1
Determining
How Costs
Behave
2
Knowing how costs
vary by identifying the
drivers of costs and by
distinguishing fixed
from variable costs are
frequently the keys to
making good
management decisions
General Issues in Estimating
Cost Functions


A cost function is a mathematical function describing cost
behavior patterns - how costs change with changes in the
cost driver.
Two assumptions are frequently made when estimating
cost functions.
 Variations in the total costs of a cost-object are explained by
variations in a single cost driver.
 Cost behavior is adequately approximated by a linear cost
function of the cost driver within a relevant range.
y = a + bX
3
S U R V E Y S OF C O M P A N Y P R A C T I C E
International Comparison of Cost
Classification by Companies
Cost Category
V
Production labor
Setup labor
Materialshandling labor
Quality-control
labor
Tooling
Energy
Building
occupancy
Depreciation
86% 6% 8%
60 25 15
M
F
V
M
F
52% 5% 43%
44 6 50
V
M
F
70% 20% 10%
45 33 22
48
34
18
23
16
61
40
30
30
34
32
26
36
35
45
30
33
29
13
31
42
12
26
31
75
43
27
21
25
-
27
28
-
52
47
-
1
1
6
7
93
92
0
0
0
0
100
100
-
-
-
The Cause-and-Effect Criterion in
Choosing Cost Drivers

The most important issue in estimating a cost
function is to determine whether a cause-and-effect
relationship exists between the cost driver and the
resulting costs.

The cause-and-effect relationship might arise in
several ways.
1. It may be due to a physical relationship between costs and cost
drivers.
2. Cause and effect can arise from a contractual arrangement.
3. Cause and effect can be implicitly established by logic and
knowledge of operations.
5
The Cause-and-Effect Criterion in
Choosing Cost Drivers

Be careful not to interpret a high correlation, or
connection, between two variables to mean that
either variable causes the other.

Only a true cause-and-effect relationship, not
merely correlation, establishes an economically
plausible relationship between costs and their cost
drivers.

Establishing economically plausibility is a vital
aspect of cost estimation.
6
7
Cost Estimation Approaches

