Cornerstonesof Managerial Accounting 3eMOWEN / HANSEN / HEITGERCOPYRIGHT 2009 South-Western/Cengage Learning

Chapter ThreeCost Behavior

Learning ObjectivesExplain the meaning of cost behavior and define and describe fixed and variable costs.Define and describe mixed and step costs.*

Learning ObjectivesSeparate mixed costs into their fixed and variable components using the high-low method, the scattergraph method, and the method of least squares(Appendix) Use a personal computer spreadsheet program to perform the method of least squares.*

OBJECTIVE

1

Explain the meaning of cost and behavior, and define and describe fixed and variable costs.

Cost BehaviorThe way costs change as the related activity changes.*A cost that does not change in total as output changesFixed Cost =

Cost BehaviorThe way costs change as the related activity changes.*Increases in total with an increase in output and decreases in total with a decrease in outputVariable Cost =

Measures of OutputTo determine if a cost is fixed or variable, we must first determine the underlying business activity and ask ourselves*What causes the cost of this particular activity to go up (or down)?In other words, we are trying to identify its driver.

Relevant RangeThe range of output over which the assumed cost relationship is valid for the normal operations of a firm.*Lets take a closer look at fixed, variable, and mixed costs, in light of the relevant range.Avoids extremely high levels of activityAvoids extremely low levels of activity

Fixed Costs*Cost that in total are constant within the relevant range as the level of output increases or decreases.

ExampleIt process up to 50,000 computers per year. The production-line manager (supervisor) is paid $32,000 per year.The company was established 5 years ago.Currently the factory produces 40,000 50,000 computers per year. Production has never fallen below 20,000 computers in a year.*Colley Computers Inc. wants to look at the cost relationship between supervision cost and the number of computers processed.Lets look at the cost of supervision at several production levels.

Example*# of Computers Produced20,00030,00040,00050,000Total Cost of Supervision$32,000$32,000$32,000$32,000We know the total cost of supervision, but what about per computer?Unit Cost

Example*# of Computers Produced20,00030,00040,00050,000Total Cost of Supervision$32,000$32,000$32,000$32,000Unit Cost$1.601.070.800.64Unit cost changes! As production increases, the per unit amount of a fixed cost decreases.

Discretionary Fixed Costs*Fixed costs that can be changed relatively easily at management discretion.

Committed Fixed Costs*A fixed costs that can not be easily changed. Often these involve a long-term contract.

Variable Costs*Costs that in total vary in direct proportion to changes in output within the relevant range.

Variable Cost Behavior Example*Each computer requires one DVD-ROM drive costing $40.The cost of DVD-ROM drives for various levels of production is as follows:Expanding our Colley Computers example.Lets look at the cost of DVD-ROMs at several production levels.

Variable Cost Behavior Example*# of Computers Produced20,00030,00040,00050,000Total Cost of DVD-ROM Drives$800,000$1,200,000$1,600,000$2,000,000Unit CostWe know the total cost increases as production increases. But what about the cost per computer?

Variable Cost Behavior Example*# of Computers Produced20,00030,00040,00050,000Total Cost of DVD-ROM Drives$800,000$1,200,000$1,600,000$2,000,000Unit Cost$40404040Unit cost stays the same! The per unit variable cost of DVD-ROM drives is always $40 per computer.

Variable Cost RelationshipTotal Variable Cost=Variable RateAmount of outputx*Lets look at the DVD-ROM costs for 50,000 computers.

Variable Cost RelationshipTotal Variable Cost=Variable RateAmount of outputx*50,000 computers$40 per computerx=$2,000,000

OBJECTIVE

2

Define and describe mixed and step costs.

Mixed Costs*Costs that have both a fixed and a variable component.Formula:Total Cost=Total Fixed Cost+Total Variable CostLets look at an example from the Colley Computers

Example*Colley Computers has 10 sales representativesLets plug this into our mixed cost formula.Each earns a salary of $30,000 per year.And a commission of $25 per computer sold.Each sales rep sells up to 50,000 computers per year.

Mixed Cost Example*Formula:Total Cost=Total Fixed Cost+Total Variable Cost($25 x # of computers sold) $30,000+=Total Cost

Step Costs*Display a constant level of cost for a range of output and then jumps to a higher level of cost at some point where it remains for a similar level of output.

OBJECTIVE

3

Separate mixed costs into their fixed and variable components using the high-low method, the scattergraph method and the method of least squares.

Separating CostsAccounting records typically show only the total cost and the associated amount of activity of a mixed cost item.*Therefore it is necessary to separate the total cost into its fixed and variable components.How do we separate the costs?

