3-1 Activity Cost Behavior Prepared by Douglas Cloud Pepperdine University Prepared by Douglas Cloud Pepperdine University.

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Activity Cost Activity Cost BehaviorBehavior

Prepared by Douglas Cloud

Pepperdine University

Prepared by Douglas Cloud

Pepperdine University

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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:

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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.

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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

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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

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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

4 8 10 12 16 0Units Produced (000)

F = $48,000

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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

4 8 10 12 16 0Units Produced (000)

F = $48,000

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Variable Variable CostCost

Variable Variable CostCost

Variable costs are costs that in total

vary in direct proportion to changes in an activity driver.

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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

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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

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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

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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

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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.

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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

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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

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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

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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

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Cost

Activity Output (units)

$500

400

300

200

100

20 40 60 80 100 120

Step-Cost BehaviorStep-Cost Behavior

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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

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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.

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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ActivityCost

0

Activity Output

The Scatterplot MethodThe Scatterplot Method

Graph A--Nonlinear RelationshipGraph A--Nonlinear Relationship

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Graph B--Upward Shift in Cost RelationshipGraph B--Upward Shift in Cost Relationship

ActivityCost

0

Activity Output

The Scatterplot MethodThe Scatterplot Method

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Graph C--Presence of OutliersGraph C--Presence of Outliers

ActivityCost

0

Activity Output

The Scatterplot MethodThe Scatterplot Method

OutlierOutlier

OutlierOutlier

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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

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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

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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

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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

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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)

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Coefficient of CorrelationCoefficient of Correlation

Positive Correlation

Machine Hours

Utilities Costs

r approaches +1

Machine Hours

Utilities Costs

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Coefficient of CorrelationCoefficient of Correlation

Negative Correlation

Hours of Safety

Training

Industrial Accidents

r approaches –1

Hours of Safety

Training

Industrial Accidents

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Coefficient of CorrelationCoefficient of Correlation

No Correlation

Hair Length

Accounting Grade

r ~ 0

Hair Length

Accounting Grade

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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

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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

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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

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The Learning Curve and Nonlinear Behavior

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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

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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

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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

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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.

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Chapter

End ofEnd of

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