COST BEHAVIOR
CHAPTER 3
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CHAPTER 3 OBJECTIVES
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
© 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a passwordprotected website for classroom use.
CHAPTER 3 OBJECTIVES
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
© 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a passwordprotected website for classroom use.
BASICS OF COST BEHAVIOR
Cost Behavior
• The term used to describe whether a cost
changes when the level of output changes
• Fixed costs do not change as output changes
• Variable costs increase in total with an
increase in output and decrease in total with
a decrease in output
LO-1
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BASICS OF COST BEHAVIOR
Cost Objects
• An item for which managers want cost
information
• For manufacturing or merchandising firms, it is
usually the tangible product
• For service firms, it is usually the service
provided
LO-1
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BASICS OF COST BEHAVIOR
Measures of Output
• Activity drivers explain changes in activity
costs by measuring changes in activity output
(usage)
• The two general categories of activity drivers
• Unit-level drivers
• Non-unit-level drivers
LO-1
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BASICS OF COST BEHAVIOR
Fixed Costs
• Fixed costs are costs that in total are
constant within the relevant range as the
level of the activity driver varies
LO-1
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BASICS OF COST BEHAVIOR
Fixed Costs
JCM Audio Systems, Inc. produces speakers
for home audio systems. One department
produces voice coils. There are two
production lines that can each make up to
100,000 voice coils per year. The productionline manager is paid $60,000 per year. For
production up to 100,000 units only one
manager is needed; above that (to 200,000
units) two managers are needed.
LO-1
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BASICS OF COST BEHAVIOR
Fixed Costs
JCM Audio Systems, Inc.
Supervision
Voice Coils
Unit Cost
Cost
Produced
$ 60,000
40,000
$1.50
60,000
80,000
0.75
60,000
100,000
0.60
120,000
120,000
1.00
120,000
160,000
0.75
120,000
200,000
0.60
The total cost of supervision remains the same
within the relevant range, but the unit cost
decreases as production increases.
LO-1
© 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a passwordprotected website for classroom use.
BASICS OF COST BEHAVIOR
Fixed Costs
JCM Audio Systems, Inc.
Supervision
Voice Coils
Unit Cost
Cost
Produced
$ 60,000
40,000
$1.50
60,000
80,000
0.75
60,000
100,000
0.60
120,000
120,000
1.00
120,000
160,000
0.75
120,000
200,000
0.60
The total cost of supervision remains the same
within the relevant range, but the unit cost
decreases as production increases
LO-1
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EXHIBIT 3.1—FIXED COST BEHAVIOR
LO-1
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BASICS OF COST BEHAVIOR
Variable Costs
• Variable costs are costs that in total vary in
direct proportion to changes in an activity
driver
• The total cost of direct materials for each
level of production varies, but the unit cost
stays the same
LO-1
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BASICS OF COST BEHAVIOR
Variable Costs
JCM Audio Systems, Inc.
Total Direct Materials Cost
of Voice Coils
$120,000
240,000
360,000
480,000
600,000
Voice Coils
Produced
Unit Direct Materials Cost
of Voice Coils
40,000
80,000
120,000
160,000
200,000
The total cost of supervision remains the same
within the relevant range, but the unit cost
decreases as production increases.
$3
3
3
3
3
LO-1
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EXHIBIT 3.2—VARIABLE COST
BEHAVIOR
LO-1
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EXHIBIT 3.3—NONLINEARITY OF
VARIABLE COSTS
LO-1
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EXHIBIT 3.4—RELEVANT RANGE FOR
VARIABLE COSTS
LO-1
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BASICS OF COST BEHAVIOR
Mixed Costs
• Mixed costs are costs that has both a fixed
and a variable component
Y = Fixed cost + Total variable cost
Y = F + VX
where
Y = Total cost (Usually a mixed cost)
LO-1
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BASICS OF COST BEHAVIOR
Mixed Costs
JCM’s sales costs are mixed. There are 10 sales
representatives who each earn $30,000 plus receive
a commission of $5 per speaker sold. This function
can be represented by the following equation
Y = $300,000 + $5X
Fixed salaries
Variable commission
LO-1
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BASICS OF COST BEHAVIOR
Mixed Cost
JCM Audio Systems, Inc.
