Determining
How Costs Behave
© 2009 Pearson Prentice Hall. All rights reserved.
COST BEHAVIOR PATTERNS
 Understanding cost behavior patterns (i.e., the
relationship between cost and activity) is important to
managers as they plan, control, and make decisions in
the operation of their organizations. (For example, a
manager must understand how costs behave across
various levels of activity before a budget can be
prepared.)
© 2009 Pearson Prentice Hall. All rights reserved.
COST BEHAVIOR PATTERNS
 Cost Estimation: The process of determining cost
behavior. Often focuses on historical data.
 Cost Behavior: The relationship between cost and
activity.
 Cost Prediction: Using knowledge of cost behavior to
forecast the level of cost at a particular level of activity.
Focus is on the future.
 Cost estimation
Cost behavior
© 2009 Pearson Prentice Hall. All rights reserved.
Cost prediction
Cost Terminology
 Variable Costs – costs that change in total in relation
to some chosen activity or output (cost driver)
 Example: the paper cost in giving exams varies with the
number of students in a class.
 Step-variable costs are nearly variable, but such costs
increase in small steps rather than in direct proportion
to cost-driver changes.
 Example: if a class is a bit larger than usual, an
additional exam proctor may have to be hired. This
increase in part-time hourly help increases by a step as
the class size grows.
© 2009 Pearson Prentice Hall. All rights reserved.
Cost Terminology
 Fixed Costs – costs that do not change in total in
relation to some chosen activity or output
 Example: a professor’s salary is fixed, and more students
enrolled in his or her course will not affect salary.
However, the salary cost per student will vary depending
on class size.
 Step-fixed costs are fixed within a wide range of
activity but will change outside that range
 Example: if a course increases by a large number of
students, it will be necessary to add another section and
hire another instructor. The fixed cost then jumps to
another step.
© 2009 Pearson Prentice Hall. All rights reserved.
Cost Terminology
 Mixed Costs – costs that have both fixed and variable
components; also called semivariable costs
 Example: a printer’s fee for brochures, which includes a
fixed set-up cost and a per-copy (i.e., variable) charge for
running the total copies needed.
© 2009 Pearson Prentice Hall. All rights reserved.
Cost Terminology
 An engineered cost is one that bears a definite
physical relationship to the cost driver.
 Example: the food cost of a restaurant, as it is
impossible to serve more meals without incurring
more food cost.
 Committed costs result from an organization’s
ownership or use of facilities and its basic
organizational structure. These costs cannot be
eliminated without endangering the entity’s overall
health and existence.
 Examples: property taxes, depreciation on buildings
and equipment, top management salaries.
© 2009 Pearson Prentice Hall. All rights reserved.
Cost Terminology
 Discretionary costs exist as the result of a
management decision. In comparison with committed
costs, such costs are more easily changed in bad
economic times without doing serious long-run harm
to the entity.
 Examples: a training program, an advertising campaign,
corporate contributions.
 Fixed costs are becoming more prevalent in many
industries because of automation and labor unions’
success in negotiating for a stable workforce. Costs
that were once variable are becoming fixed, which
makes a company less able to respond rapidly to
changing economic conditions.

© 2009 Pearson Prentice Hall. All rights reserved.
Cost Terminology
• A curvilinear cost function cannot be
represented with a straight line but instead is
represented with a curve that reflects either
increasing or decreasing marginal costs.
• Relevant range—the range of activity within
which managers expect a company to operate
and within which managers can predict cost
behavior with some certainty.
 Within the relevant range, even curvilinear costs may
behave in a linear fashion.
© 2009 Pearson Prentice Hall. All rights reserved.
Cost Functions
 A cost function is a mathematical representation of
how a cost changes with changes in the level of an
activity relating to that cost
 Examples of activities are preparing setups for
production runs and operating machines.
© 2009 Pearson Prentice Hall. All rights reserved.
Cost Function Assumptions
1.
2.
