1 chapter m4 cost behavior © 2007 pearson custom publishing

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CHAPTER M4CHAPTER M4

Cost BehaviorCost Behavior

© 2007 Pearson Custom Publishing© 2007 Pearson Custom Publishing

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Learning Objective Learning Objective 1:1:

Describe the Describe the differences between differences between

fixed costs and fixed costs and variable costs.variable costs.


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Fixed CostsFixed Costs Costs that do not change in Costs that do not change in total total as the as the

level of business activity changes are level of business activity changes are called called fixed costs.fixed costs.

An example of a fixed cost is the An example of a fixed cost is the insurance on a factory building. The insurance on a factory building. The insurance cost does not change as the insurance cost does not change as the level of production changes.level of production changes.


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Fixed Cost Per UnitFixed Cost Per Unit Although the total fixed cost does not Although the total fixed cost does not

change, the change, the fixed cost per unitfixed cost per unit does does change as the activity level changes.change as the activity level changes.

If the factory insurance cost is $5,000, If the factory insurance cost is $5,000, then the insurance cost is $1.00 per unit then the insurance cost is $1.00 per unit when 5,000 units are produced, but only when 5,000 units are produced, but only 50 cents per unit when 10,000 units are 50 cents per unit when 10,000 units are produced.produced.


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Variable CostsVariable Costs

Costs that change in direct proportion with Costs that change in direct proportion with changes in the activity level are called changes in the activity level are called variable costs.variable costs.

An example of a variable cost is the cost An example of a variable cost is the cost of sales commissions. Each sale results in of sales commissions. Each sale results in an increase in the total cost of an increase in the total cost of commissions.commissions.


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Variable Cost Per Variable Cost Per UnitUnit

The The variable cost per unitvariable cost per unit remains the remains the same regardless of the level of activity.same regardless of the level of activity.

If the sales commission is $5.00 per unit, If the sales commission is $5.00 per unit, then that commission rate is assumed to then that commission rate is assumed to remain unchanged no matter how many remain unchanged no matter how many units are sold.units are sold.

© 2007 Pearson Custom © 2007 Pearson Custom PublishingPublishing

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Classify costs by Classify costs by cost behavior.cost behavior.


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Cost BehaviorCost Behavior Cost behaviorCost behavior is the reaction of costs to is the reaction of costs to

changes in the business activity.changes in the business activity. Some costs change when the level of Some costs change when the level of

business activity changes and other costs business activity changes and other costs do not. If you consider the total costs of do not. If you consider the total costs of running a business, the cost increases as running a business, the cost increases as the activity level (sales, production, or the activity level (sales, production, or some other measure) increases.some other measure) increases.


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Cost Behavior Cost Behavior PatternsPatterns

The three most common cost The three most common cost behavior types are:behavior types are: Fixed costs Fixed costs Variable costs Variable costs Mixed costsMixed costs


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Graphical AnalysisGraphical Analysis When graphing cost behavior, the following When graphing cost behavior, the following

conventions are typically followed:conventions are typically followed: The measure of activity is shown on the X The measure of activity is shown on the X

axis. The activity base is also called the axis. The activity base is also called the independent variable.independent variable.

The measure of cost is shown on the Y axis. The measure of cost is shown on the Y axis. The cost is also called the dependent The cost is also called the dependent variable.variable.


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Graphical AnalysisGraphical Analysis

Factory Insurance Cost Sales Commissions Cost

$9,000 $9,000

$7,000 $7,000

$5,000 $5,000

$3,000 $3,000

$1,000 $1,000

2,500 5,000 7,500 10,000 2,500 5,000 7,500 10,000Units Produce d Units Sold

A fixed cost graph. A variable cost graph.© 2007 Pearson Custom © 2007 Pearson Custom PublishingPublishing

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Determining Total Determining Total CostCost

The basic cost equation is:The basic cost equation is:Total Cost = Fixed Cost + Variable CostTotal Cost = Fixed Cost + Variable Cost

Total Cost Graph

$12,500

$10,000

$7,500

$5,000

$2,500

2,500 5,000 7,500 10,000Units Sold

The graph at the rightshows the combinationof a fixed cost line and a variable cost line.


