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3-1
Activity Cost Activity Cost BehaviorBehavior
Prepared by Douglas Cloud
Pepperdine University
Prepared by Douglas Cloud
Pepperdine University
3-2
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 method of least squares.
ObjectivesObjectivesObjectivesObjectives
After studying this After studying this chapter, you should chapter, you should
be able to:be able to:
After studying this After studying this chapter, you should chapter, you should
be able to:be able to:
3-3
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.
ObjectivesObjectivesObjectivesObjectives
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Fixed CostsFixed CostsFixed CostsFixed Costs
Fixed costs are costs that in total are constant
within the relevant range as the level of the activity driver varies.
3-5
Two production lines can process 10,000 computers per year each. The workers on
each line are supervised by a production-line manager who is paid $24,000 per year. For
production up to 10,000 units, only one supervisor is needed. When production is
between 10,001 and 20,000 computers being produced, two supervisors are required.
Fixed CostsFixed CostsFixed CostsFixed Costs
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SupervisionComputers Processed
$24,000 4,000 $6.0024,000 8,000 3.0024,000 10,000 2.4048,000 12,000 4.0048,000 16,000 3.0048,000 20,000 2.40
Unit Cost
Fixed CostsFixed CostsFixed CostsFixed Costs
Total Fixed Cost GraphTotal Fixed Cost GraphT
otal
Cos
ts$60,000$50,000$40,000$30,000$20,000
$10,000
0Units Produced (000)
F = $24000
4 8 10 12 16
3-7
SupervisionComputers Processed
$24,000 4,000 $6.0024,000 8,000 3.0024,000 10,000 2.4048,000 12,000 4.0048,000 16,000 3.0048,000 20,000 2.40
Unit Cost
Fixed CostsFixed CostsFixed CostsFixed Costs
Total Fixed Cost GraphTotal Fixed Cost GraphT
otal
Cos
ts$60,000$50,000$40,000$30,000$20,000
$10,000
0Units Produced (000)
F = $24000
4 8 10 12 16
3-8
SupervisionComputers Processed
$24,000 4,000 $6.0024,000 8,000 3.0024,000 10,000 2.4048,000 12,000 4.0048,000 16,000 3.0048,000 20,000 2.40
Unit Cost
Fixed CostsFixed CostsFixed CostsFixed Costs
Total Fixed Cost GraphTotal Fixed Cost GraphT
otal
Cos
ts$60,000$50,000$40,000$30,000$20,000
$10,000
4 8 10 12 16 0Units Produced (000)
F = $48,000
3-9
SupervisionComputers Processed
$24,000 4,000 $6.0024,000 8,000 3.0024,000 10,000 2.4048,000 12,000 4.0048,000 16,000 3.0048,000 20,000 2.40
Unit Cost
Fixed CostsFixed CostsFixed CostsFixed Costs
Total Fixed Cost GraphTotal Fixed Cost GraphT
otal
Cos
ts$60,000$50,000$40,000$30,000$20,000
$10,000
4 8 10 12 16 0Units Produced (000)
F = $48,000
3-10
Variable Variable CostCost
Variable Variable CostCost
Variable costs are costs that in total
vary in direct proportion to changes in an activity driver.
3-11
A 3½-inch disk drive is added to each computer at a cost of $30 per computer. The total cost of disk drives for various
levels of production is a follows:
Variable CostVariable CostVariable CostVariable Cost
Total Cost of Disk Driver
Number of Computers Produced
Unit Cost of Disk Drives
$120,000 4,000 $30
240,000 8,000 30
360,000 12,000 30
480,000 16,000 30
600,000 20,000 30
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Variable CostVariable CostVariable CostVariable Cost
Y = VX
Y = Total variable costs
V = Variable cost per unit
X = Number of units of the driver
v
v
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Variable CostVariable CostVariable CostVariable CostCost
(in thousands)
$600
480
360
240
120
4,000 8,000 12,000 16,000 20,000
Y = $30Xv
Number of Computers Processed
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Nonlinearity of Variable CostNonlinearity of Variable CostNonlinearity of Variable CostNonlinearity of Variable Cost
Cost ($)
Units of Activity Driver0
Relevant Range
3-15
Mixed costs are costs that has
both a fixed and a variable
component.