Separating CostsHigh-Low methodScattergraph methodMethod of Least SquaresThree steps:*

Dependent Variable in the Cost Formula*Total Cost=Total Fixed Cost+Total Variable CostVariable Rate x OutputTotal Cost=Total Fixed Cost+Variable RatexOutputDependent Variable

Dependent Variable*A variable whose value depends on the value of another variable.

Independent Variable in the Cost Formula*Total Cost=Total Fixed Cost+Total Variable CostTotal Cost=Total Fixed Cost+Variable RatexOutputIndependent Variable

Independent Variable*A variable that measures output and explains changes in the cost.

Intersect*Graphically, the intersect is the point at which the cost line intercepts the cost (vertical) axis.Intercept

Intercept in the Cost Formula*Total Cost=Total Fixed Cost+Total Variable CostTotal Cost=Total Fixed Cost+Variable RatexOutputIntercept

Slope in the Cost Formula*Total Cost=Total Fixed Cost+Total Variable CostTotal Cost=Total Fixed Cost+Variable RatexOutputSlope

Slope*Corresponds to the variable rate (the variable cost per unit of output). It is the slope of the cost line.Lets work through an example.

Cornerstone 3-1HOW TO Create and Use a Cost Formula*

ExampleThe art and graphics department of State College decided to equip each faculty office with an inkjet color printer.Sufficient color printers had monthly depreciation of $250.The department purchased paper in boxes of 10,000 sheets for $35 per box.Ink cartridges cost $30 and will print, on average, 300 sheets.

*Information:

ExampleCreate a formula for the monthly cost of inkjet printing in the arts and graphics department.If the department expects to print 4,400 pages next month, what is the.Expected fixed cost?Total variable cost? Total printing cost?Required:*

Example*Total Cost=Total Fixed Cost+Total Variable CostDepreciation per month is a fixed cost.$250Total Cost of Printing=

Example*Total Cost=Total Fixed Cost+Total Variable Cost$250Total Cost of Printing=($0.1035 x No. of pages)+Paper and ink are the two variable costs.Paper is $0.0035 per sheet and ink is $0.10 per sheet.

Example*$250Total Cost of Printing=($0.1035 x No. of pages)+Using 4,400 as the number of pages.4,400

Example*$250Total Cost of Printing=($0.1035 x No. of pages)+Total Variable Cost4,400$0.1035 x$455.40

Example*$250Total Cost of Printing=($0.1035 x No. of pages)+4,400$0.1035 x$455.40Total Fixed Costs$250+=$705.40Total Costs for 4,400 pages

High-Low Method*A method of separating mixed costs into fixed and variable components by using just the high and the low data points.Step #1 Find the high point and low point.

High-Low Method*Step #2 Using the high and low points, calculate the variable rate.Variable rate =High point cost Low point costHigh point output Low point output

High-Low Method*Step #3 Calculate the fixed cost using the variable rate and either the high point or the low point.Fixed Cost =Total cost at high point (Variable rate x Output at high point)-Or Low Point

High-Low Method*Step #4 Form the cost formula based on the high-low method.Cornerstone 3-2 will walk us through an example of the High-Low method.

Cornerstone 3-2HOW TO Use the High-Low Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula*

ExampleInformation:Blue Denim Company controller wants to calculate the fixed and variable costs associated with electricity used in the factory. *

ExampleRequired:Using the High-Low method, calculate the fixed cost of electricity, calculate the variable rate per machine hour, and construct the cost formula for total electricity cost.*

Blue Denim Company*MonthJanuaryFebruaryMayElectricity Costs$3,2553,4853,3003,312Machine Hours450500470470MarchApril4,100600June2,575350July3,910570August4,200590Step #1 Identify the high and low points

Blue Denim Company*MonthJanuaryFebruaryMayElectricity Costs$3,2553,4853,3003,312Machine Hours450500470470MarchApril4,100600June2,575350July3,910570August4,200590High Point

Blue Denim Company*MonthJanuaryFebruaryMayElectricity Costs$3,2553,4853,3003,312Machine Hours450500470470MarchApril4,100600June2,575350July3,910570August4,200590Low Point

High-Low Method*Step #2 Using the high and low points, calculate the variable rate.Variable rate =High point cost Low point costHigh point output Low point output$4,100 - $2,575600 - 350Variable rate =Variable rate =$6.10 per machine hour

High-Low Method*Step #3 Calculate the fixed cost using the variable rate and either the high point or the low point.Fixed Cost =Total cost at high point (Variable rate x Output at high point)-We will choose to use the high point

High-Low Method*Fixed Cost =Total cost at high point (Variable rate x Output at high point)-$4,100- $3,660Fixed Cost =Fixed Cost =$4,100-Fixed Cost =$440($6.10 x 600)