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Explain the concept Explain the concept of relevant range of relevant range and its effect on and its effect on

cost behavior cost behavior information.information.


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Relevant RangeRelevant Range The simplifications that are made with The simplifications that are made with

regard to cost behavior patterns are regard to cost behavior patterns are assumed to be reasonable as long as the assumed to be reasonable as long as the activity level is within the activity level is within the relevant range.relevant range.

The relevant range usually cannot be The relevant range usually cannot be specifically determined, but it can be specifically determined, but it can be considered to be that range of activity considered to be that range of activity within which the company usually within which the company usually operates.operates.


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Graph of a Relevant Graph of a Relevant RangeRangeFactory Insurance Cost

$9,000 Relevant Range

$7,000

$5,000

$3,000

$1,000

2,500 5,000 7,500 10,000Units Produced


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Mixed CostsMixed Costs

Some costs exhibit cost behavior that is a Some costs exhibit cost behavior that is a combination of both a fixed element and a combination of both a fixed element and a variable element. These costs are known variable element. These costs are known as as mixed costs.mixed costs.

It is important to separate a total mixed It is important to separate a total mixed cost into its fixed component and variable cost into its fixed component and variable component.component.


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Mixed Cost GraphMixed Cost GraphEquipment Repairs Cost

$10,000

$8,000

$6,000

$4,000

$2,000

10 20 30 40 50Number of Breakdowns


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Discussion Discussion QuestionsQuestions

On the previous slide, the dashed lines On the previous slide, the dashed lines indicate a total cost of $8,000 if 40 indicate a total cost of $8,000 if 40 breakdowns occur. breakdowns occur.

What is the estimated total cost per What is the estimated total cost per breakdown?breakdown?

Estimated fixed cost per breakdown?Estimated fixed cost per breakdown? Estimated variable cost per breakdown?Estimated variable cost per breakdown?


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Besides the number of equipment Besides the number of equipment breakdowns, what other measures of breakdowns, what other measures of activity might work well when trying to activity might work well when trying to predict the amount of equipment repair predict the amount of equipment repair cost?cost?

Do you think that the selection of an Do you think that the selection of an appropriate activity measure is crucial to appropriate activity measure is crucial to making a reasonable cost estimate?making a reasonable cost estimate?


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Identify at least one cost in each of the Identify at least one cost in each of the three categories (variable, fixed, and three categories (variable, fixed, and mixed) that you incur in your personal life.mixed) that you incur in your personal life.

Do you incur more variable costs, more Do you incur more variable costs, more fixed costs, or more mixed costs?fixed costs, or more mixed costs?

Do you think a manufacturing company Do you think a manufacturing company incurs more variable costs, more fixed incurs more variable costs, more fixed costs, or more mixed costs?costs, or more mixed costs?


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Describe the Describe the characteristics of a characteristics of a

mixed cost and the four mixed cost and the four basic approaches to basic approaches to

separating a mixed cost separating a mixed cost into its fixed and into its fixed and

variable components.variable components.© 2007 Pearson Custom Publishing© 2007 Pearson Custom Publishing

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Identifying Elements of a Identifying Elements of a Mixed CostMixed Cost

The most commonly used techniques The most commonly used techniques for determining the fixed and variable for determining the fixed and variable components of a mixed cost are:components of a mixed cost are: the engineering approachthe engineering approach scatter graphingscatter graphing the high-low method the high-low method regression analysis.regression analysis.


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Engineering Engineering ApproachApproach

The The engineering approachengineering approach is based on is based on the technical judgment and expertise the technical judgment and expertise about the activity with fixed and variable about the activity with fixed and variable costs.costs.

The expert (possibly an engineer) will The expert (possibly an engineer) will analyze the cost component much like an analyze the cost component much like an investigator. An example of a technique investigator. An example of a technique used in the engineering approach would used in the engineering approach would be a time and motion study.be a time and motion study.


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Scatter GraphingScatter Graphing The The scatter graphingscatter graphing technique entails technique entails

plotting the available cost vs. activity plotting the available cost vs. activity information on a graph.information on a graph.

The cost analyst draws a line that appears to The cost analyst draws a line that appears to best fit the data. The line represents the best fit the data. The line represents the estimated cost behavior pattern.estimated cost behavior pattern.

