from the traditional approach illustrated in chapter 1. The traditional approach organizes costs in a functional format. Costs relating to production, administration, and sales are grouped together without regard to their cost behavior. The traditional approach is used primarily for external reporting purposes.
Used primarily for external reporting.
Used primarily by management.