10 - 1 learning objective 1 explain the two assumptions frequently used in cost-behavior estimation....
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Learning Objective 1Learning Objective 1
Explain the two assumptions
frequently used in
cost-behavior estimation.
Determining How Costs Behave – Chapter10
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Assumptions in Cost-BehaviorEstimation
Assumptions in Cost-BehaviorEstimation
Changes in total costs can be explained bychanges in the level of a single activity.
Cost behavior can adequately beapproximated by a linear function of theactivity level within the relevant range.
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Learning Objective 2Learning Objective 2
Describe linear cost functions
and three common ways in
which they behave.
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Cost FunctionCost 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 FunctionCost Function
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 FunctionCost 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 FunctionCost 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 FunctionCost 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 FunctionCost 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 FunctionCost 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
Cost Classificationand Estimation Function
Choice of cost object
Time span
Relevant range
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Choice of Cost Object ExampleChoice of Cost Object Example
If the number of taxis owned by a taxi companyis the cost object, annual taxi registration and
license fees would be variable costs.
If miles driven during a year on a particular taxiis the cost object, registration and license fees
for that taxi are fixed costs.
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Time SpanTime 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 RangeRelevant 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 EstimationCost 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
The Cause-and-Effect CriterionIn Choosing Cost Drivers
Physical relationship
Contractual agreements
Implicitly established by logic
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Learning Objective 3Learning Objective 3
Understand various approaches
to cost estimation.
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Cost Estimation ApproachesCost Estimation Approaches
1. Industrial engineering method
2. Conference method
3. Account analysis method
4. Quantitative analysis methods
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1. Industrial Engineering Method1. Industrial Engineering Method
A.k.a. work measurement method, estimated cost functions by analyzing the relationship between inputs and outputs in physical terms. (i.e. observing and measuring how it is done)……..may be very accurate but may be expensive and long!
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2. Conference Method2. Conference Method
Various departments share their experiences/views on how costs behave….not very accurate
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3. Account Analysis Example3. Account Analysis Example
The cost analyst uses experience andjudgment to separate total costs (found
in the ledgers) into fixed and variable.
Eg Avisha & Co. sells software programs.
Total sales = $390,000
The company sold 1,000 programs.
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3. Account Analysis Example3. 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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3. Account Analysis Example3. 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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4. Quantitative Analysis Methods4. Quantitative Analysis Methods
Uses a formal mathematical method to fit cost functions to past data observations
E.g. 1 High-Low Methods
E.g. 2 Regression Methods
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Learning Objective 4Learning Objective 4
Outline six steps in estimatinga cost function on the basisof past cost relationships.
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Steps In EstimatingA Cost Function
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
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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1. High-Low Method Example1. 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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1. High-Low Method Example1. 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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1.High-Low Method Example1.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)Note - This method uses only two data Points to estimate the cost function.
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2. Regression Analysis2. Regression Analysis
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.
Note - Regression analysis uses all availabledata to estimate the cost function.
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2. Regression Analysis2. 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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2. Regression Analysis2. 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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2. Regression Analysis2. 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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Learning Objective 5Learning Objective 5
Describe three criteria used toevaluate and choose cost drivers.
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Criteria to Evaluate andChoose Cost Drivers
Criteria to Evaluate andChoose Cost Drivers
Economic plausibility
Goodness of fit
Slope of the regression line
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Goodness of FitGoodness 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 that more than80% of the change in the dependent
variable can be explained by thechange in the independent variable.
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Slope of Regression LineSlope 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.
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Slope of Regression LineSlope of Regression Line
The closer the value of the correlationcoefficient (r) to ±1, the stronger the
statistical relation between the variables.
As (r) approaches +1, a positive relationshipis implied, meaning the dependent variable (y)
increases as the independent variable (x) increases.
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Slope of Regression LineSlope of Regression Line
As (r) approaches –1, a negative, or inverse,relationship is implied, meaning the dependent
variable (y) decreases as the independentvariable (x) increases.
Example
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Learning Objective 6Learning Objective 6
Explain and give examples
of nonlinear cost functions.
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Nonlinearity and Cost FunctionsNonlinearity and 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. Reasons include:
Economies of scale
Quantity discounts
Step cost functions
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Nonlinearity and Cost FunctionsNonlinearity and Cost Functions
Economies of scale in advertising may enablean advertising agency to double the number
of advertisements for less than double the cost.
Quantity discounts on direct materialspurchases produce a lower cost perunit purchased with larger orders.
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Nonlinearity and Cost FunctionsNonlinearity and Cost Functions
A step function is a cost function in which thecost is constant over various ranges of the level
of activity, but the cost increases by discreteamounts as the level of activity changes
from one range to the next.
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Learning Objective 7Learning Objective 7
Distinguish the cumulativeaverage-time learning model
from the incrementalunit-time learning model.
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Learning CurvesLearning Curves
A learning curve is a function that showshow labor-hours per unit decline as units
of output increase.
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Experience CurveExperience Curve
This is a function that shows how the costsper unit in various value chain areas decline
as units produced and sold increase.
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1. Cumulative Average-TimeLearning Model
1. Cumulative Average-TimeLearning Model
Cumulative average time per unit is reduced bya constant percentage each time the cumulative
quantity of units produced is doubled.
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2. Incremental Unit-TimeLearning Model
2. Incremental Unit-TimeLearning Model
The time needed to produce the last unit isreduced by a constant percentage each timethe cumulative quantity of units produced
is doubled.
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Learning Objective 8Learning Objective 8
Be aware of data problemsencountered in estimating
cost functions.
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Data Collection andAdjustment Issues
Data Collection andAdjustment Issues
The ideal database for cost estimationhas two characteristics:
1. It contains numerous reliably measuredobservations of the cost driver(s) and the
cost that is the dependent variable.
2. It considers many values for the costdriver that span a wide range.
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Data Collection andAdjustment Issues…problems
Data Collection andAdjustment Issues…problems
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 andAdjustment Issues...problems
Data Collection andAdjustment Issues...problems
Extreme values of observations occur fromerrors in recording costs.
Analysts should adjust or eliminate unusualobservations before estimating a cost relationship.
There is no homogeneous relationship.
The relationship between the cost driverand the cost is not stationary.
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Data Collection andAdjustment Issues
Data Collection andAdjustment Issues
The most difficult task in cost estimationis collecting high-quality, reliablymeasured data on the dependentvariable and the cost driver(s).