Chapter 5
Cost Behavior: Analysis and Use
Variable Costs
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
Unit Variable Cost Graph
Cost per Unit
Total Costs
Total Variable Cost Graph
$20
$15
$10
$5
0
10 20
30
Units Produced (000)
0
10 20
30
Units Produced (000)
Units
Produced
5,000
10,000
15,000
20,000
25,000
30,000
Total Cost
Cost per Unit
$ 50,000 $10
100,000 10
150,000 10
200,000 10
250,000 10
300,000 10
The Activity Base/Cost driver
Machine
hours
Units
produced
A measure of what
causes the
incurrence of a
variable cost
Miles
driven
Labor
hours
True Variable vs. Step Variable
Step Variable Costs - A cost that is obtainable only in chunks –
changes abruptly at intervals of activity.
True variable cost
Step variable cost
Volume
Volume
Step-Variable Costs
Total cost increases to a
new higher cost for the next higher
range of activity
Cost
Total cost remains
constant within a
narrow range of
activity
Activity
The Linearity Assumption and the
Relevant Range
Total Cost
A straight line
Economist’s
closely
Curvilinear Cost approximates a
Function
curvilinear
Relevant
Range
variable cost
line within the
relevant range.
Accountant’s Straight-Line
Approximation (constant
unit variable cost)
Activity
Fixed Costs
$150,000
$125,000
$100,000
$75,000
$50,000
$25,000
Unit Fixed Cost Graph
Cost per Unit
Total Costs
Total Fixed Cost Graph
$1.50
$1.25
$1.00
$.75
$.50
$.25
0
100 200 300
Units Produced (000)
0
100 200 300
Units Produced (000)
Units
Produced
Total Cost
Cost per Unit
50,000 $75,000 $1.500
100,000 75,000
.750
150,000 75,000
.500
200,000 75,000
.375
250,000 75,000
.300
300,000 75,000
.250
Types of Fixed Costs
Committed
Discretionary
Long-term, cannot be
significantly reduced
in the short term.
May be altered in the
short-term by current
managerial decisions
Examples
Examples
Depreciation on
Equipment and
Real Estate Taxes
Advertising and
Research and
Development
Step-Fixed Costs
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.
Rent Cost in Thousands
of Dollars
Step-Fixed Costs and Relevant Range
90
60
30
00
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.
1,000
2,000
3,000
Rented Area (Square Feet)
Fixed Costs and Relevant Range
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.
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.
Cost Behavior Patterns Example
Bicycles by the Sea incurs variable costs of
$52 for each of its bicycles.
Bicycles by the Sea also incurs $94,500 in
fixed costs per year
Total Costs and Unit Costs
Example
What is the unit cost when Bicycles
assembles 1,000 bicycles in a year?
Use Unit Costs Cautiously
Assume that Bicycles management uses a
unit cost of $146.50
Management is budgeting costs for
different levels of production.
What is their budgeted cost for an
estimated production of 600 bicycles?
600 × $146.50 = $87,900?
Use Unit Costs Cautiously
What is their budgeted cost for an estimated
production of 3,500 bicycles?
3,500 × $146.50 = $512,750?
Pop Quiz 
Which of the following costs would be variable with
respect to the number of cones sold at a Baskins &
Robbins shop? (There may be more than one correct
answer.)
A. The cost of lighting the store.
B. The wages of the store manager.
C. The cost of ice cream.
D. The cost of napkins for customers.
Pop Quiz 
Which of the following costs would be variable with
respect to the number of people who buy a ticket for
a show at a movie theater? (There may be more than
one correct answer.)
A. The cost of renting the film.
B. Royalties on ticket sales.
C. Wage and salary costs of theater
employees.
D. The cost of cleaning up after the show.
Mixed Costs
A mixed cost has both fixed and variable
components. Consider the example of utility cost.
Total Utility Cost
Y
Variable
Cost per KW
X
Activity (Kilowatt Hours)
Fixed Monthly
Utility Charge
Mixed Costs
The total mixed cost line can be expressed
as an equation: Y = a + bX
Where:
Total Utility Cost
Y
Y = the total mixed cost
a = the total fixed cost (the
vertical intercept of the line)
b = the variable cost per unit of
activity (the slope of the line)
X = the level of activity
Variable
Cost per KW
X
Activity (Kilowatt Hours)
Fixed Monthly
Utility Charge
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
Practice…Hospital Costs
Variable, step, mixed, discretionary or committed fixed?
•
Training costs of an administrative employee
•
Straight line depreciation
•
Cost of services of L&J Consulting
•
Nursing supervisor salaries – supervisor needed for each 45 nursing
personnel
Practice…Hospital Costs
Variable, step, mixed, discretionary or committed fixed?
•
Operating costs of x-ray equipment ($95,000 per year plus $3 per film)
•
Insurance for all full time employees
•
Costs incurred by Dr. Rath in cancer research
The Analysis of Mixed Costs
Account-Classification Method
Engineering Method
Scattergraph Method
High-Low Method
Least-Squares Regression Method
Analysis of Mixed Costs
Account Analysis and the Engineering Approach
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.
Account Classification Method
Example
Account
Indirect Labor
Indirect Material
Depreciation
Property Taxes
Insurance
Utilities
Maintenance
Totals
Overhead
Total
Cost
$
450
700
1,000
200
300
400
600
$ 3,650
Costs for 1,000 Units
Variable
Fixed
Cost
Cost
$
450
700
1,000
200
300
350
50
500
100
$ 2,000
$ 1,650
The Scattergraph Method
Plot the data points on a graph (total
cost vs. activity).
Maintenance Cost
1,000’s of Dollars
Y
20
* *
* *
10
0
0
1
2
* ** *
**
3
4
Patient-days in 1,000’s
X
High-Low Method - Cost and Activity Data
Assume the following hours of maintenance work
and the total maintenance costs for six months.
The Contribution Format
Used primarily for
external reporting.
Used primarily by
management.
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. Cost-volume-profit analysis (Chapter 6).
2. Budgeting (Chapter 9).
3. Segmented reporting of profit data (Chapter 12).
4. Special decisions such as pricing and make-or-buy
analysis (Chapter 13).