Chapter 5
Cost Behavior:
Analysis and Use
Types of Cost Behavior
Patterns
Recall the summary of our cost behavior
discussion from Chapter 2.
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Fixed
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
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The Activity Base
Units
produce
d
Machine
hours
A measure of the
event that causes
the incurrence of a
variable cost – a
cost driver
Miles
driven
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Labor
hours
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True Variable Cost Example
Total Long Distance
Telephone Bill
Your total long distance telephone bill is
based on how many minutes you talk.
Minutes Talked
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Variable Cost Per Unit Example
Per Minute
Telephone Charge
The cost per minute talked is constant. For
example, 10 cents per minute.
Minutes Talked
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Step-Variable Costs
Cost
Total cost remains
constant within a
narrow range of
activity.
Activity
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Step-Variable Costs
Cost
Total cost increases to a
new higher cost for the
next higher range of
activity.
Activity
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The Linearity Assumption and
the Relevant Range
Exh.
5-4
Total Cost
A straight line
Economist’s
closely
Curvilinear Cost approximates a
Function
curvilinear
Relevant
Range
variable cost
line within the
relevant range.
Accountant’s Straight-Line
Approximation (constant
unit variable cost)
Activity
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Exh.
5-5
Total Fixed Cost Example
Monthly Basic
Telephone Bill
Your monthly basic telephone bill is
probably fixed and does not change when
you make more local calls.
Number of Local Calls
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Exh.
5-5
Fixed Cost Per Unit Example
Monthly Basic Telephone
Bill per Local Call
The fixed cost per local call decreases as
more local calls are made.
Number of Local Calls
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Cost Behavior
Examples of normally variable costs
Merchandisers
Service Organizations
Cost of Goods Sold
Supplies and travel
Manufacturers
Merchandisers and
Manufacturers
Direct Material, Direct
Labor, and Variable
Manufacturing Overhead
Sales commissions and
shipping costs
Examples of normally fixed costs
Merchandisers, manufacturers, and
service organizations
Real estate taxes, Insurance, Sales salaries
Depreciation, Advertising
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Types of Fixed Costs
Committed
Discretionary
Long-term, cannot be
reduced in the short
term.
May be altered in the
short-term by current
managerial decisions
Examples
Examples
Depreciation on
Buildings and
Equipment
Advertising and
Research and
Development
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Fixed Costs and Relevant
Range
Example: Office space
is available at a rental
rate of $30,000 per year
in increments of 1,000
square feet. As the
business grows more
space is rented,
increasing the total cost.
Continue
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Rent Cost in
Thousands of Dollars
Fixed Costs and Relevant
Range
Exh.
5-6
90
60
30
00
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Relevant
Range
Total cost doesn’t
change for a wide
range of activity,
and then jumps to a
new higher cost for
the next higher
range of activity.
1,000
2,000
3,000
Rented Area (Square Feet)
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Fixed Costs and Relevant
Range
How does this type
of fixed cost differ
from a step-variable
cost?
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Step-variable costs
can be adjusted more
quickly and . . .
The width of the
activity steps is much
wider for the fixed
cost.
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Quick Check 
Which of the following statements about
cost behavior are true?
a Fixed costs per unit vary with the level of activity.
b Variable costs per unit are constant within the
relevant range.
c Total fixed costs are constant within the relevant
range.
d Total variable costs are constant within the
relevant range.
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Mixed Costs
A mixed cost has both fixed and variable
components. Consider the example of utility cost.
Total Utility Cost
Y
Variable
Cost per KW
X
Activity (Kilowatt
Hours)
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Fixed Monthly
Utility Charge
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Mixed Costs
The total mixed cost line can be expressed
as an equation: Y = a + bX
Where:
Total Utility Cost
Y
Y = the total mixed cost
a = the total fixed cost (the
vertical intercept of the line)
b = the variable cost per unit of
activity (the slope of the line)
X = the level of activity
Variable
Cost per KW
X
Activity (Kilowatt
Hours)
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Fixed Monthly
Utility Charge
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The Analysis of Mixed Costs
Account Analysis
Engineering Approach
Scattergraph Plot
High-Low Method
Least-Square Regression Method
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Account Analysis &
Engineering Estimates
Each account is classified as either
variable or fixed based on the analyst’s
knowledge of how the account behaves.