Mixed Mixed CostsCosts
Mixed Mixed CostsCosts
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Y = Fixed cost + Total variable cost
Y = F + VX
where
Y = Total cost
Mixed Mixed CostsCosts
Mixed Mixed CostsCosts
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Mixed CostsMixed Costs
For Days Computer, the selling cost is represented by the following equation:
Y = $300,000 + $50X
3-18
Mixed CostsMixed Costs
Days Computers, Inc.
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
3-19
Mixed Cost BehaviorMixed Cost BehaviorCost
(in thousands)
$1,500
1,300
1,100
900
700
500
300
4,000 8,000 12,000 16,000 20,000 Number of Computers Sold
Variable Costs
Fixed Cost
3-20
Basic TermsBasic TermsBasic TermsBasic Terms
When a firm acquires the resources needed to perform
an activity, it is obtaining activity capacity.
When a firm acquires the resources needed to perform
an activity, it is obtaining activity capacity.The amount of activity
capacity needed which corresponds to the level
where the activity is performed efficiency is
called practical capacity.
The amount of activity capacity needed which corresponds to the level
where the activity is performed efficiency is
called practical capacity.
3-21
Flexible ResourcesFlexible ResourcesFlexible ResourcesFlexible Resources
Flexible resources are supplied as used and needed.
They are acquired from outside sources, where the terms of acquisition do not require any long-term commitment for any given amount of the resource.
Example: Materials and energy
3-22
Committed resources are supplied in advance of usage.
They are acquired by the use of either an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the amount of the resource available is fully used or not. Committed resources may have unused capacity.
Example: Buying or leasing a building or equipment
Committed ResourcesCommitted Resources
3-23
Committed fixed expenses are costs incurred for the acquisition of long-term capacity.
Example: Plant, equipment, warehouses, vehicles, and salaries of top employees
Discretionary fixed expenses are shorter-term committed resources.
Example: The hiring of new receiving clerks
Committed ResourcesCommitted Resources
3-24
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.
Step-Cost BehaviorStep-Cost Behavior
3-25
Cost
Activity Output (units)
$500
400
300
200
100
20 40 60 80 100 120
Step-Cost BehaviorStep-Cost Behavior
3-26
Normal Operating
Range (Relevant
Range)
Cost
$150,000
100,000
50,000
2,500 5,000 7,500
Activity Usage
Step-Fixed CostsStep-Fixed Costs
3-27
Cost of orders supplied = Cost of orders used + Cost of unused orders
Step-Fixed CostsStep-Fixed Costs
7,500($20) = 6,000($20) + 1, 500($20)
$150,000 = $120,000 + $30,000
The $30,000 of excess engineering capacity means that a new product could be
introduced without increasing current spending on engineering.
3-28
The High-Low Method
The Scatterplot Method
The Method of Least Squares
Methods for Separating Mixed CostsMethods for Separating Mixed CostsMethods for Separating Mixed CostsMethods for Separating Mixed Costs
Variable Component
Fixed Component
3-29
Methods for Separating Mixed CostsMethods for Separating Mixed CostsMethods for Separating Mixed CostsMethods for Separating Mixed Costs
Y = F + VX
Total activity cost
Fixed cost component
Variable cost per unit of activity
Measure of activity output
3-30
Month Material Handling Costs No. of MovesJanuary $2,000 100February 3,090 125March 2,780 175April 1,990 200May 7,500 500June 5,300 300July 4,300 250August 6,300 400September 5,600 475October 6,240 425
The High-Low MethodThe High-Low MethodThe High-Low MethodThe High-Low Method
Step 1: Solve for variable cost (V)Step 1: Solve for variable cost (V)
3-31
V = High Cost – Low Cost
High Units – Low Units
Month Material Handling Costs No. of MovesJanuary $2,000 100February 3,090 125March 2,780 175April 1,990 200May 7,500 500June 5,300 300July 4,300 250August 6,300 400September 5,600 475October 6,240 425
The High-Low MethodThe High-Low MethodThe High-Low MethodThe High-Low Method
3-32
Month Material Handling Costs No. of MovesJanuary $2,000 100February 3,090 125March 2,780 175April 1,990 200May 7,500 500June 5,300 300July 4,300 250August 6,300 400September 5,600 475October 6,240 425
The High-Low MethodThe High-Low MethodThe High-Low MethodThe High-Low Method
V = $7,500 – Low Cost
500 – Low Units
3-33
Month Material Handling Costs No. of MovesJanuary $2,000 100February 3,090 125March 2,780 175April 1,990 200May 7,500 500June 5,300 300July 4,300 250August 6,300 400September 5,600 475October 6,240 425
The High-Low MethodThe High-Low MethodThe High-Low MethodThe High-Low Method
V = $7,500 – $2,000
500 – 100
3-34
V = $7,500 – $2,000
500 – 100
V = $13.75 V = $13.75
Step 2: Using either the high cost or low cost, solve for the total fixed cost (F).
