2009 foster school of business cost accounting l.ducharme 1 determining how costs behave chapter 10
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2009 Foster School of Business Cost Accounting L.DuCharme 1
Determining HowCosts Behave
Chapter 10
2009 Foster School of Business Cost Accounting L.DuCharme 2
Overview
1) Assumptions2) Model: Y = a + bX3) Determinates of Fixed vs. Variable costs4) Cost Estimation
Industrial EngineeringConference MethodAccount AnalysisQuantitative Analysis: H-L & OLS
5) Non-linear cost functions
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Two assumptions frequently used in cost-behavior estimation
1. Changes in total costs can be explained bychanges 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.
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Cost Function
What is a cost function?
It is a mathematical expressiondescribing how costs change
with changes in the levelof an activity.
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Cost Function—variable cost
La Playa Hotel offers an airlinethree alternative cost structures toaccommodate 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
$0
$5,000
$10,000
$15,000
$20,000
0 100 200 300
x = Number of rooms
y =
Cos
t
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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.
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Cost Function
$0
$5,000
$10,000
$15,000
$20,000
0 100 200 300
x = Number of rooms
y =
Cos
t
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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
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Cost Function
$0
$5,000
$10,000
$15,000
$20,000
0 100 200 300
x = Number of rooms
y =
Cos
t
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Cost Classificationand Estimation Function
Choice of cost object
Time span
Relevant range
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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 andlicense fees would be variable costs (number of taxis).
If the cost to operate a particular taxiis 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 respectto 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 arevalid 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 pastcost relationship between costs
and the level of an activity.
Past cost-behavior functions can helpmanagers make more accurate
cost predictions.
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The Cause-and-Effect CriterionIn Choosing Cost Drivers
Physical relationship
Contractual agreements
Implicitly established by logic
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Cost Estimation Approaches
Industrial engineering method
Conference method
Account analysis method
Quantitative analysis methods
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Steps In EstimatingA 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 5:Estimate the cost function.
Step 6:Evaluate the estimated cost function.
Step 4:Plot the data.
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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?
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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--OLS (A quantitative analysis method)
It is used to measure the average amount ofchange in a dependent variable, such aselectricity, that is associated with unit
increases in the amounts of one ormore independent variables,
such as machine-hours.
Regression analysis uses all availabledata to estimate the cost function.
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Regression Analysis
Simple regression analysis estimates therelationship between the dependent
variable and one independent variable.
Multiple regression analysis estimates therelationship between the dependent variable
and multiple independent variables.
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Regression Analysis
The regression equation and regression lineare derived using the least-squares technique.
The objective of least-squares is to developestimates of the parameters a and b.
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Regression Analysis
The vertical difference (residual term) measuresthe distance between the actual cost and the
estimated cost for each observation.
The regression method is more accurate thanthe high-low method.
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Criteria to Evaluate andChoose Cost Drivers
Economic plausibility
Goodness of fit
Slope of the regression line
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Goodness of Fit
The coefficient of determination (r2)expresses the extent to which the changes
in (x) explain the variation in (y).
An (r2) of 0.80 indicates that80% of the change in the dependent
variable can be explained by thechange in the independent variable.
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Slope of Regression Line
A relatively steep slope indicates a strongrelationship between the cost driver and costs.
A relatively flat regression line indicates a weakrelationship between the cost driver and costs.
Everything else equal:
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Slope of Regression Line
The closer the value of the correlationcoefficient (r) is to ±1, the stronger the
statistical relation between the variables.
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Excel Regression--Data
Y X1 X2
Week 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
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Excel Regression--results
• Interpret Excel regression output (in class)
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Non-linear Cost Functions
A nonlinear cost function is a cost function inwhich the graph of total costs versus the levelof a single activity is not a straight line within
the relevant range.
Economies of scale
Quantity discounts
Step cost functions
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Concave Cost Functions
Learning versus experiencecurves
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Data Issues
Data problemsencountered in estimating
cost functions.