managerial accounting garrison noreen brewer chapter 05

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

11th EditionChapter 5


Chapter Five

Cost Behavior:Analysis and Use


Summary of Variable and Fixed Cost BehaviorCost 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.

Total fixed cost remains thesame even when the activity Fixed cost per unit goes

Fixed level changes within the down as activity level goes up. relevant range.

Recall the summary of our cost behavior Recall the summary of our cost behavior discussion from an earlier chapter.discussion from an earlier chapter.

Types of Cost Behavior Patterns


The Activity Base

A measure of what causes the

incurrence of a variable cost

UnitsUnitsproducedproduced

Miles driven

Labor hours

Machine hours


Minutes Talked

Tota

l Lon

g D

ista

nce

Tele

phon

e B

ill

True Variable Cost Example

A 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.


Minutes Talked

Per M

inut

eTe

leph

one

Cha

rge

Variable Cost Per Unit Example

A variable cost remains constant if expressed on a per unit basis. The cost per minute talked is constant. For example, 10 cents per minute.


Extent of Variable Costs

The proportion of variable costs differs across organizations. For example . . .

A public utility withA public utility withlarge investments inlarge investments inequipment will tendequipment will tend

to have to have fewerfewervariable costs.variable costs.

A manufacturing companyA manufacturing companywill often have will often have manymany

variable costs.variable costs.

A merchandising companyA merchandising companyusually will have a usually will have a highhigh

proportionproportion of variable costs of variable costslike cost of sales.like cost of sales.

A service companyA service companywill normally have a will normally have a highhigh

proportionproportion of variable costs. of variable costs.


Examples of Variable Costs

1. 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.


Volume

Cos

t

True Variable Cost

Direct 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.


Step-Variable Costs

A 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 coststep-variable cost.

Volume

Cos

t


Step-Variable Costs

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

maintenance workers employed.

Volume

Cos

t


Step-Variable Costs

Only fairly wide changes in the activity level will cause a change in the number of maintenance

workers employed

Volume

Cos

t


RelevantRange

A straight line closely

approximates a curvilinear

variable cost line within the

relevant range.

Activity

Tota

l Cos

t

Economist’sCurvilinear Cost

Function

The Linearity Assumption and the Relevant Range

Accountant’s Straight-Line Approximation (constant

unit variable cost)







Let’s look at fixed cost behavior on the next Let’s look at fixed cost behavior on the next screens.screens.



Number of Local Calls

Mon

thly

Bas

ic

Tele

phon

e B

ill

Total Fixed Cost Example

A 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.


Number of Local Calls

Mon

thly

Bas

ic T

elep

hone

B

ill p

er L

ocal

Cal

l

Fixed Cost Per Unit Example

Average fixed costs per unit decrease as the activity level increases. The fixed cost per local call

decreases as more local calls are made.


ExamplesAdvertising and Research and Development

ExamplesDepreciation on Equipment and

Real Estate Taxes

Types of Fixed Costs

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

CommittedLong-term, cannot be significantly reduced

in the short term.


The Trend Toward Fixed Costs

The trend in many industries is toward greater fixed costs relative to variable costs.

As machines take overAs machines take overmany mundane tasksmany mundane taskspreviously performedpreviously performed

by humans, by humans, ““knowledge workersknowledge workers””

are demanded forare demanded fortheir minds rathertheir minds ratherthan their musclesthan their muscles

Knowledge workersKnowledge workerstend to be salaried,tend to be salaried,highly-trained andhighly-trained and

difficult to replace. Thedifficult to replace. Thecost to compensatecost to compensate

these valued employeesthese valued employeesis is relatively fixedrelatively fixed

rather than variable.rather than variable.


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.


Ren

t Cos

t in

Thou

sand

s of

Dol

lars

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

0

30

60

Fixed Costs and Relevant Range

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.



Example:Example: Office space is 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.

The relevant range of activity for a fixed cost is the range of activity over which the graph of

the cost is flat.


How does this How does this type of fixed cost type of fixed cost differ from a step-differ from a step-

variable cost?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?

1. Fixed costs per unit vary with the level of activity.

2. Variable costs per unit are constant within the relevant range.

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

4. Total variable costs are constant within the relevant range.


Fixed MonthlyUtility Charge

Variable Cost per KW

Activity (Kilowatt Hours)

Tota

l Util

ity C

ost

X

Y

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

Mixed Costs

Total mixed cost


Fixed MonthlyUtility Charge

Variable Cost per KW

Activity (Kilowatt Hours)

Tota

l Util

ity C

ost

X

Y

Mixed Costs

Total mixed cost


Mixed Costs Example

If your fixed monthly utility charge is $40, your If your fixed monthly utility charge is $40, your variable cost is $0.03 per kilowatt hour, and your variable cost is $0.03 per kilowatt hour, and your

monthly activity level is 2,000 kilowatt hours, monthly activity level is 2,000 kilowatt hours, what is the amount of your utility bill?what is the amount of your utility bill?

Y = a + bXY = $40 + ($0.03 × 2,000)Y = $100


Analysis of Mixed Costs

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

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.

Account Analysis and the Engineering ApproachAccount Analysis and the Engineering Approach


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

0 1 2 3 4

*

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ance

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000’

s of

Dol

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10

20

0

***

**

* **

*

Patient-days in 1,000’s

X

Y

The Scattergraph Method



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

0 1 2 3 4

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10

20

0

***

**

* **

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X

Y



Use 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.