Step 2: Using either the high cost or low cost, solve for the total fixed cost (F).
The High-Low MethodThe High-Low Method
3-35
Y = F + V(X) $7,500 = F + $13.75(500) $625 = F
High End
High End
Y = F + V(X) $2,000 = F + $13.75(100) $625 = F
Low End
Low End
The cost formula using the high-low method is:
Total cost = $625 + ($13.75 x # of moves)
The High-Low MethodThe High-Low Method
3-36
Material Handling Cost
Number of Moves
The Scatterplot MethodThe Scatterplot Method
Graph A--Anderson Company
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
100 200 300 400 500
| | | | |
1
2 3
6
7
8
9
10
5
4
3-37
Material Handling Cost
Number of Moves
Graph B--High-Low Line
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
100 200 300 400 500
| | | | |
1
2 3
6
7
8
9
10
5
4
The Scatterplot MethodThe Scatterplot Method
3-38
Material Handling Cost
Number of Moves
Graph C—One Possible Scattergraph LIne
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
100 200 300 400 500
| | | | |
1
2 3
6
7
8
9
10
5
4
The Scatterplot MethodThe Scatterplot Method
3-39
ActivityCost
0
Activity Output
The Scatterplot MethodThe Scatterplot Method
Graph A--Nonlinear RelationshipGraph A--Nonlinear Relationship
3-40
Graph B--Upward Shift in Cost RelationshipGraph B--Upward Shift in Cost Relationship
ActivityCost
0
Activity Output
The Scatterplot MethodThe Scatterplot Method
3-41
Graph C--Presence of OutliersGraph C--Presence of Outliers
ActivityCost
0
Activity Output
The Scatterplot MethodThe Scatterplot Method
OutlierOutlier
OutlierOutlier
3-42
2,780 2,900 -120 14,4001,990 3,200 -1,10 1,464,1007,500 6,800 700 490,0005,300 4,400 900 810,0004,300 3,800 500 250,0006,300 5,600 700 490,0005,600 6,500 -900 810,0006,240 5,900 340 115,600
Total measure of closeness 5,068,200
The Method of Least SquaresThe Method of Least SquaresThe Method of Least SquaresThe Method of Least SquaresAnnual Cost Predicted Cost Deviation Deviation Squared
$2,000 $2,000 0 03,090 2,300 790 624,100
$3,090$3,090- 2,300- 2,300
790 x 790790 x 790
3-43
The Method of Least SquaresThe Method of Least SquaresThe Method of Least SquaresThe Method of Least Squares
Material Handling Cost
0Number of Moves
Line Deviations
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
100 200 300 400 500
| | | | |
1
2
3
6
7
8
910
5
4
3-44
The Method of Least SquaresThe Method of Least SquaresThe Method of Least SquaresThe Method of Least SquaresMonth Costs # MovesJanuary $2,000 100February 3,090 125March 2,780 175April 1,990 200May 7,500 500June 5,300 300July 4,300 250August 6,300 400September 5,600 475October 6,240 425
Spreadsheet Data for Anderson Company
3-45
SUMMARY OUTPUT Regression StatisticsMultiple R 0.92894908R. Square 0.862946394Adjusted R 0.845814693
SquareStandard Error 770.4987038Observations 10
ANOVAdf SS MS F
Regression 1 29903853.98 29903853.98 50.37132077Residual 8 4749346.021 593668.2526Total 9 34653200
Coefficient Standard Error t-Stat P-valueIntercept 854.4993582 569.7810263 1.49967811 0.172079925X Variable 1 12.3915276 1.745955536 7.097275588 0.000102268
The Method of Least SquaresThe Method of Least SquaresThe Method of Least SquaresThe Method of Least Squares
Regression Output for Anderson CompanyRegression Output for Anderson Company
3-46
The results give rise to the following equation:
