Chapter 3
Cost Behaviour
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Learning Objectives
1.
2.
3.
Explain cost behaviour, define fixed and variable costs
Define mixed and step costs
Separate mixed costs into fixed and variable
components using the following methods:
•
•
•
4.
High-Low
Sattergraph
Least Squares
(Appendix) Use a computer spreadsheet program to
perform the method of least squares
3-2
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OBJECTIVE 1
Explain the meaning of cost
and behaviour, define fixed
and variable costs
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Cost Behaviour
Cost Behaviour: The way costs change
as the related activity changes
Output
Total Cost
Increase
No change
Decrease
No change
Fixed Cost =
A cost that does not
change in total as output
changes
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3-4
Cost Behaviour
Cost Behaviour: The way costs change
as the related activity changes
Output
Total Cost
Increase
Increase
Decrease
Decrease
Variable Cost =
A cost that changes in total
as output changes
3-5
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Measures of Output
To determine if a cost is fixed or
variable, we must first determine the
underlying business activity and ask…
“What causes the cost of this particular
activity to go up/down?”
In other words, we are trying to
identify its driver
3-6
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Relevant Range
The range of output over which the assumed
cost relationship is valid for the normal
operations of a firm
• Avoids extremely high levels of activity
• Avoids extremely low levels of activity
Let’s take a closer look at fixed,
variable, and mixed costs, in light
of the relevant range
3-7
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Example
SyBan Computers Inc. wants to look at the cost
relationship between supervision cost and the
number of computers processed per year
• It process up to 50,000 computers per year
• Production-line manager is paid $32,000 per year
• Factory produces 40,000 to 50,000 computers per
year
• Production has never fallen below 20,000 computers
in a year
Let’s look at the cost of
supervision at several
production levels
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3-8
Fixed Cost Example
Fixed Costs = Costs that in total are constant
within the relevant range as the level of output
increases or decreases
# of Computers
Produced
Total Cost of
Supervision
Unit Cost
20,000
$32,000
$1.60
30,000
$32,000
$1.07
40,000
$32,000
$0.80
50,000
$32,000
$0.64
3-9
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Discretionary vs. Committed
Fixed Costs
Discretionary
Fixed Costs =
Fixed costs that can be
changed relatively easily at
management discretion
Committed
Fixed Costs =
Fixed costs that can not be
easily changed
Often these involve a long-term
contract
3-10
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Variable Cost Behaviour
Example
Expanding our SyBan Computers example….
•
•
Each computer requires one DVD-ROM drive
costing $40
The cost of DVD-ROM drives for various
levels of production is as follows:
Let’s look at the cost of DVDROM’s at several production
levels
3-11
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Variable Cost Example
Variable Costs = Costs that in total vary in direct
proportion to changes in output within the relevant range
# of Computers
Total Cost of
Produced
DVD-ROM Drives
Unit Cost
20,000
$800,000
$40
30,000
$1,200,000
$40
40,000
$1,600,000
$40
50,000
$2,000,000
$40
3-12
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Variable Cost Relationship
Total Variable
Cost
$2,000,000
Amount of
output
=
Variable
Rate
×
=
$40 per
computer
50,000
× computers
Let’s look at the DVD-ROM’s
cost for 50,000 computers
3-13
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OBJECTIVE 2
Define and describe mixed
and step costs
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Mixed Costs
Costs that have both a fixed and
a variable component
Total Cost
=
Total Fixed
Cost
Total Variable
+
Cost
Let’s look at an example from
the SyBan Computers
15
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Example
SyBan Computers has 10 sales representatives
•
•
•
Each earns a salary of $30,000 per year
And a commission of $25 per computer sold
Each sales rep sells up to 50,000 computers
per year
Let’s plug this into our mixed
cost formula
3-16
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Mixed Cost Example
Total Cost
Total Cost
Total Fixed
Cost
=
=
+
$30,000 +
Total Variable
Cost
($25 × # of
computers sold)
Example:
$130,000
=
$30,000 +
($25 × 4,000
computers sold)
3-17
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Step Costs
Display a constant cost for a range of output
Then jumps to a new cost level for a
different range
$15 per unit
Example:
$10 per unit
$5 per unit
1,000 +
500 to 1,000
1 to 500 units
3-18
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OBJECTIVE 3
Separate mixed costs into their
fixed and variable components
using the high-low method, the
scattergraph method, and the
method of least squares
COPYRIGHT © 2012 Nelson Education Ltd.
