CHAPTER 3
COST BEHAVIOR
Chapter 3 provides the basics of cost behavior, focusing on expanded definitions of fixed and variable
costs and introducing the concept of mixed costs. Methods of separating mixed costs into fixed and
variable elements are presented and discussed. In addition, the resource usage model is presented. This
chapter is an important foundation for the activity-based costing system discussed in Chapter 4.
LEARNING OBJECTIVES
After studying Chapter 3, students should be able to:
1. Define and describe fixed, variable, and mixed costs.
2. Explain the use of resources and activities and their relationship to cost behavior.
3. Explain how several methods of cost estimation can be used.
4. Separate mixed costs into their fixed and variable components using the high-low method, the
scatterplot method, and the method of least squares.
5. Evaluate the reliability of the cost formula.
6. Explain how multiple regression can be used to assess cost behavior.
7. Define the learning curve, and discuss its impact on cost behavior.
8. Discuss the use of managerial judgment in determining cost behavior.
KEY TOPICS
The following major topics are covered in this chapter (related learning objectives are listed for each
topic):
1. Basics of Cost Behavior (LO 1)
2. Resources, Activities, and Cost Behavior (LO 2)
3. Methods of Determining Cost Behavior (LO 3)
4. Quantitative Methods for Separating Mixed Costs into Fixed and Variable Components (LO 4)
5. Reliability of Cost Formulas (LO 5)
6. Multiple Regression (LO 6)
7. The Learning Curve and Nonlinear Cost Behavior (LO 7)
8. Managerial Judgment (LO 8)
I. BASICS OF COST BEHAVIOR
Cost behavior refers to whether a cost changes when the level of output changes. Usually costs are placed
into one of four categories: fixed costs, variable costs, mixed costs, and step costs. These categories are
reasonably accurate within a relevant range of activity.
Remind students that activity drivers are factors that cause changes in resource usage, activity usage,
costs, and revenues. Unit-level drivers explain changes in cost as units produced change. Examples
include pounds of direct materials, kilowatt-hours used to run production machinery, and direct labor
hours. Non-unit-level drivers explain how costs change as factors other than the number of units produced
changes. Examples include the number of setups, work orders, engineering change orders, inspection
hours, and material moves.
Relevant range: The range of activity over which the assumed cost relationship is valid for the normal
operations of a firm is called the relevant range. While the cost function may not be linear, we will often
assume linearity because the function will appear to be linear within the relevant range.
Fixed costs: Fixed costs are costs that do not change in total as the activity level changes. All costs are
considered to be fixed in the short run. The term fixed cost does not infer that the cost cannot change over
time but that a change in the activity level will not cause a change in the total cost. The duration of the
short run can change depending on the cost under consideration. Total fixed costs can be described in
equation format to be:
F = Total fixed costs
Variable costs: Variable costs are costs that, in total, will vary in direct proportion to changes in activity
level, which is commonly defined as some measure of production or sales activity (e.g., direct labor
hours, units produced, or units sold). Activity level can refer to the level of any cost driver (e.g., setup
time, number of material moves, etc.) in an activity-based costing system. Total variable costs can be
described in equation format to be:
Yv = VX
where
Yv = Total variable costs
V = Variable cost per unit of activity
X = Number of units of the driver
Exhibits 3.1 (p. 76) and 3.2 (p. 77) present the graphical presentations of fixed and variable cost
behaviors.
Teaching hint: You might emphasize that the variable costs (and later fixed costs) portrayed here are total
costs, not average costs (costs per unit). Students often have difficulty with this distinction. Total variable
cost increases (decreases) as activity level increases (decreases). Average variable cost stays constant as
activity level changes.
Teaching hint: Some students have a hard time with the concept of fixed cost because they equate it to
“never changing.” However, their experience living in an inflationary economy is that costs do change
(typically upward). Thus, they think that no cost can ever be fixed. The key point is that a fixed cost does
not change because activity level changes; a fixed cost can change for other reasons. For example, a
salaried supervisor could be given a raise during the year because of excellent performance or in an effort
to keep him from taking a job with another firm. The increase in his salary would be a change in a fixed
cost. The change was not, however, due to an increase in the level of activity.
Mixed costs: Costs that have both a fixed and a variable component are classified as mixed costs. A
salesperson paid a salary of $20,000 plus a commission equal to 5 percent of sales is an example of a
mixed cost.
Total mixed costs can be described as:
Y = F + VX
where
Y = Total cost
F, V, and X are defined previously in the chapter.
Cornerstone 3.1 (p. 79) shows how the linear equation can be used to describe a mixed cost. Exhibit 3.5
(p. 81) presents a graph of mixed cost behavior.
Determining whether a cost is fixed or variable depends on the time horizon. According to economics, in
the long run, all costs are variable; in the short run, at least one cost is fixed.
