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Chapter 5
Cost Behavior: Analysis and Use
Learning Objectives
LO1.
LO2.
LO3.
LO4.
LO5.
Understand how fixed and variable costs behave and how to use them to predict costs.
Use a scattergraph plot to diagnose cost behavior.
Analyze a mixed cost using the high-low method.
Prepare an income statement using the contribution format.
(Appendix 5A) Analyze a mixed cost using the least-squares regression method.
New in this Edition
• Many new In Business boxes have been added.
• The end-of-chapter materials have been expanded by adding several new shorter exercises.
Chapter Overview
A. Types of Cost Behavior Patterns. (Exercises 5-1, 5-6, 5-7, 5-8, 5-11, and 5-12.) At
least three cost behavior patterns—variable, fixed, and mixed—are found in most organizations.
Of course, many other types of cost behavior patterns exist, but these three patterns are fairly
common and the mixed cost model can be used to provide approximations to more complex cost
behavior patterns within a relevant range. It is important for managers to understand the
behavior of each type of cost.
1.
Variable Costs. The total amount of a variable cost varies in direct proportion to changes
in the activity level. When expressed on a per unit basis, variable costs are constant.
Examples of costs that are normally variable with respect to output volume are listed in
Exhibit 5-2. Be careful to point out to students that some of these costs may be fixed in
some organizations. This is particularly true of direct labor and other employee wages and
salaries that may be effectively fixed due to labor laws in a country, custom, labor
contracts, or the organization’s personnel policies. Exhibit 5-8 in the text points out that in
practice there is a wide variation in how some of these costs are classified by individual
companies.
a. Activity base (cost driver). For a cost to be variable, it must be variable with respect to
some activity base. An activity base is a measure of whatever causes the incurrence of
a variable cost. Some of the most common activity bases are machine-hours, units
produced, and units sold. A measure of activity should be used to allocate a cost for
decision-making purposes only if it actually causes the cost.
b. True variable and step-variable costs. Some variable costs, such as direct materials,
vary in direct proportion to the level of activity. These costs are called true variable
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costs. A cost that is obtainable only in large chunks and that increases or decreases in
response to fairly wide changes in the activity level is known as a step-variable cost.
For example, direct labor may be a step-variable cost when workers are only hired on a
full-time basis. The difference between a true variable and a step-variable cost is
illustrated in Exhibit 5-3 in the text.
c. In reality, many costs are curvilinear. Most frequently, costs increase less than
proportionately with activity. Nevertheless, within any given narrow band of activity
even a curvilinear cost function is approximately linear. This narrow band of activity
within which a particular straight line is a reasonable approximation to the true
underlying cost function is called its relevant range.
• Thus, within the relevant range, variable cost per unit can be assumed to be constant.
Exhibit 5-4 in the text illustrates a curvilinear cost and the notion of the relevant
range.
• The notion of the relevant range often causes confusion. Some individuals refer to
the relevant range as the range of activity within which the company expects to
operate or has operated in the recent past. That is not what we mean by the relevant
range. The relevant range, as we use the term, is the range of activity within which a
particular straight line provides a reasonable approximation to the real underlying
cost function.
2.
Fixed Costs. A fixed cost remains constant in total dollar amount within the relevant range.
Since fixed costs remain constant in total, the amount of cost computed on a per unit basis
becomes smaller as the number of units produced increases. Care must be exercised in
interpreting fixed costs that have been expressed on a per unit basis; they should not be
misinterpreted as variable costs.
a. For planning purposes, fixed costs can be viewed as either committed or discretionary.
• Committed fixed costs. Committed fixed costs relate to investment in buildings,
equipment, and the basic organizational structure of a company. Committed fixed
costs are long-term and can’t be significantly reduced even for a short period of time
without seriously impairing long-run goals.
• Discretionary fixed costs. Discretionary fixed costs are those that management
adjusts periodically. Examples of discretionary fixed costs include advertising,
research, and management development programs. The planning horizon for
discretionary fixed costs is fairly short—usually a single year. Management may be
able to adjust these fixed costs as circumstances change.
b. The relevant range for a fixed cost is that range of activity over which total fixed cost
does not change. Exhibit 5-6 in the text illustrates this idea.
3.
Mixed Costs. A mixed cost contains both variable and fixed cost elements. Many costs are
mixed and can be expressed in terms of the cost formula Y = a + bX, where Y is the total
estimated cost, a is the estimated total fixed cost, b is the estimated variable cost per unit of
activity, and X is the amount of activity. Even when the underlying cost is not linear, this
formula can provide a reasonable approximation to the underlying cost function within the
relevant range.
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4.
Classification of costs. A cost that is considered variable in one organization may be
considered fixed in another due, for example, to differing employment policies. Exhibit 5-8
in the text shows that there is a lot of variation in how companies classify costs in terms of
behavior.