Cost estimates are based on an
evaluation of production methods,
and material, labor and overhead
requirements.
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The Scattergraph Method
Plot the data points on a
graph (total cost vs. activity).
Total Cost in
1,000’s of Dollars
Y
20
10
0
* *
* *
* ** *
**
X
0
1
2
3
4
Activity, 1,000’s of Units Produced
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Quick-and-Dirty Method
Draw a line through the data points with about an
equal numbers of points above and below the line.
Total Cost in
1,000’s of Dollars
Y
20
10
* ** *
**
* *
*
* Intercept
is the estimated
fixed cost = $10,000
0
X
0
1
2
3
4
Activity, 1,000’s of Units Produced
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Quick-and-Dirty Method
The slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units
Total Cost in
1,000’s of Dollars
Y
20
10
0
* *
*
*Horizontal
distance is
the change in
activity.
* ** *
**
Vertical distance is
the change in cost.
X
0
1
2
3
4
Activity, 1,000’s of Units Produced
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The High-Low Method
WiseCo recorded the following production activity and
maintenance costs for two months:
High activity level
Low activity level
Change
Units
8,000
5,000
3,000
Cost
$ 9,800
7,400
$ 2,400
Using these two levels of activity, compute:
the variable cost per unit;
the fixed cost; and then
express the costs in equation form Y = a + bX.
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The High-Low Method
High activity level
Low activity level
Change
Units
8,000
5,000
3,000
Cost
$ 9,800
7,400
$ 2,400
in cost in units
 Variable cost per unit = ChangeChange
in cost ÷ change
Change in units
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The High-Low Method
High activity level
Low activity level
Change
Units
8,000
5,000
3,000
Cost
$ 9,800
7,400
$ 2,400
 Variable cost per unit = $2,400 ÷ 3,000 units
= $0.80 per unit
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The High-Low Method
High activity level
Low activity level
Change
Units
8,000
5,000
3,000
Cost
$ 9,800
7,400
$ 2,400
 Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit
 Fixed cost = Total cost – Total variable cost
Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)
Fixed cost = $9,800 – $6,400 = $3,400
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The High-Low Method
High activity level
Low activity level
Change
Units
8,000
5,000
3,000
Cost
$ 9,800
7,400
$ 2,400
 Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit
 Fixed cost = Total cost – Total variable cost
Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)
Fixed cost = $9,800 – $6,400 = $3,400
 Total cost = Fixed cost + Variable cost (Y = a + bX)
Y = $3,400 + $0.80X
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Quick Check 
Sales salaries and commissions are $10,000 when
80,000 units are sold, and $14,000 when 120,000 units
are sold. Using the high-low method, what is the
variable portion of sales salaries and commission?
a. $0.08 per unit
Units
Cost
b. $0.10 per unit
High level
120,000
$ 14,000
c. $0.12 per unit
Low level
80,000
10,000
d. $0.125 per unit
Change
40,000
$ 4,000
$4,000 ÷ 40,000 units
= $0.10 per unit
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Quick Check 
Sales salaries and commissions are $10,000 when
80,000 units are sold, and $14,000 when 120,000 units
are sold. Using the high-low method, what is the
fixed portion of sales salaries and commissions?
a. $ 2,000
Total cost = Total fixed cost +
Total variable cost
b. $ 4,000
c. $10,000
$14,000 = Total fixed cost +
($0.10 × 120,000 units)
d. $12,000
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Total fixed cost
= $14,000 - $12,000
Total fixed cost
= $2,000
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Least-Squares Regression
Method
Software can be used to fit
a regression line through
the data points.
The cost analysis objective
is the same: Y = a + bx
Least-squares regression also provides a statistic,
called the R2, that is a measure of the goodness
of fit of the regression line to the data points.
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Least-Squares Regression
Method
R2 is the percentage of the variation in total cost
explained by the activity.
