Chapter 3 Cost Behaviour COPYRIGHT © 2012 Nelson Education Ltd.

Chapter 3Cost Behaviour

Chapter 3Cost Behaviour

COPYRIGHT © 2012 Nelson Education Ltd.

Learning ObjectivesLearning Objectives

1. Explain cost behaviour, define fixed and variable costs

2. Define mixed and step costs

3. Separate mixed costs into fixed and variable components using the following methods:

• High-Low• Sattergraph• Least Squares

4. (Appendix) Use a computer spreadsheet program to perform the method of least squares


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OBJECTIVE OBJECTIVE 11

Explain the meaning of cost and behaviour, define fixed

and variable costs


Cost BehaviourCost Behaviour

Cost Behaviour: The way costs change as the related activity changes

A cost that does not change in total as output

changes

Fixed Cost =

Output Total Cost

Increase No change

Decrease No change


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Cost BehaviourCost Behaviour

Cost Behaviour: The way costs change as the related activity changes

A cost that changes in total as output changesVariable Cost =

Output Total Cost

Increase Increase

Decrease Decrease


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Measures of OutputMeasures of Output

To determine if a cost is fixed or variable, we must first determine the

underlying business activity and ask…

“What causes the cost of this particular activity to go up/down?”

In other words, we are trying to identify its driver


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Relevant RangeRelevant Range

The range of output over which the assumed cost relationship is valid for the normal

operations of a firm

Let’s take a closer look at fixed, variable, and mixed costs, in light

of the relevant range

• Avoids extremely high levels of activity• Avoids extremely low levels of activity


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ExampleExample

• It process up to 50,000 computers per year• Production-line manager is paid $32,000 per year• Factory produces 40,000 to 50,000 computers per

year• Production has never fallen below 20,000 computers

in a year

SyBan Computers Inc. wants to look at the cost relationship between supervision cost and the

number of computers processed per year

Let’s look at the cost of supervision at several

production levelsCOPYRIGHT © 2012 Nelson Education Ltd.

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Fixed Cost ExampleFixed Cost Example

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# of Computers Produced

Total Cost of Supervision Unit Cost

20,000 $32,000

30,000 $32,000

40,000 $32,000

50,000 $32,000

$1.60

$1.07

$0.80

$0.64

Fixed Costs = Costs that in total are constant within the relevant range as the level of output

increases or decreases


Discretionary vs. Committed Fixed CostsDiscretionary vs. Committed Fixed Costs

Fixed costs that can be changed relatively easily at

management discretion

Discretionary Fixed Costs =

Fixed costs that can not be easily changed

Often these involve a long-term contract

Committed Fixed Costs =


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Variable Cost Behaviour ExampleVariable Cost Behaviour 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 SyBan Computers example….

Let’s look at the cost of DVD-ROM’s at several production

levels


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Variable Cost ExampleVariable Cost Example

# of Computers Produced

Total Cost of DVD-ROM Drives Unit Cost

20,000 $800,000

30,000 $1,200,000

40,000 $1,600,000

50,000 $2,000,000

$40

$40

$40

$40

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


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Variable Cost RelationshipVariable Cost Relationship

Total Variable Cost =

Variable Rate

Amount of output×

Let’s look at the DVD-ROM’s cost for 50,000 computers

$2,000,000 =$40 per

computer50,000

computers×


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Define and describe mixed and step costs


Mixed CostsMixed Costs

15

Costs that have both a fixed and a variable component

Total Cost =Total Fixed

Cost +Total Variable

Cost

Let’s look at an example from the SyBan Computers


ExampleExample

SyBan Computers has 10 sales representatives

Let’s 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


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Mixed Cost ExampleMixed Cost Example

Total Cost =Total Fixed

Cost + Total Variable Cost

($25 × # of computers sold) $30,000 +=Total Cost

($25 × 4,000 computers sold) $30,000 +=$130,000

Example:


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Step CostsStep Costs

Display a constant cost for a range of outputThen jumps to a new cost level for a

different range

1 to 500 units

500 to 1,000

1,000 +

$5 per unit

$10 per unit

$15 per unitExample:


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

method of least squares


Separating CostsSeparating Costs

Accounting records typically show only total cost and 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?1. High-Low method

2. Scattergraph method

3. Method of Least Squares

Three methods:


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Dependent Variable in the Cost FormulaDependent Variable in the Cost Formula

Total Cost

= Total Fixed Cost

+ Total Variable Cost

Total Cost =

Total Fixed Cost +

Variable Rate

Output

Dependent Variable is a variable whose value depends on the value of another variable


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×

Independent Variable in the Cost FormulaIndependent Variable in the Cost Formula

Total Cost

= Total Fixed Cost

+ Total Variable Cost

Total Cost =

Total Fixed Cost +

Variable Rate

× Output

Independent Variable is a variable that measures output and explains changes in the cost


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Intersect & SlopeIntersect & Slope

Intersect:• Point at which the cost

line intercepts the cost (vertical) axis

Intercept

Slope:Corresponds to

variable rate (variable cost

per unit of output) • Slope of the cost line

Let’s look at the formula


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Intercept & Slope in the Cost FormulaIntercept & Slope in the Cost Formula

Total Cost

=Total Fixed

Cost+

Total Variable Cost

Total Cost

= Total Fixed Cost

+ Variable Rate

× Output

Intercept Slope


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Example: Cornerstone 3-1Example: Cornerstone 3-1

• College art and graphics department decided to equip each faculty office with an inkjet colour printer

• Printers had monthly depreciation of $250• 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:

How to Create and Use a Cost Formula

• Create a formula for the monthly cost of inkjet printing• If the department expects to print 4,400 pages next month, what is…

• Expected fixed cost?• Total variable cost? • Total printing cost?

