Determining How
Costs Behave
Chapter 10
2009 Foster School of Business
Cost Accounting
L.DuCharme
1
Overview
1)
2)
3)
4)
Assumptions
Model: Y = a + bX
Determinates of Fixed vs. Variable costs
Cost Estimation
Industrial Engineering
Conference Method
Account Analysis
Quantitative Analysis: H-L & OLS
5) Non-linear cost functions
2009 Foster School of Business
Cost Accounting
L.DuCharme
2
Two assumptions frequently used
in cost-behavior estimation
1. Changes in total costs can be explained by
changes in the level of a single activity.
2. Cost behavior can adequately be
approximated by a linear function of the
activity level within the relevant range.
2009 Foster School of Business
Cost Accounting
L.DuCharme
3
Cost Function
What is a cost function?
It is a mathematical expression
describing how costs change
with changes in the level
of an activity.
2009 Foster School of Business
Cost Accounting
L.DuCharme
4
Cost Function—variable cost
La Playa Hotel offers an airline
three alternative cost structures to
accommodate its crew overnight:
1. $60 per night per room usage
y = $60x
The slope of the cost function is $60.
2009 Foster School of Business
Cost Accounting
L.DuCharme
5
Cost Function
y = Cost
$20,000
$15,000
$10,000
$5,000
$0
0
100
200
300
x = Number of rooms
2009 Foster School of Business
Cost Accounting
L.DuCharme
6
Cost Function—fixed cost
2. $8,000 per month
y = $8,000
$8,000 is called a constant or intercept.
The slope of the cost function is zero.
2009 Foster School of Business
Cost Accounting
L.DuCharme
7
Cost Function
y = Cost
$20,000
$15,000
$10,000
$5,000
$0
0
100
200
300
x = Number of rooms
2009 Foster School of Business
Cost Accounting
L.DuCharme
8
Cost Function—mixed cost
3. $3,000 per month plus $24 per room
This is an example of a mixed cost.
y = $3,000 + $24x
y = a + bx
2009 Foster School of Business
Cost Accounting
L.DuCharme
9
Cost Function
y = Cost
$20,000
$15,000
$10,000
$5,000
$0
0
100
200
300
x = Number of rooms
2009 Foster School of Business
Cost Accounting
L.DuCharme
10
Cost Classification
and Estimation Function
Choice of cost object
Time span
Relevant range
2009 Foster School of Business
Cost Accounting
L.DuCharme
11
Choice of Cost Object Example
If the total cost to operate all taxis owned by a taxi
company is the cost object, annual taxi registration and
license fees would be variable costs (number of taxis).
If the cost to operate a particular taxi
is the cost object, registration and license fees
for that taxi are fixed costs.
2009 Foster School of Business
Cost Accounting
L.DuCharme
12
Time Span
Whether a cost is variable or fixed with respect
to a particular activity depends on the time span.
More costs are variable with longer time spans.
2009 Foster School of Business
Cost Accounting
L.DuCharme
13
Relevant Range
Variable and fixed cost behavior patterns are
valid for linear cost functions only within
the given relevant range.
Costs may behave nonlinear outside the range.
2009 Foster School of Business
Cost Accounting
L.DuCharme
14
Cost Estimation
What is cost estimation?
It is the attempt to measure a past
cost relationship between costs
and the level of an activity.
Past cost-behavior functions can help
managers make more accurate
cost predictions.
2009 Foster School of Business
Cost Accounting
L.DuCharme
15
The Cause-and-Effect Criterion
In Choosing Cost Drivers
Physical relationship
Contractual agreements
Implicitly established by logic
2009 Foster School of Business
Cost Accounting
L.DuCharme
16
Cost Estimation Approaches
Industrial engineering method
Conference method
Account analysis method
Quantitative analysis methods
2009 Foster School of Business
Cost Accounting
L.DuCharme
17
Steps In Estimating
A Cost Function
Step 1:
Choose the dependent variable.
Step 2:
Identify the independent variable cost driver(s).
Step 3:
Collect data on the dependent variable
and the cost driver(s).
2009 Foster School of Business
Cost Accounting
L.DuCharme
18
Steps In Estimating
A Cost Function
Step 4:
Plot the data.
Step 5:
Estimate the cost function.
Step 6:
Evaluate the estimated cost function.
