cost behavior: analysis and use mar 3, 2004 chapter 5

Cost Behavior:Analysis and Use

Mar 3, 2004

Chapter 5

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

Cost Behavior

How a cost will react or change as the level of business activity changes

Cost can be either variable, fixed or mixed

Understanding cost behavior allows managers to predict what costs will be at various business activity levels

This information is essential for managing your business efficiently


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. i.e., hiring an

additional supervisor or maintenance worker.

Total cost increases to a new higher cost for the

next higher range of activity. i.e., hiring an

additional supervisor or maintenance worker.


Relevant Range

A range of business activity within which the assumptions made about cost behavior are valid.

Variable costs on a per unit basis remain the same within the relevant range, and in total vary directly with the level of activity

Fixed costs in total remain fixed within the relevant range, but will change on a per unit basis as the level of activity changes


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 - Examples

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 salaries,Depreciation, Advertising

Merchandisers, manufacturers, and service organizations

Real estate taxes, Insurance, Sales salaries,Depreciation, Advertising


ExamplesAdvertising and Research and Development

ExamplesAdvertising and Research and Development

ExamplesDepreciation on Buildings and

Equipment, Property Taxes

ExamplesDepreciation on Buildings and

Equipment, Property Taxes

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


Separating Variable and Fixed Costs

There are a number of methods for separating variable and fixed costs for a mixed cost total

Scattergraph

High-Low Method

Least Squares Regression


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.


Calculating the Total Cost

Y = a + bX“a” is the intersection of the slope line and the y axis (fixed cost)To find “b”, find a data point on the slope line, and determine the level of activity (x axis) and total cost (y axis)Solve for b using the above equationSee example on page 204-05Disadvantages: Outliers, accuracy of line drawn through the dots


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(Use example on page 204)


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

(or do the same calculation with the low activity level)


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


Mixed Cost Equation

If variable cost per unit is $.10 and fixed cost is $2,000 then what is the Total cost equation?

Y = $2,000 + $.10(X)


Hi-Lo Disadvantages

Utilizes only two data points out of the entire data base; not enough for accurate results in cost analysis

Outliers could cause a major discrepancy if they are selected as a high or low


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


Total Cost Formula using Least Squares Method

Use the data provided by the least squares for points a and b

See example on page 210

Result of least squares method:

Y = $3,431 + $0.759(X)


Least Squares Disadvantages

Outliers can also cause least squares to come up with a wrong answer.

Always use least squares on conjunction with scatter grade to identify, and eliminate if necessary, outliers that may erroneously impact the results.


Comparison of Methods

Scatter Graph

Y = $3,300 + $0.79(X)

High Low

Y = $3,400 + $0.80(X)

Least Squares

Y = $3,431 + $0.759(X)

Which one would you choose? Why?


Let’s put our knowledge of cost

behavior to work by preparing a

contribution format income statement.


Contribution Margin Approach

Provides the internal manager with an income statement geared directly to cost behavior; can predict future resultsContribution margin is what is left after you subtract variable costs from salesThis allows you to determine if you are selling enough product to cover your fixed costs and, therefore, earn a profitProvides ability to analyze profitability by product line, operation, etc.


The Contribution Format(Requires Segregation of variable and fixed cost)

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. Not GAAP


End of Chapter 5

cost behavior: analysis and use mar 3, 2004 chapter 5

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