Cost Accounting
Dr. Baldwin
University of Arkansas – Fort Smith
Fall 2010
Chapter 10
Determining How Costs Behave
2
Why understand cost behavior?
• Managers need to understand cost behavior in
order to make decisions about strategy and
about operations.
• For example
– Product decisions
• Apple  iPod, iPhone, iPad
• Amazon  Kindle
– Other decisions
• Fort Smith administration  enrollment
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What do we already know about the
nature of costs?
Variable Cost
Cost
Mixed Cost
Fixed Cost
Volume of Activity
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Assumptions
• Costs are linear
– or approximated by linear functions
• Each cost has a single cost driver
• Are these always true? Not always!
• We generally assume they are true within the
relevant range.
• Exercise 18.
5
Relevant Range
• The range of the activity in which total
cost and the level of activity are related.
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How to understand cost behavior?
A cost function is
• a mathematical description of how a cost
changes with changes in the volume of its
cost driver activity.
Variable Cost
Cost
Mixed Cost
Fixed Cost
Volume of Activity
7
Linear Cost Functions example
• Let’s assume you are a spin class instructor and
you have to provide your own music for class.
You spend a lot of time and money downloading
songs to use in class. uTunes is providing three
different payment options.
– Let’s look at the options and identify the cost
function for each.
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Linear Cost Functions example
• Option A
– Pay $5 per song downloaded
• Option B
– Pay $100 per month for unlimited downloads
• Option C
– Pay $50 per month plus $0.50 per download
• Create a cost function for each option using the
generic linear cost function formula.
9
Create a Linear Cost Function
Formula: Y = a + bX
• Where:
–
–
–
–
Y = total costs
a = fixed costs
b = variable cost per unit of cost driver
X = cost driver
• Option A:
• Option B:
• Option C:
Y = $0 + $5X
Y = $100 + $0X
Y = $50 + $0.50X
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How to understand cost behavior?
• Option A:
• Option B:
• Option C:
Y = $0 + $5X
Y = $100 + $0X
Y = $50 + $0.50X
Variable Cost A
Cost
Mixed Cost
Fixed Cost B
Volume of Activity (downloads)
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C
Calculate Total Cost of Each Option
Which option is least expensive?
• Assuming 40 downloads a month, what is the
total cost per month for each option?
• Option A:
• Option B:
• Option C:
Y = $0 + $5 * 40 = $200
Y = $100 + $0*40 = $100
Y = $50 + $0.50*40 = $70
• What happens if you download more or less
than 40? 100? 200?
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How to understand cost behavior?
• Option A:
• Option B:
• Option C:
Y = $0 + $5X
Y = $100 + $0X
Y = $50 + $0.50X
Variable Cost A
Cost
Mixed Cost
Fixed Cost B
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100
10
Volume of Activity (downloads)
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C
How to understand cost behavior?
Cost Estimation Methods
• Many methods to estimate costs
• Potential problems in cost estimation
– Availability of historical data
– Accuracy of data
– The estimates are only as good as the data on which
they are based.
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How to understand cost behavior?
Cost Estimation Methods
• Industrial Engineering
– Time and motion studies
• Conference
– Consensus of estimates
• Account Analysis 
• Quantitative Analysis
– High-Low Method
– Regression
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Account Analysis Method
Use knowledge of operations to
• Classify cost accounts according to their
relationship with the cost driver activity:
– variable, fixed, or mixed
• Estimate the cost/driver
relationship
• Example: Lorenzo’s Car Wash
(Exercise 20)
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Lorenzo’s Car Wash example
• Incoming cars are put on a conveyor belt.
• Cars are washed as they are carried by the
conveyor belt from start to finish.
• The cars are then dried manually.
• Workers clean and vacuum car inside.
• They are managed by a single supervisor.
• Lorenzo serviced 80,000 cars in 2009, for which
he reports the following costs:
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Lorenzo’s Car Wash example
Accounts
Car Wash Labor
Soap and Supplies
Water
Power
Salaries
Depreciation
Total Costs
$260,000
$42,000
$38,000
$72,000
$46,000
$64,000
Use knowledge of operations to
• Classify cost accounts according to their relationship
with the cost driver activity:
– variable, fixed, or mixed
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• Estimate the costs if 90,000 cars are washed in 2010.