The Method of Least SquaresThe Method of Least SquaresThe Method of Least SquaresThe Method of Least Squares
Material handling
cost= $854.50 + ($12.39 x number of items)
3-47
Coefficient of CorrelationCoefficient of Correlation
Positive Correlation
Machine Hours
Utilities Costs
r approaches +1
Machine Hours
Utilities Costs
3-48
Coefficient of CorrelationCoefficient of Correlation
Negative Correlation
Hours of Safety
Training
Industrial Accidents
r approaches –1
Hours of Safety
Training
Industrial Accidents
3-49
Coefficient of CorrelationCoefficient of Correlation
No Correlation
Hair Length
Accounting Grade
r ~ 0
Hair Length
Accounting Grade
3-50
Y = F + VY = F + V1 1 XX1 1 + V+ V2 2 XX22
X1 = Number of moves X2 = The total distance
Multiple RegressionMultiple RegressionMultiple RegressionMultiple Regression
3-51
Material Handling Number PoundsMonth Cost of Moves Moved
January $2,000 100 6,000February 3,090 125 15,000March 2,780 175 7,800April 1,990 200 600May 7,500 500 29,000June 5,300 300 23,000July 4,300 250 17,000August 6,300 400 25,000September 5,600 475 12,000October 6,240 425 22,400
Multiple RegressionMultiple RegressionMultiple RegressionMultiple Regression
3-52
Multiple RegressionMultiple RegressionMultiple RegressionMultiple Regression
Y = $507 + $7.84X + $0.11X1 2
= $507 + $7.84(350) + $0.11(17,000)
= $507 + $2.744 + $1,870
= $5,121
3-53
The Learning Curve and Nonlinear Behavior
3-54
1 100 100 1002 80 (0.8 x 100) 160 603 70.21 210.63 50.634 64 (0.8 x 80) 256 45.375 59.57 297.85 41.856 56.17 337.02 39.177 53.45 374.15 37.138 51.20 (0.8 x 64) 409.60 35.45
16 40.96 655.36 28.0632 32.77 1,048.64
Cumulative Cumulative Cumulative Individual UnitsCumulative Cumulative Cumulative Individual Units Number Average Time Total Time: Time for Number Average Time Total Time: Time for nnthth of Units per Unit in Hours Labor Hours Unit-Labor Hoursof Units per Unit in Hours Labor Hours Unit-Labor Hours (1) (2) (3) = (1) x (2) (4)(1) (2) (3) = (1) x (2) (4)
Data for Cumulative Average Time Learning Curve with 80 Percent Learning Rate
Data for Cumulative Average Time Learning Curve with 80 Percent Learning Rate
3-55
1,200 –
1,000 –
800 –
600 –
400 –
200 –
0 –1 5 10 15 20 25 30 35 36
Graph of Cumulative Total Hours Required and the Cumulative Average time per Unit
Graph of Cumulative Total Hours Required and the Cumulative Average time per Unit
Tot
al H
ours
Units
3-56
1 100 100 1002 80 (0.8 x 100) 180 903 70.21 259.21 83.404 64 (0.8 x 80) 314.21 78.555 59.57 373.78 74.766 56.17 429.95 71.667 53.45 483.40 69.068 51.20 (0.8 x 64) 534.60 66.83
16 40.96 892.00 55.75
Cumulative Individual Unit Cumulative CumulativeCumulative Individual Unit Cumulative Cumulative Number Time for Number Time for nnth Unit Total Time: Average Time perth Unit Total Time: Average Time per of Units in Labor Hours Labor Hours Unit-Labor Hoursof Units in Labor Hours Labor Hours Unit-Labor Hours (1) (2) (3) (4) = (3)/(1)(1) (2) (3) (4) = (3)/(1)
Data for an Incremental Unit-Time Learning Curve with an 80 Percent Learning Rate
Data for an Incremental Unit-Time Learning Curve with an 80 Percent Learning Rate
3-57
Managerial JudgmentManagerial JudgmentManagerial JudgmentManagerial Judgment
Managerial judgment is critically important in
determining cost behavior and is by far the most widely used
method in practice.
3-58
Chapter
End ofEnd of
3-59