Ch 5 Cost-Volume-Profit Relationships.pdf

Copyright © 2006, The McGraw-Hill Companies, Inc.
McGraw-Hill/Irwin
11th
Edition
Chapter 5

McGraw-Hill/Irwin
Chapter Five
Cost Behavior:
Analysis and Use

McGraw-Hill/Irwin
Summary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable Total variable cost is Variable cost per unit remains
proportional to the activity the same over wide ranges
level within the relevant range. of activity.
Total fixed cost remains the
same even when the activity Fixed cost per unit goes
Fixed level changes within the down as activity level goes up.
relevant range.
Recall the summary of our cost behavior
Recall the summary of our cost behavior
discussion from an earlier chapter.
discussion from an earlier chapter.
Types of Cost Behavior Patterns

McGraw-Hill/Irwin
The Activity Base
A measure of what
causes the
incurrence of a
variable cost
A measure of what
causes the
incurrence of a
variable cost
Units
Units
produced
produced
Units
Units
produced
produced
Miles
driven
Miles
driven
Labor
hours
Labor
hours
Machine
hours
Machine
hours

McGraw-Hill/Irwin
Minutes Talked
Total
Long
Distance
Telephone
Bill
True Variable Cost Example
A variable cost is a cost whose total dollar amount
varies in direct proportion to changes in the activity
level. Your total long distance telephone bill is
based on how many minutes you talk.

McGraw-Hill/Irwin
Minutes Talked
Per
Minute
Telephone
Charge
Variable Cost Per Unit Example
A variable cost remains constant if expressed on
a per unit basis. The cost per minute talked is
constant. For example, 10 cents per minute.

McGraw-Hill/Irwin
Extent of Variable Costs
The proportion of variable costs differs across
organizations. For example . . .
A public utility with
large investments in
equipment will tend
equipment will tend
to have
to have fewer
fewer
variable costs.
variable costs.
equipment will tend
equipment will tend
to have
to have fewer
fewer
variable costs.
variable costs.
A manufacturing company
will often have
will often have many
many
variable costs.
variable costs.
will often have
will often have many
many
variable costs.
variable costs.
A merchandising company
usually will have a
usually will have a high
high
proportion
proportion of variable costs
of variable costs
like cost of sales.
like cost of sales.
usually will have a
usually will have a high
high
proportion
proportion of variable costs
of variable costs
like cost of sales.
like cost of sales.
A service company
A service company
will normally have a
will normally have a high
high
proportion
proportion of variable costs.
of variable costs.
A service company
A service company
will normally have a
will normally have a high
high
proportion
proportion of variable costs.
of variable costs.

McGraw-Hill/Irwin
Examples of Variable Costs
1. Merchandising companies – cost of goods sold.
2. Manufacturing companies – direct materials,
direct labor, and variable overhead.
3. Merchandising and manufacturing companies –
commissions, shipping costs, and clerical costs
such as invoicing.
4. Service companies – supplies, travel, and
clerical.
1. Merchandising companies – cost of goods sold.
2. Manufacturing companies – direct materials,
direct labor, and variable overhead.
3. Merchandising and manufacturing companies –
commissions, shipping costs, and clerical costs
such as invoicing.
4. Service companies – supplies, travel, and
clerical.

McGraw-Hill/Irwin
Volume
Cost
True Variable Cost
Direct materials is a true or proportionately variable
cost because the amount used during a period will
vary in direct proportion to the level of production
activity.

