Cost Behavior: Analysis and Use
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Transcript of Cost Behavior: Analysis and Use
Cost Behavior:Analysis and Use
Chapter
5
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 2
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.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 3
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
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 4
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.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 5
Total Fixed Cost Example
Your monthly basic telephone bill is probably fixed and does not change when
you make more local calls.
Number of Local Calls
Mo
nth
ly B
asic
T
elep
ho
ne
Bill
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 6
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 decreases as more local calls are made.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 7
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 organizations
Real estate taxes, Insurance, Sales salariesDepreciation, Advertising
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 8
The Activity Base
Machinehours
Laborhours
Milesdriven
A measure of the event causing the incurrence of a variable cost – a cost driver
Unitsproduced
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 9
Step-Variable Costs
Activity
Co
st
Total cost remainsconstant within anarrow range of
activity.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 10
Step-Variable Costs
Activity
Co
st
Total cost increases to a new higher cost for the
next higher range of activity.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 11
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)
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 12
Activity
To
tal
Co
st
RelevantRange
The Linearity Assumption and the Relevant Range
Accountant’s Straight-Line Approximation (constant
unit variable cost)
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.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 13
ExamplesAdvertising and Research and Development
ExamplesDepreciation on Buildings and
Equipment
Types of Fixed Costs
Fixed Costs
DiscretionaryMay be altered in the short-term by current managerial decisions
CommittedLong-term, cannot be reduced in the short
term.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 14
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.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 15
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., 2002Irwin/McGraw-Hill 16
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.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 17
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.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 19
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., 2002Irwin/McGraw-Hill 20
A mixed costhas both fixed and variablecomponents.
Mixed Costs
Consider thefollowing electric utility example.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 21
Fixed Monthly
Utility Charge
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
stMixed Costs
X
Y
Total mixed cost
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 22
Total mixed cost Y
= a + bX
Fixed Monthly
Utility Charge
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
stMixed 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
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 23
Fixed Monthly
Utility Charge
Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
st
Total mixed cost Y
= a + bX
Mixed Costs
bX
aX
Y
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 24
The Analysis of Mixed Costs
Engineering Approach
Account Analysis
Scattergraph Method
Least-Square Regression Method
High-Low Method
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 25
Account Analysis
Each account is classified as eithervariable or fixed based on the analyst’s
knowledge of how the account behaves.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 26
Engineering Estimates
Cost estimates are based on an evaluation of production methods, and material, labor
and overhead requirements.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 27
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$
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 28
Unit variable cost =Changein 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
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 29
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
Unit variable cost = $3,600 ÷ 4,000 units = $0.90 per unit
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 30
Units Cost
High activity level 9,000 9,700$ Low activity level 5,000 6,100 Change 4,000 3,600$
The High-Low Method
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
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 31
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
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 32
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
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 34
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. $12,000
Quick Check
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 36
Note
How does the high-low method work when you have data for more than two periods?
Select the two periods with the lowest and highest level of activity.
Patients Admitted
Costs of Admitting
March 2,510 15,204$ April 2,550 14,976$ May 2,480 14,680$ June 2,590 15,108$ July 2,670 15,060$
Low
High
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 37
Quick Check Using the high-low method, estimate the cost
formula Y = a +bX for the patient admitting costs on the previous page.
a. Y = $9,720 + $2.00X
b. Y = $7,050 + $3.00X
c. Y = $8,385 + $2.50X
d. Y = $8,480 + $2.50X
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 39
The Scattergraph MethodPlot 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 McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 40
The Scattergraph MethodDraw a line through the data points with 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 McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 41
The Scattergraph Method
Estimated fixed cost = $10,000
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 slope of this line is the variable unit cost. (Slope is the change in total cost
for a one unit change in activity).
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 42
The Scattergraph Method
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 McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 43
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 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.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 44
0 1 2 3 4
To
tal
Co
st
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
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 45
Note
Let’s plot the data for patient admitting costs.
$14,000
$14,200
$14,400
$14,600
$14,800
$15,000
$15,200
$15,400
2,450 2,500 2,550 2,600 2,650 2,700
Patients Admitted
Pat
ient
Adm
itti
ng C
osts
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 46
Note
Problems with the high-low method:Throws away information contained in all of the data
other than the low and the high points.The low and high levels of activity tend to be
unusual.
You should always plot the data if you have more than two points to make sure it even makes sense to be using the high-low method.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 47
Let’s put our
knowledge of cost
behavior to work by
preparing a
contribution format
income statement.
The Contribution Format
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 48
The Contribution Format
Total Unit
Sales Revenue 100,000$ 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 cost behavior. Contribution margin covers fixed costs
and provides for income.
© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 49
The Contribution Format
Used primarily forexternal reporting.
Used primarily bymanagement.