B. Analysis of Mixed Costs. For planning and control purposes, mixed costs should be
broken down into variable and fixed components. A number of methods can be used to analyze
mixed costs. Account analysis and the engineering approach are mentioned briefly in this
chapter and are covered in more detail in later chapters. This chapter discusses in more depth
three techniques for analyzing past records of cost and activity—the scattergraph method, the
high-low method, and least-squares regression.
1.
The Scattergraph Method. (Exercises 5-2, 5-9, and 5-10.)
a. The data should be plotted no matter what method is ultimately used to estimate fixed
and variable costs. A graph is constructed with cost on the vertical axis and activity on
the horizontal axis. Costs at various levels of activity are then plotted on the graph.
This plot will often provide important insights concerning the underlying relationship
and can help in identifying nonlinearities and outliers (unusual points) that should be
ignored.
b. While this is not ordinarily done in practice, a line can be fitted to the plotted points by
eye with a straightedge. The line should be placed so that approximately equal numbers
of points fall above and below it. While not strictly necessary, in the text and in
problems we always draw the line through one of the points to simplify calculations.
This line can then be used to derive what we call “quick-and-dirty” estimates of the
fixed and variable costs. The fixed cost can be estimated by the vertical intercept. The
variable cost per unit can be estimated by computing the slope of the line.
2.
The High-Low Method. (Exercises 5-2, 5-4, 5-7, 5-8, 5-9, and 5-11.) The high-low
method of analyzing mixed costs focuses exclusively on the high and low levels of activity.
The difference in cost observed at these two extremes is divided by the change in activity to
estimate the variable cost per unit of activity.
A major defect of the high-low method is that it utilizes only two points and ignores all of
the other data. Generally, two points are not enough to produce accurate results. Moreover,
the periods in which the high and low activity levels occur are often not typical of most
periods.
3.
The Least-Squares Regression Method. (Exercises 5-3 and 5-12.) Using mathematical
formulas, the least-squares regression method fits a regression line that minimizes the sum
of the squared errors. Exhibit 5-13 can be used as a basis for discussing the theory of leastsquares regression.
a. We don’t go into the details of the computation of the least-squares regression
estimates since computer software is widely used for performing this chore. The
appendix to the chapter shows how to use Excel to do the necessary calculations.
b. In addition to estimates of the slope (variable cost per unit) and the intercept (total
fixed cost), least-squares regression software can produce a variety of informative
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statistics. One of the most informative is the R2, which is a measure of the goodness of
fit of the regression line. It tells us the percentage of the variation in the dependent
variable (cost) that is explained by variation in the independent variable (activity). We
do not show in the text how the R2 is computed, but you may want to discuss its
interpretation with students.
c. Multiple regression analysis should be used when the cost is caused by more than one
factor.
C. The Contribution Format. (Exercises 5-5 and 5-6.) Two major approaches can be used
to prepare an income statement. The difference between these two approaches centers on the
way in which costs are organized.
1.
The Traditional Approach. The traditional approach to the income statement organizes
data in a functional format, based on the functions of production, administration, and sales.
The emphasis is on the purposes for which the costs were incurred. No attempt is made to
identify the behavior of costs included under each functional heading. This approach is
used to prepare income statements for external reporting purposes.
2.
The Contribution Approach. The contribution approach to the income statement
organizes costs by behavior, rather than by function.
a. The contribution approach separates costs into fixed and variable categories. Variable
expenses are deducted to obtain the contribution margin. Fixed expenses are then
deducted from the contribution margin to obtain net operating income.
b. The contribution approach to the income statement makes it much easier for managers
to understand the relations between volume and expenses, and volume and profits.
Variable and fixed costs are not lumped together. Since planning and decision-making
often involve changes in the level of activity, contribution income statements can be
very useful. Unfortunately, the contribution approach is seldom used in practice.
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Assignment Materials
Assignment
Exercise 5-1
Exercise 5-2
Exercise 5-3
Exercise 5-4
Exercise 5-5
Exercise 5-6
Exercise 5-7
Exercise 5-8
Exercise 5-9
Exercise 5-10
Exercise 5-11
Exercise 5-12
Problem 5-13
Problem 5-14
Problem 5-15
Problem 5-16
Problem 5-17
Problem 5-18
Problem 5-19
Problem 5-20
Problem 5-21
Problem 5-22
Problem 5-23
Problem 5-24
Case 5-25
Case 5-26
Case 5-27
Case 5-28
Level of
Topic
Difficulty
Fixed and variable cost behavior
Basic
High-low method; scattergraph analysis............................................
Basic
(Appendix 5A) Least-squares regression ...........................................
Basic
High-low method ...............................................................................
Basic
Contribution format income statement ..............................................
Basic
Cost behavior; contribution format income statement .......................
Basic
High-low method; predicting cost .....................................................
Basic
High-low method; predicting cost ....................................................
Basic
Scattergraph analysis; high-low method ............................................
