Cost Estimation

Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

11Cost Estimation

11-2

Costprediction

Using results ofcost estimation

to forecast alevel of cost at

a particularactivity. Focusis on the future.

Existingrelationship

betweencost andactivity.

Process ofestimating relationship

between costsand cost driveractivities that

cause those costs.

Costestimation

Costbehavior

Introduction

11-3

Learning Objective 1

11-4

Management needsto know the costs that

are likely to beincurred for each

alternative.

How muchwill costs increaseif sales increase

10 percent?

What will mycosts be if I introducethe new model in a

foreign market?

Reasons for Estimating Costs

11-5

Increasedcompany

value

More accurate cost estimates

Better informed decisions about:• efficient business processes• alternative courses of action• performance standards• financial forecasts


11-6

Relationship between activities and costs

Relationship between activities and costs

ActivitiesActivities

CostsCosts

3. To reduce these

1. First identify this

We estimate costs to:

manage costsmake decisions

plan and set standards.

We estimate costs to:

manage costsmake decisions

plan and set standards.

2. Then manage these

Exh.11-1


11-7

Summary of variable and fixed cost behavior

Cost In total Per unit

Variable Total variable cost changes Variable cost per unit remainsas activity level changes. the same over wide ranges

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.

Total Costs = Fixed costs + Variable costsTC = F + VXV is the variable cost per cost driver unit (cost driver rate).X is the number of cost driver units.

Basic Cost Behavior Patterns

11-8


11-9

Intercept = Fixed Cost

Intercept = Fixed Cost

Slope = Cost Driver Rate

Slope = Cost Driver Rate

$.16

One Cost Driver and Fixed/Variable Cost Behavior

Exh.11-2

11-10

Multiple Cost Drivers and Complex Cost Behavior

In cases of complex cost behavior and

multiple cost drivers, the cost-benefit test

should be considered when developing a

cost estimation model.

In cases of complex cost behavior and

multiple cost drivers, the cost-benefit test

should be considered when developing a

cost estimation model.

11-11

Step Cost•A cost that increases in steps as the amount of the cost driver volume increases.

•Also called a “semifixed cost”

Step Cost•A cost that increases in steps as the amount of the cost driver volume increases.

•Also called a “semifixed cost”

Total cost remains unchanged over a narrow

range of activity. As activity increases to the

next range, total cost steps up to the next level.

Total cost remains unchanged over a narrow

range of activity. As activity increases to the

next range, total cost steps up to the next level.

Co

st

Activity

Step Costs

11-12

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.

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.

Continue

Step Costs

11-13

Rent Cost

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

$30,000

$60,000

$90,000

Total cost remains unchanged for a range of activity, then jumps to a

higher cost for the next range of activity.

Step Costs

11-14

The activity limits within which acost projection may be valid is the relevant range of activity.

Unit variable costsremain unchanged.

Total fixed costsremain unchanged.

Relevant Range of Activity

11-15

Mixed Costs

A mixed cost is one that has both a

fixed and a variable component.

For example, a cellular phone plan that charges $40 for

the first 600 minutes and $0.10

per minute thereafter.

11-16

CurvilinearCost Function

Relevant Range

Activity

To

tal

Co

st

A nonlinear cost pattern (e.g. changes in unit variable cost)

may often approximate a straight line (when

the unit variable cost is constant) within the

relevant range.

Nonlinear Costs

11-17

Engineering method

Account analysis

Scattergraph and high-low estimates

Statistical methods (regression analysis)

Methods of Estimating Costs

11-18

Simply plotting past cost behavior on a graph may be a helpful first step in analyzing costs

regardless of the estimation method ultimately chosen.

It can reveal outlier data points and suggest possible relationships between the variables.

The Scattergraph

11-19

****

**

**

*

*

0 1 2 3 4

$10,000

$20,000

0

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

Activity: Units produced (‘000)

Total cost

The ScattergraphThe Scattergraph

11-20

Draw a line through the plotted data points so that about an equal amount of points falls above and below the line.

0 1 2 3 40

****

**

**

*

*


Total Cost

The Scattergraph

Estimated fixed cost = $10,000

The Scattergraph

$20,000

$10,000

11-21

0 1 2 3 40

****

**

**

*

*

The slope of this line is the unit variable cost. (Slope is the change in total cost for a one-unit change in activity).


