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Cost Behavior:Analysis and Use
Chapter 5
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Summary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable Total variable cost is Variable cost per unit remainsproportional to the activity the same over wide ranges
level within the relevant range. of activity.
Fixed Total fixed cost remains the Fixed cost per unit goessame even when the activity down as activity level goes up.
level changes within therelevant range.
Recall the summary of our cost behavior discussion from Chapter 2.
Types of Cost Behavior Patterns
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
The Activity Base
A measure of the event that causes the incurrence of a
variable cost – a cost driver
A measure of the event that causes the incurrence of a
variable cost – a cost driver
Unitsproduced
Unitsproduced
Miles driven
Miles driven
Labor hours
Labor hours
Machine hours
Machine hours
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Minutes Talked
To
tal L
on
g D
ista
nce
Tel
eph
on
e B
ill
True Variable Cost Example
Your total long distance telephone bill is based on how many minutes you talk.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Minutes Talked
Per
Min
ute
Tel
eph
on
e C
har
ge
Variable Cost Per Unit Example
The cost per minute talked is constant. For example, 10 cents per minute.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Step-Variable Costs
Activity
Co
st
Total cost remainsconstant within anarrow range of
activity.
Total cost remainsconstant within anarrow range of
activity.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Step-Variable Costs
Activity
Co
st
Total cost increases to a new higher cost for the
next higher range of activity.
Total cost increases to a new higher cost for the
next higher range of activity.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
RelevantRange
A straight line closely
approximates a curvilinear
variable cost line within the
relevant range.
A straight line closely
approximates a curvilinear
variable cost line within the
relevant range.
Activity
To
tal
Co
st
Economist’sCurvilinear Cost
Function
The Linearity Assumption and the Relevant Range
Accountant’s Straight-Line Approximation (constant
unit variable cost)
Exh.5-4
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Number of Local Calls
Mo
nth
ly B
asic
T
elep
ho
ne
Bill
Total Fixed Cost Example
Your monthly basic telephone bill is probably fixed and does not change when
you make more local calls.
Exh.5-5
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Number of Local Calls
Mo
nth
ly B
asic
Tel
eph
on
e B
ill p
er L
oca
l Cal
l
Fixed Cost Per Unit Example
The fixed cost per local call decreases as more local calls are made.
Exh.5-5
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Cost Behavior
MerchandisersCost of Goods Sold
MerchandisersCost of Goods Sold
ManufacturersDirect Material, Direct Labor, and Variable
Manufacturing Overhead
ManufacturersDirect Material, Direct Labor, and Variable
Manufacturing Overhead
Merchandisers and Manufacturers
Sales commissions and shipping costs
Merchandisers and Manufacturers
Sales commissions and shipping costs
Service Organizations Supplies and travel
Service Organizations Supplies and travel
Examples of normally variable costsExamples of normally variable costs
Examples of normally fixed costsExamples of normally fixed costs
Merchandisers, manufacturers, and service organizations
Real estate taxes, Insurance, Sales salariesDepreciation, Advertising
Merchandisers, manufacturers, and service organizations
Real estate taxes, Insurance, Sales salariesDepreciation, Advertising
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
ExamplesAdvertising and Research and Development
ExamplesAdvertising and Research and Development
ExamplesDepreciation on Buildings and
Equipment
ExamplesDepreciation on Buildings and
Equipment
Types of Fixed Costs
DiscretionaryMay be altered in the short-term by current managerial decisions
DiscretionaryMay be altered in the short-term by current managerial decisions
CommittedLong-term, cannot be reduced in the short
term.
CommittedLong-term, cannot be reduced in the short
term.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
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.
Fixed Costs and Relevant Range
Continue
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Ren
t C
ost
in
T
ho
usa
nd
s o
f D
oll
ars
0 1,000 2,000 3,000 Rented Area (Square Feet)
0
30
60
Fixed Costs and Relevant Range
90
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.
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.
Exh.5-6
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
How does this type of fixed cost differ
from a step-variable cost?
Step-variable costs can be adjusted more
quickly and . . .
The width of the activity steps is much
wider for the fixed cost.
Fixed Costs and Relevant Range
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
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.
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.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Fixed Monthly
Utility Charge
Variable
Cost per KW
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
st
X
Y
A mixed cost has both fixed and variablecomponents. Consider the example of utility cost.
A mixed cost has both fixed and variablecomponents. Consider the example of utility cost.
Mixed Costs
Total mixed cost
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Fixed Monthly
Utility Charge
Variable
Cost per KW
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
st
X
Y
Mixed Costs
Total mixed cost Y
= a + bX
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
The Analysis of Mixed Costs
Engineering Approach
Account Analysis
High-Low Method
Least-Square Regression Method
Scattergraph Plot
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Account Analysis & Engineering Estimates
Each account is classified as eithervariable or fixed based on the analyst’s
knowledge of how the account behaves.
Each account is classified as eithervariable 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.
Cost estimates are based on an evaluation of production methods, and material, labor and overhead
requirements.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Plot the data points on a graph (total cost vs. activity).
Plot the data points on a graph (total cost vs. activity).
