cost behaviour lecture 3

Cost Behavior:Analysis and Use

Chapter 5

© The McGraw-Hill Companies, Inc., 2003McGraw-Hill/Irwin

Summary of Variable and Fixed Cost Behavior

Cost In Total Per Unit

Variable Total variable cost is Variable cost per unit remainsproportional to the activity the same over wide ranges

level within the relevant range. of activity.

Fixed Total fixed cost remains the Fixed cost per unit goessame even when the activity down as activity level goes up.

level changes within therelevant range.

Recall the summary of our cost behavior discussion from Chapter 2.

Types of Cost Behavior Patterns


The Activity Base

A measure of the event that causes the incurrence of a

variable cost – a cost driver

A measure of the event that causes the incurrence of a

variable cost – a cost driver

Unitsproduced

Unitsproduced

Miles driven

Miles driven

Labor hours

Labor hours

Machine hours

Machine hours


Minutes Talked

To

tal L

on

g D

ista

nce

Tel

eph

on

e B

ill

True Variable Cost Example

Your total long distance telephone bill is based on how many minutes you talk.


Minutes Talked

Per

Min

ute

Tel

eph

on

e C

har

ge

Variable Cost Per Unit Example

The cost per minute talked is constant. For example, 10 cents per minute.


Step-Variable Costs

Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.

Total cost remainsconstant within anarrow range of

activity.


Step-Variable Costs

Activity

Co

st

Total cost increases to a new higher cost for the

next higher range of activity.

Total cost increases to a new higher cost for the

next higher range of activity.


RelevantRange

A straight line closely

approximates a curvilinear

variable cost line within the

relevant range.

A straight line closely

approximates a curvilinear

variable cost line within the

relevant range.

Activity

To

tal

Co

st

Economist’sCurvilinear Cost

Function

The Linearity Assumption and the Relevant Range

Accountant’s Straight-Line Approximation (constant

unit variable cost)

Exh.5-4


Number of Local Calls

Mo

nth

ly B

asic

T

elep

ho

ne

Bill

Total Fixed Cost Example

Your monthly basic telephone bill is probably fixed and does not change when

you make more local calls.

Exh.5-5


Number of Local Calls

Mo

nth

ly B

asic

Tel

eph

on

e B

ill p

er L

oca

l Cal

l

Fixed Cost Per Unit Example

The fixed cost per local call decreases as more local calls are made.

Exh.5-5


Cost Behavior

MerchandisersCost of Goods Sold

MerchandisersCost of Goods Sold

ManufacturersDirect Material, Direct Labor, and Variable

Manufacturing Overhead

ManufacturersDirect Material, Direct Labor, and Variable

Manufacturing Overhead

Merchandisers and Manufacturers

Sales commissions and shipping costs

Merchandisers and Manufacturers

Sales commissions and shipping costs

Service Organizations Supplies and travel

Service Organizations Supplies and travel

Examples of normally variable costsExamples of normally variable costs

Examples of normally fixed costsExamples of normally fixed costs

Merchandisers, manufacturers, and service organizations

Real estate taxes, Insurance, Sales salariesDepreciation, Advertising

Merchandisers, manufacturers, and service organizations

Real estate taxes, Insurance, Sales salariesDepreciation, Advertising


ExamplesAdvertising and Research and Development

ExamplesAdvertising and Research and Development

ExamplesDepreciation on Buildings and

Equipment

ExamplesDepreciation on Buildings and

Equipment

Types of Fixed Costs

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

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

CommittedLong-term, cannot be reduced in the short

term.

CommittedLong-term, cannot be reduced in the short

term.


Example: Office space is available at a rental

rate of $30,000 per year in increments of 1,000

square feet. As the business grows more

space is rented, increasing the total

cost.

Fixed Costs and Relevant Range

Continue


Ren

t C

ost

in

T

ho

usa

nd

s o

f D

oll

ars

0 1,000 2,000 3,000 Rented Area (Square Feet)

0

30

60


90

Relevant

Range

Total cost doesn’t change for a wide range of activity,

and then jumps to a new higher cost for

the next higher range of activity.

Total cost doesn’t change for a wide range of activity,

and then jumps to a new higher cost for

the next higher range of activity.

Exh.5-6


How does this type of fixed cost differ

from a step-variable cost?

Step-variable costs can be adjusted more

quickly and . . .