Separating Costs
Accounting records typically show only total cost
and associated amount of activity of a mixed cost
item
Therefore it is necessary to separate the total
cost into its fixed and variable components
Three methods:
1. High-Low method
2. Scattergraph method
3. Method of Least Squares
How do we separate
the costs?
3-20
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Dependent Variable in the
Cost Formula
Total
Cost
= Total Fixed +
Cost
Total Variable
Cost
Total
Cost
Total Fixed
Variable × Output
=
+
Cost
Rate
Dependent Variable is a variable whose value
depends on the value of another variable
3-21
COPYRIGHT © 2012 Nelson Education Ltd.
Independent Variable in the
Cost Formula
Total
Cost
= Total Fixed +
Cost
Total Variable
Cost
Total
Cost
Total Fixed
Variable × Output
=
+
Cost
Rate
Independent Variable is a variable that measures
output and explains changes in the cost
3-22
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Intersect & Slope
Intersect:
• Point at which the cost
line intercepts the cost
(vertical) axis
Slope:
Corresponds to
variable rate
(variable cost
per unit of output)
• Slope of the cost line
Let’s look at the
formula
Intercept
3-23
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Intercept & Slope
in the Cost Formula
Total
Cost
Total Fixed
=
+
Cost
Total
Cost
=
Total Fixed
Cost
+
Total Variable
Cost
Variable
× Output
Rate
Intercept
Slope
3-24
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Example: Cornerstone 3-1
How to Create and Use a Cost Formula
Information:
• College art and graphics department decided to equip each faculty
office with an inkjet colour printer
• Printers had monthly depreciation of $250
• Department purchased paper in boxes of 10,000 sheets for $35
per box
• Ink cartridges cost $30 and will print, on average, 300 sheets
Required:
• Create a formula for the monthly cost of inkjet printing
• If the department expects to print 4,400 pages next month, what is…
• Expected fixed cost?
• Total variable cost?
• Total printing cost?
3-25
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Example Continued
Total Cost = Total Fixed Cost + Total Variable Cost
Total Cost =
$250
+ ($0.1035 × No. of pages)
Using 4,400 as the # of pages….
($0.1035 × 4,400)
$705.40 =
Total Costs for
4,400 pages
$250
Total Fixed
Costs
+
$455.40
Total Variable
Cost
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3-26
High-Low Method
A method of separating mixed costs into fixed & variable
components by using just the high and low data points
Step 1: Find the high point and low point
Step 2: Using the high and low points, calculate the
variable rate
Variable rate =
High point cost – Low point cost
High point output – Low point output
3-27
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High-Low Method
Step 3: Calculate the fixed cost using the variable
rate and either the high point or the low point
Total cost at
(Variable rate x Output
Fixed Cost =
high point
at high point)
Or Low Point
Step 4: Form the cost formula based on the high-low
method
Cornerstone 3-2 will walk us
through an example
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3-28
Example: Cornerstone 3-2
How to use the High-Low Method
Information:
Blue Denim Company controller wants to calculate the fixed and
variable costs associated with electricity used in the factory
Required:
Using the High-Low method, calculate:
• fixed cost of electricity
• the variable rate per machine hour
• construct the cost formula for total electricity cost
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3-29
Blue Denim Company
Step 1: Identify the high and low points
Month
Electricity Costs
Machine Hours
January
February
$3,255
3,485
March
April
May
June
July
August
4,100
3,300
3,312
2,575
3,910
4,200
450
500
600
470
470
350
570
590
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3-30
Blue Denim Company
Month
Electricity Costs
Machine Hours
January
February
$3,255
3,485
March
April
May
June
July
August
4,100
3,300
3,312
2,575
3,910
4,200
450
500
600
470
470
350
570
590
High Point
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Blue Denim Company
Month
Electricity Costs
Machine Hours
January
February
$3,255
3,485
March
April
May
June
July
August
4,100
3,300
3,312
2,575
3,910
4,200
450
500
600
470
470
350
570
590
Low Point
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3-32
High-Low Method
Step 2: Calculate the variable rate
High point cost – Low point cost
Variable rate =
High point output – Low point output
Variable rate =
$4,100 – $2,575
600 – 350
Variable rate = $6.10 per machine hour
3-33
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High-Low Method
Step 3: Calculate the fixed cost using the variable rate
and either the high point or the low point
Fixed Cost =
Total cost at
(Variable rate ×
–
high point
Output at high point)
Fixed Cost =
$4,100
– ($6.10 × 600)
Fixed Cost =
$4,100
– $3,660
Fixed Cost =
$440
3-34
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High-Low Method
Step 4: Construct a cost formula
Total electricity cost = $440 + ($6.10 x Machine hrs.)
