CHAPTER M4
Cost Behavior
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Learning Objective 1:
Describe the differences
between fixed costs and
variable costs.
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Fixed Costs
 Costs that do not change in total as the
level of business activity changes are
called fixed costs.
 An example of a fixed cost is the
insurance on a factory building. The
insurance cost does not change as the
level of production changes.
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Fixed Cost Per Unit
 Although the total fixed cost does not
change, the fixed cost per unit does
change as the activity level changes.
 If the factory insurance cost is $5,000,
then the insurance cost is $1.00 per unit
when 5,000 units are produced, but only
50 cents per unit when 10,000 units are
produced.
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Variable Costs
 Costs that change in direct proportion with
changes in the activity level are called
variable costs.
 An example of a variable cost is the cost
of sales commissions. Each sale results in
an increase in the total cost of
commissions.
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Variable Cost Per Unit
 The variable cost per unit remains the
same regardless of the level of activity.
 If the sales commission is $5.00 per unit,
then that commission rate is assumed to
remain unchanged no matter how many
units are sold.
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Learning Objective 2:
Classify costs by cost
behavior.
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Cost Behavior
 Cost behavior is the reaction of costs to
changes in the business activity.
 Some costs change when the level of
business activity changes and other costs
do not. If you consider the total costs of
running a business, the cost increases as
the activity level (sales, production, or
some other measure) increases.
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Cost Behavior Patterns
 The three most common cost
behavior types are:
 Fixed costs
 Variable costs
 Mixed costs
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Graphical Analysis
 When graphing cost behavior, the following
conventions are typically followed:
 The measure of activity is shown on the X
axis. The activity base is also called the
independent variable.
 The measure of cost is shown on the Y axis.
The cost is also called the dependent
variable.
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Graphical Analysis
Factory Insurance Cost
Sales Commissions Cost
$9,000
$9,000
$7,000
$7,000
$5,000
$5,000
$3,000
$3,000
$1,000
$1,000
2,500 5,000 7,500
Units Produce d
10,000
A fixed cost graph.
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2,500
5,000 7,500
Units Sold
10,000
A variable cost graph.
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Determining Total Cost
 The basic cost equation is:
Total Cost = Fixed Cost + Variable Cost
The graph at the right
shows the combination
of a fixed cost line and
a variable cost line.
Tota l Cost Gra ph
$12,500
$10,000
$7,500
$5,000
$2,500
2,500
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5,000 7,500 10,000
Units Sold
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Learning Objective 3:
Explain the concept of
relevant range and its
effect on cost behavior
information.
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Relevant Range
 The simplifications that are made with
regard to cost behavior patterns are
assumed to be reasonable as long as the
activity level is within the relevant range.
 The relevant range usually cannot be
specifically determined, but it can be
considered to be that range of activity
within which the company usually
operates.
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Graph of a Relevant Range
Factory Insurance Cost
$9,000
Re levant Range
$7,000
$5,000
$3,000
$1,000
2,500
5,000
7,500
Units Produce d
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10,000
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Mixed Costs
 Some costs exhibit cost behavior that is a
combination of both a fixed element and a
variable element. These costs are known
as mixed costs.
 It is important to separate a total mixed
cost into its fixed component and variable
component.
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Mixed Cost Graph
Equipment Re pairs Cost
$10,000
$8,000
$6,000
$4,000
$2,000
10
20
30
40
Number of Breakdowns
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Discussion Questions
 On the previous slide, the dashed lines
indicate a total cost of $8,000 if 40
breakdowns occur.
 What is the estimated total cost per
breakdown?
 Estimated fixed cost per breakdown?
 Estimated variable cost per breakdown?
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Discussion Questions
 Besides the number of equipment
breakdowns, what other measures of
activity might work well when trying to
predict the amount of equipment repair
cost?
 Do you think that the selection of an
appropriate activity measure is crucial to
making a reasonable cost estimate?
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Discussion Questions
 Identify at least one cost in each of the
three categories (variable, fixed, and
mixed) that you incur in your personal life.
 Do you incur more variable costs, more
fixed costs, or more mixed costs?
 Do you think a manufacturing company
incurs more variable costs, more fixed
costs, or more mixed costs?
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Learning Objective 4:
Describe the
characteristics of a mixed
cost and the four basic
approaches to separating a
mixed cost into its fixed
and variable components.
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Identifying Elements of a
Mixed Cost
 The most commonly used techniques
for determining the fixed and variable
components of a mixed cost are:




the engineering approach
scatter graphing
the high-low method
regression analysis.
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Engineering Approach
 The engineering approach is based on
the technical judgment and expertise
about the activity with fixed and variable
costs.
 The expert (possibly an engineer) will
analyze the cost component much like an
investigator. An example of a technique
used in the engineering approach would
be a time and motion study.
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Scatter Graphing
 The scatter graphing technique entails
plotting the available cost vs. activity
information on a graph.
 The cost analyst draws a line that appears to
best fit the data. The line represents the
estimated cost behavior pattern.