II. RESOURCES, ACTIVITIES, AND COST BEHAVIOR
Resources are economic elements that permit one to perform activities. Common resources include direct
materials, direct labor, equipment, etc. Resources can be categorized as either flexible or committed.
Flexible resources are supplied as used and needed (e.g., direct materials).
Committed resources are supplied in advance of usage. These resources are acquired by the use of either
an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the amount of
the resource available is fully used or not. Committed resources may have unused capacity (e.g., buying
or leasing a building or equipment).
Activities are tasks such as setting up equipment, purchasing materials, and assembling materials. Activity
capacity is the ability to perform activities. When a company acquires resources necessary to perform an
activity, it is obtaining activity capacity. Practical capacity is the efficient level of activity performance.
A step-cost function has the property of displaying a constant level of cost for a range of activity and then
jumping to a higher level of cost at some point, where it remains for a similar range of activity. A step-
cost function is illustrated in Exhibit 3.6 (p. 84).
A step-variable cost is simply a step-cost that changes for relatively narrow ranges of activity. This type
of cost is usually treated as if it were a pure variable cost because of the narrow ranges of activity.
Step-costs that have relatively wide levels of activity are known as step-fixed costs. The difference
between step-variable and step-fixed costs is the range of activity included at each step. For example, a
step-variable cost may increase for every 100 units produced, while a step-fixed cost may increase for
every 10,000 units produced. A step-fixed cost is usually treated as a fixed cost. Exhibit 3.7 (p. 84)
displays a step-fixed cost.
A traditional cost management system typically provides information only about the cost of the resources
supplied. A contemporary cost management system provides information about how much of the activity
is used and the cost of its usage.
The relationship between resources supplied and resources used is expressed by either of the following
equations:
Activity availability = Activity output + Unused capacity
Cost of activity supplied = Cost of activity used + Cost of unused activity
Cornerstone 3.2 (p. 85) illustrates the way a company may determine the cost of capacity used and unused
capacity.
When activities use a mix of resources that are acquired in advance and resources that are acquired as
needed, they display mixed cost behavior. In practice, companies use a variety of methods of estimating
cost, including the industrial engineering method, the account analysis method, and a variety of
quantitative and statistical methods.
III. METHODS OF DETERMINING COST BEHAVIOR
The industrial engineering method is a forward-looking method of determining, through physical
observation and analysis, just what activities, in what amounts, are needed to complete a process. The
account analysis method is used to estimate costs by classifying accounts in the general ledger as fixed,
variable, or mixed. To use the account analysis method, the accountant uses judgment and experience to
separate the accounts into two categories—fixed and variable. Once the fixed categories are known, the
average monthly cost can be computed and this is the fixed amount. The variable categories need to be
further separated into categories according to the driver the accountant wishes to associate with the
account. Cornerstone 3.3 (p. 87) shows how the account analysis method can be used to separate fixed
and variable costs, determine a cost function, and use that cost function in budgeting.
IV. QUANTITATIVE METHODS FOR SEPARATING MIXED COSTS INTO FIXED AND
VARIABLE COMPONENTS
To facilitate planning and decision making, managers need to know the fixed and variable components of
mixed costs. The text presents three methods used to separate a mixed cost into its fixed and variable
components: the high-low method, the scatterplot method, and the method of least squares.
A. The High-Low Method
When using the high-low method, the highest point and the lowest point are used for creating the cost
formula. The high point is defined as the point with the highest activity level and the low point as the
point with the lowest activity level. The independent variable should be used when selecting the highest
and lowest activity levels. Always make sure that the high and low activity points are representative of the
rest of the points. A scatterplot would be helpful to see whether the two points are representative of the
others.
Letting (X1, Y1) be the low point and (X2, Y2) be the high point, the equations for determining the slope
parameter and intercept parameter are, respectively:
V = Change in cost/Change in activity
= (Y2 – Y1)/(X2 – X1)
F = Total mixed cost – Variable cost
= Y2 – VX2
or
F = Y1 – VX1
Cornerstone 3.4 (p. 90) shows how the high-low method can be used to determine the fixed cost and
variable rate.
Teaching hint: Tell the students that the high-low method is nothing more than finding the equation of a
line through two points.
B. Scatterplot Method
Using the scatterplot method, the manager plots the observations of cost and activity level on a graph.
The manager selects two points by visual inspection of the scattergraph and fits a line to these two points.
This is accomplished by using the slope-intercept method from basic algebra. The slope is the change in
cost divided by the change in activity. Once the slope is known, simply substitute the slope and the values
of one of the two points into the linear cost formula (Y = F + VX) and solve for the fixed component, F (F
= Y – VX).