McGraw-Hill/Irwin
Step-Variable Costs
A resource that is obtainable only in large chunks (such
as maintenance workers) and whose costs increase or
decrease only in response to fairly wide changes in
activity is known as a step-variable cost
step-variable cost.
Volume
Cost

McGraw-Hill/Irwin
Step-Variable Costs
Small changes in the level of production are
not likely to have any effect on the number of
maintenance workers employed.
Small changes in the level of production are
not likely to have any effect on the number of
maintenance workers employed.
Volume
Cost

McGraw-Hill/Irwin
Step-Variable Costs
Only fairly wide changes in the activity level will
cause a change in the number of maintenance
workers employed
Only fairly wide changes in the activity level will
cause a change in the number of maintenance
workers employed
Volume
Cost

McGraw-Hill/Irwin
Relevant
Range
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
Total
Cost
Economist’s
Curvilinear Cost
Function
The Linearity Assumption and the Relevant Range
Accountant’s Straight-Line
Approximation (constant
unit variable cost)

McGraw-Hill/Irwin
Summary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable Total variable cost is Variable cost per unit remains
proportional to the activity the same over wide ranges
level within the relevant range. of activity.
Total fixed cost remains the
same even when the activity Fixed cost per unit goes
Fixed level changes within the down as activity level goes up.
relevant range.
Let’s look at fixed cost behavior on the next
Let’s look at fixed cost behavior on the next
screens.
screens.
Types of Cost Behavior Patterns

McGraw-Hill/Irwin
Number of Local Calls
Monthly
Basic
Telephone
Bill
Total Fixed Cost Example
A fixed cost is a cost whose total dollar amount remains
constant as the activity level changes. Your monthly
basic telephone bill is probably fixed and does not
change when you make more local calls.

McGraw-Hill/Irwin
Number of Local Calls
Monthly
Basic
Telephone
Bill
per
Local
Call
Fixed Cost Per Unit Example
Average fixed costs per unit decrease as the activity
level increases. The fixed cost per local call
decreases as more local calls are made.

McGraw-Hill/Irwin
Examples
Advertising and
Research and
Development
Examples
Advertising and
Research and
Development
Examples
Depreciation on
Equipment and
Real Estate Taxes
Examples
Depreciation on
Equipment and
Real Estate Taxes
Types of Fixed Costs
Discretionary
May be altered in the
short-term by current
managerial decisions
Discretionary
May be altered in the
short-term by current
managerial decisions
Committed
Long-term, cannot be
significantly reduced
in the short term.
Committed
Long-term, cannot be
significantly reduced
in the short term.

McGraw-Hill/Irwin
The Trend Toward Fixed Costs
The trend in many industries is toward
greater fixed costs relative to variable costs.
As machines take over
many mundane tasks
many mundane tasks
previously performed
by humans,
by humans,
“
“knowledge workers
knowledge workers”
”
are demanded for
are demanded for
their minds rather
their minds rather
than their muscles
than their muscles
many mundane tasks
many mundane tasks
by humans,
by humans,
“
“knowledge workers
knowledge workers”
”
are demanded for
are demanded for
their minds rather
their minds rather
than their muscles
than their muscles
Knowledge workers
Knowledge workers
tend to be salaried,
highly-trained and
highly-trained and
difficult to replace. The
cost to compensate
cost to compensate
these valued employees
is
is relatively fixed
relatively fixed
rather than variable.
Knowledge workers
Knowledge workers
highly-trained and
highly-trained and
cost to compensate
cost to compensate
is
is relatively fixed
relatively fixed

McGraw-Hill/Irwin
Is Labor a Variable or a Fixed Cost?
The behavior of wage and salary costs can
differ across countries, depending on labor
regulations, labor contracts, and custom.
In France, Germany, China, and Japan management has
little flexibility in adjusting the size of the labor force.
Labor costs are more fixed in nature.
In France, Germany, China, and Japan management has
little flexibility in adjusting the size of the labor force.
Labor costs are more fixed in nature.
In the United States and the United Kingdom management
has greater latitude. Labor costs are more variable in nature.
In the United States and the United Kingdom management
has greater latitude. Labor costs are more variable in nature.

McGraw-Hill/Irwin
Rent
Cost
in
Thousands
of
Dollars
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.

McGraw-Hill/Irwin
Example:
Example: Office space is
Office space is
available at a rental rate of
$30,000 per year in
$30,000 per year in
increments of 1,000 square
feet. As the business grows
more space is rented,
increasing the total cost.
Example:
Example: Office space is
Office space is
$30,000 per year in
$30,000 per year in
The relevant range of activity for a fixed cost
is the range of activity over which the graph of
the cost is flat.