Variations in the level of a single activity (the cost
driver) explain the variations in the related total
costs
Cost behavior is approximated by a linear cost
function within the relevant range

Graphically, the total cost versus the level of a single
activity related to that cost is a straight line within the
relevant range
© 2009 Pearson Prentice Hall. All rights reserved.
Bridging Accounting & Statistical
Terminology
Accounting
Statistics
Variable Cost
Slope
Fixed Cost
Intercept
Mixed Cost
Linear Cost Function
© 2009 Pearson Prentice Hall. All rights reserved.
The Linear Cost Function
y = a + bX
The Dependent
Variable:
The cost that is
being predicted
The Independent
Variable:
The cost driver
The Intercept:
Fixed Costs
The slope of
the line:
variable cost
per unit
© 2009 Pearson Prentice Hall. All rights reserved.
Linear Cost Functions Illustrated
© 2009 Pearson Prentice Hall. All rights reserved.
Criteria for Classifying Variable & Fixed
Components of a Cost
1.
2.
3.
Choice of Cost Object – different objects may result
in different classification of the same cost
Time Horizon – the longer the period, the more
likely the cost will be variable
Relevant Range – behavior is predictable only within
this band of activity
© 2009 Pearson Prentice Hall. All rights reserved.
The
Relevant
Range
Illustrated
© 2009 Pearson Prentice Hall. All rights reserved.
Cause & Effect as it relates to
Cost Drivers
 The most important issue in estimating a cost function
is determining whether a cause-and-effect relationship
exists between the level of an activity and the costs
related to that level of activity.
© 2009 Pearson Prentice Hall. All rights reserved.
Cause & Effect as it relates to
Cost Drivers
 A cause-and-effect relationship might arise as a result
of:
 A physical relationship between the level of activity and
costs
 A contractual agreement
 Knowledge of operations
 Note: a high correlation (connection) between
activities and costs does not necessarily mean causality
© 2009 Pearson Prentice Hall. All rights reserved.
Cost Estimation Methods
1.
2.
3.
4.
Industrial Engineering Method
Conference Method
Account Analysis Method
Quantitative Analysis Methods
High-Low Method
2. Regression Analysis
1.
© 2009 Pearson Prentice Hall. All rights reserved.
Industrial Engineering Method
 Estimates cost functions by analyzing the relationship
between inputs and outputs in physical terms
 Includes time-and-motion studies
 Very thorough and detailed, but also costly and timeconsuming
 Also called the Work-Measurement Method
© 2009 Pearson Prentice Hall. All rights reserved.
Conference Method
 Estimates cost functions on the basis of analysis and
opinions about costs and their drivers gathered from
various departments of a company
 Pools expert knowledge
 Reliance on opinions still make this method subjective
© 2009 Pearson Prentice Hall. All rights reserved.
Account Analysis Method
 The account-classification method (also called
account analysis) requires the study of an account in
the general ledger. The experienced analyst uses the
account information as well as his or her own
judgment to determine future cost behavior
 estimates cost functions by classifying various cost
accounts as variable, fixed or mixed with respect to the
identified level of activity
 Is reasonably accurate, cost-effective, and easy to use,
but is subjective
© 2009 Pearson Prentice Hall. All rights reserved.
Quantitative Analysis Method
 Uses a formal mathematical method to fit cost
functions to past data observations
 Advantage: results are objective
© 2009 Pearson Prentice Hall. All rights reserved.
Steps in Estimating a Cost Function Using
Quantitative Analysis
Choose the dependent variable (the cost to be
predicted)
2. Identify the independent variable or cost driver
3. Collect data on the dependent variable and the
cost driver
4. Plot the data
5. Estimate the cost function using the High-Low
Method or Regression Analysis
6. Evaluate the cost driver of the estimated cost
function
1.
© 2009 Pearson Prentice Hall. All rights reserved.
AN EXAMPLE
Week
Cost Driver :
machine Hours
(X)
1
68
Indirect Manufacturing:
Labor Costs ($)
(Y)
1,190
2
88
1,211
3
62
1,004
4
72
917
5
60
770
6
96
1,456
7
78
1,180
8
46
710
9
82
1,316
10
94
1,032
11
68
752
12
48
963
Total
862
12,501
© 2009 Pearson Prentice Hall. All rights reserved.