Basic
Scattergraph analysis .........................................................................
Basic
Cost behavior; high-low method........................................................
Basic
(Appendix 5A) Least-squares regression ...........................................
Basic
Cost behavior; high-low method; contribution income
statement .......................................................................................
Basic
Contribution format versus traditional income statement ..................
Basic
(Appendix 5A) Least-squares regression; scattergraph; cost
behavior .......................................................................................
Basic
Identifying cost behavior patterns......................................................
Medium
High-low and scattergraph analysis ...................................................
Medium
(Appendix 5A) Least-squares regression method ..............................
Medium
Scattergraph analysis .........................................................................
Medium
(Appendix 5A) Least-squares regression method ..............................
Medium
(Appendix 5A) Least-squares regression analysis;
contribution income statement .....................................................
Medium
High-low method; cost of goods manufactured .................................
Difficult
High-low method; predicting cost .....................................................
Difficult
High-low method; predicting cost .....................................................
Difficult
(Appendix 5A) Analysis of mixed costs, job-cost system,
and activity-based costing .............................................................
Difficult
Scattergraph analysis; selection of an activity base ...........................
Medium
Analysis of mixed costs in a pricing decision....................................
Difficult
(Appendix 5A) Mixed cost analysis by three methods ......................
Difficult
Suggested
Time
15 min.
45 min.
30 min.
20 min.
20 min.
20 min.
30 min.
20 min.
30 min.
30 min.
20 min.
30 min.
45 min.
45 min.
45 min.
30 min.
45 min.
30 min.
30 min.
30 min.
45 min.
45 min.
45 min.
45 min.
90 min.
45 min.
90 min.
90 min.
Essential Problems: Problem 5-13, Problem 5-17 or Problem 5-19, Problem 5-23 or Problem 524
Supplementary Problems: Problem 5-14, Problem 5-16, Problem 5-22, Case 5-25, Case 5-26,
Case 5-27, Case 5-28
Appendix 5A Essential Problems: Problem 5-15
Appendix 5A Supplementary Problems: Problem 5-18, Problem 5-20, Problem 5-21
Linked problems and exercises:
Exercise 5-3 should be assigned in conjunction with Exercise 5-2
Exercise 5-9 should be assigned in conjunction with Exercise 5-8
Problem 5-18 should be assigned in conjunction with Problem 5-17
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Chapter 5
Lecture Notes
Helpful Hint: The McGraw-Hill/Irwin Managerial/Cost
Accounting video library does not contain a segment
that relates to Chapter 5.
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I.
Chapter theme: 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.
Types of cost behavior patterns
A. Variable costs
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i. A variable cost is a cost whose total dollar amount
varies in direct proportion to changes in the
activity level.
1. 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.
a. 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
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miles driven, machine hours, or labor
hours.
2. 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.
ii. Variable costs remain constant if expressed on a
per unit basis.
1. Referring to the telephone example, the cost
per minute talked is constant (e.g., 10 cents
per minute)
iii. Extent of variable costs
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1. The proportion of variable costs differs
across organizations. For example:
a. A public utility like Florida Power
and Light, with large investments in
equipment, will tend to have fewer
variable costs.
b. A manufacturing company like
Black and Decker will often have
many variable costs associated with
the manufacture and distribution of
its products to customers.
c. A merchandising company like
Wal-Mart will usually have a high
proportion of variable costs such as
the cost of merchandise purchased
for resale.
d. Some service companies, such as
restaurants, have a high proportion of
variable costs due to their raw
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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.
iv. Common examples of variable costs
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1. Merchandising companies  cost of goods
sold
2. Manufacturing companies  direct materials,
direct labor, and variable overhead.
3. Merchandising and manufacturing
companies  commissions, shipping costs,
and clerical costs such as invoicing.
4. Service companies  supplies, travel, and
clerical.
Helpful Hint: Students tend to assume that a certain
type of cost is always variable or fixed. They should
examine the facts of each situation before deciding
whether a cost is fixed or variable. For example, a
company’s employment policy may determine whether
direct labor costs are fixed or variable with respect to
volume of output.
B. True variable versus step-variable costs
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i. True variable costs  the amount used during the
period varies in direct proportion to the activity
level.
1. The long distance phone bill was one
example of a true variable cost.
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2. Direct material is another example of a cost
that behaves in a true variable pattern.
a. Direct materials purchased but not
used can be stored and carried
forward to the next period as
inventory.
ii. Step-variable costs  A resource that is obtainable
only in large chunks and whose costs change only
in response to fairly wide changes in activity.
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1. For example, maintenance workers are often
considered to be a variable cost, but this
labor cost does not behave as a true variable
cost.
a. Small changes in the level of
production are not likely to have any
effect on the number of maintenance
workers employed.
b. Only fairly wide changes in the
activity level will cause a change in
the number of maintenance workers
employed.
i. Maintenance workers are
obtainable only in large chunks
of a whole person who is capable
of working approximately 2,000
hours a year.