Fixed Cost
of Selling
$300,000
300,000
300,000
300,000
300,000
Variable Cost
Total Cost
of Selling
$200,000
400,000
600,000
800,000
1,000,000
$ 500,000
700,000
900,000
1,100,000
1,300,000
Speakers
Sold
40,000
80,000
120,000
160,000
200,000
Selling Cost
Per Unit
$12.50
8.75
7.50
6.88
6.50
LO-1
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EXHIBIT 3.5—MIXED COST BEHAVIOR
LO-1
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RESOURCES, ACTIVITIES, AND COST
BEHAVIOR
Resources
• Economic elements that enable one to perform
activities
• When a firm acquires the resources needed to
perform an activity, it obtains activity capacity
• Practical capacity is the activity level where the
activity is performed efficiently
LO-2
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RESOURCES, ACTIVITIES, AND COST
BEHAVIOR
Flexible Resources
• Supplied as needed and used
• Quantity of resource supplied equals quantity
demanded
• No unused capacity
LO-2
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RESOURCES, ACTIVITIES, AND COST
BEHAVIOR
Committed Resources
• Supplied in advance of usage
• A given quantity is obtained, whether or not that full
amount is used
• Unused capacity is possible
LO-2
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RESOURCES, ACTIVITIES, AND COST
BEHAVIOR
Step-Cost Behavior
• A step cost function displays a constant
level of cost for a range of output and then
jumps to a higher level of cost at some point
LO-2
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RESOURCES, ACTIVITIES, AND COST
BEHAVIOR
Step-Cost Behavior
Step-variable Costs
• Follow a step-cost behavior with narrow steps
Step-fixed Costs
• Follow a step-cost function
• Exceed the relevant range, and the costs increase
“one step”
LO-2
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EXHIBIT 3.6— STEP COST FUNCTION
LO-2
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EXHIBIT 3.7—STEP-FIXED COSTS
LO-2
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RESOURCES, ACTIVITIES, AND COST
BEHAVIOR
Activities and Mixed Cost Behavior
• Many activities have characteristics of both
flexible and committed resources
• For example, a power department acquires longterm capacity for supplying power by investing in
a building and equipment
• It also acquires fuel to produce power on an asneeded basis
LO-2
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RESOURCES, ACTIVITIES, AND COST
BEHAVIOR
Need for Cost Separation
• Sometimes it is easy to spot the variable and
fixed portion of a cost
• Other times it is not; thus there is a need for a
method to separate costs into their fixed and
variable components
LO-2
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METHODS OF DETERMINING COST
BEHAVIOR
The Industrial Engineering Method
• 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
• Used to estimate costs by classifying accounts in the
general ledger as fixed, variable, or mixed
LO-3
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QUANTITATIVE METHODS FOR SEPARATING MIXED
COSTS INTO FIXED AND VARIABLE COMPONENTS
Y = F + VX
where
Y = Total cost (the dependent variable)
F = Fixed cost (the intercept parameter)
V = Variable cost per unit (the slope parameter)
X = Measure of output (the independent variable)
LO-4
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QUANTITATIVE METHODS FOR SEPARATING MIXED
COSTS INTO FIXED AND VARIABLE COMPONENTS
The High-Low Method
• Take two points (the high and the low by
volume of activity) and determine the slope
and intercept
• Slope is variable rate
• Intercept is fixed cost
LO-4
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QUANTITATIVE METHODS FOR SEPARATING MIXED
COSTS INTO FIXED AND VARIABLE COMPONENTS
The High-Low Method
Advantages
• It is objective
• It is simple to calculate
Disadvantages
• The high and low points may be “outliers”
• Other pairs of points may clearly be more
representative
LO-4
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QUANTITATIVE METHODS FOR SEPARATING MIXED
COSTS INTO FIXED AND VARIABLE COMPONENTS
Scatterplot Method
• Uses a scattergraph to visually assess the
relationship between cost and output
• Intercept is fixed cost
• Slope is variable rate
LO-4
© 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a passwordprotected website for classroom use.
