Cost Behaviour: Analysis and Use Chapter 5
Cost Behaviour:Analysis and Use
Chapter
5
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5-2
LEARNING OBJECTIVES
1. Explain the effect of a change in activity onboth total variable costs and per unit variablecosts.
2. Explain the effect of a change in activity onboth total fixed costs and fixed costsexpressed on a per unit.
3. Use a cost formula to predict costs at a newlevel of activity.
4. Analyze a mixed cost using the high-lowmethod.
After studying this chapter, you should be able to:
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LEARNING OBJECTIVES
5. Analyze a mixed cost using the scattergraphmethod.
6. Explain the least-squares regression method ofanalyzing a mixed cost.
7. Prepare an income statement using thecontribution format.
8. (Appendix 5A) Analyze a mixed cost using theleast-squares regression method.
After studying this chapter, you should be able to:
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Types of Cost Behaviour Patterns
Summary of Variable and Fixed Cost Behaviour
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 behaviourdiscussion from Chapter 2.
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Total Variable Cost Example
Your total long distance telephone bill isbased on how many minutes you talk.
Minutes Talked
To
tal L
on
g D
ista
nc
eT
elep
ho
ne
Bil
l
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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. Forexample, 10 cents per minute.
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Total Fixed Cost Example
Your monthly basic telephone bill isprobably fixed and does not change when
you make more local calls.
Number of Local Calls
Mo
nth
ly B
asic
Tel
eph
on
e B
ill
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Fixed Cost Per Unit Example
Number of Local Calls
Mo
nth
ly B
asic
Tel
eph
on
eB
ill p
er L
oca
l C
all
The fixed cost per local call decreases asmore local calls are made.
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Cost Behaviour
MerchandisersCost of Goods Sold
ManufacturersDirect Material, DirectLabour, and Variable
Manufacturing Overhead
Merchandisers andManufacturers
Sales commissions andshipping costs
Service Organizations Supplies and travel
Examples of normally variable costs
Examples of normally fixed costs
Merchandisers, manufacturers, andservice organizations
Real estate taxes, Insurance, Sales salariesAmortization, Advertising
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The Activity Base
Machinehours
Labourhours
Unitsproduced
Milesdriven
A measure of the event causing the occurrence of a variable cost – a cost driver
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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
Activity
Co
st
Total cost increases to a new higher cost for the
next higher range ofactivity.
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The Linearity Assumption and theRelevant Range
Activity
To
tal C
ost
Economist’sCurvilinear Cost
Function
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Activity
To
tal C
ost
Economist’sCurvilinear Cost
Function
Accountant’s Straight-LineApproximation (constant
unit variable cost)
The Linearity Assumption and theRelevant Range
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Activity
To
tal C
ost
RelevantRange
The Linearity Assumption and theRelevant Range
Accountant’s Straight-LineApproximation (constant
unit variable cost)
Economist’sCurvilinear Cost
Function
A straight lineclosely
approximatesa curvilinearvariable costline within the
relevantrange.
A straight lineclosely
approximatesa curvilinearvariable costline within the
relevantrange.
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Types of Fixed Costs
Fixed Costs
Discretionary
May be altered in theshort-term by currentmanagerial decisions
Committed
Long-term, cannot bereduced in the short
term.
Examples
Amortization onBuildings and
Equipment
Examples
Advertising andResearch andDevelopment
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Trend Toward Fixed Costs
Increased automation.
Increase in salaried “knowledge” workerswho are difficult to train and replace.
Implications
Managers are more “locked-in” with fewer decisionalternatives.
Planning becomes more crucial because fixed costs aredifficult to change with current operating decisions.
Implications
Managers are more “locked-in” with fewer decisionalternatives.
Planning becomes more crucial because fixed costs aredifficult to change with current operating decisions.
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Example: Office spaceis available at a rental
rate of $30,000 peryear in increments of1,000 square feet. As
the business growsmore space is rented,
increasing the totalcost.
Fixed Costs and Relevant Range
Continue
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Re
nt
Co
st i
nT
ho
usa
nd
s o
f D
olla
rs
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’tchange for a widerange of activity,
and then jumps to anew higher cost for
the next higherrange of activity.
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How does this typeof fixed cost differ
from a step-variablecost?
Step-variable costscan be adjusted more
quickly and . . .
The width of theactivity steps is much
wider for the fixedcost.
Fixed Costs and Relevant Range
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A mixed costhas both fixedand variablecomponents.
Mixed Costs
Consider thefollowing electricutility example.
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Fixed Monthly
Utility Charge
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal U
tilit
y C
os
tMixed Costs
X
Y
Total mixed cost
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Total mixed cost Y
= a + bX
Fixed Monthly
Utility Charge
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal U
tilit
y C
os
tMixed Costs
X
Y
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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Fixed Monthly
Utility Charge
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal U
tilit
y C
os
t
Total mixed cost Y
= a + bX
Mixed Costs
bX
aX
Y
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The Analysis of Mixed Costs
Engineering Approach
Account Analysis
Scattergraph Method
Least-Square 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, labour
and overhead requirements.
