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Chapter 3:
Cost Behavior
Cornerstones of Managerial Accounting, 4e
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Learning Objectives
1. Explain the meaning of cost behavior, and define and
describe fixed and variable costs.
2. Define and describe mixed and step costs.
3. Separate mixed costs into their fixed and variable
components using the high-low method, the scattergraph
method, and the method of least squares.
4. (Appendix 3A) Use a personal computer spreadsheet
program to perform the method of least squares.
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1
Basics of Cost Behavior
► Cost behavior is the foundation upon which managerial
accounting is built.
► Cost behavior is the general term for describing whether a
cost changes when the level of output changes.
► Costs can be variable, fixed, or mixed.
► A cost that does not change in total as output changes is a
fixed cost.
► A variable cost, on the other hand, increases in total with an
increase in output and decreases in total with a decrease in
output.
► Knowing how costs change as output changes is essential to
planning, controlling, and decision making.
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1
Measures of Output and the
Relevant Range
► Fixed and variable costs have meaning
only when related to some output
measure.
► A cost driver is a causal factor that
measures the output of the activity
that leads (or causes) costs to change.
► Identifying and managing drivers helps
managers better predict and control
costs.
► For example, weather is a significant
driver in the airline industry.
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1
Relevant Range and Cost
Relationships
► The relevant range is the range of output over which the
assumed cost relationship is valid for the normal operations
of a firm.
► The relevant range limits the cost relationship to the range of
operations that the firm normally expects to occur.
As this graph
shows, the
concept of the
relevant range
allows
managerial
accountants to
assume a
linear cost
relationship.
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1
Fixed Costs
► Fixed costs are costs that in total are constant within the relevant range as
the level of output increases or decreases.
► In this example of Colley Computers, notice while the total fixed cost of
supervision remains the same, the unit cost decreases as more computers
are produced.
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1
►
►
►
►
Fixed Costs
(continued)
The number of computers produced is called the output measure, or driver.
Even though fixed costs may change, this possibility does not make them
variable.
They are fixed at a new higher (or lower) rate.
A graph of Colley’s fixed supervision costs is shown below:
Supervision
cost is fixed
with respect
to the number
of computers
produced.
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Discretionary
Fixed
Costs
and
1
Committed Fixed Costs
► Two types of fixed costs are commonly recognized:
discretionary fixed costs and committed fixed costs.
► Discretionary fixed costs are fixed costs that can be changed
or avoided relatively easily at management discretion.
► Committed fixed costs, on the other hand, are fixed costs
that cannot be easily changed.
Advertising
Lease cost
is a discretionary fixed
cost, because it
depends on a
management decision.
is a committed fixed
cost because it
involves a long-term
contract.
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1
Variable Costs
► Variable costs are costs that in total vary in direct proportion to changes
in output within the relevant range.
► Variable costs can also be represented by a linear equation.
► Total variable costs depend on the level of output.
► This relationship can be described by the following equation or graphs:
Total variable costs = Variable rate x Amount of output
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1
The Reasonableness of
Straight-Line Cost Relationships
► Caution should be taken when applying cost behavior assumptions to output
levels that fall outside of the company’s relevant range of operations.
► Straight-line cost relationships that are assumed within the relevant range
may actually be semi-variable costs.
For example, at extremely
low levels of output, workers
often use more materials per
unit or require more time per
unit than they do at higher
levels of output.
Likewise, as the level of
output increases, workers
learn how to use materials
and time more efficiently so
that the variable cost per unit
decreases as more and
more output is produced.
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2
Mixed Costs
► Mixed costs are costs that have both a fixed and a variable
component. For example, overhead for a company may consist of a
fixed supervisor salary plus the cost of supplies that vary with the
quantity of output produced. The formula and graph depiction for a
mixed cost is as follows:
Total cost = Total fixed cost + Total variable cost
Volume
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2
Step Costs: Narrow Steps
► Some cost functions may be
discontinuous.
► These costs are known as step
costs (or semi-fixed).
► A step cost displays a constant
level of cost for a range of output
and then jumps to a higher level
(or step) of cost at some point,
where it remains for a similar
range of output.
► If a step cost has relatively narrow
steps, it means that the cost changes
in response to fairly small changes in
output and we can approximate it as a
variable cost (i.e., the red line).
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2
Step Costs: Wide Steps
► Step cost with relatively wide steps
are more characteristic of fixed
costs.
► For example, a company may have
to lease production machinery. If
the machine can only produce
1,000 units and the company
grows, they will have to lease
additional machines for each 1,000
units of production needed
(resulting in the wide steps shown
in the graph).