The accuracy of the line in describing the The accuracy of the line in describing the relationship among the variables is suspect.relationship among the variables is suspect.


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High-Low MethodHigh-Low Method In the In the high-low method,high-low method, only two of the only two of the

data points are used to determine the fixed data points are used to determine the fixed and variable cost components.and variable cost components.

The highest and lowest observations are The highest and lowest observations are picked, with the choice being based on the picked, with the choice being based on the independent variable (machine hours) independent variable (machine hours) rather than the dependent variable rather than the dependent variable (overhead cost).(overhead cost).


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Regression AnalysisRegression Analysis Regression analysisRegression analysis is a statistical is a statistical

approach that can be used to determine the approach that can be used to determine the fixed and variable cost components with a fixed and variable cost components with a high degree of accuracy.high degree of accuracy.

Calculations done by hand are very tedious. Calculations done by hand are very tedious. However, many software packages can However, many software packages can make these calculations for you. Let’s use make these calculations for you. Let’s use the same sample data and view the output the same sample data and view the output from a popular spreadsheet program.from a popular spreadsheet program.


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Determine the fixed Determine the fixed and variable and variable

components of a mixed components of a mixed cost using scatter cost using scatter

graphs, the high-low graphs, the high-low method, and the results method, and the results of regression analysis.of regression analysis.


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Scatter Graph Scatter Graph ExampleExample

We will use the following data in an effort to We will use the following data in an effort to predict overhead costs on the basis of machine predict overhead costs on the basis of machine hours.hours.

MonthMachine

HoursOverhead

CostsJanuary 4,500 $10,800February 3,900 8,000March 2,500 6,200April 2,000 6,000May 3,000 6,600June 3,500 7,250July 4,300 8,750August 4,500 8,850September 5,000 10,500


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Scatter Graph Scatter Graph ExampleExample

Scatter Graph

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0 1,000 2,000 3,000 4,000 5,000 6,000

Machine Hours

Ove

rhea

d C

ost

s


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Draw the Best Fit Draw the Best Fit LineLineScatter Graph

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0 1,000 2,000 3,000 4,000 5,000 6,000

Machine Hours

Ove

rhea

d C

ost

s


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Determine Line Determine Line ParametersParameters

The line appears to intersect the Y axis at The line appears to intersect the Y axis at about $2,000. This would be our best about $2,000. This would be our best estimate of the fixed cost component.estimate of the fixed cost component.

The line also goes through the data point for The line also goes through the data point for March where X= 2,500 and Y = $6,200. March where X= 2,500 and Y = $6,200. Subtracting the $2,000 fixed cost from Subtracting the $2,000 fixed cost from $6,200, leaves $4,200 as the estimate of total $6,200, leaves $4,200 as the estimate of total variable cost at this level of volume.variable cost at this level of volume.


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Estimate the Total Cost Estimate the Total Cost FormulaFormula

To determine the variable cost per machine To determine the variable cost per machine hour, simply divide the total variable cost by the hour, simply divide the total variable cost by the number of machine hours:number of machine hours:$4,200 / 2,500 hours = $1.68 per hour.$4,200 / 2,500 hours = $1.68 per hour.

Thus, our estimated overhead cost is $2,000 per Thus, our estimated overhead cost is $2,000 per month plus $1.68 per machine hour.month plus $1.68 per machine hour.

TC = FC + (VC x V)TC = FC + (VC x V) TC = $2,000 + ($1.68 x 2,500 hours)TC = $2,000 + ($1.68 x 2,500 hours)

TC = $6,200TC = $6,200


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High-Low MethodHigh-Low Method Using the same data as before, the high Using the same data as before, the high

and low activity months are:and low activity months are: High: SeptemberHigh: September 5,000 hours, $10,500 5,000 hours, $10,500

costcost Low: AprilLow: April 2,000 hours, $ 6,000 cost2,000 hours, $ 6,000 cost

The next step is to analyze the data to The next step is to analyze the data to determine the variable cost (based on the determine the variable cost (based on the cost change from low to high) and the cost change from low to high) and the fixed cost.fixed cost.© 2007 Pearson Custom Publishing© 2007 Pearson Custom Publishing