Y
Total Cost
20
* ** *
**
* *
* * R2 for this relationship is near
10
100% since the data points are
very close to the regression line.
0
0
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1
2
3
Activity
4
X
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Cost Estimation Methods
Regression Analysis
A statistical method used to create an
equation relating independent (or X)
variables to dependent (or Y) variables.
Past data is used to estimate relationships
between costs and activities.
Independent variables
are the cost drivers that
are correlated with the
dependent variables.
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Dependent variables are
caused by the
independent variables.
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Cost Estimation Methods
Regression Analysis
The simple cost model is actually a
regression model:
TC = F + VX
This model will only
be useful within a
relevant range of
activity.
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Caution: Before doing
the analysis, take time
to determine if a
logical relationship
between the variables
exists.
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Cost Estimation Methods
Regression Analysis
A set of data can be regressed using several
techniques:
•Manual computations
•SPSS or SAS Statistical Software
•Excel or other spreadsheet
The result of the
regression process is a
regression model:
TC = F + VX
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Each regression model
has an R-square (R2)
measure of how good the
model is.
Range of R2 = 0 to 1.0
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Simple Regression Analysis
Example
Fasco wants to
know it’s average
fixed cost and
variable cost per
unit.
Using the data to
the right, let’s see
how to do a
regression using
Excel.
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Month
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
Total Costs
$6,720
7,260
7,270
11,060
12,580
8,660
8,580
9,550
13,050
11,060
7,320
7,370
6,790
7,480
6,990
11,400
Units (Meals)
1,280
1,810
1,620
2,830
3,630
2,610
2,460
2,640
3,620
2,840
1,820
1,650
1,260
1,850
1,710
2,940
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Simple Regression Analysis
Example
You will need three pieces
of information from your
regression analysis:
1. Estimated Variable Cost
per Unit (line slope)
2. Estimated Fixed Costs
(line intercept)
3. Goodness of fit, or R2
To get these three pieces
of information we will
need to use THREE
different excel functions.
LINEST, INTERCEPT, & RSQ
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Month
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
Total Costs
$6,720
7,260
7,270
11,060
12,580
8,660
8,580
9,550
13,050
11,060
7,320
7,370
6,790
7,480
6,990
11,400
Units (Meals)
1,280
1,810
1,620
2,830
3,630
2,610
2,460
2,640
3,620
2,840
1,820
1,650
1,260
1,850
1,710
2,940
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Simple Regression Using Excel 2000
First, open
the excel file
with your
data and
click on
“Insert” and
“Function”
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Simple Regression Using Excel 2000
When the
function box
opens, click
on
“Statistical”,
then on
“LINEST”
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Simple Regression Using Excel
2000
By clicking on the
buttons to the
left, you can
highlight the
desired cells
directly from the
spreadsheet.
1. Enter the cell range for the cost amounts in the
“Known_y’s” box.
2. Enter the cell range for the quantity amounts in
the “Known_x’s” box.
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Simple Regression Using Excel 2000
The Slope, or estimated variable cost per unit, is
identified here. Click OK to put this value on your
spreadsheet.
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Simple Regression Using Excel 2000
Repeat the
procedure
using
“Intercept”,
to estimate
fixed cost.
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Simple Regression Using Excel 2000
The estimated fixed cost is
identified here.
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As previously,
enter the
appropriate cell
ranges in their
appropriate
places.
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Simple Regression Using Excel 2000
Finally,
determine the
“goodness of
fit”, or R2, by
using the RSQ
function.
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Simple Regression Using Excel 2000
The estimated R2 for your estimated
cost function is identified here.
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As previously,
enter the
appropriate cell
ranges in their
appropriate
places.
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Let’s put our
knowledge of cost
behavior to work by
preparing a
contribution format
income statement.
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The Contribution Format
Sales Revenue
Less: Variable costs
Contribution margin
Less: Fixed costs
Net operating income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
Unit
$ 50
30
$ 20
The contribution margin format emphasizes cost
behavior. Contribution margin covers fixed costs
and provides for income.
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The Contribution Format
Used primarily for
external reporting.
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Used primarily by
management.
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End of Chapter 5
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