Chapter 5
Cost Behavior:
Analysis and Use
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Types of Cost Behavior Patterns
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 1.
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Total Variable Cost Example
Your total long distance telephone bill is based on how many minutes you talk.
Minutes Talked
To
tal L
on
g D
ista
nce
Tel
eph
on
e B
ill
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Variable Cost Per Unit Example
Minutes Talked
Per
Min
ute
Tel
eph
on
e C
har
ge
The cost per minute talked is constant.For example, 10 cents per minute.
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Total Fixed Cost Example
Your monthly basic telephone bill is probably fixed and does not changewhen you make more local calls.
Number of Local Calls
Mo
nth
ly B
asic
T
elep
ho
ne
Bill
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Fixed Cost Per Unit Example
Number of Local Calls
Mo
nth
ly B
asic
Tel
eph
on
e B
ill p
er L
oca
l Cal
l
The fixed cost per local call decreasesas more local calls are made.
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Cost Behavior
MerchandisersCost of Goods Sold
ManufacturersDirect Material, Direct Labor, and Variable
Manufacturing Overhead
Merchandisers and Manufacturers
Sales commissions and shipping costs
Service Organizations Supplies and travel
Examples of normally variable costs
Examples of normally fixed costs
Merchandisers, manufacturers, and service organizationsReal estate taxes, Insurance, Sales salaries
Depreciation, Advertising
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The Activity Base
Machinehours
Laborhours
Milesdriven
A measure of the event causing the incurrence of a variable cost – a cost driver
Unitsproduced
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Step-Variable Costs
Activity
Co
st
Total cost remainsconstant within anarrow range of
activity.
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Step-Variable Costs
Total cost increases to a new higher cost for the
next higher range of activity.
Activity
Co
st
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RelevantRange
The Linearity Assumption and the Relevant Range
Accountant’s Straight-Line Approximation (constant
unit variable cost)
Activity
To
tal
Co
st
Economist’sCurvilinear Cost
Function
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.
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Types of Fixed Costs
Discretionary
•One-year planning horizon
•Can be cut for short periods of time
Discretionary
•One-year planning horizon
•Can be cut for short periods of time
Committed
•Multi-year planning horizon
•Cannot be cut for short periods of time
Committed
•Multi-year planning horizon
•Cannot be cut for short periods of time
ExamplesDepreciation on Buildings and
Equipment
ExamplesDepreciation on Buildings and
Equipment
ExamplesAdvertising and Research and Development
ExamplesAdvertising and Research and Development
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Trend Toward Fixed Costs
Increased automation.
Increase in salaried knowledge workers who are difficult to train and replace.
Implications
Managers are more “locked-in” with fewer decision alternatives.
Planning becomes more crucial because fixed costs are difficult to change with current operating decisions.
Implications
Managers are more “locked-in” with fewer decision alternatives.
Planning becomes more crucial because fixed costs are difficult to change with current operating decisions.
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Fixed if work force is stable because managementis reluctant to increase/decrease the number of
employees in response to short-term fluctuationsin business activity.
Fixed if work force is stable because managementis reluctant to increase/decrease the number of
employees in response to short-term fluctuationsin business activity.
Variable if size of work force is easily adjusted forshort-term fluctuations in business activity.
Variable if size of work force is easily adjusted forshort-term fluctuations in business activity.
Labor Costs: Fixed or Variable?
May be both fixed and variable if temporary workers are employed to accommodate short-term
fluctuations in business activity.
May be both fixed and variable if temporary workers are employed to accommodate short-term
fluctuations in business activity.
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Fixed Costs and Relevant Range
Continue
Example: Office spaceis available at a rental rate
of $30,000 per year inincrements of 1,000 square
feet. As the business grows, more space is rented,
increasing the total cost.
Example: Office spaceis available at a rental rate
of $30,000 per year inincrements of 1,000 square
feet. As the business grows, more space is rented,
increasing the total cost.
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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.
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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.
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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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.
Quick Check
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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
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A mixed costhas both fixed and variablecomponents.
Mixed Costs
Consider thefollowing electric utility example.
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Fixed Monthly
Utility Charge
Variable
Utility Charge
Mixed Costs
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
st
X
Y
Total mixed cost
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Fixed Monthly
Utility Charge
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
st
X
Y
Total mixed cost
Mixed Costs The total mixed cost line can be expressed as an equation: Y = a + bX
Where: Y = the total mixed cost
a = the total fixed cost (thevertical intercept of the line)
b = the variable cost per unit ofactivity (the slope of the line)
X = the level of activity
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Mixed Costs
bX
a
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
st
X
Y
Total mixed cost = Y = a + bX
Fixed Monthly
Utility Charge
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The Analysis of Mixed Costs
Engineering Approach
Account Analysis
Scattergraph Plot
Least-Squares Regression Method
High-Low Method
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Account Analysis
Each account is classified as eithervariable or fixed based on the analyst’s
knowledge of how the account behaves.
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Engineering Estimates
Cost estimates are based on an evaluation of production methods, and material, labor
and overhead requirements.
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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 Plot
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Draw a line through the data pointswith about an equal numbers of
points above and below the line.
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 Plot
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Estimated fixed cost = $10,000
The slope of this line is the variable unit cost. (Slope is the change in total cost
for a one unit change in activity).
0 1 2 3 4
To
tal
Co
st i
n1,
000’
s o
f D
oll
ars
10
20
0
***
**
**
*
*
Activity, 1,000’s of Units Produced
X
Y
The Scattergraph Plot
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Slope = Change in costChange in units
Horizontal distance is the change in activity.
0 1 2 3 4
*
To
tal
Co
st i
n1,
000’
s o
f D
oll
ars
10
20
0
***
**
**
*
*
Activity, 1,000’s of Units Produced
X
Y
Vertical distance
is the change in cost.
