Determining How
Costs Behave
Chapter 10
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Learning Objective 1
Explain the two assumptions
frequently used in
cost-behavior estimation.
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Assumptions in Cost-Behavior
Estimation
Changes in total costs can be explained by
changes in the level of a single activity.
Cost behavior can adequately be
approximated by a linear function of the
activity level within the relevant range.
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Learning Objective 2
Describe linear cost functions
and three common ways in
which they behave.
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Cost Function
What is a cost function?
It is a mathematical expression
describing how costs change
with changes in the level
of an activity.
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Cost Function
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.
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Cost Function
y = Cost
$20,000
$15,000
$10,000
$5,000
$0
0
100
200
300
x = Number of rooms
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Cost Function
2. $8,000 per month
y = $8,000
$8,000 is called a constant or intercept.
The slope of the cost function is zero.
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Cost Function
y = Cost
$20,000
$15,000
$10,000
$5,000
$0
0
100
200
300
x = Number of rooms
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Cost Function
3. $3,000 per month plus $24 per room
This is an example of a mixed cost.
y = $3,000 + $24x
y = a + bx
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Cost Function
y = Cost
$20,000
$15,000
$10,000
$5,000
$0
0
100
200
300
x = Number of rooms
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Cost Classification
and Estimation Function
Choice of cost object
Time span
Relevant range
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Choice of Cost Object Example
If the number of taxis owned by a taxi company
is the cost object, annual taxi registration and
license fees would be variable costs.
If miles driven during a year on a particular taxi
is the cost object, registration and license fees
for that taxi are fixed costs.
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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.
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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.
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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.
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The Cause-and-Effect Criterion
In Choosing Cost Drivers
Physical relationship
Contractual agreements
Implicitly established by logic
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Learning Objective 3
Understand various approaches
to cost estimation.
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Cost Estimation Approaches
Industrial engineering method
Conference method
Account analysis method
Quantitative analysis methods
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Account Analysis Example
The cost analyst uses experience and
judgment to separate total costs into
fixed and variable.
Avisha & Co. sells software programs.
Total sales = $390,000
The company sold 1,000 programs.
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Account Analysis Example
Cost of goods sold = $130,000
Manager’s salary = $60,000
Secretary’s salary = $29,000
Commissions = 12% of sales
What is the total fixed cost?
$60,000 + $29,000 = $89,000
What is the fixed cost per unit sold?
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Account Analysis Example
$89,000 ÷ 1,000 = $89.00
What is the variable cost per unit sold?
Cost of goods sold: $130,000
Commissions: $390,000 × .12 = $46,800
($130,000 + $46,800) ÷ 1,000 = $176.80
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Learning Objective 4
Outline six steps in estimating
a cost function on the basis
of past cost relationships.
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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).
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Steps In Estimating
A Cost Function
Step 4:
Plot the data.
Step 5:
Estimate the cost function.
Step 6:
Evaluate the estimated cost function.
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High-Low Method Example
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?
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High-Low Method Example
($80,450 – $64,200) ÷ (55,000 – 30,000)
$16,250 ÷ 25,000 = $0.65
What is the fixed cost?
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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)
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Regression Analysis
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.
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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.
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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.
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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.
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Learning Objective 5
Describe three criteria used to
evaluate and choose cost drivers.
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Criteria to Evaluate and
Choose Cost Drivers
Economic plausibility
Goodness of fit
Slope of the regression line
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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 more than
80% of the change in the dependent
variable can be explained by the
change in the independent variable.
2
2
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Slope of Regression Line
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.
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Slope of Regression Line
The closer the value of the correlation
coefficient (r) to ±1, the stronger the
statistical relation between the variables.
As (r) approaches +1, a positive relationship
is implied, meaning the dependent variable (y)
increases as the independent variable (x) increases.
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Slope of Regression Line
As (r) approaches –1, a negative, or inverse,
relationship is implied, meaning the dependent
variable (y) decreases as the independent
variable (x) increases.
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Learning Objective 6
Explain and give examples
of nonlinear cost functions.
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Nonlinearity and 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
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Nonlinearity and Cost Functions
Economies of scale in advertising may enable
an advertising agency to double the number
of advertisements for less than double the cost.
Quantity discounts on direct materials
purchases produce a lower cost per
unit purchased with larger orders.
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Nonlinearity and Cost Functions
A step function is a cost function in which the
cost is constant over various ranges of the level
of activity, but the cost increases by discrete
amounts as the level of activity changes
from one range to the next.
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Learning Objective 7
Distinguish the cumulative
average-time learning model
from the incremental
unit-time learning model.
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Learning Curves
A learning curve is a function that shows
how labor-hours per unit decline as units
of output increase.
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Experience Curve
This is a function that shows how the costs
per unit in various value chain areas decline
as units produced and sold increase.
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Cumulative Average-Time
Learning Model
Cumulative average time per unit is reduced by
a constant percentage each time the cumulative
quantity of units produced is doubled.
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Incremental Unit-Time
Learning Model
The time needed to produce the last unit is
reduced by a constant percentage each time
the cumulative quantity of units produced
is doubled.
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Learning Objective 8
Be aware of data problems
encountered in estimating
cost functions.
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Data Collection and
Adjustment Issues
The ideal database for cost estimation
has two characteristics:
1. It contains numerous reliably measured
observations of the cost driver(s) and the
cost that is the dependent variable.
2. It considers many values for the cost
driver that span a wide range.
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Data Collection and
Adjustment Issues
Time periods do not match.
Fixed costs are allocated as if they were variable.
Data are either not available or not reliable.
Inflation may play a role.
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Data Collection and
Adjustment Issues
Extreme values of observations occur from
errors in recording costs.
Analysts should adjust or eliminate unusual
observations before estimating a cost relationship.
There is no homogeneous relationship.
The relationship between the cost driver
and the cost is not stationary.
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Data Collection and
Adjustment Issues
The most difficult task in cost estimation
is collecting high-quality, reliably
measured data on the dependent
variable and the cost driver(s).
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End of Chapter 10
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