 The accuracy of the line in describing the
relationship among the variables is suspect.
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High-Low Method
 In the high-low method, only two of the
data points are used to determine the fixed
and variable cost components.
 The highest and lowest observations are
picked, with the choice being based on the
independent variable (machine hours)
rather than the dependent variable
(overhead cost).
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Regression Analysis
 Regression analysis is a statistical
approach that can be used to determine the
fixed and variable cost components with a
high degree of accuracy.
 Calculations done by hand are very tedious.
However, many software packages can
make these calculations for you. Let’s use
the same sample data and view the output
from a popular spreadsheet program.
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Learning Objective 5:
Determine the fixed and
variable components of a
mixed cost using scatter
graphs, the high-low
method, and the results of
regression analysis.
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Scatter Graph Example
 We will use the following data in an effort to
predict overhead costs on the basis of
machine hours.
Month
January
February
March
April
May
June
July
August
September
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Machine
Hours
4,500
3,900
2,500
2,000
3,000
3,500
4,300
4,500
5,000
Overhead
Costs
$10,800
8,000
6,200
6,000
6,600
7,250
8,750
8,850
10,500
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Scatter Graph Example
Scatter Graph
$12,000
Overhead Costs
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0
1,000
2,000
3,000
4,000
5,000
6,000
Machine Hours
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Draw the Best Fit Line
Scatter Graph
$12,000
Overhead Costs
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0
1,000
2,000
3,000
4,000
5,000
6,000
Machine Hours
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Determine Line Parameters
 The line appears to intersect the Y axis at
about $2,000. This would be our best
estimate of the fixed cost component.
 The line also goes through the data point for
March where X= 2,500 and Y = $6,200.
Subtracting the $2,000 fixed cost from
$6,200, leaves $4,200 as the estimate of total
variable cost at this level of volume.
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Estimate the Total Cost
Formula
 To determine the variable cost per machine hour,
simply divide the total variable cost by the
number of machine hours:
$4,200 / 2,500 hours = $1.68 per hour.
 Thus, our estimated overhead cost is $2,000 per
month plus $1.68 per machine hour.
 TC =
FC + (VC x V)
TC = $2,000 + ($1.68 x 2,500 hours)
TC = $6,200
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High-Low Method
 Using the same data as before, the high
and low activity months are:
High: September 5,000 hours, $10,500 cost
 Low: April
2,000 hours, $ 6,000 cost

 The next step is to analyze the data to
determine the variable cost (based on the
cost change from low to high) and the
fixed cost.
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The High-Low Line
High-Low Method
$12,000
Overhead Costs
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0
1,000
2,000
3,000
4,000
5,000
6,000
Machine Hours
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High-Low Calculations
 Step 1: Calculate the variable cost:
Change in cost $10,500 - $6,000
Change in hours
5,000 - 2,000
 $4,500
3,000 hrs. = $1.50 per machine hour
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High-Low Calculations
 Step 2: Calculate the fixed cost: (NOTE: you
can use either month for this step.)
 TC = FC + (UVC x V) or TC – (UVC x V) = FC
 April total cost -- variable cost = fixed cost
 $6,000 -- ($1.50 X 2,000 hours) = $3,000
 Thus, the overhead is estimated at $3,000 per
month plus $1.50 per machine hour.
 TC = FC + (UVC x V)
 TC = $3,000 + ($1.20 X Machine hours)
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Regression Analysis
Output
Regression Statistics
R Square
86.12%
Adjusted R Square
84.14%
Standard Error
$
704.53
Observations
9
Intercept
X Variable 1
Coefficients Standard Error Lower 95% Upper 95%
$ 2,134.15 $
935.93 $ (78.97) $ 4,347.27
$
1.62 $
0.25 $ 1.04 $
2.20
The blue text is used to highlight the variable and
fixed cost estimates using regression analysis.
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Estimates Using
Regression Analysis
 Based on the output data, the estimate of fixed
cost is $2,134 and the estimate of variable cost
is $1.62 per machine hour.
 TC = $2,134 + ($1.62 x Machine hours)
 The remaining output data provides information
related to the expected accuracy of our
overhead cost estimates. The measures of
probable error are major advantages of
regression analysis over the other methods.
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Cost Equation
 The basic format used for cost equations
is:
 Y = a + bX, where
Y = estimated total cost
X = expected or actual activity level
a = estimated fixed cost per period
b = estimated variable cost per unit of activity
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Comparison of the Methods
 Each of the three analyses gives us a different
cost equation for predicting overhead costs
based on 4,000 machine hours.
 Scatter graph:$2,000 + $1.68 x 4,000 = $8,720
 High-low:
$3,000 + $1.50 x 4,000 = $9,000
 Regression: $2,134 + $1.62 x 4,000 = $8,614
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Discussion Questions
 Of the three cost equations, which one do
you think would be most reliable (i.e.,
gives the most accurate predictions)?
 Consider the fact that we only used data
from nine months. What implications does
this have for your assessment of how
accurate our predictions might be?
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The End of Chapter M4
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