3-35
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Example: Cornerstone 3-3
How to use the High-Low Method to Calculate Predicted
Total Variable Cost and Total Cost for Budgeted Output
Information:
Blue Denim’s formula for monthly electrical cost:
Total electricity
cost
=
$440 + ($6.10 × Machine Hrs)
Required:
Assume that 550 machine hours are budgeted for the month of September.
Using the formula calculate the following:
• Total variable electricity cost for October
• Total electricity cost for October
3-36
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Example
Monthly Electricity Cost Formula:
Total electricity cost = $440 + ($6.10 × Machine hrs.)
Total electricity cost = $440 + ($6.10 × 550)
Total electricity cost = $440 +
550 machine
$3,355
hours
Total electricity cost = $3,795
Total variable
electricity cost
3-37
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High-Low Method
Disadvantages:
•
High and low points can be outliers and may
represent atypical cost-activity relationships
•
Even if these points are not outliers, other
pairs of points may clearly be more
representative
The scattergraph method does a better job
of separating the costs
3-38
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Scattergraph Method
Purpose of the Method:
• To see whether a straight line reasonably
describes the cost relationship
• To reveal one or more points that do not
seem to fit the general pattern of
behaviour
3-39
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Scattergraph Method
Applying the Method:
• Draw a graph with units on the x-axis and cost on the y-axis
• Plot the data points on the graph
• Visually fit a line to the data points on the graph
• The intercept is the fixed cost
• Use the high-low method using the points from the graph to
determine the variable rate
Disadvantage:
Lack of any objective criterion for choosing the best fitting line
3-40
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Method of Least Squares
A statistical way to find the best-fitting line through a set
of data points
What does best fitting mean?
The line is one in which the data points are
closer to the line than to any other line
Steps:
•Measure distance from points to line
•Then square the differences
•Add up all the squared differences
▪
▪▪ ▪ ▪
▪
▪ ▪
3-41
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Example: Cornerstone 3-4
How to use the Regression Method to
calculate fixed cost and variable rate, construct
a cost formula and to determine budgeted cost
Information:
Blue Denim’s electricity cost and machine hours data for the past nine months
Coefficients shown by regression program:
Intercept
321
X Variable
6.38
Required:
Using the results of regression, calculate:
•
•
•
The fixed cost of electricity and the variable rate per machine hour
Construct the cost formula for total electricity cost
Calculate the budgeted cost for next month assuming 550 budgeted machine hours
3-42
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Example
The fixed cost and the variable rate are given
directly by regression
Fixed Cost = $321
Variable Rate = $6.38
Intercept
X Variable
Total Electricity Cost
=
Fixed Cost
+ Variable Cost
Total Electricity Cost
=
$321
+ ($6.38 × 550)
Total Electricity Cost
=
$3,830
Budgeted machine hours
3-43
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Managerial Judgment
Instead of the three methods
previously discussed, many managers
use their experience and past
observation of cost relationships to
determine fixed and variable costs
Statistical techniques are highly
accurate in depicting the past, but
they cannot foresee the future
3-44
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