Cost Behavior Analysis & Use)

Cost Behavior: Analysis and UseChapter Five

McGraw-Hill/Irwin

Copyright 2006, The McGraw-Hill Companies, Inc.

Types of Cost Behavior PatternsRecall the summary of our cost behavior discussion from an earlier chapter.Summary of Variable and Fixed Cost BehaviorCost Variable In Total Total variable cost is proportional to the activity level within the relevant range. Total fixed cost remains the same even when the activity level changes within the relevant range. Per Unit Variable cost per unit remains the same over wide ranges of activity. Fixed cost per unit goes down as activity level goes up.

Fixed

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The Activity BaseUnits Units produced produced A measure of what A measure of what causes the causes the incurrence of a incurrence of a variable cost variable cost Miles Miles driven drivenMcGraw-Hill/Irwin

Machine Machine hours hours

Labor Labor hours hoursCopyright 2006, The McGraw-Hill Companies, Inc.

True Variable Cost ExampleA variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level. Your total long distance telephone bill is based on how many minutes you talk.Total Long Distance Telephone BillMinutes TalkedMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.


Fixed

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Variable Cost Per Unit ExampleA variable cost remains constant if expressed on a per unit basis. The cost per minute talked is constant. For example, 10 cents per minute.Per Minute Telephone ChargeMinutes TalkedMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Extent of Variable CostsThe proportion of variable costs differs across organizations. For example . . .A public utility with large investments in equipment will tend to have fewer variable costs. A service company will normally have a high proportion of variable costs.McGraw-Hill/Irwin

A manufacturing company will often have many variable costs.

A merchandising company usually will have a high proportion of variable costs like cost of sales.Copyright 2006, The McGraw-Hill Companies, Inc.

Examples of Variable Costs1. Merchandising companies cost of goods sold. 2. Manufacturing companies direct materials, direct labor, and variable overhead. 3. Merchandising and manufacturing companies commissions, shipping costs, and clerical costs such as invoicing. 4. Service companies supplies, travel, and clerical.

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True Variable CostDirect materials is a true or proportionately variable cost because the amount used during a period will vary in direct proportion to the level of production activity.

Cost

VolumeMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Step-Variable CostsA resource that is obtainable only in large chunks (such as maintenance workers) and whose costs increase or decrease only in response to fairly wide changes in activity is known as a step-variable cost. cost

Cost


Step-Variable Costs

Small changes in the level of production are Small changes of not likely to have any effect on the number of not likely to have any effect on the maintenance workers employed. maintenance workers employed.

Cost


Step-Variable CostsOnly fairly wide changes in the activity level will cause a change in the number of maintenance workers employed

Cost


The Linearity Assumption and the Relevant Range

A straight line A straight line Economists closely closely Curvilinear Cost approximates a approximates a Function curvilinear curvilinear

Total Cost

Relevant Range

variable cost variable cost line within the line within the relevant range. relevant range.

Accountants Straight-Line Approximation (constant unit variable cost) Activity

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Types of Cost Behavior PatternsLets look at fixed cost behavior on the next screens.Summary of Variable and Fixed Cost BehaviorCost Variable In Total Total variable cost is proportional to the activity level within the relevant range. Total fixed cost remains the same even when the activity level changes within the relevant range. Per Unit Variable cost per unit remains the same over wide ranges of activity. Fixed cost per unit goes down as activity level goes up.

Fixed

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Total Fixed Cost ExampleA fixed cost is a cost whose total dollar amount remains constant as the activity level changes. Your monthly basic telephone bill is probably fixed and does not change when you make more local calls.Monthly Basic Telephone BillNumber of Local CallsMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.


Fixed

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Fixed Cost Per Unit ExampleAverage fixed costs per unit decrease as the activity level increases. The fixed cost per local call decreases as more local calls are made.Monthly Basic Telephone Bill per Local CallNumber of Local CallsMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Types of Fixed Costs

Committed CommittedLong-term, cannot be Long-term, cannot be significantly reduced significantly reduced in the short term. in the short term.

Discretionary DiscretionaryMay be altered in the May be altered in the short-term by current short-term by current managerial decisions managerial decisions

ExamplesDepreciation on Equipment and Real Estate TaxesMcGraw-Hill/Irwin

Examples ExamplesAdvertising and Advertising and Research and Research and Development DevelopmentCopyright 2006, The McGraw-Hill Companies, Inc.