“In Business Insights”
Step-variable costs can change for reasons that have
nothing to do with changes in the activity level. For
example:
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“Coping with the Fallout from September 11” (page
186)
 Filterfresh is a company that services coffee
machines located in commercial offices.
 Post September 11, heightened security clearance
measures at customer locations have added about
one hour per day to each deliveryman’s route.
 This has required Filterfresh to hire 24 more
delivery people to do the same work it did prior
to September 11.
C. The linearity assumption and the relevant range
i. Economists correctly point out that many costs that
accountants classify as variable costs actually
behave in a curvilinear fashion.
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ii. Nonetheless, within a narrow band of activity
known as the relevant range, a curvilinear cost can
be satisfactorily approximated by a straight line.
1. The relevant range is that range of activity
within which the assumptions made about
cost behavior are valid.
Helpful Hint: Slide 13 can be tied in with economics
courses students have taken. Ask what happens to
average costs when the cost curve bends downward and
what economists call this part of the curve. Average
costs are falling and this is roughly equivalent to what
economists call “increasing returns to scale.” You can
repeat the same question for the part of the curve that
bends upward.
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D. Fixed costs
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i. A fixed cost is a cost whose total dollar amount
remains constant as the activity level changes.
1. For example, your monthly basic telephone
bill is probably fixed and does not change
when you make more local calls.
ii. Average fixed costs per unit decrease as the
activity level increases.
1. For example, the fixed cost per local call
decreases as more local calls are made.
E. Types of fixed costs
i. Committed fixed costs
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1. These costs are long-term in nature (i.e.,
greater than one year).
2. These costs cannot be significantly
reduced even for short periods of time
without seriously impairing the profitability
or long-run goals of the organization.
a. Examples of committed-fixed costs
include depreciation on buildings and
equipment, and real estate taxes.
“In Business Insights”
Committed fixed costs may be more flexible than they
would appear at first glance. For example:
“Sharing Office Space to Reduce Committed Fixed
Costs” (page 191)
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 Doctors in private practice have been under
enormous pressure in recent years to cut costs.
 Dr. Edward Betz of California reduced the
committed fixed costs of maintaining his office by
letting a urologist use the office on Wednesday
afternoons and Friday mornings for $1,500 per
month.
 Dr. Betz uses these times to work on paperwork at
home. He also makes up for lost time by treating
patients on Saturdays.
ii. Discretionary fixed costs
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1. These costs usually arise from annual
decisions by management to spend in
certain fixed cost areas.
2. These costs can be cut for short periods of
time with minimal damage to the long-run
goals of the organization.
a. Examples of discretionary fixed costs
include advertising and research and
development.
3. A cost may be discretionary or committed
depending upon management’s strategy.
a. 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.
“In Business Insights”
The extent of a company’s discretionary fixed costs is a
function of management choices. For example:
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“Cost Structure: A Management Choice” (page 184)
 Nucor Steel is the most successful U.S. steel
company of recent years due in large part to its
cost-efficiency.
 Nucor treats all employees alike. There are no
management dining rooms, company yachts or
airplanes, no first-class travel for executives, and
no support staff to pamper the upper echelons.
 All of these management actions serve to lower
discretionary fixed costs for Nucor.
 In addition, Nucor relies upon fewer layers of
management. In fact, although Nucor is the
largest steel company in the U.S., its headquarters
employs only 20 people.
iii. The trend toward fixed costs
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1. The trend in many industries is toward
greater fixed costs relative to variable
costs. For example:
a. H&R Block employees used to fill
out tax returns for customers by
hand. Now, computer software is
used to complete tax returns.
b. Safeway and Kroger employees
used to key-in prices by hand on cash
registers. Now, barcode readers enter
price and other product information
automatically.
c. As machines take over many
mundane tasks previously performed
by humans, “knowledge workers”
are demanded for their minds rather
than their muscles.
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i. Knowledge workers tend to be
salaried, highly-trained and
difficult to replace; consequently,
the cost of compensating these
valued employees in relatively
fixed rather than variable.
“In Business Insights”
By making investments in technology many internet
companies have created radically different cost
structures from their “bricks and mortar” counterparts.
For example:
“Selling Online” (page 185)
 Onsale, an internet auctioneer of discontinued
computers and House of Fabrics, a traditional
retailer, each has roughly the same revenue of
about $250 million per year.
 However, House of Fabrics, with 5,500
employees, has revenue per employee of about
$90,000. At Onsale, with only 200 employees, the
figure is $1.18 million per employee.
 Onsale relies upon investments in technology to
reduce its labor cost.
iv. Is labor a variable or a fixed cost?
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1. The behavior of wage and salary costs can
differ across countries, depending on labor
regulations, labor contracts, and custom.
For example:
a. In France, Germany, China, and
Japan management has little
flexibility in adjusting the size of the
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labor force; hence, labor costs are
more fixed in nature.