Industrial Engineering Method

Conference Method

Account Analysis Method

Quantitative Analysis of Current or
Past Cost Relationships
These approaches differ in the costs of conducting the analysis, the
assumptions they make, and the evidence they provide about
accuracy of the estimated cost function.
8
Industrial Engineering Method
 The industrial engineering method(or work-
measurement method) estimates cost
functions by analyzing the relationship
between inputs and outputs in physical terms.
 Time-and-motion study
 It can be very time-consuming
 Organizations use this approach for direct-
cost categories such as materials and labor but
not for indirect-cost categories.
9
Conference Method
 The conference method estimates cost
functions on the basis of analysis and opinions
about costs and their drivers gathered from
various departments of an organization.
 This method allows cost functions and cost
estimates to be developed quickly.
 The accuracy of the cost estimates largely
depends on the care and detail taken by the
people providing the inputs.
10
Account Analysis Method
 The account analysis method estimates cost
functions by classifying cost accounts in the
ledger as variable, fixed, or mixed with
respect to identified cost driver.
 Typically, managers use qualitative rather
than quantitative analysis when making these
cost-classification decisions.
 The account analysis approach is widely
used.
11
Quantitative Analysis
of Cost Relationships
Quantitative analysis of cost relationships are
formal methods to fit linear cost functions to past
data observations
Steps in Estimating A
Cost Function
Step 1 : Choose the Dependent Variable
Step 2 : Identify the Cost Driver(s)
Step 3 : Collect Data on the Dependent Variable and
Cost Driver(s)
Step 4 : Plot the Data
Step 5 : Estimate the Cost Function
Step 6 : Evaluate the Estimated Cost Function
12
13
High-Low Method
Highest Observation
Lowest Observation
Difference
MH
96
46
50
IMLC
$1,456
$710
$746
^
b = $746/50 = $14.92
^a = $1,456-($14.92*96)
= $23.68
IMLC = $23.68+($14.92*MH)
Regression Analysis Method
IMLC = $300.98+($10.31*MH)
IMLC = $744.67+($7.72*DMLC)
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15
Quality Implement Corporation (QIC) produces
farm implements for large vehicles used for farming.
QIC is refining its cost system and is currently
studying the costs of the maintenance activity.
Activity analysis indicates that maintenance activity
consists primarily of labor setting up machines using
certain supplies. Costs include labor, supplies, and
energy. QIC employs two full-time mechanics to
perform maintenance. The annual salary of a
maintenance mechanic is $25,000 (fixed cost). Two
plausible cost drivers have been suggested: units
produced and number of setups. QIC has performed
the first four steps in the cost estimation process.
You are asked to estimate and evaluate the
prospective cost functions.
MAINTENANCE COSTS
(THOUSANDS)
16
$30
$25
$20
$15
$10
$5
Plant closed three weeks
in March due to storm
damage
$0
0
10
20
NUMBER OF SETUPS
30
17
MAINTENANCE COSTS
(THOUSANDS)
$30
$25
$20
$15
$10
$5
$0
0
1
2
Plant closed three
weeks in March due to
storm damage
3
UNITS PRODUCED (THOUSANDS)
4
MAINTENANCE COSTS
(THOUSANDS)
18
$30
$25
$20
$15
$10
$5
$0
0
10
20
30
NUMBER OF SETUPS
MAINTENANCE COSTS
(THOUSANDS)
$30
$25
$20
$15
$10
$5
$0
0
1
2
3
UNITS PRODUCED (THOUSANDS)
4
Using the visual fit
method, determine
the monthly fixed
maintenance cost
and the variable
maintenance cost
per driver unit
based on each
potential cost
driver. How should
the March data be
treated?
MAINTENANCE COSTS
(THOUSANDS)
19
$30
$25
How should the March
data be treated?
$20
$15
$10
$5
$0
0
10
20
30
NUMBER OF SETUPS
MAINTENANCE COSTS
(THOUSANDS)
$30
$25
$20
$15
$10
$5
$0
0
1
2
3
UNITS PRODUCED (THOUSANDS)
4
As indicated on page
355 of the text, extreme
values of observations
occur from
nonrepresentative time
periods. Such data
should be eliminated
before estimating cost
relationships.
20
REGRESSION ANALYSIS RESULTS
MAINTENANCE COSTS
(THOUSANDS)
$30
y = 0.7511x + 5.162
2
R = 0.8519
$25
$20
$15
$10
$5
$0
0
5
10
15
20
25
30
MAINTENANCE COSTS
(THOUSANDS)
NUMBER OF SETUPS
$30
y = 2.1653x + 13.108
$25
R = 0.2052
2
$20
$15
$10
$5
$0
0
1
2
3
4
UNITS PRODUCED (THOUSANDS)
5
Which cost
driver best
meets the
criteria for
choosing cost
functions:
economic
plausibility,
goodness-of-fit,
and slope of the
regression line?
21
MAINTENANCE COSTS
(THOUSANDS)
$30
y = 0.7511x + 5.162
2
R = 0.8519
$25
$20
$15
$10
$5
$0
0
5
10
15
20
25
30
NUMBER OF SETUPS
MAINTENANCE COSTS
(THOUSANDS)
Both cost drivers appear to be
economically plausible. However,
if maintenance activity is
primarily associated with a
batch-level activity such as
setups, the setup driver is
preferred. Of the costs
associated with maintenance
activity, supplies and energy are
primarily variable and salaries
are fixed at a monthly amount of
$4,167 [2*25,000/12]. The