Visual-Fit method
 With the visual-fit method, an analyst examines a
cost by plotting points on a graph (called a scatter
diagram) and places a line through the points to yield
a cost function.
 This method is more objective than the accountclassification method, but it is still lacking because
two cost analysts could visually fit different lines.

 The visual-fit method is useful because it helps spot
nonrepresentative data points, or outliers.
© 2009 Pearson Prentice Hall. All rights reserved.
Sample Cost – Activity Plot
© 2009 Pearson Prentice Hall. All rights reserved.
High-Low Method
 Simplest method of quantitative analysis
 Uses only the highest and lowest observed values
© 2009 Pearson Prentice Hall. All rights reserved.
Steps in the High-Low Method
1.
Calculate variable cost per unit of activity
Variable
Cost per
Unit of Activity
=
{
Cost associated with
highest activity level
Highest activity level
-
Cost associated with
lowest activity level
Lowest activity level
(c) 2009 Pearson Prentice Hall. All rights reserved.
}
Steps in the High-Low Method
2.
Calculate Total Fixed Costs
Total Cost from either the highest or lowest activity level
- (Variable Cost per unit of activity X Activity associated with above total cost)
Fixed Costs
3.
Summarize by writing a linear equation
Y = Fixed Costs + ( Variable cost per unit of Activity * Activity )
Y = FC + (VCu * X)
(c) 2009 Pearson Prentice Hall. All rights reserved.
AN EXAMPLE
Week
Cost Driver :
machine Hours
(X)
1
68
Indirect Manufacturing:
Labor Costs ($)
(Y)
1,190
2
88
1,211
3
62
1,004
4
72
917
5
60
770
6
96
7
78
8
46
9
82
1,316
10
94
1,032
11
68
752
12
48
963
Total
862
12,501
© 2009 Pearson Prentice Hall. All rights reserved.
1,456 Highest Level
1,180
710 lowest level
High low Method
Cost Driver:
Indirect Manufacturing
Machine Hours (X)
Labor Costs(Y)
Highest observation of cost driver ( week 6)
96
1,456
lowest observation of cost driver ( week 8)
46
710
Difference
50
746
The Slope Co-efficient is calculated as:
Difference between costs associated with Highest and
Lowest observations of the cost driver
Slope Co-efficient = ____________________________________________
Difference between Highest and Lowest observations of the
cost driver
= 746/50 Machine hours
= $14.92 per machine-hour
© 2009 Pearson Prentice Hall. All rights reserved.
High low Method
 At the highest observation of the cost driver, the
constant, a, is calculated as :
Constant= $1,456-($14.92 per machine hr * 96 Machine hrs) = $23.68
 At the lowest observation of the cost driver
Constant= $710-($14.92 per machine hr * 46 Machine hrs) = $23.68
 Thus, the high-low estimate of the cost function is :
Y= a + bX
Y= $23.68 + ($14.92 per Machine Hr * Number of Machine Hrs)
© 2009 Pearson Prentice Hall. All rights reserved.
High – Low Method Plot
© 2009 Pearson Prentice Hall. All rights reserved.
Regression Analysis
 Regression analysis is a statistical method that
measures the average amount of change in the
dependent variable associated with a unit change in
one or more independent variables
 Is more accurate than the High-Low method
because the regression equation estimates costs
using information from all observations; the HighLow method uses only two observations
© 2009 Pearson Prentice Hall. All rights reserved.
Types of Regression
 Simple – estimates the relationship between the
dependent variable and one independent variable
 Multiple – estimates the relationship between the
dependent variable and two or more independent
variables
© 2009 Pearson Prentice Hall. All rights reserved.