The Trend Toward Fixed CostsThe trend in many industries is toward greater fixed costs relative to variable costs.As machines take over As machines take over many mundane tasks many mundane tasks previously performed previously performed by humans, by humans, knowledge workers knowledge workers are demanded for are demanded for their minds rather their minds rather than their muscles than their musclesMcGraw-Hill/Irwin

Knowledge workers Knowledge workers tend to be salaried, tend to be salaried, highly-trained and highly-trained and difficult to replace. The difficult to replace. The cost to compensate cost to compensate these valued employees these valued employees is relatively fixed is relatively fixed rather than variable. rather than variable.Copyright 2006, The McGraw-Hill Companies, Inc.

Is Labor a Variable or a Fixed Cost?The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom.In France, Germany, China, and Japan management has little flexibility in adjusting the size of the labor force. Labor costs are more fixed in nature. In the United States and the United Kingdom management has greater latitude. Labor costs are more variable in nature.

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Fixed Costs and Relevant Range

Rent Cost in Thousands of Dollars

90 Relevant RangeTotal cost doesnt Total cost doesnt change for a wide change for a wide range of activity, range of activity, and then jumps to a and then jumps to a new higher cost for new higher cost for the next higher the next higher range of activity. range of activity.

60

30 0 0

1,000 2,000 3,000 Rented Area (Square Feet)Copyright 2006, The McGraw-Hill Companies, Inc.

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Fixed Costs and Relevant RangeThe relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat.Example: Office space is Example: Office space is available at a rental rate of available at a rental rate of $30,000 per year in $30,000 per year in increments of 1,000 square increments of 1,000 square feet. As the business grows feet. As the business grows more space is rented, more space is rented, increasing the total cost. increasing the total cost.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Fixed Costs and Relevant Range

How does this type of fixed cost differ from a stepvariable cost?McGraw-Hill/Irwin

Step-variable costs can be adjusted more quickly and . . . The width of the activity steps is much wider for the fixed cost.Copyright 2006, The McGraw-Hill Companies, Inc.

Quick Check Which of the following statements about cost Which of the following statements about cost behavior are true? behavior are true?1. Fixed costs per unit vary with the level of 1. Fixed costs per unit vary with the level of activity. activity. 2. Variable costs per unit are constant within the 2. Variable costs per unit are constant within the relevant range. relevant range. 3. Total fixed costs are constant within the 3. Total fixed costs are constant within the relevant range. relevant range. 4. Total variable costs are constant within the 4. Total variable costs are constant within the relevant range. relevant range.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Quick Check Which of the following statements about cost Which of the following statements about cost behavior are true? behavior are true?1. Fixed costs per unit vary with the level of 1. Fixed costs per unit vary with the level of activity. activity. 2. Variable costs per unit are constant within the 2. Variable costs per unit are constant within the relevant range. relevant range. 3. Total fixed costs are constant within the 3. Total fixed costs are constant within the relevant range. relevant range. 4. Total variable costs are constant within the 4. Total variable costs are constant within the relevant range. relevant range.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Mixed CostsA mixed cost has both fixed and variable A mixed cost has both fixed and variable components. Consider the example of utility cost. components. Consider the example of utility cost.Y

Total Utility Cost

st co d i xe m al t To

Variable Cost per KW

Activity (Kilowatt Hours)McGraw-Hill/Irwin

X

Fixed Monthly Utility ChargeCopyright 2006, The McGraw-Hill Companies, Inc.

Mixed Costs

Y

Total Utility Cost

st co d i xe m al t To

Variable Cost per KW

Activity (Kilowatt Hours)McGraw-Hill/Irwin

X

Fixed Monthly Utility ChargeCopyright 2006, The McGraw-Hill Companies, Inc.

Mixed Costs ExampleIf your fixed monthly utility charge is $40, your variable cost is $0.03 per kilowatt hour, and your monthly activity level is 2,000 kilowatt hours, what is the amount of your utility bill?

Y = a + bX Y = $40 + ($0.03 2,000) Y = $100McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Analysis of Mixed CostsAccount Analysis and the Engineering ApproachEach account is classified as either Each account is classified as either variable or fixed based on the analysts variable or fixed based on the analysts knowledge of how the account behaves. knowledge of how the account behaves.

Cost estimates are based on an Cost estimates are based on an evaluation of production methods, and evaluation of production methods, and material, labor and overhead material, labor and overhead requirements. requirements.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

The Scattergraph MethodPlot the data points on a graph Plot the data points on a graph (total cost vs. activity). (total cost vs. activity).