Required:


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Example ContinuedExample Continued

Total Cost = Total Fixed Cost + Total Variable Cost

$250Total Cost = ($0.1035 × No. of pages)+

Using 4,400 as the # of pages….

Total Variable Cost

($0.1035 × 4,400)

$455.40

Total Fixed Costs

$250 +=$705.40

Total Costs for 4,400 pages


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High-Low MethodHigh-Low Method

A method of separating mixed costs into fixed & variable components by using just the high and low data points

Step 1: Find the high point and low point

Step 2: Using the high and low points, calculate the variable rate

Variable rate =High point cost – Low point cost

High point output – Low point output


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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

Step 4: Form the cost formula based on the high-low method

Cornerstone 3-2 will walk us through an example


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How to use the High-Low Method

Information:

Blue Denim Company controller wants to calculate the fixed and

variable costs associated with electricity used in the factory

Required:

Using the High-Low method, calculate:

• fixed cost of electricity

• the variable rate per machine hour

• construct the cost formula for total electricity cost


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Blue Denim CompanyBlue Denim Company

Month

January

February

May

Electricity Costs

$3,255

3,485

3,300

3,312

Machine Hours

450

500

470

470

MarchApril

4,100 600

June 2,575 350

July 3,910 570

August 4,200 590

Step 1: Identify the high and low points


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Month

January

February

May

Electricity Costs

$3,255

3,485

3,300

3,312

Machine Hours

450

500

470

470

MarchApril

4,100 600

June 2,575 350

July 3,910 570

August 4,200 590

High Point



Month

January

February

May

Electricity Costs

$3,255

3,485

3,300

3,312

Machine Hours

450

500

470

470

MarchApril

4,100 600

June 2,575 350

July 3,910 570

August 4,200 590

Low Point


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Step 2: Calculate the variable rate

Variable rate =High point cost – Low point cost

High point output – Low point output

$4,100 – $2,575

600 – 350Variable rate =

Variable rate = $6.10 per machine hour


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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 × Output at high point)–

$4,100 –

$3,660

Fixed Cost =

Fixed Cost = $4,100 –

Fixed Cost = $440

($6.10 × 600)


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Step 4: Construct a cost formula

Total electricity cost = $440 ($6.10 x Machine hrs.)+


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Blue Denim’s formula for monthly electrical cost:

Information:

Total electricity cost

$440 ($6.10 × Machine Hrs)= +

How to use the High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for Budgeted Output

• Total variable electricity cost for October• Total electricity cost for October

Required:

Assume that 550 machine hours are budgeted for the month of September.

Using the formula calculate the following:


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ExampleExample

Total electricity cost = $440 ($6.10 × Machine hrs.)+

Monthly Electricity Cost Formula:

550 machine hours

Total electricity cost =

$440 + ($6.10 × 550)

Total variable electricity cost

Total electricity cost = $440 + $3,355

Total electricity cost = $3,795


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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


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Scattergraph MethodScattergraph Method

Purpose of the Method:

• To see whether a straight line reasonably describes the cost relationship

• To reveal one or more points that do not seem to fit the general pattern of behaviour


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Scattergraph MethodScattergraph Method

Applying the Method:• Draw a graph with units on the x-axis and cost on the y-axis

• Plot the data points on the graph

• Visually fit a line to the data points on the graph

• The intercept is the fixed cost

• Use the high-low method using the points from the graph to determine the variable rate

Disadvantage:Lack of any objective criterion for choosing the best fitting line


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Method of Least SquaresMethod of Least Squares

Steps:• Measure distance from points to line• Then square the differences• Add up all the squared differences

▪▪▪

▪▪▪ ▪▪

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 than to any other line

What does best fitting mean?


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How to use the Regression Method to calculate fixed cost and variable rate, construct a cost formula and to determine budgeted cost

Coefficients shown by regression program:

Intercept 321

X Variable 6.38

Blue Denim’s electricity cost and machine hours data for the past nine monthsInformation:

Using 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 550 budgeted machine hours

Required:


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ExampleExample

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

Fixed Cost = $321

Variable Rate = $6.38

Intercept

X Variable

Total Electricity Cost =

Fixed Cost + Variable Cost

$321 + ($6.38 × 550)

Total Electricity Cost =

Budgeted machine hoursTotal Electricity Cost = $3,830


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Managerial JudgmentManagerial Judgment

Instead of the three methods previously discussed, many managers

use their experience and past observation of cost relationships to determine fixed and variable costs

Statistical techniques are highly accurate in depicting the past, but

they cannot foresee the future


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Chapter 3 Cost Behaviour COPYRIGHT © 2012 Nelson Education Ltd.

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Transcript of Chapter 3 Cost Behaviour COPYRIGHT © 2012 Nelson Education Ltd.