AN EXAMPLE
Week
Cost Driver :
machine Hours
(X)
1
68
Indirect Manufacturing:
Labor Costs ($)
(Y)
1,190
2
88
1,211
3
62
1,004
4
72
917
5
60
770
6
96
1,456
7
78
1,180
8
46
710
9
82
1,316
10
94
1,032
11
68
752
12
48
963
Total
862
12,501
© 2009 Pearson Prentice Hall. All rights reserved.
Sample Regression Model Plot
© 2009 Pearson Prentice Hall. All rights reserved.
AN EXAMPLE
Month
Cost Driver :
Direct Labor Hours
(X)
January
34,000
Indirect Manufacturing:
Electricity Costs ($)
(Y)
640
February
30,000
620
March
34,000
620
April
39,000
590
May
42,000
500
June
32,000
530
July
26,000
500
August
26,000
500
September
31,000
530
October
35,000
550
November
43,000
580
December
48,000
680
Total
420,000
6,840
© 2009 Pearson Prentice Hall. All rights reserved.
Alternative Regression Model Plot
© 2009 Pearson Prentice Hall. All rights reserved.
Terminology
 Goodness of Fit – indicates the strength of the
relationship between the cost driver and costs
 Residual Term – measures the distance between actual
cost and estimated cost for each observation
© 2009 Pearson Prentice Hall. All rights reserved.
Criteria for Evaluating
Alternative Cost Drivers
1.
2.
3.
Economic Plausibility
Goodness of Fit
Significance of the Independent Variable
© 2009 Pearson Prentice Hall. All rights reserved.
Nonlinear Cost Functions
Economies of Scale
Quantity Discounts
Step Cost Functions – resources increase in “lotsizes”, not individual units
4. Learning Curves – labor hours consumed decrease
as workers learn their jobs and become better at
them
5. Experience Curve – broader application of
learning curve that includes Downstream
activities including marketing and distribution
1.
2.
3.
© 2009 Pearson Prentice Hall. All rights reserved.
Nonlinear Cost Functions Illustrated
© 2009 Pearson Prentice Hall. All rights reserved.
A learning curve is a function that measures how
labor-hours per unit decline as unit of production
increase because workers are learning and becoming
better at their jobs.
© 2009 Pearson Prentice Hall. All rights reserved.
Types of Learning Curves
 Cumulative Average-Time Learning Model –
cumulative average time per unit declines by a
constant percentage each time the cumulative
quantity of units produced doubles. Rayburn has an
80% learning curve.
 Incremental Unit-Time Learning Model –
incremental time needed to produce the last unit
declines by a constant percentage each time the
cumulative quantity of units produced doubles
© 2009 Pearson Prentice Hall. All rights reserved.
Sample Cumulative Average-Time
Model
© 2009 Pearson Prentice Hall. All rights reserved.
Sample Incremental Unit-Time
Model
© 2009 Pearson Prentice Hall. All rights reserved.
Time Learning Model Comparative
Plots
© 2009 Pearson Prentice Hall. All rights reserved.
Predicting Costs Using Alternative
Time Learning Models
© 2009 Pearson Prentice Hall. All rights reserved.
The Ideal Database
1.
2.
The database should contain numerous reliably
measured observations of the cost driver and the
costs
In relation to the cost driver, the database should
consider many values spanning a wide range
© 2009 Pearson Prentice Hall. All rights reserved.
Data Problems
 The time period for measuring the dependent variable
does not match the period for measuring the cost
driver
 Fixed costs are allocated as if they are variable
 Data are either not available for all observations or are
not uniformly reliable
© 2009 Pearson Prentice Hall. All rights reserved.
Data Problems
 Extreme values of observations occur from errors in
recording costs
 There is no homogeneous relationship between the
cost driver and the individual cost items in the
dependent variable-cost pool. A homogeneous
relationship exists when each activity whose costs are
included in the dependent variable has the same cost
driver
© 2009 Pearson Prentice Hall. All rights reserved.
Data Problems
 The relationship between the cost driver and the cost
is not stationary
 Inflation has affected costs, the driver, or both
© 2009 Pearson Prentice Hall. All rights reserved.
© 2009 Pearson Prentice Hall. All rights reserved.