QUANTITATIVE METHODS FOR SEPARATING MIXED
COSTS INTO FIXED AND VARIABLE COMPONENTS
Scatterplot Method
Advantages
• Allows for visual inspection of the data
• Identifies nonlinearity, outliers, and shifts in
the cost relationship
Disadvantages
• It is subjective
LO-4
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EXHIBIT 3.8—SCATTERGRAPH FOR ANDERSON
COMPANY’S MATERIALS HANDLING COSTS
LO-4
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EXHIBIT 3.8—SCATTERGRAPH FOR ANDERSON
COMPANY’S MATERIALS HANDLING COSTS
(CONTINUED)
LO-4
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EXHIBIT 3.8—SCATTERGRAPH FOR ANDERSON
COMPANY’S MATERIALS HANDLING COSTS
(CONTINUED)
LO-4
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EXHIBIT 3.9—SCATTERGRAPH FOR
VARIOUS COST BEHAVIOR PATTERNS
LO-4
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EXHIBIT 3.9—SCATTERGRAPH FOR VARIOUS
COST BEHAVIOR PATTERNS (CONTINUED)
LO-4
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EXHIBIT 3.9—SCATTERGRAPH FOR VARIOUS
COST BEHAVIOR PATTERNS (CONTINUED)
LO-4
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EXHIBIT 3.10—DEVIATIONS OF DATA
FROM A LINE
LO-4
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EXHIBIT 3.11—SPREADSHEET DATA FOR ANDERSON
COMPANY’S MATERIALS HANDLING COST
LO-4
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QUANTITATIVE METHODS FOR SEPARATING MIXED
COSTS INTO FIXED AND VARIABLE COMPONENTS
Using Regression Programs
• Enter the data
• Choose the “Tools” menu
• Choose the “Data Analysis” option
• If this is not available, you may have to manage
add-ins
• Scroll down to “Regression”
• Click on “Input Y Range” and highlight the cost cells
• Click on “Input X Range” and highlight the driver cells
• Choose your preferred location for output
• Click ok
LO-4
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EXHIBIT-3.12— REGRESSION RESULTS FOR ANDERSON
COMPANY’S MATERIALS HANDLING COST
LO-4
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QUANTITATIVE METHODS FOR SEPARATING MIXED
COSTS INTO FIXED AND VARIABLE COMPONENTS
Using Regression Programs
• Interpreting the results
• Under “coefficients” in the bottom left of the
output find the intercept and the slope
• Write the equation
• Y = $12.39X + $854.50
• Use the equation to make a point estimate
• At a point of 350 moves, total cost is predicted
• Y = $12.39(350) + $854.50
• Y = $4,336.50
LO-4
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RELIABILITY OF COST FORMULAS
• Three statistical assessments concerning the
cost formula’s reliability
• Hypothesis test of cost parameters
• Goodness of fit
• Confidence intervals
LO-5
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RELIABILITY OF COST FORMULAS
• Hypothesis Test of Cost Parameters
• The “t Stat” tests the hypothesis that the
parameters are different from zero
• The “P-value” is the level of significance achieved
• Generally, a P-value of 0.05 or less is needed for
significance
LO-5
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RELIABILITY OF COST FORMULAS
Goodness of Fit Measures
• The coefficient of determination, or R2, shows the
percentage of variability in the dependent variable
explained by the independent variable
• Since R2 is the percentage of variability explained, it
always has a value between 0 and 1.00
• Typically, the Adjusted R Square is used because
this value has been adjusted for the number of
variables included in the equation
LO-5
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RELIABILITY OF COST FORMULAS
Coefficient of Correlation
• It is the square root of the coefficient of
determination when there is one independent
variable
• Range between −1 and +1
• The higher the magnitude, the greater the
correlation
• A coefficient of correlation value close to zero
indicates no correlation
LO-5
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EXHIBIT 3.13—CORRELATION
ILLUSTRATED
LO-5
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RELIABILITY OF COST FORMULAS
• Confidence Intervals
Yf ± tSe
• This is the formula for calculating the desired level
of confidence