McGraw-Hill/Irwin
How does this
How does this
type of fixed cost
type of fixed cost
differ from a step-
differ from a step-
variable cost?
variable cost?
Step-variable costs
can be adjusted
more quickly and . . .
The width of the
activity steps is
much wider for the
fixed cost.

McGraw-Hill/Irwin
Quick Check 
Which of the following statements about cost
behavior are true?
1. Fixed costs per unit vary with the level of
activity.
2. Variable costs per unit are constant within the
relevant range.
3. Total fixed costs are constant within the
relevant range.
4. Total variable costs are constant within the
relevant range.
Which of the following statements about cost
behavior are true?
1. Fixed costs per unit vary with the level of
activity.
2. Variable costs per unit are constant within the
relevant range.
3. Total fixed costs are constant within the
relevant range.
4. Total variable costs are constant within the
relevant range.

McGraw-Hill/Irwin
Fixed Monthly
Utility Charge
Variable
Cost per KW
Activity (Kilowatt Hours)
Total
Utility
Cost
X
Y
A mixed cost has both fixed and variable
components. Consider the example of utility cost.
A mixed cost has both fixed and variable
components. Consider the example of utility cost.
Mixed Costs
Total mixed cost

McGraw-Hill/Irwin
Fixed Monthly
Utility Charge
Variable
Cost per KW
Activity (Kilowatt Hours)
Total
Utility
Cost
X
Y
Mixed Costs
Total mixed cost

McGraw-Hill/Irwin
Mixed Costs Example
If your fixed monthly utility charge is $40, your
variable cost is $0.03 per kilowatt hour, and your
monthly activity level is 2,000 kilowatt hours,
what is the amount of your utility bill?
Y = a + bX
Y = $40 + ($0.03 × 2,000)
Y = $100

McGraw-Hill/Irwin
Analysis of Mixed Costs
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.
requirements.
requirements.
requirements.
Account Analysis and the Engineering Approach

McGraw-Hill/Irwin
Plot the data points on a graph
(total cost vs. activity).
0 1 2 3 4
*
Maintenance
Cost
1,000’s
of
Dollars
10
20
0
*
*
*
*
*
*
*
*
*
Patient-days in 1,000’s
X
Y
The Scattergraph Method

McGraw-Hill/Irwin
Draw a line through the data points with about an
equal numbers of points above and below the line.
0 1 2 3 4
*
Maintenance
Cost
1,000’s
of
Dollars
10
20
0
*
*
*
*
*
*
*
*
*
X
Y

McGraw-Hill/Irwin
Use one data point to estimate the total level of activity
and the total cost.
and the total cost.
and the total cost.
and the total cost.
Intercept = Fixed cost: $10,000
0 1 2 3 4
*
Maintenance
Cost
1,000’s
of
Dollars
10
20
0
*
*
*
*
*
*
*
*
*
X
Y
Patient days = 800
Patient days = 800
Total maintenance cost = $11,000
Total maintenance cost = $11,000

McGraw-Hill/Irwin
Make a quick estimate of variable cost per unit and
determine the cost equation.
Variable cost per unit =
$1,000
800
= $1.25/patient-day
$1.25/patient-day
Y = $10,000 + $1.25X
Y = $10,000 + $1.25X
Y = $10,000 + $1.25X
Y = $10,000 + $1.25X
Total maintenance at 800 patients 11,000
$
Less: Fixed cost 10,000
Estimated total variable cost for 800 patients 1,000
$
Total maintenance cost
Total maintenance cost Number of patient days
Number of patient days

McGraw-Hill/Irwin
The High-Low Method
Assume the following hours of maintenance work and
the total maintenance costs for six months.