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2
Accounting Records and
Need for Cost Separation
► Only through a formal effort to separate costs can all costs be
classified into the appropriate cost behavior categories.
► If mixed costs are a very small percentage of total costs,
formal cost separation may be more trouble than it’s worth.
► In this case, mixed costs could be assigned to either the fixed
or variable cost category without much concern for the
classification error or its effect on decision making.
► Alternatively, the total mixed cost could be arbitrarily divided
between the two cost categories. (This is rarely done and not
a good option.)
► Typically, mixed costs for many firms are large enough to call
for separation.
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3 Methods for Separating Mixed Costs
into Fixed and Variable Components
►Three methods of separating a mixed cost into its
fixed and variable components are commonly used:
►the high-low method
►the scattergraph method
►the method of least squares
►Each method requires the simplifying assumption of
a linear cost relationship.
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Methods for Separating Mixed Costs
3
into Fixed and Variable Components
(continued)
► Recall the expression of cost as an equation for a straight line is:
►Total cost = Fixed cost + (Variable rate x Output)
► The dependent variable is a variable whose value depends on the value of
another variable. In the previous equation, total cost is the dependent
variable; it is the cost we are trying to predict.
► The independent variable is a variable that measures output and explains
changes in the cost or other dependent variable.
► A good independent variable is one that causes or is closely
associated with the dependent variable.
► Therefore, many managers refer to an independent variable as a cost
driver.
► The intercept corresponds to fixed cost.
► The slope of the cost line corresponds to the variable rate.
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3
Cornerstone 3-1
Creating and Using A Cost Formula
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3
Cornerstone 3-1
Creating and Using A Cost Formula
(continued)
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3
The High-Low Method
► Given two points, the slope and the intercept can be determined.
► The high-low method is method of separating mixed costs into fixed and
variable components by using just the high and low data points.
► To demonstrate, we will use data from materials handling costs at
Anderson Company:
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3
The High-Low Method
► Four steps must be taken in the high-low method:
►Step 1: Find the high point and the low point for a given data
set.
►Step 2: Using the high and low point, calculate the variable rate.
►Variable rate = (High point cost - Low point cost) ÷ (High
point output - Low point output)
►Step 3: Calculate the fixed cost using the variable rate (from
Step 2) and either the high point or low point.
►Fixed cost = Total cost at high point - (Variable rate x
Output at high point)
►Step 4: Form the cost formula for materials handling based on
the high-low method.
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Cornerstone 3-2
Using The High-Low Method to Calculate
Fixed Cost and the Variable Rate and to
Construct a Cost Formula
Solution:
Step 1—Find the high and low points: The high number of machine hours is in March, and the low number of
machine hours is in June. (Hint: Did you notice that the high cost of $4,200 was for August? Yet August is not the high point because its
number of machine hours is not the highest activity level. Remember, the high point is associated with the highest activity
level; the low point is associated with the lowest activity level.)
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3
Cornerstone 3-2
Using The High-Low Method to
Calculate Fixed Cost and the Variable
Rate and to Construct a Cost Formula
(continued)
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Cornerstone 3-3
3
Using The High-Low Method to Calculate
Predicted Total Variable Cost and Total Cost for
Budgeted Output
Information:
Recall that BlueDenim Company constructed the following formula for monthly electricity cost. (Refer to
Cornerstone 3-2 to see how the fixed cost per month and the variable rate were computed.)
Total electricity cost = $440 + ($6.10 x Machine hours)
Required:
Assume that 550 machine hours are budgeted for the month of October. Use the previous cost formula for the
following calculations:
1. Calculate total variable electricity cost for October.
2. Calculate total electricity cost for October.
Solution:
1. Total variable electricity cost = Variable rate x Machine hours
= $6.10 x 550
= $3,355
2. Total electricity cost = Fixed cost + (Variable rate x Machine hours)
= $440 + ($6.10 x 550)
= $440 + $3,355
= $3,795
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Cornerstone 3-4
3
Using The High-Low Method to Calculate
Predicted Total Variable Cost and Total Cost for
A Time Period that Differs from the Data Period
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3
Cornerstone 3-4
Using The High-Low Method to
Calculate Predicted Total Variable Cost
and Total Cost for A Time Period that
Differs from the Data Period (continued)
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3
Scattergraph Method
► The scattergraph method is a way to see the cost relationship
by plotting the data points on a graph.