“In Business Insights”
Survey research supports the assertion that labor costs
are viewed as more fixed in nature in certain countries.
For example:
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“Cost Behavior in the U.S. and Japan” (page 195)
 A total of 257 American and 40 Japanese
manufacturing companies responded to a
questionnaire concerning their management
practices.
 The findings indicate that approximately 40% of
the Japanese companies surveyed viewed
production labor as a fixed cost, while
approximately 10% of U.S. companies surveyed
viewed production labor as a fixed cost.
b. In the United States and the United
Kingdom, management typically has
much greater latitude; hence, labor
costs are more variable in nature.
“In Business Insights”
Regulatory requirements can influence the fixed versus
variable nature of labor costs in American companies.
For example:
“The Regulatory Burden” (page 193)
 Peter Drucker claims that “the driving force
behind the steady growth of temps…is the
growing burden of rules and regulations for
employers.”
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 According to the Small Business Administration,
the owner of a small business spends up to a
quarter of his or her time on employment-related
paperwork. Furthermore, the cost of complying
with government regulations is over $5,000 per
employee per year.
 This motivates small businesses to rely upon
temporary workers, thus converting labor from a
fixed cost to a variable cost.
2. 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.
“In Business Insights”
Managers can view labor costs differently depending upon
their strategy. For example:
“A Twist on Fixed and Variable Costs” (page 191)
 Mission Controls designs and installs automation
systems for food and beverage manufacturers.
 When sales drop, the founders of this company slash
their own salaries rather than laying off workers.
 This makes their own salaries somewhat variable,
while the wages and salaries of workers act more
like fixed costs. The payoff is a loyal and committed
work force.
“Labor at Southwest Airlines” (page 192)
 Southwest Airlines is the most profitable airline in
the United States.
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 Prior to stepping down as President and CEO of the
airline in 2001, Herb Kelleher wrote “The thing that
would disturb me the most to see after I’m no longer
CEO is layoffs at Southwest. Nothing kills your
company’s culture like layoffs.”
 Because of Southwest Airline’s commitment to its
employees, all wages and salaries are basically
committed fixed costs.
F. Fixed costs and the relevant range
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i. The relevant range of activity for a fixed cost is the
range of activity over which the graph of the cost is
flat.
1. For example, assume office space is
available at a rental rate of $30,000 per year
in increments of 1,000 square feet.
2. Fixed costs would increase in a step fashion
at a rate of $30,000 for each additional 1,000
square feet.
ii. 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.
1. Step-variable costs can often be adjusted
quickly as conditions change, whereas fixed
costs cannot be changed easily.
2. The width of the steps for fixed costs is
wider than the width of the steps for stepvariable costs.
a. For example, a step-variable cost
such as maintenance workers may
have steps with a width of 40 hours a
week.
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b. However, fixed costs may have steps
that have a width of thousands or tens
of thousands of hours of activity.
Helpful Hint: Discuss with students that over a given
level of production, certain costs, such as custodial
salaries, would remain fixed. However, if activity
increases to the point where a second shift is needed,
custodial salaries would need to increase since activity
is outside the relevant range.
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Quick Check  cost behavior patterns
G. Mixed costs (also called semivariable costs)
i. A mixed cost contains both variable and fixed cost
elements.
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1. For example, utility bills often contain fixed
and variable cost components.
a. 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.
b. The variable portion of the bill varies
in direct proportion to the
consumption of kilowatt hours.
ii. 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.
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II.
1. The equation is Y = a + bX
a. Y = The total mixed cost.
b. a = The total fixed cost (the vertical
intercept of the line).
c. b = The variable cost per unit of
activity (the slope of the line).
d. X = The level of activity.
iii. For example, if your fixed monthly utility charge is
$40, your variable cost is .03 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.
The analysis of mixed costs
A. Account analysis and the engineering approach
i. In account analysis, each account under
consideration is classified as variable or fixed based
on the analyst’s prior knowledge about how costs
behave.
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1. 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.
ii. The engineering approach classifies costs based
upon an industrial engineer’s evaluation of
production methods, material specifications, labor
requirements, equipment usage, power
consumption, as so on.
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1. This approach is particularly useful when no
past experience is available concerning
activity and costs.
B. The scattergraph plot (also called the quick-and-dirty
method)
i. The first step when using this method to analyze a
mixed cost is to plot the data on a scattergraph.
1. The cost, which is known as the dependent
variable, is plotted on the Y axis.
2. The activity, which is known as the
independent variable, is plotted on the X
axis.
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ii. 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.
1. 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.
31
iii. 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.
301
32
33
35
302
34
iv. The fourth step is to identify the Y intercept.
1. This intercept represents the estimated fixed
cost portion of the mixed cost ($10,000 in
this example).
32
33
v. The fifth step is to estimate the variable cost per
unit of the activity.