The width of the activity steps is much

wider for the fixed cost.



Quick Check

Which of the following statements about cost behavior are true?

a Fixed costs per unit vary with the level of activity.b Variable costs per unit are constant within the

relevant range.c Total fixed costs are constant within the relevant

range.d Total variable costs are constant within the

relevant range.

Which of the following statements about cost behavior are true?

a Fixed costs per unit vary with the level of activity.b Variable costs per unit are constant within the

relevant range.c Total fixed costs are constant within the relevant

range.d Total variable costs are constant within the

relevant range.


Fixed Monthly

Utility Charge

Variable

Cost per KW

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

X

Y

A mixed cost has both fixed and variablecomponents. Consider the example of utility cost.

A mixed cost has both fixed and variablecomponents. Consider the example of utility cost.

Mixed Costs

Total mixed cost


Fixed Monthly

Utility Charge

Variable

Cost per KW

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

X

Y

Mixed Costs

Total mixed cost Y

= a + bX


The Analysis of Mixed Costs

Engineering Approach

Account Analysis

High-Low Method

Least-Square Regression Method

Scattergraph Plot


Account Analysis & Engineering Estimates

Each account is classified as eithervariable or fixed based on the analyst’s

knowledge of how the account behaves.

Each account is classified as eithervariable or fixed based on the analyst’s

knowledge of how the account behaves.

Cost estimates are based on an evaluation of production methods, and material, labor and overhead

requirements.

Cost estimates are based on an evaluation of production methods, and material, labor and overhead

requirements.


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

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

0 1 2 3 4

*

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*

Activity, 1,000’s of Units Produced

X

Y

The Scattergraph Method


0 1 2 3 4

*

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*


X

Y

Quick-and-Dirty Method

Intercept is the estimated fixed cost = $10,000

Intercept is the estimated fixed cost = $10,000

Draw a line through the data points with about anequal numbers of points above and below the line.

Draw a line through the data points with about anequal numbers of points above and below the line.


0 1 2 3 4

*

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*


X

Y

Quick-and-Dirty MethodThe slope is the estimated variable cost per unit.

Slope = Change in cost ÷ Change in units

The slope is the estimated variable cost per unit.

Slope = Change in cost ÷ Change in units

Vertical distance is the change in cost.

Vertical distance is the change in cost.

Horizontal distance is

the change in activity.

Horizontal distance is

the change in activity.


WiseCo recorded the following production activity and maintenance costs for two months:

Using these two levels of activity, compute: the variable cost per unit; the fixed cost; and then express the costs in equation form Y = a + bX.

The High-Low Method


Changein costChange in units

The High-Low Method

Variable cost per unit = Change in cost ÷ change in units


The High-Low Method

Variable cost per unit = $2,400 ÷ 3,000 units

= $0.80 per unit


The High-Low Method

Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit Fixed cost = Total cost – Total variable cost

Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)

Fixed cost = $9,800 – $6,400 = $3,400


Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit Fixed cost = Total cost – Total variable cost

Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)

Fixed cost = $9,800 – $6,400 = $3,400 Total cost = Fixed cost + Variable cost (Y = a + bX) Y = $3,400 + $0.80X

The High-Low Method


Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission?

a. $0.08 per unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit

Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission?

a. $0.08 per unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit

Quick Check

$4,000 ÷ 40,000 units = $0.10 per unit

Units Cost

High level 120,000 14,000$

Low level 80,000 10,000

Change 40,000 4,000$


Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions?

a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions?

a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

Quick Check


Software can be used to fit a regression line through the data points.

The cost analysis objective is the same: Y = a + bx

Least-Squares Regression Method

Least-squares regression also provides a statistic,

called the R2, that is a measure of the goodness

of fit of the regression line to the data points.

Least-squares regression also provides a statistic,

called the R2, that is a measure of the goodness

of fit of the regression line to the data points.


0 1 2 3 4

To

tal

Co

st

10

20

0

Activity

****

**

****

Least-Squares Regression Method

R2 is the percentage of the variation in total cost explained by the activity.

R2 is the percentage of the variation in total cost explained by the activity.

R2 for this relationship is near100% since the data points are

very close to the regression line.

X

Y


Cost Estimation MethodsRegression Analysis

A statistical method used to create an equation relating independent (or X)

variables to dependent (or Y) variables.

Past data is used to estimate relationships between costs and activities.