► The first step in applying the scattergraph method is to plot
the data points so that the relationship between materials
handling costs and activity output can be seen.
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3
Scattergraph Method (continued)
► Then we inspect the scattergraph to see if it reveals one or
more points (outliers) that do not seem to fit the general
pattern of behavior.
► This knowledge might justify their elimination and perhaps
lead to a better estimate of the underlying cost function.
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3
Scattergraph Method (continued)
► Next, we should question whether the line determined by the high and low points
is representative of the overall relationship.
► Notice that three points lie above the high-low line, but five points lie below it.
► This does not give us confidence in the high-low results for fixed and variable
costs.
► In particular, we might wonder if the variable cost (slope) is somewhat higher than
it should be and the fixed cost is somewhat lower than it should be.
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3
Scattergraph Method (continued)
► Finally, we can use the scattergraph to visually fit a line to the data points on the
graph.
► Of course, the manager or cost analyst will choose the line that appears to fit the
points the best, and perhaps that choice will take into account past experience
with the behavior of the cost item.
► An infinite number of lines might go through the data, but this one goes through
the point for January (100, $2,000) and intersects the y-axis at $800.
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3
Scattergraph Method (continued)
► First, remember that our two points are (100,
$2,000) and (0, $800). Next, use these two
points to compute the variable rate (the slope):
Variable rate = ($2,000 - $800)
$100 - 0
= $1,200/100
= $12
► Thus the variable rate is $12 per material move.
► The fixed cost and variable rate for materials
handling cost have now been identified.
► The cost formula for the materials handling
activity can be expressed as:
Total cost = $800 + ($12 x Number of moves)
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3
Using the Formula from the
Scattergraph Method
► Using this formula, the total cost of materials handling for between
100 and 500 moves can be predicted and then broken down into
fixed and variable components.
► For example, assume that 350 moves are planned for November.
► Using the cost formula, the predicted cost is:
$5,000 = $800 + ($12 x 350)
► Of this total cost, $800 is fixed, and $4,200 is variable.
► Unfortunately, the scattergraph method suffers from the lack
of any objective criterion for choosing the best-fitting line.
► The quality of the cost formula depends on the quality of the
subjective judgment of the analyst.
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3
The Method of Least Squares
►The method of least squares (regression) is a
statistical way to find the best-fitting line through a
set of data points.
►One advantage of the method of least squares is that
for a given set of data, it will always produce the
same cost formula.
►Basically, the best-fitting line is the one in which the
data points are closer to the line than to any other
line.
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3
Line Deviations
► The regression line better describes
the pattern of the data than other
possible lines.
► This best description results because
the squared deviations between the
regression line and each data point
are, in total, smaller than the sum of
the squared deviations of the data
points and any other line.
► The least squares statistical formulas
can find the one line with the smallest
sum of squared deviations or the line
which minimizes the cost prediction
errors or differences between
predicted costs (i.e., on the regression
line) and actual costs (i.e., the actual
data points).
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Cornerstone 3-5
3
Using The Regression Method to Calculate Fixed
Cost and the Variable Rate and to Construct a Cost
Formula and to Determine Budgeted Cost
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Cornerstone 3-5
3
Using The Regression Method to Calculate Fixed
Cost and the Variable Rate and to Construct a Cost
Formula and to Determine Budgeted Cost (continued)
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3
Comparison of Methods
►Knowing how costs change in relation to
changes in output is essential to planning,
controlling, and decision making.
►Each of the methods for separating mixed
costs into fixed and variable components help
managers understand cost behavior and
consequently make good business decisions.
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Comparison of Methods
3
for Separating Fixed Costs
into Fixed and Variable Components
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3
Managerial Judgment
► Managerial judgment is critically important in determining
cost behavior and is by far the most widely used method in
practice.
► Many managers simply use their experience and past
observation of cost relationships to determine fixed and
variable costs.
► This method, however, may take a number of forms.
►Some managers simply assign some costs to the fixed
category and others to the variable category and ignore
the possibility of mixed costs.
►Other managers may identify mixed costs and divide these
into fixed and variable components.
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3
Managerial Judgment
(continued)
► Finally, management may use experience and judgment to
refine statistical estimation results.
► Perhaps the experienced manager might ‘‘eyeball’’ the data
and throw out several points as being highly unusual or revise
the results of estimation account for projected changes in
cost structure or technology.
► The advantage of using managerial judgment to separate
fixed and variable costs is its simplicity.
► In situations in which the manager has a deep understanding
of the firm and its cost patterns, this method can give good
results.