regression results indicate a
fixed cost of $5,162 using setups,
compared to $13,108 using units.
Thus, number of setups is the
preferred cost driver based on
economic plausibility.
$30
y = 2.1653x + 13.108
$25
R = 0.2052
2
$20
$15
$10
$5
$0
0
1
2
3
4
UNITS PRODUCED (THOUSANDS)
5
22
Units produced has an R2 of
only 0.2052 so it does not
pass the goodness-of-fit
test. Number of setups has
an R2 of 0.8519, passing the
goodness-of-fit test.
MAINTENANCE COSTS
(THOUSANDS)
$30
y = 0.7511x + 5.162
2
R = 0.8519
$25
$20
$15
$10
$5
$0
0
5
10
15
20
25
30
NUMBER OF SETUPS
MAINTENANCE COSTS
(THOUSANDS)
The coefficient of
determination, R2, measures
the percentage of variation
in maintenance cost
explained by number of
setups or units produced.
Generally, an R2 of 0.30 or
higher passes the
goodness-of-fit test.
$30
y = 2.1653x + 13.108
$25
R = 0.2052
2
$20
$15
$10
$5
$0
0
1
2
3
4
UNITS PRODUCED (THOUSANDS)
5
MAINTENANCE COSTS
(THOUSANDS)
$30
23
y = 0.7511x + 5.162
2
R = 0.8519
$25
Do changes in the
economically plausible cost
driver result in significant
changes in maintenance
cost?
$20
$15
$10
$5
$0
0
5
10
15
20
NUMBER OF SETUPS
25
30
MAINTENANCE COSTS
(THOUSANDS)
$30
24
y = 0.7511x + 5.162
2
R = 0.8519
$25
Do changes in the
economically plausible cost
driver result in significant
changes in maintenance
cost?
$20
$15
$10
$5
$0
0
5
10
15
20
25
30
NUMBER OF SETUPS
Coefficients Standard Error t Stat
Intercept
5.16
1.98 2.61
SETUPS
0.75
0.10 7.20
MAINTENANCE COSTS
(THOUSANDS)
$30
25
y = 0.7511x + 5.162
2
R = 0.8519
$25
Do changes in the
economically plausible cost
driver result in significant
changes in maintenance
cost?
$20
$15
$10
$5
$0
0
5
10
15
20
25
30
NUMBER OF SETUPS
Coefficients Standard Error t Stat
Intercept
5.16
1.98 2.61
SETUPS
0.75
0.10 7.20
The slope of the regression line is 0.75, meaning that each
additional setup performed results in an average increase
in maintenance costs of $750. The importance of setups in
driving maintenance costs is measured by the t statistic.
Both t statistics are greater than 2.23 implying a significant
relationship exists.
Learning Curve and
Nonlinear Cost Functions
 A learning curve is a function that shows how labor-hours per unit
decline as units of production increases and workers learn and
become better at what they do.
 Managers use learning curves to predict how labor-hours(or labor
costs) will change as more units are produced.
 Managers are now extending the learning-curve notion to include
other cost areas in the value chain such as marketing, distribution,
and customer service.
 The term experience curve describes this broader application of the
learning curve.
 An experience curve is a function that shows how full product
costs per unit(including manufacturing, marketing, distribution, and
so on) declines as units of output increase.
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Cumulative Average-Time Learning Model
120
100
80
60
40
20
0
1
17
16
33
32
49
48
6465
81
80
97 112
113 128
96
Cumulative units
4000
3000
2000
1000
0
1
17
16
33
32
49
48
6465
81
80
Cumulative units
97 112
113 128
129
96
In the cumulative
average-time learning
model, the cumulative
average time per unit
declines by a constant
percentage each time the
cumulative quantity of
units doubles.
27
Incremental Unit-Time Learning Model
28
120
100
In the incremental unittime learning model, the
incremental unit time (the
time needed to produce
the last unit) declines by a
constant percentage each
time the cumulative
quantity of units doubles.
80
60
40
20
0
1
17
16
33
32
49
48
65
64
81
80
97 112
113 128
96
Cumulative units
4000
3000
2000
1000
0
1
17
16
3233
49 6465
48
8081
Cumulative units
97 112
113 128
96
Data Collection and
Adjustment Issues
The ideal data base for estimating cost
functions quantitatively has two
characteristics
1. It contains numerous reliably measured observations
of the cost driver(s) and the dependent variable.
2. It contains many values for the cost driver over a wide
range.
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Some Frequently Encountered
Data Problems
1. The time period for measuring the dependent variable does not
properly match the period for measuring cost driver(s).
2. Fixed costs are allocated as if they are variable.
3. Data are either not available for all observations or are not uniformly
reliable.
4. Extreme values of observations occur from errors in recording costs;
from nonrepresentative time periods; or from observations being
outside the relevant range.
5. There is no homogeneous relationship between the individual cost
items in the dependent variable pool and the cost driver.
6. The relationship between cost and the cost driver is not stationary; that
is, the underlying process that generated the observations has not
remained stable over time.
7. Inflation has affected the dependent variable, the cost driver, or both.
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