1. 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 called the contribution approach.
Chapter 5
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

2. The Activity Base (also called a cost driver)
5-2
The Activity Base (also called a cost driver)
Units produced
Machine 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 total 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.
Miles driven
Labor hours
5-2

3. True Variable Cost – An Example
5-3
True Variable Cost – An Example
As an example of an activity base, consider overage charges on a cell phone bill. The activity base is the number of minutes used above the allowed minutes in the calling plan.
Total Overage Charges on Cell Phone Bill
As an example of an activity base, consider overage charges on a cell phone bill. The activity base is the number of minutes used above the allowed minutes in the calling plan.
Minutes Talked
5-3

4. Variable Cost Per Unit – An Example
5-4
Variable Cost Per Unit – An Example
Referring to the cell phone example, the cost per overage minute is constant, for example 45 cents per overage minute.
Per Minute Overage Charge
Remember that a variable cost remains constant if expressed on a per unit basis. Referring to the cell phone example, the cost per overage minute is constant, for example 45 cents per overage minute.
Minutes Talked
5-4

5. Examples of Variable Costs
5-5
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.
Here are some examples of variable costs that are likely present in many types of businesses.
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.
5-5

6. 5-6
True Variable Costs
The amount of a true variable cost used during the period varies in direct proportion to the activity level. The overage charge on a cell 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.
Cost
The amount of a true variable cost used during the period varies in direct proportion to the activity level.
The overage charge on a cell phone bill was one example of a true variable cost.
Direct material is an 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 of inventory.
Volume
5-6

7. 5-7
Step-Variable Costs
A step-variable cost is a resource that is obtainable only in large chunks (such as maintenance workers) and whose costs change only in response to fairly wide changes in activity.
Volume
Cost
A step-variable cost is a resource that is obtainable only in large chucks 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.
5-7

8. The Linearity Assumption and the Relevant Range
5-8
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
Accountant’s Straight-Line Approximation (constant unit variable cost)
Part I
Economists correctly point out that many costs which 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 that range of activity within which the assumptions made about cost behavior are valid.
Activity
5-8

9. Total Fixed Cost – An Example
5-9
Total Fixed Cost – An Example
For example, your cell phone bill probably includes a fixed amount related to the total minutes allowed in your calling plan. The amount does not change when you use more or less allowed minutes.
Monthly Basic Cell Phone Bill
For example, your cell phone bill probably includes a fixed amount related to the total minutes allowed in your calling plan. The amount does not change when you use more or less allowed minutes.
Number of Minutes Used within Monthly Plan
5-9

10. Fixed Cost Per Unit Example
5-10
Fixed Cost Per Unit Example
For example, the fixed cost per minute used decreases as more allowed minutes are used.
Cost Per Cell Phone Call
For example, the fixed cost per minute used decreases as more allowed minutes are used.
As you make more and more allowed calls, the basic rate cost per call decreases. If your basic rate is $39 per month and you make one allowed call per month, the average basic rate is $39 per call. However, if you make 100 allowed calls per month, the average basic rate per call drops to 39 cents per call.
Number of Minutes Used within Monthly Plan
5-10

11. Is Labor a Variable or a Fixed Cost?
5-11
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.
In the United States and the United Kingdom, management has greater latitude. Labor costs are more variable in nature.
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.
In the United States and United Kingdom, management typically has much greater latitude to adjust the size of the labor force; hence, labor costs are more variable in nature.
Within countries managers can view labor costs differently depending upon their strategy. Nonetheless, most companies in the United States continue to view direct labor as a variable cost.
Within countries managers can view labor costs differently
depending upon their strategy. Most companies in the
United States continue to view direct labor as a variable cost.
5-11

12. Fixed Costs and the Relevant Range
5-12
Fixed Costs and the Relevant Range 90
The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat.
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)
5-12