YMaintenance Cost 1,000s of Dollars

20

10

* * * *0 1 2

* ** * **X

0

3

4

Patient-days in 1,000sMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

The Scattergraph MethodDraw a line through the data points with about an Draw a line through the data points with about an equal numbers of points above and below the line. equal numbers of points above and below the line. YMaintenance Cost 1,000s of Dollars

20

10

* * * *0 1 2

* ** * **X

0

3

4

Patient-days in 1,000sMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

The Scattergraph MethodUse one data point to estimate the total level of activity Use one data point to estimate the total level of activity and the total cost. and the total cost. Y Total maintenance cost = $11,000Maintenance Cost 1,000s of Dollars

20

10

* * * *0 1 2

* ** * **X

Intercept = Fixed cost: $10,000

0

3

4

Patient-days in 1,000s Patient days = 800McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

The Scattergraph MethodMake a quick estimate of variable cost per unit and Make a quick estimate of variable cost per unit and determine the cost equation. determine the cost equation.Total maintenance at 800 patients Less: Fixed cost Estimated total variable cost for 800 patients $ 11,000 10,000 $ 1,000

Variable cost per unit =

$1,000 800

= $1.25/patient-day

Y = $10,000 + $1.25XTotal maintenance costMcGraw-Hill/Irwin

Number of patient daysCopyright 2006, The McGraw-Hill Companies, Inc.

The High-Low MethodAssume the following hours of maintenance work and the total maintenance costs for six months.

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The High-Low MethodThe variable cost per hour of maintenance is equal to the change in cost divided by the change in hours. $2,400 = $8.00/hour 300

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The High-Low Method

Total Fixed Cost = Total Cost Total Variable Cost Total Fixed Cost = $9,800 ($8/hour 800 hours) Total Fixed Cost = $9,800 $6,400 Total Fixed Cost = $3,400McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

The High-Low Method

The Cost Equation for Maintenance

Y = $3,400 + $8.00XMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Quick Check Sales salaries and commissions are $10,000 when Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is units are sold. Using the high-low method, what is the variable portion of sales salaries and the variable portion of sales salaries and commission? commission? a. $0.08 per unit a. $0.08 per unit b. $0.10 per unit b. $0.10 per unit c. $0.12 per unit c. $0.12 per unit d. $0.125 per unit d. $0.125 per unit

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Quick Check Sales salaries and commissions are $10,000 when Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is units are sold. Using the high-low method, what is the variable portion of sales salaries and the variable portion of sales salaries and commission? commission? Units Cost a. $0.08 per unit High level a. $0.08 per unit 120,000 $ 14,000 b. $0.10 per unit Low level 80,000 10,000 b. $0.10 per unit 40,000 $ 4,000 c. $0.12 per unit Change c. $0.12 per unit d. $0.125 per unit d. $0.125 per unit $4,000 40,000 units= $0.10 per unit

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Quick Check Sales salaries and commissions are $10,000 when Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? the fixed portion of sales salaries and commissions? a. $ 2,000 a. $ 2,000 b. $ 4,000 b. $ 4,000 c. $10,000 c. $10,000 d. $12,000 d. $12,000

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Quick Check Sales salaries and commissions are $10,000 when Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? the fixed portion of sales salaries and commissions? a. $ 2,000 a. $ 2,000 b. $ 4,000 b. $ 4,000 c. $10,000 c. $10,000 d. $12,000 d. $12,000

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Least-Squares Regression MethodA method used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables.This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost.

The goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors.Copyright 2006, The McGraw-Hill Companies, Inc.

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Least-Squares Regression Method Software can be used to fit a regression line through the data points. The cost analysis objective is the same: Y = a + bXLeast-squares regression also provides a statistic, Least-squares regression also provides a statistic, called the R2,, that is a measure of the goodness called the R2 that is a measure of the goodness of fit of the regression line to the data points. of fit of the regression line to the data points.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Least-Squares Regression MethodR2 is the percentage of the variation in total cost R2 is the percentage of the variation in total cost explained by the activity. explained by the activity. Y 20

Total Cost

10

* * * *0 1

* ** * **

R2 varies from 0% to 100%, and the higher the percentage the better. 0 2 3 Activity 4 X

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Comparing Results From the Three MethodsThe three methods just discussed provide The three methods just discussed provide slightly different estimates of the fixed and slightly different estimates of the fixed and variable cost components of the mixed cost. variable cost components of the mixed cost. This is to be expected because each method This is to be expected because each method uses differing amounts of the data points to uses differing amounts of the data points to provide estimates. provide estimates. Least-squares regression provides the most Least-squares regression provides the most accurate estimate because it uses all the data accurate estimate because it uses all the data points. points.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Lets put our knowledge of cost behavior to work by preparing a contribution format income statement.