The Scattergraph Plot
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WiseCo recorded the following production activity and maintenance costs for two months:
Using these two levels of activity, compute: the variable cost per unit; the fixed cost; and then express the costs in equation form Y = a + bX.
The High-Low Method
Units Cost
High activity level 9,000 9,700$ Low activity level 5,000 6,100 Change 4,000 3,600$
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Unit variable cost =Changein costChange in units
The High-Low Method
Units Cost
High activity level 9,000 9,700$ Low activity level 5,000 6,100 Change 4,000 3,600$
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The High-Low Method
Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
Units Cost
High activity level 9,000 9,700$ Low activity level 5,000 6,100 Change 4,000 3,600$
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The High-Low Method
Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit Fixed cost = Total cost – Total variable cost
Fixed cost = $9,700 – ($0.90 per unit × 9,000 units)
Fixed cost = $9,700 – $8,100 = $1,600
Units Cost
High activity level 9,000 9,700$ Low activity level 5,000 6,100 Change 4,000 3,600$
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Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit Fixed cost = Total cost – Total variable cost
Fixed cost = $9,700 – ($0.90 per unit × 9,000 units)
Fixed cost = $9,700 – $8,100 = $1,600 Total cost = Fixed cost + Variable cost (Y = a + bX) Y = $1,600 + $0.90X
Units Cost
High activity level 9,000 9,700$ Low activity level 5,000 6,100 Change 4,000 3,600$
The High-Low Method
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If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, 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
If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, 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
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If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, 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
If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, 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$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$
Quick Check
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If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
Quick Check
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If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
Total cost = Total fixed cost + Total variable cost
$14,000 = Total fixed cost +($0.10 × 120,000 units)
Total fixed cost = $14,000 - $12,000
Total fixed cost = $2,000
Quick Check
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• How does the high-low method work when you have data for more than two periods?
• Select the two periods with the lowest and highest level of activity.
• How does the high-low method work when you have data for more than two periods?
• Select the two periods with the lowest and highest level of activity.
March 2,510 15,204$ April 2,550 14,976$ May 2,480 14,680$ June 2,590 15,108$ July 2,670 15,060$
Low month
High month
Note
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Quick Check Using the high-low method, estimate the cost
formula Y = a + bX for the patient admitting costs.
a. Y = $9,720 + $2.00X
b. Y = $7,050 + $3.00X
c. Y = $8,385 + $2.50X
d. Y = $8,480 + $2.50X
Using the high-low method, estimate the cost formula Y = a + bX for the patient admitting costs.
a. Y = $9,720 + $2.00X
b. Y = $7,050 + $3.00X
c. Y = $8,385 + $2.50X
d. Y = $8,480 + $2.50X
March 2,510 15,204$ April 2,550 14,976$ May 2,480 14,680$ June 2,590 15,108$ July 2,670 15,060$
Low month
High month
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Using the high-low method, estimate the cost formula Y = a + bX for the patient admitting costs.
a. Y = $9,720 + $2.00X
b. Y = $7,050 + $3.00X
c. Y = $8,385 + $2.50X
d. Y = $8,480 + $2.50X
Using the high-low method, estimate the cost formula Y = a + bX for the patient admitting costs.
a. Y = $9,720 + $2.00X
b. Y = $7,050 + $3.00X
c. Y = $8,385 + $2.50X
d. Y = $8,480 + $2.50X
March 2,510 15,204$ April 2,550 14,976$ May 2,480 14,680$ June 2,590 15,108$ July 2,670 15,060$
Low month
High month
Quick Check
b = = = $2
a = $15,060 – $2 × 2,670 = $15,060 – $5,340 = $9,720
b = = = $2
a = $15,060 – $2 × 2,670 = $15,060 – $5,340 = $9,720
$15,060 – $14,680 2,670 – 2,480
$380 190
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Let’s plot the data for patient admitting costs.
$14,000
$14,200
$14,400
$14,600
$14,800
$15,000
$15,200
$15,400
2,450 2,500 2,550 2,600 2,650 2,700
Patients Admitted
Pat
ient
Adm
itti
ng C
osts
Note
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Problems with the high-low method:• Disregards information contained in all of the data
other than the low and the high points.
• The low and high levels of activity tend to be unusual.
Always plot the data if you have more than two points to make sure it even makes sense to use the high-low method.
Problems with the high-low method:• Disregards information contained in all of the data
other than the low and the high points.
• The low and high levels of activity tend to be unusual.
Always plot the data if you have more than two points to make sure it even makes sense to use the high-low method.
Note
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• Software can be used to fit a regression line through the data points.
• The cost analysis objective is the same: Y = a + bx
• Software can be used to fit a regression line through the data points.
• The cost analysis objective is the same: Y = a + bx
Least-squares regression also provides a statistic, called
the adjusted R2, that is a measure of the goodness
of fit of the regression line to the data points.
Least-squares regression also provides a statistic, called
the adjusted R2, that is a measure of the goodness
of fit of the regression line to the data points.
Least Squares Regression
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0 1 2 3 4
To
tal
Co
st
10
20
0
Activity
****
**
****
R2 is the percentage of the variationin total cost explained by the activity.
R2 for this relationship is near100% since the data points are
very close to the regression line.X
Y
Least Squares Regression
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Let’s put our
knowledge of cost
behavior to work by
preparing a
contribution format
income statement.
The Contribution Format
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Total Unit
Sales Revenue 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Net income 10,000$
The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs
and provides for income.
The Contribution Format
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Used primarily forexternal reporting.
Used primarily bymanagement.
The Contribution Format
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End of Chapter 5