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COST MANAGEMENT
Guan Hansen Mowen
COPYRIGHT 2009 South-Western Publishing, a division of Cengage Learning.Cengage Learning and South-Western are trademarks used herein under license. 1
Chapter 3Cost Behavior
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Study 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. Separate mixed costs into their fixed and variable components
using the high-low method, the scatterplot method, and the methodof least squares.
4. Evaluate the reliability of the cost formula.
5. Explain how multiple regression can be used to assess cost
behavior.6. Define the learning curve, and discuss its impact on cost behavior.
7. Discuss the use of managerial judgment in determining cost
behavior.
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Two production lines can process 10,000computers per year each. The workers on eachline are supervised by a production-line manager
who is paid $24,000 per year. For production upto 10,000 units, only one supervisor is needed.
When production is between 10,001 and 20,000units, two supervisors are required.
Cost Behavior: Fixed Costs
Fixed costsarecosts that in to tal areconstant within the relevant range asthe level of the activity driver varies.
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Supervision
Computers
Processed
$54,000 4,00054,000 8,000
54,000 10,000
108,000 12,000
108,000 16,000108,000 20,000
Days Computers, Inc.
Cost Behavior: Fixed Costs
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Supervision
Computers
Processed
$54,000 4,00054,000 8,000
54,000 10,000
108,000 12,000
108,000 16,000108,000 20,000
Days Computers, Inc.
Cost Behavior: Fixed Costs
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Supervision
Computers
Processed Unit Cost
$54,000 4,000 $13.5054,000 8,000 6.75
54,000 10,000 5.40
108,000 12,000 9.00
108,000 16,000 6.75108,000 20,000 5.40
Days Computers, Inc.
Cost Behavior: Fixed Costs
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Cost Behavior: Fixed Costs
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Variable costs are costs that in to talvary in direct proportion to changes inan activity driver.
A CD-ROM disk drive is added to eachcomputer at a cost of $30 per computer.
The total cost of disk drives for each level of
production varies.
Cost Behavior: Variable Costs
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Cost Behavior: Variable Costs
Total Cost of
CD-ROMs
Number of
Computers
Processed
$120,000 4,000
240,000 8,000
360,000 12,000
480,000 16,000
600,000 20,000
Days Computers, Inc.
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Cost Behavior: Variable Costs
Total Cost of
CD-ROMs
Number of
Computers
Processed
Unit Cost of
CD-ROMs
$120,000 4,000 $30.00
240,000 8,000 30.00
360,000 12,000 30.00
480,000 16,000 30.00
600,000 20,000 30.00
Days Computers, Inc.
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Cost Behavior: Variable Costs
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Mixed costs are costs that have both afixed and a variable component.
Ten sales representatives each earn anannual salary of $30,000plusa commissionof $50 per computer sold. 10,000 computers
are sold.
Cost Behavior: Mixed Costs
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Y= Fixed cost + Total variable cost
Y= F+ VX
where
Y= Total cost
For Days Computer, the selling cost is:
Y = $300,000 + $50X
Cost Behavior: Mixed Costs
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Cost Behavior: Mixed Costs
Fixed Cost of
Selling
Variable
Cost of
Selling Total Cost
Computers
Sold
Selling Cost
per Unit
$300,000 $200,000 $500,000 4,000 $125.00
300,000 400,000 700,000 8,000 87.50
300,000 600,000 900,000 12,000 75.00
300,000 800,000 1,100,000 16,000 68.75
300,000 1,000,000 1,300,000 20,000 65.00
Days Computers, Inc.
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Cost Behavior: Mixed Costs
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Flexible resources
Acquired as used and needed
Usually considered variable costs
Examples: materials, energy
Committed resources
Acquired in advance of usage
Usually considered fixed costs
Examples: buying or leasing buildings, contractswith employees
Resources, Activities,and Cost Behavior
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Resources, Activities,and Cost Behavior
Step cost behaviordisplays a constantlevel of cost for a range of output and then
jumps to a higher level of cost at some
point Step-Variable costs
Narrow increments Approximate as a strictly variable assumption
Step-Fixed costs Wide increments Assigned to the fixed cost category
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Resources, Activities,and Cost Behavior
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Methods for Separating Mixed Costsinto Fixed and Variable Components
The High-Low Method
The Scatterplot Method The Method of Least Squares
Variable
Component
FixedComponent
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Y = F + VX
Methods for Separating Mixed Costsinto Fixed and Variable Components
whereY = Total activity cost
F = Fixed cost componentV = Variable cost per unit
X = Measure of activity output
Straight-line equation:
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Step 1: Solve for variable cost (V)V= Change in cost Change in activity
High-Low Method
Month
Materials
Handling Cost
Number of
Moves
January $2,000 100
February 3,090 125
March 2,780 175
April 1,990 200May 7,500 500
June 5,300 300
July 4,300 250
August 6,300 400
September 5,600 475October 6,240 425
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High-Low Method
$7,500 - $2,000Step1: $13.75
