Cost Behavior: Analysis and Use - · PDF file4 Types of Cost Behavior Patterns Recall the...

1

Cost Behavior:Analysis and Use

M. En C. Eduardo Bustos Farías

3

Assumptions in Cost-BehaviorEstimation

Changes in total costs can be explained bychanges in the level of a single activity.

Cost behavior can adequately beapproximated by a linear function of theactivity level within the relevant range.

4

Types of Cost Behavior Patterns

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

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.

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.

5

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 drivenMiles driven

Labor hoursLabor hours

Machine hours

Machine hours

6

True Variable Cost Example

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

Tota

l Lon

g D

ista

nce

Tele

phon

e B

ill

Minutes Talked

7

Variable Cost Per Unit Example

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

Minutes Talked

Per M

inut

eTe

leph

one

Cha

rge

8

Step-Variable Costs

Activity

Cos

t

Total cost remainsconstant within anarrow range of

activity.

Total cost remainsconstant within anarrow range of

activity.

9

Step-Variable Costs

Activity

Cos

t

Total cost increases to anew higher cost for the next higher range of

activity.

Total cost increases to anew higher cost for the next higher range of

activity.

10

The Linearity Assumption and the Relevant Range

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.

Tota

l Cos

t

Economist’sCurvilinear Cost

Function

Accountant’s Straight-Line Approximation (constant

unit variable cost)

Activity

11

Total Fixed Cost Example

Number of Local Calls

Mon

thly

Bas

ic

Tele

phon

e B

ill

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

you make more local calls.

12

Fixed Cost Per Unit Example

Number of Local Calls

Mon

thly

Bas

ic T

elep

hone

B

ill p

er L

ocal

Cal

l

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

13

Cost BehaviorExamples of normally variable costsExamples of normally variable costs

Service OrganizationsSupplies and travel

Service OrganizationsSupplies and travel

MerchandisersCost of Goods SoldMerchandisers

Cost of Goods Sold

Merchandisers and Manufacturers

Sales commissions and shipping costs

Merchandisers and Manufacturers

Sales commissions and shipping costs

ManufacturersDirect Material, Direct Labor, and Variable

Manufacturing Overhead

ManufacturersDirect Material, Direct Labor, and Variable

Manufacturing Overhead

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

14

Types of Fixed Costs

ExamplesAdvertising and Research and Development

ExamplesAdvertising and Research and Development

ExamplesDepreciation on Buildings and

Equipment

ExamplesDepreciation on Buildings and

Equipment

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.

comprometidos

15

Fixed Costs and Relevant Range

Continue

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.

16


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

0

30

60

90

RelevantRange

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.R

ent C

ost i

n Th

ousa

nds

of D

olla

rs

17


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.

18

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.

19

Mixed Costs

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.

Fixed MonthlyUtility Charge

Variable Cost per KW

Activity (Kilowatt Hours)

Tota

l Util

ity C

ost

X

Y

Total mixed cost

20

Mixed Costs

Fixed MonthlyUtility Charge

Variable Cost per KW

Activity (Kilowatt Hours)

Tota

l Util

ity C

ost

X

Y

The total mixed cost line can be expressed as an equation: Y = a + bX

Where: Y = the total mixed costa = the total fixed cost (the

vertical intercept of the line)b = the variable cost per unit of

activity (the slope of the line)X = the level of activity

The total mixed cost line can be expressed as an equation: Y = a + bX

Where: Y = the total mixed costa = the total fixed cost (the

vertical intercept of the line)b = the variable cost per unit of

activity (the slope of the line)X = the level of activity

Total mixed cost Y = a + bX

21

The Analysis of Mixed Costs

Engineering Approach

Account Analysis

High-Low Method

Least-Square Regression Method

Scattergraph Plotdispersión

22

Engineering Estimates

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.

23

Account Analysis

Each account is classified as eithervariable or fixed based on the analyst’sknowledge of how the account behaves.

Each account is classified as eithervariable or fixed based on the analyst’sknowledge of how the account behaves.

24

Account Analysis Example

The cost analyst uses experience andjudgment to separate total costs into

fixed and variable.Avisha & Co. sells software programs.

Total sales = $390,000The company sold 1,000 programs.

25


Cost of goods sold = $130,000Manager’s salary = $60,000Secretary’s salary = $29,000Commissions = 12% of salesWhat is the total fixed cost?

$60,000 + $29,000 = $89,000What is the fixed cost per unit sold?

26


$89,000 ÷ 1,000 = $89.00What is the variable cost per unit sold?

Cost of goods sold: $130,000Commissions: $390,000 × .12 = $46,800($130,000 + $46,800) ÷ 1,000 = $176.80

27

The Scattergraph Methoddispersión

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

*

Tota

l Cos

t in

1,00

0’s

of D

olla

rs

10

20

0

***

**

* **

*

Activity, 1,000’s of Units Produced

X

Y

28

0 1 2 3 4

*

Tota

l Cos

t in

1,00

0’s

of D

olla

rs

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.

Al tanteo

29

0 1 2 3 4

*

Tota

l Cos

t in

1,00

0’s

of D

olla

rs

10

20

0

***

**

* **

*


X

Y

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

Slope = Change in cost ÷ Change in unitsThe 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.

30

The High-Low Method

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 thenexpress the costs in equation form Y = a + bX.