Lorenzo’s Car Wash example
• Classify: variable, fixed, or mixed
Accounts
Car Wash Labor
Soap and Supplies
Water
Power
Salaries
Depreciation
Total Costs
$260,000
$42,000
$38,000
$72,000
$46,000
$64,000
Variable
$412,000
Fixed
$110,000
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Lorenzo’s Car Wash example
• Variable Costs for 2009
$ 412,000
80,000 cars = $5.15 per car
• Fixed Costs
$110,000
• Total average cost per car =
(412,000 + 110,000)
80,000 cars
= $6.53 per car
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Lorenzo’s Car Wash example
Estimate Lorenzo’s 2010 costs (90,000 washes)
• Variable Costs
90,000 cars * $5.15 per car = $463,500
• Fixed Costs
$110,000
• Total costs =
$463,500 + $110,000 = $573,500
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How to understand cost behavior?
Cost Estimation Methods
• Industrial Engineering
– Time and motion studies
• Conference
– Consensus of estimates
• Account Analysis 
• Quantitative Analysis 
– High-Low Method
– Regression
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Quantitative Analysis
• Uses formal mathematical methods to fit cost
functions to past data observations.
• Remember, a cost function is a mathematical
description of how a cost changes with changes
in the level of its cost driver activity.
– Total costs = FC + VCUNIT * activity
– Lorenzo’s cost function:
• $110,000 + $5.15 per car * number of cars
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Estimate a Linear Cost Function
• Formula: Y = a + bX
• Where:
–
–
–
–
Y = total costs
a = fixed costs
b = variable cost per unit of cost driver
X = cost driver
• Two methods
– High-Low Method
– Regression Analysis
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High-Low Method
• Uses two points (the high and the low) to find
the equation of the cost line y = a + bx
– slope = b = change in y/change in x
– intercept = a = y - bx
• Strengths
– Simple to compute
– Easy to understand
• Weaknesses
– Only two points used - what if they are not
representative of normal relationship?
• Exercise 16.
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Regression Analysis
• Uses all the observations to find the equation of
the cost line y = a + bx
– slope = change in y/change in x
– intercept = a = y - bx
• Regression minimizes the sum of the squared
differences between the observed data and the
predicted line
• Strengths
– More accurate than the high-low method
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Statistical Output
Provides
• estimates of the two parameters in the cost function: Y
= a + bX
– a = intercept = fixed costs
– b = slope = variable costs per unit
• Measures of goodness of fit
– Co-efficient of determination = r2
• Measures the % variation in Y explained by X
Larger is
better
– T-statistic = b/standard error of estimated co-efficient
• t tells us if b is different from zero
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Statistical Output
What do we do with it?
• Check goodness of fit measures
– Want r2  .3 (or perhaps even higher)
– Want t  2
• Compare cost drivers to see which is best
• Estimate Y (total costs) for future period.
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Non-Linear Functions
Costs are not always linear!
For example:
• Quantity discounts
– Costs decrease as volume increases
• Step cost functions
– Costs increase by discrete amounts over narrow ranges
• Step fixed-cost functions
– Cost remain the same over wider intervals
• Learning curves

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Learning Curves
A learning curve is a function that measures how laborhours per unit decline as unites of production increase
because workers are learning and becoming better at
their jobs. Two types:
• Cumulative average-time learning model
– Average time per unit declines at a constant rate
• Incremental unit-time learning model
– Time to produce last unit decreases at a constant rate
Learning curves are given as a percentage
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Learning Curves
• Formula: Y = pXq
• Where:
– Y = cumulative average time or incremental
time
– p = labor hours on first unit
– X = cumulative # of units
– q reflects the learning rate (log of learning
curve)
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Learning Curves
• Learning is faster in which model?
– (cumulative model)
• Which of these models will predict higher costs?
– (incremental model)
• Which of these models is better?
– It depends! Case by case basis decision.
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Learning Curves
• What are implications for product costing?
– Charge more initially and decrease price as time to
produce declines?
• Will the customers put up with that?
– Price down the learning curve - set price based on
what we expect costs to be in the future
• Why might companies do this?
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Summary 1
• Managers have to understand cost behavior in order to
make decisions about strategy and about operations.
• Most of the time we assume costs are linear and each
has single cost driver.
• A cost function is a mathematical description of how a
cost changes with changes in the level of its cost driver
activity.
– Formula:
Y = a + bX
• Costs are not always linear (e.g. learning curves).
34
Summary 2
Cost Estimation Methods help us understand cost
behavior.
• Industrial Engineering (Time & motion studies)
• Conference (consenses)
• Account Analysis
• Quantitative Analysis
– High-Low Method
– Regression
35
Summary 3
• Many methods to estimate costs
• Potential problems in cost estimation
– Availability of historical data
– Accuracy of data
– The estimates are only as good as the data on which
they are based.
• Don’t forget to read the appendix which
discusses regression.
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