2-1 HANSEN & MOWEN Cost Management ACCOUNTING AND CONTROL.

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HANSEN & MOWENHANSEN & MOWEN

Cost ManagementCost ManagementACCOUNTING AND CONTROLACCOUNTING AND CONTROL

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Cost BehaviorCost Behavior3

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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.

Basics of Cost BehaviorBasics of Cost Behavior 1

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.

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Supervision Computers Processed Unit Cost

$24,000 4,00024,000 8,00024,000 10,00048,000 12,00048,000 16,00048,000 20,000

Days Computers, Inc.

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$24,000 4,00024,000 8,00024,000 10,000

48,000 12,00048,000 16,00048,000 20,000

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$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


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4,000 8,000 12,000 16,000 20,000

$48,000

24,000

Supervision

Cost

F = $48,000

Fixed Cost BehaviorFixed Cost Behavior

Number of Computers Processed

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Variable CostsVariable CostsVariable CostsVariable Costs

Variable costs are costs that in total vary in direct proportion to

changes in an activity driver.


A 3½-inch disk drive is added to each computer at a cost of $30 per computer. The total cost of disk

drives for each level of production varies.

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Total Cost of Number of Unit Cost ofDisk Drives Computers Produced 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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Total Cost of Number of Unit Cost ofDisk Drives Computers Produced Disk Drives

$120,000 4,000 $30240,000 8,000 30360,000 12,000 30480,000 16,000 30600,000 20,000 30


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4,000 8,000 12,000 16,000 20,000

$600

120

Cost

VYV = $30X

Variable Cost BehaviorVariable Cost Behavior

(in thousands)

480

360

240

Number of Computers Processed

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Cost

Nonlinearity of Variable CostsNonlinearity of Variable Costs

($)

Units of Activity Driver

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Cost

Nonlinearity of Variable CostsNonlinearity of Variable Costs

($)

X*

Units of Activity Driver

Large

Error

Region

Error

Relevant Range

0

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Mixed costs are costs that has both a fixed and a variable component.

Mixed Mixed CostsCosts



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Y = Fixed cost + Total variable cost

Y = F + VX

where

Y = Total cost

For Days Computer, the selling cost is represented by the following equation:

Y = $300,000 + $50X

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Selling Cost Per Unit

Mixed CostsMixed Costs


Fixed Cost of Selling

Variable Cost of Selling

Total Cost

Computers Sold

$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

Number of Computers Sold

Variable Costs

Fixed Cost

500

300

700

900

1,100

1,300

4,000 8,000 12,000 16,000 20,000


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Resources, Activities, and Cost Resources, Activities, and Cost BehaviorBehavior 2

ResourcesResources

Flexible resources are acquired as used and needed. They are usually considered variable costs.

Example: Materials, energy

Committed resources are acquired in advance of usage. They are usually considered fixed costs.

Example: Buying or leasing a building or equipment

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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.

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Step-Cost FunctionStep-Cost Function

Cost

$600

100 120

100

200

20 40 60 80Activity Outputs (Units)

300

400

500

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Step-Fixed CostsStep-Fixed Costs

Cost

$150,000

100,000

50,000

2,500 5,000 7,500

Activity Output (Number of Engineering Change Orders)

Normal Operating

Range (Relevant

Range)

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The High-Low Method The Scatterplot Method The Method of Least

Squares

Variable Component

Fixed Component

Methods for Separating Mixed Costs Methods for Separating Mixed Costs into Fixed and Variable Componentsinto Fixed and Variable Components 3

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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

Step 1: Solve for variable cost (V)V = Change in cost / Change in activity

Step 1: Solve for variable cost (V)V = Change in cost / Change in activity

The High-Low MethodThe High-Low Method


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Low

High

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



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).



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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)



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Mat

eria

l Han

dlin

g C

ost

Number of Moves

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

The Scattergraph for Anderson CompanyThe Scattergraph for Anderson Company


2-29Number 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


Mat

eria

l Han

dlin

g C

ost


2-30Number 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

3M

ater

ial H

andl

ing

Cos

t

Methods for Separating Mixed Costs Methods for Separating Mixed Costs into Fixed and Variable Componentsinto Fixed and Variable Components


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ActivityCost

0

Activity Output

Graph A--Nonlinear Relationship

Cost Behavior PatternsCost Behavior Patterns


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Graph B--Upward Shift in Cost RelationshipActivity

Cost

0

Activity Output



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Graph C--Presence of OutliersActivity

Cost

0

Activity OutputOutlierOutlier

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 Squares

Annual 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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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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Month 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

Regression Output for Anderson CompanyRegression Output for Anderson Company



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The results give rise to the following equation:

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

Reliability of Cost FormulasReliability of Cost Formulas 4

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Negative Correlation

Hours of Safety

Training

Industrial Accidents

r approaches –1

Hours of Safety

Training

Industrial Accidents



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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 Regression 5

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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


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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 The Learning Curve and Nonlinear Cost BehaviorNonlinear Cost Behavior 6

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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 Units Number Average Time Total Time: Time for nth of Units per Unit in Hours Labor Hours Unit-Labor Hours (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

Cumulative total hours required

Cumulative average time

per unit


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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 Cumulative Number Time for nth Unit Total Time: Average Time per of Units in Labor Hours Labor Hours Unit-Labor Hours (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 Judgment 7

Managerial judgment is critically important in determining cost

behavior and is by far the most widely used method in practice.

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End of End of Chapter 3Chapter 3

2-1 HANSEN & MOWEN Cost Management ACCOUNTING AND CONTROL.

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