1. Select one point on the scattergraph that
intersects the straight line.
2. Determine the total cost and the total
activity level at the chosen point.
3. Subtract the fixed costs from the total costs
to arrive at the total variable costs for the
chosen activity level.
4. Divide the total variable costs by the activity
level at the chosen point. This is the variable
cost per unit of activity.
5. Construct an equation that can be used to
estimate total costs at any activity level.
C. The high-low method
34
i. 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 following information.
ii. The first step is to choose the data points
pertaining to the highest and lowest activity levels
(high = 800 units; low = 500 units).
35
1. Notice, this method relies upon two data
points to estimate the fixed and variable
303
35
36
304
37
portions of a mixed cost, as opposed to one
data point with the scattergraph method.
iii. The second step is to determine the total costs
associated with the two chosen points (high =
$9,800; low = $7,400).
35
Helpful Hint: Emphasize that the high and low points
are identified by the level of activity and not by the level
of the cost.
iv. 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).
1. The quotient represents an estimate of
variable cost per unit of activity ($8.00 per
unit).
v. 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).
36
37
1. 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).
vi. 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).
305
38
39
40
41
42
43
306
38-41
Quick Check  the high-low method
D. The least-squares regression method
i. This method can be used to analyze mixed costs if
a scattergraph plot reveals an approximately linear
relationship between the X and Y variables.
42
ii. 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.
iii. 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.
iv. 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.
43
1. The output from the regression analysis can
be used to create an equation that enables
you to estimate total costs at any activity
level.
307
43
44
308
43
v. The key statistic to look at when evaluating
regression results is called R2, which is a measure
of “goodness of fit.”
1. The R2 quantifies the percentage of the
variation in the dependent variable that is
explained by variation in the independent
variable. The R2 varies from 0% to 100%,
and the higher the percentage the better.
44
vi. This example assumes that a single factor drives
the variable cost component of a mixed cost. If
more than one factor drives the variable cost
component, multiple regression can be used to
perform the mixed cost analysis.
“In Business Insights”
Least-squares regression can be used by companies to
estimate the fixed and variable components of mixed costs.
For example:
“Managing Power Consumption” (page 205)
 The Tata Iron Steel Company is one of the largest
companies in India.
 Management used simple least-squares regression to
estimate the fixed and variable components of its
power consumption.
 Total power consumption was the dependent
variable and tons of steel processed was the
independent variable.
 The regression model estimated the fixed power
consumption per month and the variable power cost
per ton of steel processed.
309
45
46
48
49
310
47
E. Comparing results from the three methods
45
III.
i. 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.
The contribution approach income statement
46
A. The contribution approach provides an income
statement format geared directly to cost behavior,
which has been the focus of discussion in this chapter.
47
i. This approach separates costs into fixed and
variable categories. Sales  variable costs =
contribution margin. The contribution margin 
fixed costs = net operating income.
ii. This approach is used as an internal planning and
decision making tool. For example, this approach
is useful for:
48
49
1. Cost-volume-profit analysis (chapter 6).
2. Budgeting (chapter 9).
3. Segmented reporting of profit data (chapter
12).
4. Special decisions such as pricing and make
or buy analysis (chapter 13).
iii. The contribution approach differs from the
traditional approach illustrated in chapter 2.
311
49
50
52
312
51
49
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.
2. The traditional approach is used primarily
for external reporting purposes.
Helpful Hint: The income statement from the annual
report of a well-known local manufacturing firm can be
used to illustrate the functional income statement. Ask
if the various expense categories on the income
statement contain both fixed and variable costs. Also
ask how to estimate the increase in profit that would
result from a 4% increase in sales using the functional
statement. There is no way to do this with reasonable
accuracy, since there is no way to tell on a functional
income statement what costs would increase.
IV. Appendix 5A: least-squares regression using Microsoft
Excel (Slide #50 is a title slide)
A. The data set
51
52
i. Assume that you have the following data set and
that you wish to use Microsoft Excel to estimate the
variable and fixed cost components of your total
meals cost.
ii. You will need to calculate three key pieces of
information: the estimated variable cost per unit
(called the slope of the line), the estimated fixed
cost (called the intercept), and the R2.
313
52
53
54
55
56
57
58
59
60
314
52
1. To get these three pieces of information you
will need three Excel functions, namely
LINEST, INTERCEPT, and RSQ.
53
iii. The first step within Excel is to place your cursor in
cell F4 and press the = key. Click on the pull down
menu and scroll down to “More Functions.”
54
iv. When the function box opens, click on
“Statistical” and then on “LINEST.”
55
v. Enter the cell range for the cost amounts in the
“Known_y’s” box. Enter the cell range for the
quantity amounts in the “Known_x’s” box.
56
57
58
59
60
1. The slope, or estimated variable cost per
unit, is identified on the screen as shown.