2009 Foster School of Business
Cost Accounting
L.DuCharme
19
High-Low Method Example
(A quantitative analysis method)
High capacity December: 55,000 machine-hours
Cost of electricity: $80,450
Low capacity September: 30,000 machine-hours
Cost of electricity: $64,200
What is the variable rate?
2009 Foster School of Business
Cost Accounting
L.DuCharme
20
High-Low Method Example
($80,450 – $64,200) ÷ (55,000 – 30,000)
$16,250 ÷ 25,000 = $0.65
What is the fixed cost?
2009 Foster School of Business
Cost Accounting
L.DuCharme
21
High-Low Method Example
$80,450 = Fixed cost + (55,000 × $0.65)
Fixed cost = $80,450 – $35,750 = $44,700
$64,200 = Fixed cost + (30,000 × $0.65)
Fixed cost = $64,200 – $19,500 = $44,700
y = a + bx
y = $44,700 + ($0.65 × Machine-hours)
2009 Foster School of Business
Cost Accounting
L.DuCharme
22
Regression Analysis--OLS
(A quantitative analysis method)
It is used to measure the average amount of
change in a dependent variable, such as
electricity, that is associated with unit
increases in the amounts of one or
more independent variables,
such as machine-hours.
Regression analysis uses all available
data to estimate the cost function.
2009 Foster School of Business
Cost Accounting
L.DuCharme
23
Regression Analysis
Simple regression analysis estimates the
relationship between the dependent
variable and one independent variable.
Multiple regression analysis estimates the
relationship between the dependent variable
and multiple independent variables.
2009 Foster School of Business
Cost Accounting
L.DuCharme
24
Regression Analysis
The regression equation and regression line
are derived using the least-squares technique.
The objective of least-squares is to develop
estimates of the parameters a and b.
2009 Foster School of Business
Cost Accounting
L.DuCharme
25
Regression Analysis
The vertical difference (residual term) measures
the distance between the actual cost and the
estimated cost for each observation.
The regression method is more accurate than
the high-low method.
2009 Foster School of Business
Cost Accounting
L.DuCharme
26
Criteria to Evaluate and
Choose Cost Drivers
Economic plausibility
Goodness of fit
Slope of the regression line
2009 Foster School of Business
Cost Accounting
L.DuCharme
27
Goodness of Fit
The coefficient of determination (r )
expresses the extent to which the changes
in (x) explain the variation in (y).
An (r ) of 0.80 indicates that
80% of the change in the dependent
variable can be explained by the
change in the independent variable.
2
2
2009 Foster School of Business
Cost Accounting
L.DuCharme
28
Slope of Regression Line
Everything else equal:
A relatively steep slope indicates a strong
relationship between the cost driver and costs.
A relatively flat regression line indicates a weak
relationship between the cost driver and costs.
2009 Foster School of Business
Cost Accounting
L.DuCharme
29
Slope of Regression Line
The closer the value of the correlation
coefficient (r) is to ±1, the stronger the
statistical relation between the variables.
2009 Foster School of Business
Cost Accounting
L.DuCharme
30
Excel Regression--Data
Week
Y
X1
X2
MOH
MH
DLH
1
$
1,190.00
68
30
2
$
1,211.00
88
35
3
$
1,004.00
62
36
4
$
917.00
72
20
5
$
770.00
60
47
6
$
1,456.00
96
45
7
$
1,180.00
78
44
8
$
710.00
46
38
9
$
1,316.00
82
70
10
$
1,032.00
94
30
11
$
752.00
68
29
12
$
963.00
48
38
2009 Foster School of Business
Cost Accounting
L.DuCharme
31
Excel Regression--results
• Interpret Excel regression output (in class)
2009 Foster School of Business
Cost Accounting
L.DuCharme
32
Non-linear Cost Functions
A nonlinear cost function is a cost function in
which the graph of total costs versus the level
of a single activity is not a straight line within
the relevant range.
Economies of scale
Quantity discounts
Step cost functions
2009 Foster School of Business
Cost Accounting
L.DuCharme
33
Concave Cost Functions
Learning versus experience
curves
2009 Foster School of Business
Cost Accounting
L.DuCharme
34
Data Issues
Data problems
encountered in estimating
cost functions.
2009 Foster School of Business
Cost Accounting
L.DuCharme
35