Exhibit 3.8 (p. 93) presents a plot of data points, along with the graph of a line for the high-low method
and a possible scattergraph line. Exhibit 3.9 (p. 95) presents three graphs illustrating (1) a nonlinear
relationship, (2) an upward shift in a cost relationship, and (3) the presence of outliers in the data set.
C. The Method of Least Squares
The method of least squares identifies the line that best fits the data points (the sum of the squared
deviations is minimized). This method is the most sophisticated and provides the user with a measure of
the goodness of fit, which can be used to assess the usefulness of the cost formula. If the fit is not very
good, then a search for additional activity variables may be needed.
Computing the regression formula manually is tedious and best left to a statistics course. Exhibits 3.11 (p.
97) and 3.12 (p. 98) illustrate the use of a Microsoft Excel® worksheet to identify the intercept and X
variable (e.g., fixed and variable cost). The output not only provides estimates of the coefficients, it also
provides information that can be used to determine the reliability of the cost equation. The same program
can be used for multiple regression as well. Cornerstone 3.5 (p. 99) displays how to take the results of the
regression program and to use them to construct a cost formula. That cost formula can then be used to
determine the predicted cost given an estimate of the independent variable.
V. RELIABILITY OF COST FORMULAS
There are two basic measures for determining the reliability of cost formulas: coefficient of determination
and coefficient of correlation. The coefficient of determination (R2) is a measure of the goodness of fit. It
shows the percent of the variation in the dependent variable that is explained by the independent variable
(or variables). The higher the percentage of variability explained, the better the fit. The coefficient of
correlation (r) is the square root of the coefficient of determination. If the coefficient of correlation is
positive, the independent variable and the dependent variable move together in the same direction. If it is
negative, the independent variable and the dependent variable move in a predictable fashion in opposite
directions.
Constructing a confidence interval allows one to state with a specified degree of confidence the range in
which a predicted cost should fall. Exhibit 3.14 (p. 103) provides a table for use in constructing a
confidence interval at the 90 percent, 95 percent, and 99 percent confidence level. Cornerstone 3.6 (p.
103) illustrates the construction of a confidence interval.
VI. MULTIPLE REGRESSION
Multiple regression can be used to predict a cost function when there is more than one independent
variable. When using a spreadsheet to perform regression analysis, multiple regression is no more
difficult than simple regression. Exhibit 3.15 (p. 106) illustrates the results of running a multiple
regression program in Excel. Cornerstone 3.7 (p. 106) shows how and why to construct a cost equation
using the results of multiple regression.
VII. THE LEARNING CURVE AND NONLINEAR COST BEHAVIOR
The learning curve shows how the labor hours worked per unit decrease as the volume produced
increases. The use of the learning curve enables management to be more accurate in budgeting and in
performance evaluations for processes in which learning occurs. In order to use a learning curve model,
management must estimate a learning rate for a process, usually on the basis of past experience. The
learning curve model takes two common forms: (1) the cumulative average-time learning curve model
and (2) the incremental unit-time learning curve model.
The cumulative average-time learning curve model assumes that the cumulative average time per unit
decreases by a constant percentage, or learning rate, each time the cumulative quantity of units produced
doubles. Cornerstone 3.8 (p. 109) shows how to calculate the amount of time needed for producing
successive units given the learning rate and direct labor hours for the first unit. Then, Exhibit 3.16 (p.
111) displays an Excel screenshot of the results for the cumulative average-time learning model. Exhibit
3.17 (p. 112) shows the graph of both the cumulative average time per unit (the bottom line) and the
cumulative total hours required (top line).
The incremental unit-time learning curve model assumes that the time necessary for production decreases
by a constant percentage each time the cumulative quantity of units produced doubles.
VIII. MANAGERIAL JUDGMENT
Managerial judgment is a simple approach to classifying costs as variable or fixed. When managers have
a thorough understanding of the firm and its cost patterns, this method can give good results. If the
manager has poor judgment, errors will occur. With regard to using judgment, the manager may want to:
(1) consider past experience, (2) confirm results with operating personnel, and (3) use common sense to
confirm statistical studies.
IX. INFORMATION ABOUT EXERCISES, PROBLEMS, AND CASES
Exercises and problems are described below and on the following page according to coverage of content,
learning objective(s), and level of difficulty. The time required to solve the problems is roughly
proportional to the level of difficulty.
In general, basic exercises/problems are fairly simple and straightforward. The text material is relatively
brief; only one or two concepts are covered. Basic exercises and problems should take about 15 to 20
minutes each.
Moderate exercises/problems may take longer and involve more concepts. These problems may have a
“twist” and require more thought. Moderate exercises and problems may take 20 to 40 minutes each.
Challenging problems are more comprehensive and may cover more concepts. The text material is
relatively longer and may include some ambiguity. Challenging problems may take 60 to 90 minutes
each.
