Chapter 10 - Determining How Costs Behave
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Transcript of Chapter 10 - Determining How Costs Behave
Chapter Ten
Determining How Costs Behave
1-2
Define cost functionsCausality and cost functionsLinear functionsQuantitative cost estimation techniquesNon-linear functionsData problems
Learning Objectives
1-3
Cost FunctionA mathematical representation of the behavior of costs relative to activity levelVariable costs—costs that change in relation to a
chosen activity or outputFixed costs—costs that do not change in relation to a
chosen activity or outputMixed costs—costs that have both fixed and variable
components; also called semi-variable costs
1-4
Cost Estimation: Variable Costs Variable Costs – Directly
based on resource usage
Number of Pay Per View shows watched
Tota
l Pay
Per
Vie
w Bi
llVariable Step Costs - Total cost is fixed within a narrow range
Volume purchase – buy 5 movies for $10
1-5
Cost Estimation: Fixed Costs
Fixed Costs – constant no matter how much of a resource is used
Number of hours watched
Mon
thly
Bas
ic Ca
ble
Bill
Fixed Step Costs - constant for a wide range of activity, then jumps to a higher level
Rent an additional floor in an office tower
1-6
The Relevant Range
1-7
Criteria for Classifying Variable and Fixed Costs
Choice of cost object Different objects may result in different
classificationsTime horizon
The longer the period, the more likely the cost will be variable
Relevant rangeBehavior is predictable only within a band of activityExtrapolation vs. interpolation
1-8
Linear Cost Functions
y = a + bXThe dependent
variable:the cost that isbeing predicted
The independentvariable:
the cost driver
The intercept:fixed costs
The slope ofthe line:
variable cost per unit
1-9
Accounting and Mathematical Terminology
Accounting MathematicalVariable Cost Slope
Fixed Cost InterceptMixed Cost Linear Cost Function
1-10
Linear Cost Functions
1-11
Cause and EffectA cause-and-effect relationship might arise as a result of:
A physical relationship between the level of activity and costs
A contractual agreementKnowledge of operations
Correlation does not necessarily mean causality
1-12
Cost Estimation Methods
1. Industrial engineering method2. Conference method3. Account analysis method4. Quantitative analysis methods
1. High-low method2. Regression analysis
1-13
Industrial Engineering Method
Analyze the relationship between inputs and outputs in physical terms
Time-and-motion studiesVery thorough and detailed, but also costly and
time-consumingAlso called the work-measurement method
1-14
Conference Method
Gather analyses and opinions about costs and their drivers from various departments
Pool expert knowledgeSubjective
1-15
Account Analysis Method
Classify cost accounts as variable, fixed, or mixed with respect to the identified level of activity
Is reasonably accurate, cost-effective, and easy to use
Subjective
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Quantitative Analysis
Uses a formal mathematical method to fit cost functions to data observations
Advantage: results are objectiveHigh-Low Method - uses algebra to determine a
unique equation between representative high and low cost points
Least-Squares Regression Method - Uses statistical techniques to determine the relationship between activity and cost
1-17
Estimating a Cost Function Using Quantitative Analysis
1. Choose the dependent variable (the cost to be predicted)
2. Identify the independent variable or cost driver3. Collect data on the dependent variable and the cost
driver4. Plot the data5. Estimate the cost function using the high-low method
or regression analysis6. Evaluate the viability of the model
1-18
Sample Cost—Activity Plot
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Sample Cost—Activity Plot
High-Low Method
1. Calculate variable cost per unit of activity
Variable Cost associated with Cost associated withCost per = highest activity level lowest activity level
Unit of Activity Highest activity level - Lowest activity level
{ - }
High-Low Method2. Calculate total fixed costs
3. Summarize by writing a linear equation.
Total Cost from either the highest or lowest activity level- (Variable Cost per unit of activity X Activity associated with above total cost)Fixed Costs
Y = Fixed Costs + ( Variable cost per unit of Activity * Activity )
Y = FC + (VCu * X)
1-22
High-Low Method
Not resistant to unusual situations
9-23
Using the High-Low Method
What are the variable and the “fixed” costs for this situation?
Y = a + (bX)
Where Y = the value of the est imated costX = the cost drivera = a fi xed quantity that represents Y when X is zerob = the slope of the line (unit variable cost)
9-24
The High-Low Method
Pros:Requires less effort than regression analysis Provides a reasonable cost equation from which you
can estimate future costsCons:Relies on only two subjectively determined pointsRegression analysis, based on statistical estimation,
would provide more accurate estimates
1-25
Regression Analysis
A statistical method that;Measures an average amount of change in the
dependent variable Associated with a unit change in one or more
independent variablesMore accurate than the high-low method
Uses information from all observations
1-26
Types of Regression
Simple — estimates the relationship between the dependent variable and one independent variable
Multiple — estimates the relationship between the dependent variable and two or more independent variables
9-27
Regression Analysis
Minimize the sum of the squares of the estimation errors:An error is the distance measured from the regression
line to the data pointReferred to as least-squares regression
1-28
Criteria for Evaluating Alternative Cost Drivers
1. Economic plausibility2. Goodness of fit3. Significance of the independent variable
1-29
Sample Regression Model Plot
1-30
Alternative Regression Model Plot
9-31
Regression AnalysisPros:
Objective, statistically preciseProvides quantitative measures of its precision and
reliability the statistical goodness of fit & validity of the
regression, measured by R2, t-values, and p-values)Readily available software will do the calculations
Cons:Can be influenced by “outlier” data points
1-32
Nonlinear Cost FunctionsEconomies of scale
Quantity discountsStep cost functions
Resources increase in “lot-sizes”, not individual unitsLearning curves
Labor hours decrease as workers learn their jobs Experience curve
Broader application of learning curve that includes downstream activities such as marketing and distribution
1-33
Nonlinear Cost Functions
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A cost that is influenced by learning Repetitive labor that becomes more proficient over time
Learning curve analysis is a systematic method for estimating learning based costs
The learning rate is the percentage by which average time falls from previous levels as output doubles
A learning rate ranges from 1.0 (no learning) to 0.5 (infinite learning)
Learning Curve
8-35
Y = aXb
Where: Y = the average time per unit of outputa = the time required f or the fi rst unit of outputX = cumulative outputb = the learning index
Learning Curve
The general equation used in learning-curve analysis:
1-36
Learning Curve
Cumulative Production Output
Aver
age
Labo
rTi
me
per
Uni
t
Learning effectsare large initially
Learning effectsbecome smaller, eventually
reaching steady state
1-37
Types of Learning Curves
Cumulative average-time learning modelCumulative average time per unit declines by a
constant percentage each time the cumulative quantity of units produced doubles
Incremental unit-time learning modelIncremental time to produce the last unit declines by
a constant percentage each time the cumulative quantity of units produced doubles
1-38
Cumulative Average-Time Model
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Incremental Unit-Time Model
1-40
The Ideal Database
Should contain numerous reliably measured observations of the cost driver and the costs
1-41
Data Problems
The time period for measuring the dependent variable does not match the period for measuring the cost driver
Fixed costs are allocated as if they are variableData are either not available for all observations or are
not uniformly reliableExtreme values occur from errors in recording costsThe relationship between the cost driver and the cost is
not static Inflation has affected costs, the driver, or both