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The Contribution FormatSales Revenue Less: Variable costs Contribution margin Less: Fixed costs Net operating income Total $ 100,000 60,000 $ 40,000 30,000 $ 10,000 Unit $ 50 30 $ 20

The contribution margin format emphasizes The contribution margin format emphasizes cost behavior. Contribution margin covers fixed cost behavior. Contribution margin covers fixed costs and provides for income. costs and provides for income.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Uses of the Contribution FormatThe contribution income statement format is used The contribution income statement format is used as an internal planning and decision making tool. as an internal planning and decision making tool. We will use this approach for: We will use this approach for: 1. Cost-volume-profit analysis (Chapter 6). 1. Cost-volume-profit analysis (Chapter 6). 2. Budgeting (Chapter 9). 2. Budgeting (Chapter 9). 3. Segmented reporting of profit data (Chapter 12). 3. Segmented reporting of profit data (Chapter 12). 4. Special decisions such as pricing and make-or4. Special decisions such as pricing and make-orbuy analysis (Chapter 13). buy analysis (Chapter 13).McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

The Contribution FormatComparison of the Contribution Income Statement with the Traditional Income Statement Traditional Approach (costs organized by function) Sales $ 100,000 Less cost of goods sold 70,000 Gross margin $ 30,000 Less operating expenses 20,000 Net operating income $ 10,000 Contribution Approach (costs organized by behavior) Sales $ 100,000 Less variable expenses 60,000 Contribution margin $ 40,000 Less fixed expenses 30,000 Net operating income $ 10,000

Used primarily for external reporting.McGraw-Hill/Irwin

Used primarily by management.Copyright 2006, The McGraw-Hill Companies, Inc.

Appendix 5A

Least-Squares Regression Using Microsoft Excel.

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Simple Regression Analysis ExampleMatrix, Inc. wants to Matrix, Inc. wants to know its average know its average fixed cost and fixed cost and variable cost per unit. variable cost per unit. Using the data to the Using the data to the right, lets see how to right, lets see how to do a regression using do a regression using Microsoft Excel. Microsoft Excel.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Simple Regression Using ExcelYou will need three pieces of You will need three pieces of information from your information from your regression analysis: regression analysis: 1. Estimated Variable Cost per 1. Estimated Variable Cost per Unit (line slope) Unit (line slope) 2. Estimated Fixed Costs (line 2. Estimated Fixed Costs (line intercept) intercept) 3. Goodness of fit, or R22 3. Goodness of fit, or R To get these three pieces To get these three pieces information we will need to information we will need to use three different Excel use three different Excel functions. functions. LINEST, INTERCEPT, & RSQ LINEST, INTERCEPT, & RSQMcGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Simple Regression Using ExcelPlace your cursor in Place your cursor in cell F4 and press the cell F4 and press the = key. Click on the = key. Click on the pull down menu and pull down menu and scroll down to More scroll down to More Functions .. .. . Functions .

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Simple Regression Using Excel

Scroll down to the Scroll down to the Statistical, Statistical, functions. Now functions. Now scroll down the scroll down the statistical statistical functions until you functions until you highlight highlight LINEST LINEST

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1. In the Known_ys box enter C4:C19 for the range. 1. In the Known_ys box enter C4:C19 for the range. 2. In the Known_xs box enter D4:D19 for the range. 2. In the Known_xs box enter D4:D19 for the range.

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Here is the estimate of the slope of the line.

1. In the Known_ys box enter C4:C19 for the range. 1. In the Known_ys box enter C4:C19 for the range. 2. In the Known_xs box enter D4:D19 for the range. 2. In the Known_xs box enter D4:D19 for the range.

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Simple Regression Using ExcelWith you cursor in cell With you cursor in cell F5, press the = key F5, press the = key and go to the pull and go to the pull down menu for down menu for special functions. special functions. Select Statistical and Select Statistical and scroll down to scroll down to highlight the highlight the INTERCEPT function. INTERCEPT function.

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Here is the estimate of the fixed costs.

1. In the Known_ys box enter C4:C19 for the range. 1. In the Known_ys box enter C4:C19 for the range. 2. In the Known_xs box enter D4:D19 for the range. 2. In the Known_xs box enter D4:D19 for the range.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

Simple Regression Using ExcelFinally, we will Finally, we will determine the determine the goodness of goodness of fit, or R22,, by fit, or R by using the RSQ using the RSQ function. function.

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Here is the estimate of R2.

1. In the Known_ys box enter C4:C19 for the range. 1. In the Known_ys box enter C4:C19 for the range. 2. In the Known_xs box enter D4:D19 for the range. 2. In the Known_xs box enter D4:D19 for the range.McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

End of Chapter 5

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Cost Behavior Analysis & Use)