High-Low Method*Step #4 Form the cost formula based on the high-low method.Total electricity cost = $440 ($6.10 x Machine hrs.)+

Cornerstone 3-3HOW TO Use the High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for Budgeted Output*

ExampleBlue Denims formula for monthly electrical cost:*Information:Total electricity cost $440 ($6.10 x Machine Hrs)= +

ExampleTotal variable electricity cost for OctoberTotal electricity cost for OctoberRequired:*Assume that 550 machine hours are budgeted for the month of September. Using the formula calculate the following:

ExampleTotal electricity cost = $440 ($6.10 x Machine hrs.)+Monthly Electricity Cost Formula550 machine hoursTotal electricity cost = $440+ ($6.10 x 550)

ExampleTotal electricity cost = $440 ($6.10 x Machine hrs.)+Monthly Electricity Cost FormulaTotal variable electricity costTotal electricity cost = $440+ ($6.10 x 550)Total electricity cost = $440+ $3,355

ExampleTotal electricity cost = $440 ($6.10 x Machine Hrs)+Monthly Electricity Cost FormulaTotal electricity cost = $440+ ($6.10 x 550)Total electricity cost = $440+ $3,355Total electricity cost = $3,795

High-Low Method*Disadvantages:High and low points can be outliers and may represent atypical cost-activity relationships.Even if these points are not outliers, other pairs of points may clearly be more representative.The scattergraph method does a better job of separating the costs.

Cornerstone 3-4HOW TO Use the High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for a Time Period That Differs from the Data Period.*

ExampleBlue Denims formula for monthly electrical cost:*Information:Total electricity cost $440 ($6.10 x Machine hrs.)= +

ExampleTotal variable electricity cost for the yearTotal fixed electricity cost for the yearTotal electricity cost for the coming year.Assume that 6,500 machine hours are budgeted for the coming year. Use the formula to make the following calculations:*Required:

Example*Total Variable Electricity Cost=Variable RatexMachine hoursTotal Variable Electricity Cost=$6.10 x6,500Total Variable Electricity Cost=$39,650

Example*Total Fixed Cost=Monthly Fixed Costx12 Months$440 x12 MonthsTotal Fixed Cost=Total Fixed Cost=$5,280

Example*Total Electricity Cost=Fixed Cost+Variable Cost$5,280+$39,650Total Electricity Cost=Total Electricity Cost=$44,930

Scattergraph MethodPurpose of the method:To see whether a straight line reasonably describes the cost relationshipTo reveal one or more points that do not seem to fit the general pattern of behavior*

Scattergraph MethodApplying the method:Draw a graph with units on the x-axis and cost on the y-axisPlot the data points on the graphVisually fit a line to the data points on the graphThe intercept is the fixed costUse the high-low method to determine the variable rate*

Scattergraph Method*Disadvantage:Lack of any objective criterion for choosing the best fitting line.We need a method that is objective and produces the best-fitting line.

Method of Least Squares*A statistical way to find the best-fitting line through a set of data points. The line is one in which the data points are closer to the line to any other line.What does best fitting mean?

Method of Least Squares*Measure distance from points to line. Then square the differences. Add up all the squared differences.

Method of Least Squares*Spreadsheet programs have packages to calculate the best-fitting line (called regression line).

Cornerstone 3-5HOW TO Use the Regression Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula and to Determine Budgeted Cost*

Example*Coefficients shown by regression program: Intercept 321 X Variable 6.38

Blue Denims electricity cost and machine hours data for the past nine months (given in Cornerstone 3-2)Information:

ExampleUsing the results of regression, calculate:The fixed cost of electricity and the variable rate per machine hour.Construct the cost formula for total electricity cost.Calculate the budgeted cost for next month assuming that 550 machine hours are budgeted.*Required:

Example*The fixed cost and the variable rate are given directly by regression.

Fixed Cost = $321 Variable Rate = $6.38

InterceptX Variable

Example*Total Electricity Cost=Fixed Cost+Variable Cost$321+($6.38 x 550)Total Electricity Cost=Budgeted machine hours

Example*Total Electricity Cost=Fixed Cost+Variable Cost$321+($6.38 x 550)Total Electricity Cost=Total Electricity Cost=$3,830

Managerial Judgment*Instead of the three methods previously discussed, many managers simply use their experience and past observation of cost relationships to determine fixed and variable costs.

Managerial Judgment with Estimation*Managers may use experience and judgment to refine statistical estimation results.Statistical techniques are highly accurate in depicting the past, but they cannot foresee the future.

****