Intercept = Fixed cost: $10,000

0 1 2 3 4

*

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10

20

0

***

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* **

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X

Y

Patient days = 800Patient days = 800

Total maintenance cost = $11,000Total maintenance cost = $11,000



Make 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.

Variable cost per unit = $1,000 800

= $1.25/patient-day$1.25/patient-day

Y = $10,000 + $1.25XY = $10,000 + $1.25X

Total maintenance at 800 patients 11,000$ Less: Fixed cost 10,000 Estimated total variable cost for 800 patients 1,000$

Total maintenance costTotal maintenance cost Number of patient daysNumber of patient days


The High-Low Method

Assume the following hours of maintenance work and the total maintenance costs for six months.


The High-Low Method

The The variable cost variable cost per hourper hour of of

maintenance is maintenance is equal to the change equal to the change

in cost divided by in cost divided by the change in hours.the change in hours.

= $8.00/hour$8.00/hour$2,400300


The High-Low Method

Total Fixed Cost = Total Cost – Total Variable CostTotal Fixed Cost = Total Cost – Total Variable Cost

Total Fixed Cost = $9,800 – ($8/hour Total Fixed Cost = $9,800 – ($8/hour × 800 hours)× 800 hours)

Total Fixed Cost = $9,800 – $6,400Total Fixed Cost = $9,800 – $6,400

Total Fixed Cost = Total Fixed Cost = $3,400$3,400


The High-Low Method

Y = $3,400 + $8.00Y = $3,400 + $8.00XXThe Cost Equation for Maintenance


Quick Check

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 unitb. $0.10 per unit c. $0.12 per unitd. $0.125 per unit


Quick Check

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 unitb. $0.10 per unit c. $0.12 per unitd. $0.125 per unit $4,000 ÷ 40,000 units

= $0.10 per unit

Units CostHigh level 120,000 14,000$ Low level 80,000 10,000 Change 40,000 4,000$


Quick Check

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. $ 2,000b. $ 4,000 c. $10,000d. $12,000


Least-Squares Regression Method

A method used to analyze mixed costs if a scattergraph plot reveals an approximately linear

relationship between the X and Y variables.

This method uses This method uses allall of the of thedata points to estimatedata points to estimatethe fixed and variablethe fixed and variablecost components of acost components of a

mixed cost.mixed cost.The goal of this method isThe goal of this method isto fit a straight line to theto fit a straight line to thedata that data that minimizes theminimizes the

sum of the squared errorssum of the squared errors..



• 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 also provides a statistic,

called the R2, that is a measure of the goodnessof fit of the regression line to the data points.


0 1 2 3 4

Tota

l Cos

t

10

20

0

Activity

****

**

* ***


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

R2 varies from 0% to 100%, andthe higher the percentage the better.

X

Y


Comparing Results From the Three Methods

The 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.


Let’s put our knowledge of cost

behavior to work by preparing a

contribution format income statement.


The Contribution Format

Total UnitSales 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 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.


Uses of the Contribution Format

The 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:

1.1. Cost-volume-profit analysis (Chapter 6).Cost-volume-profit analysis (Chapter 6).

2.2. Budgeting (Chapter 9).Budgeting (Chapter 9).

3.3. Segmented reporting of profit data (Chapter 12).Segmented reporting of profit data (Chapter 12).

4.4. Special decisions such as pricing and make-or-Special decisions such as pricing and make-or-buy analysis (Chapter 13).buy analysis (Chapter 13).


The Contribution Format

Used primarily forUsed primarily forexternal reporting.external reporting.

Used primarily byUsed primarily bymanagement.management.


Appendix 5A

Least-Squares Regression Using Microsoft Excel.


Simple Regression Analysis Example

Matrix, 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, let’s see how to right, let’s see how to do a regression using do a regression using

Microsoft Excel.Microsoft Excel.


Simple Regression Using Excel

You will need three pieces of You will need three pieces of information from your information from your regression analysis:regression analysis:

1.1. Estimated Variable Cost per Estimated Variable Cost per Unit (line slope)Unit (line slope)

2.2. Estimated Fixed Costs (line Estimated Fixed Costs (line intercept)intercept)

3.3. Goodness of fit, or RGoodness of fit, or R22

To get these three pieces To get these three pieces information we will need to information we will need to useuse three three different Excel different Excel functions.functions.

LINEST, INTERCEPT, & RSQLINEST, INTERCEPT, & RSQ



Place 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 . . .”



Scroll down to the Scroll down to the ““StatisticalStatistical”, ”,

functions. Now functions. Now scroll down the scroll down the

statistical statistical functions until you functions until you

highlight highlight ““LINESTLINEST””



1. In the Known_y’s box enter C4:C19 for the range.

2. In the Known_x’s box enter D4:D19 for the range.





Here is the Here is the estimate of the estimate of the

slope of the line.slope of the line.



With 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 Select Statistical Statistical and and

scroll down to scroll down to highlight the highlight the

INTERCEPTINTERCEPT function. function.





Here is the Here is the estimate of the estimate of the

fixed costs.fixed costs.



Finally, we will Finally, we will determine the determine the ““goodness of goodness of fitfit”, or ”, or RR22, by , by

using the using the RSQRSQ function.function.





Here is the Here is the estimate of estimate of RR22..


End of Chapter 5

managerial accounting garrison noreen brewer chapter 05

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