McGraw-Hill/Irwin
The High-Low Method
The
The variable cost
variable cost
per hour
per hour of
of
maintenance is
maintenance is
equal to the change
equal to the change
in cost divided by
in cost divided by
the change in hours.
The
The variable cost
variable cost
per hour
per hour of
of
maintenance is
maintenance is
equal to the change
equal to the change
in cost divided by
in cost divided by
= $8.00/hour
$8.00/hour
$2,400
300

McGraw-Hill/Irwin
The High-Low Method
Total Fixed Cost = Total Cost – Total Variable Cost
Total Fixed Cost = Total Cost – Total Variable Cost
Total Fixed Cost = $9,800 – ($8/hour
Total Fixed Cost = $9,800 – ($8/hour × 800 hours)
× 800 hours)
Total Fixed Cost = $9,800 – $6,400
Total Fixed Cost = $9,800 – $6,400
Total Fixed Cost =
Total Fixed Cost = $3,400
$3,400

McGraw-Hill/Irwin
The High-Low Method
Y = $3,400 + $8.00
Y = $3,400 + $8.00X
X
The Cost Equation for Maintenance

McGraw-Hill/Irwin
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
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
commission?
a. $0.08 per unit
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit

McGraw-Hill/Irwin
Quick Check 
commission?
a. $0.08 per unit
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
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
$

McGraw-Hill/Irwin
Quick Check 
the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000

McGraw-Hill/Irwin
Least-Squares Regression Method
A method used to analyze mixed costs if a
scattergraph plot reveals an approximately linear
relationship between the X and Y variables.
This method uses
This method uses all
all of the
of the
data points to estimate
the fixed and variable
cost components of a
mixed cost.
mixed cost.
This method uses
This method uses all
all of the
of the
mixed cost.
mixed cost.
The goal of this method is
to fit a straight line to the
data that
data that minimizes the
minimizes the
sum of the squared errors
sum of the squared errors.
.
data that
data that minimizes the
minimizes the
sum of the squared errors
sum of the squared errors.
.

McGraw-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 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.

McGraw-Hill/Irwin
0 1 2 3 4
Total
Cost
10
20
0
Activity
*
*
*
*
*
*
*
*
*
*
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
varies from 0% to 100%, and
the higher the percentage the better.
X
Y

McGraw-Hill/Irwin
Comparing Results From the Three Methods
The three methods just discussed provide
slightly different estimates of the fixed and
variable cost components of the mixed cost.
This is to be expected because each method
uses differing amounts of the data points to
provide estimates.
provide estimates.
Least-squares regression provides the most
accurate estimate because it uses all the data
points.
points.
provide estimates.
provide estimates.
points.
points.

McGraw-Hill/Irwin
Let’s put our
knowledge of cost
behavior to work by
preparing a
contribution format
income statement.

McGraw-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.

McGraw-Hill/Irwin
Uses of the Contribution Format
The contribution income statement format is used
as an internal planning and decision making tool.
We will use this approach for:
1.
1. Cost-volume-profit analysis (Chapter 6).
Cost-volume-profit analysis (Chapter 6).
2.
2. Budgeting (Chapter 9).
Budgeting (Chapter 9).
3.
3. Segmented reporting of profit data (Chapter 12).
Segmented reporting of profit data (Chapter 12).
4.
4. Special decisions such as pricing and make-or-
Special decisions such as pricing and make-or-
buy analysis (Chapter 13).
1.
1. Cost-volume-profit analysis (Chapter 6).
Cost-volume-profit analysis (Chapter 6).
2.
2. Budgeting (Chapter 9).
Budgeting (Chapter 9).
3.
3. Segmented reporting of profit data (Chapter 12).
Segmented reporting of profit data (Chapter 12).
4.
4. Special decisions such as pricing and make-or-
Special decisions such as pricing and make-or-

McGraw-Hill/Irwin
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 operating income 10,000
$ Net operating income 10,000
$
Used primarily for
Used primarily for
external reporting.
external reporting.
Used primarily by
Used primarily by
management.
management.