Click “OK” to put this value on your
spreadsheet.
vi. Return to the function box and click on
“Statistical” and then on “INTERCEPT.”
1. The estimated fixed cost is identified on the
screen as shown.
vii. Return to the function box and click on
“Statistical” and then on “RSQ.”
1. The estimated R2 for your estimated cost
function is identified on the screen as
shown.
315
Chapter 5
Transparency Masters
316
TM 5-1
AGENDA: COST BEHAVIOR
1.
Variable cost behavior.
2.
Types of fixed costs: committed and discretionary.
3.
Behavior of fixed costs in total and on a unit basis.
4.
Mixed costs (combination of fixed and variable).
5.
Scattergraph plot of a mixed cost.
6.
High-low method of mixed cost analysis.
7.
Least-squares regression method of mixed cost analysis.
8.
Contribution income statement.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-2
VARIABLE COST BEHAVIOR
Many costs can be described as variable, fixed, or mixed.
A variable cost changes in total in proportion to changes in
activity; a variable cost is constant on a per-unit basis.
EXAMPLE: Each bicycle requires one bicycle chain costing $8.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-3
EXAMPLES OF COSTS THAT ARE NORMALLY VARIABLE WITH
RESPECT TO OUTPUT VOLUME
Merchandising company
Costs of goods (merchandise) sold
Manufacturing company
Manufacturing costs:
Prime costs:
Direct materials
Direct labor*
Variable portion of manufacturing overhead:
Indirect materials
Lubricants
Supplies
Power
Both merchandising and manufacturing companies
Selling, general, and administrative costs:
Commissions
Clerical costs, such as invoicing
Shipping costs
Service organizations
Supplies, travel, clerical
*Whether direct labor is fixed or variable will depend on the labor
laws of the country, custom, and the company’s employment
contracts and policies.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-4
FIXED COST BEHAVIOR
A fixed cost remains constant in total amount throughout wide
ranges of activity.
EXAMPLE: Fashion photographer Lori Yang rents studio spaces in
a prestige location for $50,000 a year. She measures her company’s
activity in terms of the number of photo sessions.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-5
FIXED COST BEHAVIOR (cont’d)
A fixed cost varies inversely with activity if expressed on a per unit
basis.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-6
TYPES OF FIXED COSTS
• Committed fixed costs relate to investment in plant, equipment,
and basic administrative structure. It is difficult to reduce these
fixed costs in the short-term. Examples include:
• Depreciation on plant facilities.
• Taxes on real estate.
• Salaries of key operating personnel.
• Discretionary fixed costs arise from annual decisions by
management to spend in certain areas. These costs can often be
reduced in the short-term. Examples include:
• Advertising.
• Research.
• Public relations.
• Management development programs.
TREND TOWARD FIXED COSTS
The trend is toward greater fixed costs relative to variable costs. The
reasons for this trend are:
• Increased automation of business processes.
• Shift from laborers paid by the hour to salaried knowledge
workers.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-7
MIXED COSTS
A mixed (or semi-variable) cost contains elements of both variable
and fixed costs.
Example: Lori Yang leases an automated photo developer for
$2,500 per year plus 2¢ per photo developed.
Equation of a straight line: Y = a + bX
Y = $2,500 + $0.02X
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-8
MIXED COSTS (cont’d)
A cost that is considered fixed in one company might be
considered variable or mixed in another company.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-9
SCATTERGRAPH METHOD
As the first step in the analysis of a mixed cost, the cost and its
activity base should be plotted on a scattergraph. This helps to
quickly diagnose the nature of the relation between the cost and the
activity base.
Example: Piedmont Wholesale Florists has maintained records of the
number of orders and billing costs in each quarter over the past
several years.
Number
Quarter of Orders
Year 1—1st
2nd
3rd
4th
Year 2—1st
2nd
3rd
4th
Year 3—1st
2nd
3rd
1,500
1,900
1,000
1,300
2,800
1,700
2,100
1,100
2,000
2,400
2,300
Billing
Costs
$42,000
$46,000
$37,000
$43,000
$54,000
$47,000
$51,000
$42,000
$48,000
$53,000
$49,000
These data are plotted on the next page, with the activity (number of
orders) on the horizontal X axis and the cost (billing costs) on the
vertical Y axis.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-10
A COMPLETED SCATTERGRAPH
Y
$60,000
Regression Line
Billing Costs
$50,000
$48,000
$40,000
$30,000
$20,000
$10,000
X
$0
0
500
1,000
1,500
2,000
2,500
3,000
Number of Orders
The relation between the number of orders and the billing cost is
approximately linear. (A straight line that seems to reflect this basic
relation was drawn with a ruler on the scattergraph.)
Since a straight line seems to be a reasonable fit to the data, we can
proceed to estimate the variable and fixed elements of the cost using
one of the following three methods.
1) Quick-and-dirty method based on the line in the scattergraph.
2) High-low method.