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WiseCo recorded the following production activityand maintenance costs for two months:
Using these two levels of activity, compute:υ the variable cost per unit;ϖ the fixed cost; and thenω 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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υ Unit variable cost =Change in costChange in units
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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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
υ Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
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Units Cost
High activity level 9,000 9,700$ Low activity level 5,000 6,100
Change 4,000 3,600$
The High-Low Method
υ Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
ϖ 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
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υ Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
ϖ 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
ω 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 $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the variableportion 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 $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the variableportion 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
The High-Low Method
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If sales salaries and commissions are $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the variableportion 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 $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the variableportion 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
The High-Low Method
$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$
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If sales salaries and commissions are $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the fixed portionof sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
If sales salaries and commissions are $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the fixed portionof sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
The High-Low Method
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If sales salaries and commissions are $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the fixed portionof sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
If sales salaries and commissions are $10,000when 80,000 units are sold and $14,000 when120,000 units are sold, what is the fixed portionof sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
The High-Low Method
Tota l cost = Tota l fixed cost + Tota l variable cost
$14,000 = Tota l fixed cost +($0.10 × 120,000 units)
Tota l fixed cost = $14,000 - $12,000
Tota l fixed cost = $2,000
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The Scattergraph MethodPlot the data points on a
graph (total cost vs. activity).
0 1 2 3 4
*
To
tal C
ost
(00
0’s
of
Do
llars
)
10
20
0
***
**
**
*
*
Activity (000’s of Units Produced)
X
Y
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The Scattergraph MethodDraw a line through the data points with about anequal numbers of points above and below the line.
0 1 2 3 4
*
To
tal C
ost
(00
0’s
of
Do
llars
)
10
20
0
***
**
**
*
*
Activity (000’s of Units Produced)
X
Y
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The Scattergraph Method
Estimated fixed cost = $10,000
0 1 2 3 4
*
To
tal C
ost
(00
0’s
of
Do
llars
)
10
20
0
***
**
**
*
*
Activity (000’s of Units Produced)
X
Y
The slope of this line is the variable unitcost. (Slope is the change in total cost
for a one unit change in activity).
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The Scattergraph Method
Slope = Change in costChange in units
Horizontal distance isthe change in activity.
0 1 2 3 4
*
To
tal C
ost
(00
0’s
of
Do
llars
)
10
20
0
***
**
**
*
*
Activity (000’s of Units Produced)
X
Y
Verticaldistance
is thechangein cost.
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! Accountants and managersmay use computer softwareto fit a regression linethrough the data points.
! The cost analysis objectiveis the same: Y = a + bx
Least-Squares Regression Method
Least-squares regression also provides a statistic, called
the adjusted R2, that is a measure of the goodness
of fit of the regression line to the data points.
Least-squares regression also provides a statistic, called
the adjusted R2, that is a measure of the goodness
of fit of the regression line to the data points.
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0 1 2 3 4
To
tal C
ost
10
20
0
Activity
****
**
****
Least-Squares Regression Method
R2 is the percentage of the variationin total cost explained by the activity.
R2 for this relationship is near100% since the data points are
very close to the regression line.X
Y
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Let’s put our
knowledge of cost
behaviour to work
by preparing a
contribution format
income statement.
The Contribution Format
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The Contribution Format
Total Unit
Sales Revenue 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Net income 10,000$
The contribution margin format emphasizes costbehaviour. Contribution margin covers fixed costs
and provides for income.
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The Contribution Format
Comparison of the Contribution Income Statement with the Traditional Income Statement
Traditional Approach Contribution Approach (costs organized by function) (costs organized by behavior)
Sales 100,000$ Sales 100,000$ Less cost of goods sold 70,000 Less variable expenses 60,000 Gross margin 30,000$ Contribution margin 40,000$ Less operating expenses 20,000 Less fixed expenses 30,000 Net income 10,000$ Net income 10,000$
Used primarily forexternal reporting.
Used primarily bymanagement.
Least-Squares RegressionCalculations
Appendix
5A
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Least-Squares Regression
This method provides the most objective and precisebreakdown of mixed costs into variable and fixedcomponents.
This method also uses the most complex calculations.However, most business calculators and severalcomputer software programs can quickly complete thecalculations required.
This method mathematically places the line in the mostfavourable location by ensuring that the total of thesquares of all points off the line is minimized.
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Least-Squares RegressionCalculations:
b = n(∑XY-(∑X)(∑Y)
n(∑X2) - (∑X)2
a = (∑Y) - b(∑X)
n
where X= the level of activity (Independent variable)
Y= the total mixed cost (dependent variable)
a = the total fixed cost (vertical intercept of line)
b = the variable cost per unit of activity (slope ofline)
n = number of observations
∑ = sum across all n observations
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End of Chapter 5