► However, if the manager does not have good judgment,
errors will occur.
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3
Ethical Decisions
► There are ethical implications to the use of managerial
judgment.
► Managers use their knowledge of fixed and variable costs to
make important decisions, such as whether to switch
suppliers, expand or contract production, or lay off workers.
► These decisions affect the lives of workers, suppliers, and
customers.
► Ethical managers will make sure that they have the best
information possible when making these decisions.
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3
You Decide
Choosing a Cost Estimation Method
Assume that you work as a financial analyst for Royal Caribbean
Cruises Ltd. The company operates some of the world’s biggest cruise
ships, such as The Allure of the Seas, which weighs 222,000 tons and
carries 5,400 guests, as well as 1,650 crew members. As an internal
financial analyst, one of your most important tasks is to estimate the costs
that Royal will incur on the many cruises it offers to customers each year.
The accuracy with which you predict Royal’s most important cruiserelated costs will affect many of the strategic and operating decisions
made by management. You are familiar with several common cost
estimation methods, including scattergraph, high-low, and regression.
However, you also are aware that each method has its advantages and
disadvantages.
Which cost estimation method should you employ?
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3
You Decide
Choosing a Cost Estimation Method (continued)
If the scattergraph method were used, the analysis would be quite easy as you could employ Excel
to quickly create a plot of the important costs against various potential cost drivers. However, this
method does not involve quantitative analysis, which some individuals believe is a significant
weakness. If the high-low method were adopted, the analysis would be quantitative in nature and
relatively easy to conduct and explain to management. However, this method can be subject to
considerable inaccuracy if one or both of the two data points used to construct the cost formula is
an outlier. Finally, regression overcomes many of the weaknesses of high-low because it
incorporates all of the data into its estimate of the cost formula. Nevertheless, regression can
require considerably more time than other methods to collect the necessary input data, ensure
their accuracy, and explain the results to the ultimate users of the results. There is no obvious,
one-size-fits-all answer as to the best cost estimation method to employ. Instead, you would be
wise to consult the managers who will be using your analysis. For example, does management
need a general ‘‘ball park’’ estimate or does it need the most accurate estimate possible? The
results from your cost analysis, along with the competitive pressures facing Royal, will affect
important decisions such as how much to pay cruise ship employees to ensure a high quality
customer experience, the prices to charge customers to ensure affordability yet exclusivity, and the
types and quantities of food, beverages, and shopping to offer onboard the ships. Regardless of
the cost estimation method ultimately selected, you likely will supplement the results with a dose of
managerial judgment to help management make the best decisions possible.
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4
APPENDIX 3A:
Using the Regression Programs
► Computing the regression formula manually is tedious, even
with only a few data points.
► As the number of data points increases, manual computation
becomes impractical.
► Fortunately, spreadsheet packages like Microsoft Excel have
regression routines that perform these computations.
► All you need to do is input the data and the spreadsheet
regression program supplies more than the estimates of the
coefficients.
► It also provides information that can be used to see how
reliable the cost equation is—a feature that is not available
for the scattergraph and high-low methods.
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4
Spreadsheet Data
► The first step in using the computer to calculate regression coefficients is to enter
the data. The exhibit here shows the computer screen that you would see if you
entered the data on material moves into a spreadsheet.
► It is a good idea to label your variables as is done in the exhibit.
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4
Regression Output
► Once we run the
regression, we find the
fixed cost is 789 and the
variable rate is 12.38
(rounded).
► Using this information, the
cost formula for materials
handling cost is:
Materials handling cost = $789
+ $12.38 x number of moves
► For 350 moves, the total
materials handling cost
predicted by the least squares
line is: $5,122 = $789 + ($12.38 X
350)
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4
Goodness of Fit
► Regression routines provide information on goodness of fit.
► Goodness of fit tells us how well the independent variable
predicts the dependent variable.
► The percentage of variability in the dependent variable
explained by an independent variable (in this case, a measure
of activity output) is called the coefficient of determination
(R-squared).
► The higher the percentage of cost variability explained, the
better job the independent variable does of explaining the
dependent variable.
► Since R-squared is the percentage of variability explained, it
always has a value between 0 and 1.00.
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4
Regression Output
► Note that the summary output
shows that the coefficient of
determination, labeled as R
Square (R2) is 0.85.
► In other words, material moves
explain about 85 percent of the
variability in the materials
handling cost.
► This is not bad.
► However, something else
explains the remaining 15
percent. The company’s
controller may want to keep
this in mind when using the
regression results.
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