3-1Copyright © 2004 by Nelson, a division of Thomson Canada Limited.

Activity Cost Activity Cost BehaviourBehaviour

33

PowerPresentation® prepared by PowerPresentation® prepared by

David J. McConomy, Queen’s UniversityDavid J. McConomy, Queen’s University

3-2Copyright © 2004 by Nelson, a division of Thomson Canada Limited.

Learning Objectives

Define and describe cost behaviour for fixed, variable, and mixed costs.

Explain the role of the resource usage model in understanding cost behaviour.

Learning Objectives Learning Objectives

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Separate mixed costs into their fixed and

variable components using the high-low

method, the scatterplot method, and the

method of least squares.

Learning ObjectivesLearning Objectives(continued) (continued)

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Learning Objectives (continued)Learning Objectives (continued)

Evaluate the reliability of a cost equation.

Explain the role of multiple regression in assessing cost behaviour.

Describe the use of managerial judgment in determining cost behaviour.

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Cost BehaviourCost Behaviour

Fixed-Cost Behaviour Variable-Cost Behaviour

$ $Relevant Range

Units Produced Units Produced

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Mixed-Cost BehaviourMixed-Cost Behaviour

Total Costs

Cost

Number of Units Produced

Fixed Costs Variable Costs

Linearity Assumption

Total cost = Fixed cost + Total variable cost

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Activity Cost Behaviour ModelActivity Cost Behaviour Model

Inputs:

Materials

Energy

Labour

Capital

Cost Behaviour

Activities Activity Output

Changes in Input Cost Changes in Output

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Basic TermsBasic Terms

The linearity assumption assumes that variable costs increase in direct proportion to the number of units produced (or activity units used).

Practical capacity is the efficient level of activity performance.

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Types of ResourcesTypes of Resources

Flexible Resources

Committed Resources

Discretionary Fixed Costs

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Flexible 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

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Committed ResourcesCommitted Resources

Committed resources are resources that 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.

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Discretionary Fixed CostsDiscretionary Fixed Costs

Discretionary fixed costs are shorter-term committed resources

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Step-Cost FunctionStep-Cost Function

Cost

Activity Output (units)

Narrow Width

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Step-Fixed CostsStep-Fixed Costs

Cost

Activity Usage

Normal Operating

Range

(Relevant Range)

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Resource RelationshipsResource Relationships

The relationship between resources supplied and resources used is expressed by the following equation:

Resources available = Resources used + Unused capacity

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Resource Relationships ExampleResource Relationships Example

Three engineers hired at $50,000 each

Each engineer is capable of processing 2,500 change orders

$90,000 was spent on supplies for the engineering activity

There were 6,000 orders processed

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Resource Relationships Example Resource Relationships Example (continued)(continued)

Available orders = Orders used + Orders unused

7,500 orders = 6,000 orders + 1,500 orders

Fixed engineering rate = $150,000/7,500

= $20 per change order

Variable engineering rate = $90,000/6,000

= $15 per change order

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Resource Relationships Example Resource Relationships Example (continued)(continued)

Cost of orders supplied = Cost of orders used + Cost of unused orders

= [($20 + $15) x 6,000] + ($20 x 1,500)

= $240,000

Of course, the $240,000 is precisely equal to the $150,000 spent on engineers and the $90,000 spent on supplies.

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

The High-Low Method

The Scatterplot Method

The Method of Least Squares

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Month Setup Costs Setup Hours

January $1,000 100

February 1,250 200

March 2,250 300

April 2,500 400

May 3,750 500

High-Low Method: An ExampleHigh-Low Method: An Example

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The High-Low Method (continued)The High-Low Method (continued)

Variable Rate (V)= Change in cost/Change in output

V = (High cost - Low cost) / (High output - Low output)

V = ($3,750 - $1,000) / (500 - 100)

V = $2,750 / 400

V = $6.875 per setup hour

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The High-Low Method (continued)The High-Low Method (continued)

3,750 = Fixed costs + $6.875 (500)

Fixed costs = $3,750.00 - $3,437.50

Fixed costs = $312.50

The cost formula using the high-low method is:

Total cost = $312.50 + ($6.875 x setup hours)

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Activity Hours

Activity

Cost

$4,000

3,000

2,000

1,000

0100 200 300 400 500

.

Scatterplot MethodScatterplot Method

.

. .

.

Analyst can fit line

based on his or her

experience

Important: Cost function is only

relevant within relevant range

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Nonlinear Relationship`Nonlinear Relationship`

ActivityCost

0 Activity Output

*

*

***

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Upward Shift in Cost RelationshipUpward Shift in Cost Relationship

ActivityCost

0 Activity Output

**

*

**

*

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Presence of OutliersPresence of Outliers

ActivityCost

0 Activity Output

**

*

*

**

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Least SquaresLeast Squares

Constant 125

Standard Error of Y Est 299.304749934466

R squared 0.944300518134715

No. of Observations 5

Degrees of Freedom 3

X Coefficient(s) 6.75

Standard Error of Coef. 0.9464847243

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Least Squares (continued)Least Squares (continued)

The results give rise to the following equation:

Setup Costs = $125 + ($6.75 x # of setup hours)

R2 = .944, or 94.4 percent of the variation in

setup costs is explained by the

number of setup hours variable.

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TC = b0 + b1X1 + b2X2 + . . .

b0 = the fixed cost or intercept

bi = the variable rate for the ith independent variable

Xi = the ith independent variable

Multiple RegressionMultiple Regression

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Multiple Regression (continued)Multiple Regression (continued)Utility

Month MHrs Summer Cost

January 1,340 0 $1,688

February 1,298 0 1,636

March 1,376 0 1,734

April 1,405 0 1,770

May 1,500 1 2,390

June 1,432 1 2,304

July 1,322 1 2,166

August 1,416 1 2,284

September 1,370 1 1,730

October 1,580 0 1,991

November 1,460 0 1,840

December 1,455 0 1,833

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Multiple Regression (continued)Multiple Regression (continued)

Constant 243.11149907159

Std Error of Y Est 55.5082829356447

R squared 0.96717927255452

No. of Observations 12

Degrees of Freedom 9

X Coefficient(s) 1.09715750519456 510.49073361447

Std Err of Coef. 0.210226332115593 32.5489645352191

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Multiple Regression (continued)Multiple Regression (continued)

The results gives rise to the following equation:

Utilities cost = $243.11 + $1.097(MH) + $510.49(Summer)

R2 = .967, or 96.7 percent of the variation in utilities cost is explained by the machine hours and summer variables.

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Cost Behaviour and Managerial Cost Behaviour and Managerial JudgmentJudgment

Use past experience Try to confirm results with operating

personnel Use common sense to confirm

statistical studies

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