3
Activity Cost
Behaviour
PowerPresentation® prepared by
David J. McConomy, Queen’s University
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-1
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.
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-2
Learning Objectives
(continued)

Separate mixed costs into their fixed and
variable components using the high-low
method, the scatterplot method, and the
method of least squares.
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-3
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.
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-4
Cost Behaviour
Fixed-Cost Behaviour
$
Variable-Cost Behaviour
$
Relevant Range
Units Produced
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Units Produced
3-5
Mixed-Cost Behaviour
Linearity Assumption
Total Costs
Cost
Fixed Costs
Variable Costs
Number of Units Produced
Total cost = Fixed cost + Total variable cost
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-6
Activity Cost Behaviour Model
Inputs:
Materials
Energy
Activities
Activity Output
Labour
Capital
Cost Behaviour
Changes in Input Cost
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
Changes in Output
3-7
Basic 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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3-8
Types of Resources

Flexible Resources

Committed Resources

Discretionary Fixed
Costs
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3-9
Flexible Resources

Flexible resources are supplied as
used and needed.
They are acquired from outside
sources, where the terms of
acquisition do not require any longterm commitment for any given
amount of the resource
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3-10
Committed 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.
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-11
Discretionary Fixed Costs

Discretionary fixed costs are shorterterm committed resources
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3-12
Step-Cost Function
Cost
Narrow Width
Activity Output (units)
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3-13
Step-Fixed Costs
Cost
Normal
Operating
Range
(Relevant Range)
Activity Usage
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3-14
Resource 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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3-15
Resource 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
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-16
Resource Relationships Example
(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
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-17
Resource Relationships Example
(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.
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-18
Methods for Separating Mixed Costs into
Fixed and Variable Components

The High-Low Method

The Scatterplot Method

The Method of Least Squares
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3-19
High-Low Method: An Example
Month
January
February
March
April
May
Setup Costs
$1,000
1,250
2,250
2,500
3,750
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Setup Hours
100
200
300
400
500
3-20
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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3-21
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)
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-22
Activity
Cost
Scatterplot Method
$4,000
3,000
Important: Cost function is only
relevant within relevant range
.
2,000
1,000
0
.
100
.
200
.
Analyst can fit line
based on his or her
experience
300
400
Activity Hours
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
.
500
3-23
Nonlinear Relationship`
Activity
Cost
*
*
*
*
*
0
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Activity Output
3-24
Upward Shift in Cost Relationship
Activity
Cost
*
*
*
*
*
*
0
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Activity Output
3-25
Presence of Outliers
Activity
Cost
*
*
*
*
*
*
0
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Activity Output
3-26
Least Squares
Constant
Standard Error of Y Est
R squared
No. of Observations
Degrees of Freedom
X Coefficient(s)
Standard Error of Coef.
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
125
299.304749934466
0.944300518134715
5
3
6.75
0.9464847243
3-27
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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3-28
Multiple Regression
TC = b0 + b1X1 + b2X2 + . . .
b0 = the fixed cost or intercept
bi = the variable rate for the ith independent variable
Xi = the ith independent variable
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3-29
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
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
3-30
Multiple Regression (continued)
Constant
Std Error of Y Est
R squared
No. of Observations
Degrees of Freedom
243.11149907159
55.5082829356447
0.96717927255452
12
9
X Coefficient(s) 1.09715750519456
Std Err of Coef. 0.210226332115593
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510.49073361447
32.5489645352191
3-31
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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3-32
Cost Behaviour and Managerial
Judgment
Some Tips



Use past experience
Try to confirm results with operating
personnel
Use common sense to confirm
statistical studies
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3-33