Cornerstone
Exercise (CS)/
Exercise/
Problem/Case
Topic
Learning
Objective
Degree of
Difficulty
CS 3.1
Mixed Costs and Cost Formula
LO 1
Basic
CS 3.2
Activity Availability, Capacity Used, Unused Capacity
LO 2
Basic
CS 3.3
Account Analysis to Determine Cost Behavior
LO 3
Basic
CS 3.4
High-Low Method to Determine Fixed Cost and
Variable Rate
LO 4
Basic
CS 3.5
Using Regression Results to Construct and Apply a
Cost Formula
LO 4
Basic
CS 3.6
Constructing a Confidence Interval Using Regression
Results
LO 5
Basic
CS 3.7
Using Multiple Regression Results to Construct and
Apply a Cost Formula
LO 6
Basic
CS 3.8
Cumulative Average-Time Learning Curve
LO 7
Basic
3.9
Variable, Fixed, and Mixed Costs
LO 1
Basic
3.10
Cost Behavior
LO 1
Basic
3.11
Types of Costs
LO 1
Basic
3.12
Resource Usage Model and Cost Behavior
LO 2
Basic
3.13
Resource Usage and Supply, Activity Rates, Service
Organization
LO 2
Basic
3.14
Step Costs, Relevant Range
LO 1, 2
Basic
3.15
Account Analysis Method
LO 3
Basic
3.16
Account Analysis Method
LO 3
Basic
3.17
Scattergraph Method, High-Low Method
LO 4
Basic
3.18
Method of Least Squares, Goodness of Fit
LO 4, 5
Moderate
3.19
High-Low Method, Cost Formulas
LO 4
Moderate
3.20
Method of Least Squares, Evaluation of Cost Equation
LO 4, 5
Moderate
3.21
Multiple Regression
LO 6
Moderate
3.22
Multiple Regression
LO 6
Moderate
3.23
Learning Curve
LO 7
Moderate
3.24
Learning Curve
LO 7
Moderate
3.25
Cost Behavior Patterns
LO 1, 2
Moderate
3.26
CPA-Type Exercise
LO1
Basic
3.27
CPA-Type Exercise
LO1
Basic
3.28
CPA-Type Exercise
LO6
Basic
3.29
CPA-Type Exercise
LO1
Basic
3.30
CPA-Type Exercise
LO1
Basic
3.31
Cost Behavior, Resource Usage, Excess Capacity
LO 1, 2
Moderate
3.32
Cost Behavior, High-Low Method, Pricing Decision
LO 1, 4
Moderate
3.33
High-Low Method, Method of Least Squares,
Correlation, Confidence Interval
LO 2, 4, 5
Moderate
3.34
Cost Formulas, Single and Multiple Activity Drivers,
Coefficient of Correlation
LO 1, 4, 5, 6
Moderate
3.35
Scatterplot, High-Low Method, Regression
LO 4, 5, 6
Moderate
3.36
Method of Least Squares
LO 1, 4, 5, 6
Moderate
3.37
High-Low Method, Scatterplot, Regression
LO 2, 4, 5, 6
Moderate
3.38
Comparison of Regression Equations
LO 1, 4, 5, 6
Challenging
3.39
Multiple Regression, Confidence Intervals, Reliability
LO 2, 5, 6
Challenging
of Cost Formulas
3.40
Simple and Multiple Regression, Evaluating Reliability
of an Equation
LO 2, 4, 5
Challenging
3.41
Learning Curve
LO 7
Moderate
3.42
Learning Curve
LO 7
Moderate
3.43
Cyber Research Case
LO 7
Challenging
LIST OF ILLUSTRATIONS
Illustration
Topic
Exhibit 3.1
Fixed Cost Behavior
Exhibit 3.2
Variable Cost Behavior
Exhibit 3.3
Nonlinearity of Variable Costs
Exhibit 3.4
Relevant Range for Variable Costs
Exhibit 3.5
Mixed Cost Behavior
Exhibit 3.6
Step-Cost Function
Exhibit 3.7
Step-Fixed Costs
Exhibit 3.8
Scattergraph for Anderson Company’s Materials Handling Costs
Exhibit 3.9
Scattergraphs for Various Cost Behavior Patterns
Exhibit 3.10
Deviations of Data from a Line
Exhibit 3.11
Spreadsheet Data for Anderson Company’s Materials Handling Cost
Exhibit 3.12
Regression Results for Anderson Company’s Materials Handling Cost
Exhibit 3.13
Correlation Illustrated
Exhibit 3.14
Table of Selected Values: t Distribution
Exhibit 3.15
Multiple Regression Results for Anderson Company’s Materials Handling Cost
Exhibit 3.16
Spreadsheet for Cumulative Average-Time Learning Model
Exhibit 3.17
Graph of Cumulative Total Hours Required and the Cumulative Average Time per
Unit