Chapter 10 - Determining How Costs Behave

Chapter Ten

Determining How Costs Behave

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Define cost functionsCausality and cost functionsLinear functionsQuantitative cost estimation techniquesNon-linear functionsData problems

Learning Objectives

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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

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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

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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

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The Relevant Range

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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

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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

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Accounting and Mathematical Terminology

Accounting MathematicalVariable Cost Slope

Fixed Cost InterceptMixed Cost Linear Cost Function

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Linear Cost Functions

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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

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Cost Estimation Methods

1. Industrial engineering method2. Conference method3. Account analysis method4. Quantitative analysis methods

1. High-low method2. Regression analysis

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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

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Conference Method

Gather analyses and opinions about costs and their drivers from various departments

Pool expert knowledgeSubjective

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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

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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

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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)

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High-Low Method

Not resistant to unusual situations

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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)

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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

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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

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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

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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

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Criteria for Evaluating Alternative Cost Drivers

1. Economic plausibility2. Goodness of fit3. Significance of the independent variable

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Sample Regression Model Plot

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Alternative Regression Model Plot

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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

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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

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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

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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:

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Learning Curve

Cumulative Production Output

Aver

age

Labo

rTi

me

per

Uni

t

Learning effectsare large initially

Learning effectsbecome smaller, eventually

reaching steady state

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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

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Cumulative Average-Time Model

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Incremental Unit-Time Model

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The Ideal Database

Should contain numerous reliably measured observations of the cost driver and the costs

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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