13. Fixed Monthly Utility Charge
5-13
Mixed Costs X Y
Total mixed cost
Total Utility Cost
The mixed cost line can be expressed with the equation Y = a + bX. This equation should look familiar, from your algebra and statistics classes.
In the equation, Y is the total mixed cost; a is the total fixed cost (or the vertical intercept of the line); b is the variable cost per unit of activity (or the slope of the line), and X is the actual level of activity.
In our utility example, Y is the total mixed cost; a is the total fixed monthly utility charge; b is the cost per kilowatt hour consumed, and X is the number of kilowatt hours consumed.
Variable Cost per KW
Fixed Monthly Utility Charge
Activity (Kilowatt Hours)
5-13

14. The Scattergraph Method
5-14
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
Intercept = Fixed cost: $10,000
Part I
The fourth step is to identify the Y intercept. This is the point where the straight line crosses the Y axis determines the estimate of total fixed costs. In this case, the fixed costs are $10,000.
Part II
The fifth step is to estimate the variable cost per unit of the activity. Select one data point on the scattergraph that intersects the straight line. Determine the total cost ($11,000) and the total activity level (800 patient-days) at the chosen point.
Patient days = 800
5-14

15. The High-Low Method – An Example
5-15
The High-Low Method – An Example
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. In this case, the high level of activity was in June at 850 hours of maintenance and the low level of activity is in February with 450 hours of maintenance. Notice that this method relies upon two data points to estimate the fixed and variable portions of a mixed cost, as opposed to one data point with the scattergraph method.
Part II
The second step is to determine the total costs associated with the two chosen points. We incurred costs of $9,800 at the high level of activity and $7,400 at the low level of activity.
The third step is to calculate the change in cost between the two data points. The change in maintenance hours was 400 hours and the change in maintenance dollars was $2,400. Notice, this method relies upon two data points to estimate the fixed and variable portions of a mixed costs, as opposed to one data point with the scattergraph method.
For this example, we divide $2,400 by 400 and determine that the variable cost per hour of maintenance is $6.00.
= $6.00/hour
$2,
5-15

16. The High-Low Method – An Example
5-16
The High-Low Method – An Example
Total Fixed Cost = Total Cost – Total Variable Cost
Part I
The fourth step is to take the total cost at either activity level (in this case, $9,800).
Part II
Deduct the variable cost component ($6 per hour times 850 hours) for the total cost of $9,800.
Part III
The difference represents the estimate of total fixed costs ($4,700).
Total Fixed Cost = $9,800 – ($6/hour × 850 hours)
Total Fixed Cost = $9,800 – $5,100
Total Fixed Cost = $4,700
5-16

17. The High-Low Method – An Example
5-17
The High-Low Method – An Example
The fifth step is to construct an equation that can be used to estimate the total cost at any activity level (Y = $4,700 + $6.00X). The basic equation of Y is equal to $4,700 (the total fixed cost) plus $6 times the actual level of activity.
You can verify the equation by calculating total maintenance costs at 450 hours, the low level of activity. It will be worth your time to make the calculation.
Y = $4,700 + $6.00X
The Cost Equation for Maintenance
5-17

18. Least-Squares Regression Method
5-18
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.
This method can be used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables.
The least-squares regression method is a more sophisticated approach to isolating the fixed and variable portion of a mixed cost. This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost. This method is superior to the scattergraph plot method that relies upon 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.
5-18

19. Least-Squares Regression Method
5-19
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, computer software can perform the calculations quickly. The observed values of the X and Y variables are entered into the computer program and all necessary calculations are made.
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 key statistic to look at when evaluating regression results is called R squared, which is a measure of the “goodness of fit.”
In the appendix to this chapter, we show you how to use Microsoft Excel to complete a least-squares regression analysis.
Least-squares regression also provides a statistic, called the R2, which is a measure of the goodness of fit of the regression line to the data points.
5-19

20. End of Chapter 5
End of chapter 5.
5-20