3) Least-squares regression method.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-11
THE QUICK-AND-DIRTY METHOD
The straight line drawn on the scattergraph can be used to make a
quick-and-dirty estimate of the fixed and variable elements of billing
costs.
Recall that we are trying to estimate the fixed cost, a, and the
variable cost per unit, b, in the linear equation Y= a + bX.
• The vertical intercept, approximately $30,000 in this case, is a
rough estimate of the fixed cost.
• The slope of the straight line is an estimate of the variable cost
per unit
Select a point falling on the line (in this case 2,000 orders):
Total billing cost for 2,000 orders ........
Less fixed cost element (intercept)......
Variable cost element for 2,000 orders
$48,000
30,000
$18,000
Variable cost per unit = $18,000 ÷ 2,000 orders = $9 per order.
Therefore, the cost formula for billing costs is $30,000 per quarter
plus $9 per order or:
Y = $30,000 + $9X,
where X is the number of orders.
Because of the imprecision of this method of estimating the variable
and fixed cost components of a mixed cost, it is seldom used in
practice.
Nevertheless, it is always a good idea to plot the data on a
scattergraph before using the more precise high-low or least-squares
regression methods.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-12
ANALYSIS OF MIXED COSTS: HIGH-LOW METHOD
EXAMPLE: Kohlson Company has incurred the following shipping
costs over the past eight months:
Units
Sold
January ..... 6,000
February ... 5,000
March ....... 7,000
April .......... 9,000
May .......... 8,000
June ......... 10,000
July........... 12,000
August ...... 11,000
Shipping
Cost
$66,000
$65,000
$70,000
$80,000
$76,000
$85,000
$100,000
$87,000
With the high-low method, only the periods in which the lowest
activity and the highest activity occurred are used to estimate the
variable and fixed components of the mixed cost.
High activity level, July .......
Low activity level, February
Change .............................
Variable cost=
Units
Sold
12,000
5,000
7,000
Shipping
Cost
$100,000
65,000
$ 35,000
Change in cost
$35,000
=
=$5 per unit
Change in activity 7,000 units
Fixed cost = Total cost - Variable cost element
= $100,000 - (12,000 units × $5 per unit)
= $40,000
The cost formula for shipping cost is:
Y = $40,000 + $5X
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-13
EVALUATION OF THE HIGH-LOW METHOD
Y
high
level of
activity
Shipping Costs
$100,000
$80,000
low level
of
activity
Variable
Cost
$5/unit
$60,000
$40,000
Fixed
Cost
$40,000
$20,000
X
$0
0
2,000
4,000
6,000
8,000 10,000 12,000
Units Sold
The high-low method suffers from two major defects:
1. It throws away all but two data points.
2. The high and low volume periods are often unusual.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-14
LEAST-SQUARES REGRESSION METHOD
The least-squares regression method for analyzing mixed costs
uses mathematical formulas to determine the regression line that
minimizes the sum of the squared “errors.”
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-15
LEAST-SQUARES REGRESSION (cont’d)
Example: Montrose Hospital operates a cafeteria for employees.
Management would like to know how cafeteria costs are affected by
the number of meals served.
April ...........
May ............
June ...........
July ............
August ........
September ..
Meals
Served
X
4,000
1,000
3,000
5,000
10,000
7,000
Total
Cost
Y
$9,500
$4,000
$8,000
$10,000
$19,500
$14,000
Statistical software or a spreadsheet program can do the
computations required by the least-squares method. The results in
this case are:
Intercept (fixed cost) ...........
Slope (variable cost) ............
R2 ........................................
$2,433
$1.68
0.99
The fixed cost is therefore $2,433 per month and the variable cost is
$1.68 per meal served, or:
Y = $2,433 + $1.68X,
where X is meals served.
R2 is a measure of the goodness of fit of the regression line. In this case, it
indicates that 99% of the variation in cafeteria costs is due to the number of
meals served. This suggests a very good fit.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.
TM 5-16
TRADITIONAL VERSUS CONTRIBUTION INCOME STATEMENT
Traditional Approach
(costs organized by function)
Sales ..............................
Less cost of goods sold* .
Gross margin ..................
Less operating expenses:
Selling* .......................
Administrative* ............
Net operating income ......
Contribution Approach
(costs organized by behavior)
$60,000
34,000
26,000
$15,000
6,000
21,000
$ 5,000
Sales
Less variable expenses:
Variable production ..... $12,000
Variable selling ............
3,000
Variable administrative
1,000
Contribution margin .......
Less fixed expenses:
Fixed production .........
22,000
Fixed selling ................
12,000
Fixed administrative.....
5,000
Net operating income .....
$60,000
16,000
44,000
39,000
$ 5,000
* Contains both variable and fixed elements since this is the income statement for a manufacturing
company. If this were a merchandising company, then the cost of goods sold would be entirely variable.
© The McGraw-Hill Companies, Inc., 2006. All rights reserved.