• Yf is the predicted cost for a given level of activity
• t is the t distribution (get this from the table in your
book
• Se is the standard error shown in the regression
output
LO-5
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EXHIBIT 3.14—TABLE OF SELECTED
VALUES: T DISTRIBUTION
LO-5
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MULTIPLE REGRESSION
• Whenever least squares is used to fit an equation
involving two or more independent variables, the
method is called multiple regression
• In the case of two explanatory variables, the linear
equation is expanded to include the additional
variable
Y = F + V1X1 + V2X2
where
X1 = Number of moves
X2 = Number of pounds moved
LO-6
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MULTIPLE REGRESSION
• Adding another independent variable might
increase the explanatory power of our
model
• Performing the regression is very similar to
simple regression
• Input the data – make sure the two independent
variables are side by side.
• Follow the same directions, but select both
independent variable columns for the “input X
range”
LO-6
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MULTIPLE REGRESSION
Month
Materials
Handling Cost
Number of
Moves
Pounds
Moved
January
$2,000
100
6,000
February
3,090
125
15,000
March
2,780
175
7,800
April
1,990
200
600
May
7,500
500
29,000
June
5,300
300
23,000
July
4,300
250
17,000
August
6,300
400
25,000
September
5,600
475
12,000
October
6,240
425
22,400
LO-6
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EXHIBIT 3.15—MULTIPLE REGRESSION RESULTS FOR
ANDERSON COMPANY’S MATERIALS HANDLING COST
LO-6
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MULTIPLE REGRESSION
• Interpreting the results
• Under “coefficients” in the bottom left of the
output find the intercept and the slope
• Write the equation
• Y = $507.31 + $7.84X1 + $0.11X2
• Examine reliability of the new model
• Adjusted R2 is 99% - a significant improvement
• The p-values are all very good as well
• the t statistic drops to 7 degrees of freedom
because another independent variable is used
LO-6
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THE LEARNING CURVE AND NONLINEAR
COST BEHAVIOR
• The learning curve shows how labor hours
per unit decreases as units produced
increases
• The experience curve relates cost to
increased efficiency – the more you perform
a task the lower the cost is of doing it
LO-7
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THE LEARNING CURVE AND NONLINEAR
COST BEHAVIOR
Cumulative Average-Time Learning Curve
• States that the cumulative average time per
unit decreases by a constant percentage
• The learning rate is expressed as a percent
LO-7
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THE LEARNING CURVE AND NONLINEAR
COST BEHAVIOR
Incremental Unit-Time Learning Curve
• The incremental unit-time learning curve
model decreases by a constant percentage
each time the cumulative quantity of units
produced doubles
LO-7
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EXHIBIT 3.16—SPREADSHEET FOR CUMULATIVE
AVERAGE-TIME LEARNING MODEL
LO-7
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EXHIBIT 3.17—GRAPH OF CUMULATIVE TOTAL
HOURS REQUIRED AND THE CUMULATIVE AVERAGE
TIME PER UNIT
LO-7
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MANAGERIAL JUDGMENT
• The most widely used method in practice
• Managers may just use their experiences
and observations to determine fixed and
variable costs
• Managers may identify mixed costs and use
experience to determine what part is fixed –
thus denoting the rest as variable
LO-8
© 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a passwordprotected website for classroom use.
MANAGERIAL JUDGMENT
• This is a simple method and can yield good
results when the manager has a good
understanding of the processes
• However poor judgment yields poor results
LO-8
© 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a passwordprotected website for classroom use.
END OF CHAPTER 3
© 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a passwordprotected website for classroom use.