500 - 100V
Low Activity
High Activity
Month
Materials
Handling Cost
Number of
Moves
January $2,000 100
February 3,090 125
March 2,780 175
April 1,990 200May 7,500 500
June 5,300 300
July 4,300 250
August 6,300 400
Septembe 5,600 475
October 6,240 425
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High-Low Method
$7,500 - $2,000$13.75
500 - 100V
Step 2: Using either the high cost or low cost, solve forthe total fixed costs F
Step 1: Solve for variable cost (V)V= Change in cost Change in activity
( )
$2,000 $13.75(100)$625
Y F V X
FF
Low cost
( )$7,500 $13.75(500)
$625
Y F V X
F
F
High cost
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Scatterplot Method
Step 1: Plot the data points on a scattergraph
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Method of Least Squares
ActualCost
PredictedCost Deviation
DeviationSquared
2,000 1,742 258 66,564
3,090 2,088 1,002 1,004,004
2,780 2,780 - -1,990 3,126 (1,136) 1,290,496
7,500 7,278 222 49,284
5,300 4,510 790 624,100
4,300 3,818 482 232,3246,300 5,894 406 164,836
5,600 6,932 (1,332) 1,774,224
6,240 6,240 - -
5,205,832Total measure of closeness
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Regression Programs
The best-fitting lineis the line with thesmallest sum of squared deviations
Regression analysis determines the linearfunction with the minimum sum of squareddeviations
Utilize spreadsheet packages such as
Microsoft Excel to perform thecomputation
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Spreadsheet Data forAnderson Company
Regression Analysisfor the Method of Least Squares
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.92894908
R. Square 0.862946394
Adjusted R 0.845814693
SquareStandard Error 770.4987038
Observations 10
ANOVA
df SS MS F
Regression 1 29903853.98 29903853.98 50.37132077Residual 8 4749346.021 593668.2526
Total 9 34653200
Coefficient Standard Error t-Stat P-value
Intercept 854.4993582 569.7810263 1.49967811 0.172079925
X Variable 1 12.3915276 1.745955536 7.097275588 0.000102268
Regression Output forAnderson Company
Regression Analysisfor the Method of Least Squares
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The regression analysis gives rise to the following
equation for Andersons material handling cost:
Regression Analysisfor the Method of Least Squares
$854.50 + ($12.39 number of moves)
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Reliability of Cost Formulas
Hypothesis test of parameters
The lower the P-value, the more likely that thetrue parameter is significantly different from 0
Traditional benchmarks of significance are
0.10, 0.05 or 0.01
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Reliability of Cost Formulas
Goodness of fit
R2 is the coefficient of determination
Measures the percentage of change in thedependent variable explained by changes in
the independent variable
The closer to 1.0, the better; no benchmark
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Reliability of Cost Formulas
Confidence intervals
The standard error is used to determine the range of possible values around the
predicted value:
Standard Confidencet-statisticError Interval
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X1= first explanatory variable
X2= second explanatory variable
Multiple Regression
Least-squares method is used to fit anequation involving two or moreexplanatory variables
Y = F + V1X
1+ V
2X
2etc.
where
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Multiple Regression
Spreadsheet Data forAnderson Company
Month
Materials
Handling
Cost
Number
of Moves
Pounds
MovedJanuary $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 23,000July 4,300 250 17,000
August 6,300 400 25,000
Septembe 5,600 475 12,000
October 6,240 425 22,400
X2
X1
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Multiple Regression Analysisfor the Method of Least Squares
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.999420
R Square 0.998841
Adjusted R Square 0.998509
Standard Error 75.762721
Observations 10
ANOVA
df SS MS F
Regression 2 34613020.07 17306510.04 3015.076722
Residual 7 40179.92954 5739.989934
Total 9 34653200
Coefficients Standard Error t Stat P-value
Intercept 507.309711 57.322496 8.850098 0.000048
X Variable 1 7.835162 0.234048 33.476720 0.000000
X Variable 2 0.107181 0.003742 28.642864 0.000000
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Y= $507 + $7.84X1 + $0.11X
2
Y= $507 + $7.84(350) + $0.11(17,000)= $507 + $2,744 + $1,870
= $5,121
Multiple Regression
Based on the multiple regression analysis, thecost formula is written as:
In November the company expects to make 350moves with a weight of 17,000 pounds. Thepredicted cost of material handling is:
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1 100 100 100
2 80 (80% 100) 160 60
3 70.21 210.63 50.63
4 64 (80% 80) 256 45.37
5 59.57 297.85 41.85
6 56.17 337.02 39.17
7 53.45 374.15 37.13
8 51.20 (80% 64) 409.60 35.45
16 40.96 655.36 28.06
32 32.77 1,048.64
Cumulative Cumulative Cumulative Individual Units
Number Average Time Total Time: Time for nth
of Units per Unit in Hours Labor Hours Unit-Labor Hours
(1) (2) (3) = (1) (2) (4)
Cumulative Average Time LearningCurve with 80% Learning Rate
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Graph of Cumulative Total Hours Requiredand the Cumulative Average Time per Unit
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Managerial Judgment
Managerial judgment is critically important
in determining cost behavior and is by far
the most widely used method in practice Advantage simplicity
Disadvantage poor judgment leads to errors
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COST MANAGEMENT
Guan Hansen Mowen
End Chapter 3