A statistical method used to create an equation relating independent (or X)

variables to dependent (or Y) variables.

Past data is used to estimate relationships between costs and activities.

Dependent variables are caused by the

independent variables.

Dependent variables are caused by the

independent variables.

Independent variables are the cost drivers that are correlated with the dependent variables.

Independent variables are the cost drivers that are correlated with the dependent variables.


Caution: Before doing the analysis, take time

to determine if a logical relationship

between the variables exists.

Caution: Before doing the analysis, take time

to determine if a logical relationship

between the variables exists.


The simple cost model is actually a regression model:

TC = F + VX

The simple cost model is actually a regression model:

TC = F + VX

This model will only be useful within a relevant range of

activity.

This model will only be useful within a relevant range of

activity.



A set of data can be regressed using several techniques:

•Manual computations•SPSS or SAS Statistical Software

•Excel or other spreadsheet

A set of data can be regressed using several techniques:

•Manual computations•SPSS or SAS Statistical Software

•Excel or other spreadsheet

The result of the regression process is a

regression model:

TC = F + VX

The result of the regression process is a

regression model:

TC = F + VX

Each regression model has an R-square (R2)

measure of how good the model is.

Range of R2 = 0 to 1.0

Each regression model has an R-square (R2)

measure of how good the model is.

Range of R2 = 0 to 1.0


Simple Regression AnalysisExample

Fasco wants to know its average

fixed cost and variable cost per

unit.

Using the data to the right, let’s see

how to do a regression using

Excel.

Fasco wants to know its average

fixed cost and variable cost per

unit.

Using the data to the right, let’s see

how to do a regression using

Excel.


Simple Regression AnalysisExample

You will need three pieces of information from your

regression analysis:

1. Estimated Variable Cost per Unit (line slope)

2. Estimated Fixed Costs (line intercept)

3. Goodness of fit, or R2

You will need three pieces of information from your

regression analysis:

1. Estimated Variable Cost per Unit (line slope)

2. Estimated Fixed Costs (line intercept)

3. Goodness of fit, or R2

To get these three pieces of information we will need to use THREE

different excel functions.

LINEST, INTERCEPT, & RSQ

To get these three pieces of information we will need to use THREE

different excel functions.

LINEST, INTERCEPT, & RSQ


Simple Regression Using Excel 2000

First, open the excel file

with your data and click on

“Insert” and “Function”

First, open the excel file

with your data and click on

“Insert” and “Function”



When the function box opens, click

on “Statistical”,

then on “LINEST”

When the function box opens, click

on “Statistical”,

then on “LINEST”



1. Enter the cell range for the cost amounts in the “Known_y’s” box.

2. Enter the cell range for the quantity amounts in the “Known_x’s” box.

1. Enter the cell range for the cost amounts in the “Known_y’s” box.

2. Enter the cell range for the quantity amounts in the “Known_x’s” box.

By clicking on the buttons to the left, you can highlight the desired cells

directly from the spreadsheet.

By clicking on the buttons to the left, you can highlight the desired cells

directly from the spreadsheet.



The Slope, or estimated variable cost per unit, is identified here. Click OK to put this value on your

spreadsheet.

The Slope, or estimated variable cost per unit, is identified here. Click OK to put this value on your

spreadsheet.



Repeat the procedure

using “Intercept”, to estimate fixed cost.

Repeat the procedure

using “Intercept”, to estimate fixed cost.



As previously, enter the

appropriate cell ranges in their

appropriate places.



appropriate places.

The estimated fixed cost is identified here.

The estimated fixed cost is identified here.



Finally, determine the “goodness of fit”, or R2, by

using the RSQ function.

Finally, determine the “goodness of fit”, or R2, by

using the RSQ function.





appropriate places.



appropriate places.

The estimated R2 for your estimated cost function is identified here.

The estimated R2 for your estimated cost function is identified here.


Let’s put our knowledge of cost

behavior to work by preparing a

contribution format income statement.


The Contribution Format

Total Unit

Sales Revenue 100,000$ 50$

Less: Variable costs 60,000 30

Contribution margin 40,000$ 20$

Less: Fixed costs 30,000

Net operating income 10,000$

The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs

and provides for income.


The Contribution Format

Used primarily forexternal reporting.

Used primarily bymanagement.


End of Chapter 5

cost behaviour lecture 3

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