Units CostHigh activity level 8,000 9,800$ Low activity level 5,000 7,400 Change 3,000 2,400$

31

The High-Low Method


Change in costChange in units

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

32

The High-Low Method


Variable cost per unit = $2,400 ÷ 3,000 units = $0.80 per unit

33

The High-Low Method


Variable cost = $2,400 ÷ 3,000 units = $0.80 per unitFixed cost = Total cost – Total variable costFixed cost = $9,800 – ($0.80 per unit × 8,000 units)Fixed cost = $9,800 – $6,400 = $3,400

34

The High-Low Method


Variable cost = $2,400 ÷ 3,000 units = $0.80 per unitFixed cost = Total cost – Total variable costFixed cost = $9,800 – ($0.80 per unit × 8,000 units)Fixed cost = $9,800 – $6,400 = $3,400Total cost = Fixed cost + Variable cost (Y = a + bX)Y = $3,400 + $0.80X

35

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 thevariable portion of sales salaries and commission?a. $0.08 per unitb. $0.10 per unit c. $0.12 per unitd. $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 thevariable 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$

36

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

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

Total cost = Total fixed cost + Total variable cost

$14,000 = Total fixed cost +($0.10 × 120,000 units)

Total fixed cost = $14,000 - $12,000

Total fixed cost = $2,000

40

Least-Squares Regression Method

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 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.

41

Least-Squares Regression Method

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 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

42

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.

43


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.

44


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

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

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

46

Simple Regression AnalysisExample

Month Total Costs Units (Meals)January $6,720 1,280February 7,260 1,810March 7,270 1,620April 11,060 2,830May 12,580 3,630June 8,660 2,610July 8,580 2,460August 9,550 2,640September 13,050 3,620October 11,060 2,840November 7,320 1,820December 7,370 1,650January 6,790 1,260February 7,480 1,850March 6,990 1,710April 11,400 2,940

Fasco wants to know it’s 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 it’s average

fixed cost and variable cost per

unit.

Using the data to the right, let’s see

how to do a regression using

Excel.

47

Simple Regression AnalysisExample

Month Total Costs Units (Meals)January $6,720 1,280February 7,260 1,810March 7,270 1,620April 11,060 2,830May 12,580 3,630June 8,660 2,610July 8,580 2,460August 9,550 2,640September 13,050 3,620October 11,060 2,840November 7,320 1,820December 7,370 1,650January 6,790 1,260February 7,480 1,850March 6,990 1,710April 11,400 2,940

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

48

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”

49


When the function box opens, click

on“Statistical”,

then on “LINEST”

When the function box opens, click

on“Statistical”,

then on “LINEST”

50


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.

51


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.

52


Repeat the procedure

using “Intercept”, to estimate fixed cost.

Repeat the procedure

using “Intercept”, to estimate fixed cost.

53


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.

54


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.

55




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.

69

Let’s put our knowledge of cost

behavior to work by preparing a

contribution format income statement.

70

PELICULA

71

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 cost behavior. Contribution margin covers fixed costs

and provides for income.

72

The Contribution Format

Comparison of the Contribution Income Statement with the Traditional Income Statement

Traditional Approach Contribution Approach (costs organized by function) (costs organized by behavior)

Sales 100,000$ Sales 100,000$ Less cost of goods sold 70,000 Less variable expenses 60,000 Gross margin 30,000$ Contribution margin 40,000$ Less operating expenses 20,000 Less fixed expenses 30,000 Net operating income 10,000$ Net operating income 10,000$

Used primarily forexternal reporting.

Used primarily bymanagement.

73

PROBLEM

An analysis of past janitorial costs indicates that janitorial cost is an average of $0.80 per machine-hour at an activity level of 40,000 machine-hours and $1.00 per machine-hour at an activity level of 32,000 machine-hours. Assuming that this activity is within the relevant range, what is the total expected janitorial cost if the activity level is 37,000 machine-hours?

74

Solution

Using the data provided above, janitorial costs are fixed (rather than variable or mixed) in nature; that is, they total $32,000 at both 40,000 and 32,000 machine hours.

Accordingly, janitorial costs would be expected to be $32,000 at 37,000 machine hours (or at any other level of machine hours within the relevant range).

75

PROBLEM

Shipping expense is $10,000 for 1,000 pounds shipped and $13,750 for 1,500 pounds shipped. Assuming that this activity is within the relevant range, if the company ships 1,250 pounds, what is its expected shipping expense?

76

Solution

Using the high-low method, the company’s variable cost per unit for shipping costs can be calculated as follows:

Variable cost per unit = Change in costs ÷ Change in unitsVariable cost per unit = ($13,750 – $10,000) ÷ (1,500 – 1,000)Variable cost per unit = $3,750 ÷ 500 = $7.50 per pound

shipped. Then, the company’s fixed shipping cost can be calculated as follows:

Total cost = Total variable cost + Total fixed cost orTotal fixed cost = Total cost – Total variable costTotal fixed cost = $10,000 – (1,000 pounds x $7.50 per pound) Total fixed cost = $10,000 – $7,500 = $2,500

Finally, if the company ships 1,250 pounds, its total shipping cost can be estimated as follows:

Total cost = Total variable cost + Total fixed costTotal cost = (1,250 pounds x $7.50 per pound) + $2,500Total cost = $9,375 + $2,500 = $11,875

77

PROBLEM

The following information has been provided by the Batavia Office Supply Store for the first quarter of the year:

What is the contribution margin of Batavia Office Supply Store for the first quarter?

78

Solution

79

PROBLEM

Lewis Company has provided the following data for the second quarter of the most recent year:

Assume that direct labor is a variable cost and that there were no beginning or ending inventories. What was the total contribution margin of Lewis Company for the second quarter?

80

Solution

Cost Behavior: Analysis and Use - · PDF file4 Types of Cost Behavior Patterns Recall the...

Documents

Transcript of Cost Behavior: Analysis and Use - · PDF file4 Types of Cost Behavior Patterns Recall the...