McGraw-Hill/Irwin
Appendix 5A
Least-Squares
Regression Using
Microsoft Excel.

McGraw-Hill/Irwin
Simple Regression Analysis Example
Matrix, Inc. wants to
know its average
know its average
fixed cost and
fixed cost and
variable cost per unit.
Using the data to the
right, let’s see how to
do a regression using
Microsoft Excel.
Microsoft Excel.
know its average
know its average
fixed cost and
fixed cost and
Microsoft Excel.
Microsoft Excel.

McGraw-Hill/Irwin
Simple Regression Using Excel
You will need three pieces of
information from your
regression analysis:
1.
1. Estimated Variable Cost per
Estimated Variable Cost per
Unit (line slope)
Unit (line slope)
2.
2. Estimated Fixed Costs (line
Estimated Fixed Costs (line
intercept)
intercept)
3.
3. Goodness of fit, or R
Goodness of fit, or R2
2
1.
1. Estimated Variable Cost per
Estimated Variable Cost per
Unit (line slope)
Unit (line slope)
2.
2. Estimated Fixed Costs (line
Estimated Fixed Costs (line
intercept)
intercept)
3.
3. Goodness of fit, or R
Goodness of fit, or R2
2
To get these three pieces
information we will need to
use
use three
three different Excel
different Excel
functions.
functions.
LINEST, INTERCEPT, & RSQ
use
use three
three different Excel
different Excel
functions.
functions.

McGraw-Hill/Irwin
Place your cursor in
cell F4 and press the
= key. Click on the
= key. Click on the
pull down menu and
pull down menu and
scroll down to “More
Functions . . .”
Functions . . .”
= key. Click on the
= key. Click on the
pull down menu and
pull down menu and
Functions . . .”
Functions . . .”

McGraw-Hill/Irwin
Scroll down to the
Scroll down to the
“
“Statistical
Statistical”,
”,
functions. Now
functions. Now
scroll down the
scroll down the
statistical
statistical
functions until you
functions until you
highlight
highlight
“
“LINEST
LINEST”
”
Scroll down to the
Scroll down to the
“
“Statistical
Statistical”,
”,
functions. Now
functions. Now
scroll down the
scroll down the
statistical
statistical
functions until you
functions until you
highlight
highlight
“
“LINEST
LINEST”
”

McGraw-Hill/Irwin
1. In the Known_y’s box enter C4:C19 for the range.
2. In the Known_x’s box enter D4:D19 for the range.

McGraw-Hill/Irwin
Here is the
Here is the
estimate of the
estimate of the
slope of the line.
slope of the line.

McGraw-Hill/Irwin
With you cursor in cell
F5, press the = key
F5, press the = key
and go to the pull
and go to the pull
down menu for
down menu for
special functions.
special functions.
Select
Select Statistical
Statistical and
and
scroll down to
scroll down to
highlight the
highlight the
INTERCEPT
INTERCEPT function.
function.
F5, press the = key
F5, press the = key
and go to the pull
and go to the pull
down menu for
down menu for
special functions.
special functions.
Select
Select Statistical
Statistical and
and
scroll down to
scroll down to
highlight the
highlight the
INTERCEPT
INTERCEPT function.
function.

McGraw-Hill/Irwin
Here is the
Here is the
estimate of the
estimate of the
fixed costs.
fixed costs.

McGraw-Hill/Irwin
Finally, we will
Finally, we will
determine the
determine the
“
“goodness of
goodness of
fit
fit”, or
”, or R
R2
2
, by
, by
using the
using the RSQ
RSQ
function.
function.
Finally, we will
Finally, we will
determine the
determine the
“
“goodness of
goodness of
fit
fit”, or
”, or R
R2
2
, by
, by
using the
using the RSQ
RSQ
function.
function.

McGraw-Hill/Irwin
Here is the
Here is the
estimate of
estimate of R
R2
2
.
.

McGraw-Hill/Irwin
End of Chapter 5

Ch 5 Cost-Volume-Profit Relationships.pdf

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