0 1 2 3 4
*
To
tal
Co
st i
n1,
000’
s o
f D
oll
ars
10
20
0
***
**
**
*
*
Activity, 1,000’s of Units Produced
X
Y
The Scattergraph Method
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
0 1 2 3 4
*
To
tal
Co
st i
n1,
000’
s o
f D
oll
ars
10
20
0
***
**
**
*
*
Activity, 1,000’s of Units Produced
X
Y
Quick-and-Dirty Method
Intercept is the estimated fixed cost = $10,000
Intercept is the estimated fixed cost = $10,000
Draw a line through the data points with about anequal numbers of points above and below the line.
Draw a line through the data points with about anequal numbers of points above and below the line.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
0 1 2 3 4
*
To
tal
Co
st i
n1,
000’
s o
f D
oll
ars
10
20
0
***
**
**
*
*
Activity, 1,000’s of Units Produced
X
Y
Quick-and-Dirty MethodThe slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units
The slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units
Vertical distance is the change in cost.
Vertical distance is the change in cost.
Horizontal distance is
the change in activity.
Horizontal distance is
the change in activity.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
WiseCo recorded the following production activity and maintenance costs for two months:
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.
The High-Low Method
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Changein costChange in units
The High-Low Method
Variable cost per unit = Change in cost ÷ change in units
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
The High-Low Method
Variable cost per unit = $2,400 ÷ 3,000 units
= $0.80 per unit
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
The High-Low Method
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
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
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
The High-Low Method
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
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
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
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
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
Quick Check
$4,000 ÷ 40,000 units = $0.10 per unit
Units Cost
High level 120,000 14,000$
Low level 80,000 10,000
Change 40,000 4,000$
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
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
b. $ 4,000
c. $10,000
d. $12,000
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
b. $ 4,000
c. $10,000
d. $12,000
Quick Check
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
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 Method
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.
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.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
0 1 2 3 4
To
tal
Co
st
10
20
0
Activity
****
**
****
Least-Squares Regression Method
R2 is the percentage of the variation in total cost explained by the activity.
R2 is the percentage of the variation in total cost explained by the activity.
R2 for this relationship is near100% since the data points are
very close to the regression line.
X
Y
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Cost Estimation MethodsRegression 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.
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.
Dependent variables are caused by the
independent variables.
Dependent variables are caused by the
independent variables.
Independent variables are the cost drivers that are correlated with the dependent variables.
Independent variables are the cost drivers that are correlated with the dependent variables.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Caution: Before doing the analysis, take time
to determine if a logical relationship
between the variables exists.
Caution: Before doing the analysis, take time
to determine if a logical relationship
between the variables exists.
Cost Estimation MethodsRegression Analysis
The simple cost model is actually a regression model:
TC = F + VX
The simple cost model is actually a regression model:
TC = F + VX
This model will only be useful within a relevant range of
activity.
This model will only be useful within a relevant range of
activity.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Cost Estimation MethodsRegression Analysis
A set of data can be regressed using several techniques:
•Manual computations•SPSS or SAS Statistical Software
•Excel or other spreadsheet
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
The result of the regression process is a
regression model:
TC = F + VX
Each regression model has an R-square (R2)
measure of how good the model is.
Range of R2 = 0 to 1.0
Each regression model has an R-square (R2)
measure of how good the model is.
Range of R2 = 0 to 1.0
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression AnalysisExample
Fasco wants to know its average
fixed cost and variable cost per
unit.
Using the data to the right, let’s see
how to do a regression using
Excel.
Fasco wants to know its average
fixed cost and variable cost per
unit.
Using the data to the right, let’s see
how to do a regression using
Excel.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression AnalysisExample
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
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
To get these three pieces of information we will need to use THREE
different excel functions.
LINEST, INTERCEPT, & RSQ
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression Using Excel 2000
First, open the excel file
with your data and click on
“Insert” and “Function”
First, open the excel file
with your data and click on
“Insert” and “Function”
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression Using Excel 2000
When the function box opens, click
on “Statistical”,
then on “LINEST”
When the function box opens, click
on “Statistical”,
then on “LINEST”
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression Using Excel 2000
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.
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.
By clicking on the buttons to the left, you can highlight the desired cells
directly from the spreadsheet.
By clicking on the buttons to the left, you can highlight the desired cells
directly from the spreadsheet.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
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.
The Slope, or estimated variable cost per unit, is identified here. Click OK to put this value on your
spreadsheet.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression Using Excel 2000
Repeat the procedure
using “Intercept”, to estimate fixed cost.
Repeat the procedure
using “Intercept”, to estimate fixed cost.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression Using Excel 2000
As previously, enter the
appropriate cell ranges in their
appropriate places.
As previously, enter the
appropriate cell ranges in their
appropriate places.
The estimated fixed cost is identified here.
The estimated fixed cost is identified here.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression Using Excel 2000
Finally, determine the “goodness of fit”, or R2, by
using the RSQ function.
Finally, determine the “goodness of fit”, or R2, by
using the RSQ function.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Simple Regression Using Excel 2000
As previously, enter the
appropriate cell ranges in their
appropriate places.
As previously, enter the
appropriate cell ranges in their
appropriate places.
The estimated R2 for your estimated cost function is identified here.
The estimated R2 for your estimated cost function is identified here.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
Let’s put our knowledge of cost
behavior to work by preparing a
contribution format income statement.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
The Contribution Format
Total Unit
Sales Revenue 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Net operating income 10,000$
The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs
and provides for income.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
The Contribution Format
Used primarily forexternal reporting.
Used primarily bymanagement.
© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin
End of Chapter 5
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