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The High-Low LineThe High-Low LineHigh-Low Method

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0 1,000 2,000 3,000 4,000 5,000 6,000

Machine Hours

Ove

rhea

d C

ost

s


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High-Low High-Low CalculationsCalculations

Step 1:Step 1: Calculate the variable cost: Calculate the variable cost:

Change in cost Change in cost $10,500 - $6,000$10,500 - $6,000Change in hoursChange in hours 5,000 - 2,000 5,000 - 2,000

$4,500 $4,500 3,000 hrs. = $1.50 per machine hour3,000 hrs. = $1.50 per machine hour


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High-Low High-Low CalculationsCalculations

Step 2:Step 2: Calculate the fixed cost: (NOTE: you Calculate the fixed cost: (NOTE: you can use either month for this step.)can use either month for this step.) TC = FC + (UVC x V) or TC – (UVC x V) = FCTC = FC + (UVC x V) or TC – (UVC x V) = FC April total cost -- variable cost = fixed costApril total cost -- variable cost = fixed cost $6,000 -- ($1.50 X 2,000 hours) = $3,000$6,000 -- ($1.50 X 2,000 hours) = $3,000 Thus, the overhead is estimated at $3,000 per Thus, the overhead is estimated at $3,000 per

month plus $1.50 per machine hour.month plus $1.50 per machine hour. TC = FC + (UVC x V) TC = FC + (UVC x V) TC = $3,000 + ($1.20 X Machine hours)TC = $3,000 + ($1.20 X Machine hours)


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Regression Analysis Regression Analysis OutputOutput

Regression StatisticsR Square 86.12%Adjusted R Square 84.14%Standard Error 704.53$ Observations 9

Coefficients Standard Error Lower 95% Upper 95%

Intercept 2,134.15$ 935.93$ (78.97)$ 4,347.27$ X Variable 1 1.62$ 0.25$ 1.04$ 2.20$

The blue text is used to highlight the variable and fixed cost estimates using regression analysis.


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Estimates Using Estimates Using Regression AnalysisRegression Analysis

Based on the output data, the estimate of fixed Based on the output data, the estimate of fixed cost is $2,134 and the estimate of variable cost cost is $2,134 and the estimate of variable cost is $1.62 per machine hour.is $1.62 per machine hour.

TC = $2,134 + ($1.62 x Machine hours)TC = $2,134 + ($1.62 x Machine hours) The remaining output data provides information The remaining output data provides information

related to the expected accuracy of our related to the expected accuracy of our overhead cost estimates. The measures of overhead cost estimates. The measures of probable error are major advantages of probable error are major advantages of regression analysis over the other methods.regression analysis over the other methods.


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Cost EquationCost Equation The basic format used for cost equations The basic format used for cost equations

is:is:

Y = a + bX, whereY = a + bX, where

Y = estimated total costY = estimated total costX = expected or actual activity levelX = expected or actual activity levela = estimated fixed cost per perioda = estimated fixed cost per periodb = estimated variable cost per unit of activityb = estimated variable cost per unit of activity


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Comparison of the Comparison of the MethodsMethods

Each of the three analyses gives us a different Each of the three analyses gives us a different cost equation for predicting overhead costs cost equation for predicting overhead costs based on 4,000 machine hours.based on 4,000 machine hours.

Scatter graph:$2,000 + $1.68 x 4,000 = $8,720Scatter graph:$2,000 + $1.68 x 4,000 = $8,720 High-low:High-low: $3,000 + $1.50 x 4,000 = $9,000$3,000 + $1.50 x 4,000 = $9,000 Regression:Regression: $2,134 + $1.62 x 4,000 = $2,134 + $1.62 x 4,000 =

$8,614$8,614


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Of the three cost equations, which one do Of the three cost equations, which one do you think would be most reliable (i.e., you think would be most reliable (i.e., gives the most accurate predictions)?gives the most accurate predictions)?

Consider the fact that we only used data Consider the fact that we only used data from nine months. What implications does from nine months. What implications does this have for your assessment of how this have for your assessment of how accurate our predictions might be? accurate our predictions might be?


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The End of Chapter The End of Chapter M4M4


1 chapter m4 cost behavior © 2007 pearson custom publishing

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