Total Cost

The Scattergraph

Vertical distance

is the change in cost.

Horizontal distance is the change in activity.

The Scattergraph

$20,000

$10,000

11-22

The high-low method uses two data points to estimate the general cost equation TC = F VX

TC = the estimated total cost

F = a fixed quantity that represents the value of Y when X = zero

V = the slope of the line(equivalent to the unit variable cost)

X = units of the cost driver activity

The High-Low Method

11-23

0 1 2 3 4

$10,000

$20,000

0

****

**

**

*

*

The high-low method uses two data points to estimate the general

cost equation TC = F + VX

The two points should be representative ofthe cost and activity relationship over the range

of activity for which the estimation is made.


Total Cost

The High-Low Method

11-24

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 TC = F + VX.

Units Cost

High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$

The High-Low Method

11-25

Unit variable cost = $3,600 ÷ 4,000 units = $.90 per unit Fixed cost = Total cost – Total variable cost

Fixed cost = $9,700 – ($.90 per unit × 9,000 units)

Fixed cost = $9,700 – $8,100 = $1,600 Total cost = Fixed cost + Variable cost (TC = F + VX) TC = $1,600 + $0.90X

Units Cost

High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$

The High-Low MethodThe High-Low Method

11-26


11-27

Regression Analysis

A statistical method used to create an equation relating dependent (or Y) variables

to independent (or X) variables.

Data from the past are used to estimate relationships between costs and activities.

A statistical method used to create an equation relating dependent (or Y) variables

to independent (or X) variables.

Data from the past are used to estimate relationships between costs and activities.

Independent variables are the cost drivers that

drive the variation in dependent variables.

Independent variables are the cost drivers that

drive the variation in dependent variables.

Before doing the analysis, take time to determine if a logical

relationship between the variables exists.

Before doing the analysis, take time to determine if a logical

relationship between the variables exists.

11-28

The objective of the regression method is still a linear equation to estimate costs TC = F + VX

TC = value of the dependent variable(estimated total cost)

F = a fixed quantity, the intercept, that represents the value of TC when X = 0

V = the unit variable cost, the coefficient of the independent variable measuring the increase in TC for each unit increase in X

X = value of the independent variable, the cost driver

Regression AnalysisRegression Analysis

11-29

A statistical procedure that finds the unique line through data points that minimizes the sum of

squared distances from the data points to the line.

50 100 150 200

400

350

300

250

200

De

pen

de

nt

Va

ria

ble

Independent Variable


11-30

50 100 150 200

400

350

300

250

200

De

pen

de

nt

Va

ria

ble


V = the slope of the regression line or the coefficient of the independent variable. Here it represents the increase in TC for each unit increase in X.

F = a fixed quantity, the intercept


11-31

Outlier

proper line, excluding the outlierimproper line, influenced by outlier

Outliers may be discarded toobtain a regression that is more

representative of the data. 50 100 150 200

400

350

300

250

200

De

pen

de

nt

Va

ria

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11-32

The correlation coefficient (r) is a measure of the linear relationship between variables such as cost and activity.

0 1 2 3 4

Total Cost

$10,000

$20,000

0

***

**

****


*

The correlation coefficient is highly positive (close to 1.0) if the data points

are close to the regression line.

Regression Analysis

11-33

0 1 2 3 4

Total Cost

$10,000

$20,000

0


*

*

*

*

*

*

**

* *

The correlation coefficient is near zero if little or no relationshipexists between the variables.


Regression Analysis

11-34

0 1 2 3 4

Total Cost

$10,000

$20,000

0


*

*

*

** *

***

*This relationship has a negative

correlation coefficient, approachinga maximum value of –1.0


Regression Analysis

11-35

50 100 150 200

400

350

300

250

200

Regression withhigh R2 (close to 1.0)

De

pen

de

nt

Va

ria

ble


R2, the coefficient of determination, is a measureof the goodness of fit. R2 tells us the amount

of the variation of the dependent variable thatis explained by the independent variable.


11-36

Regression withlow R2 (close to 0)

50 100 150 200

400

350

300

250

200

De

pen

de

nt

Va

ria

ble


The coefficient ofdetermination, R2,is the correlation

coefficient squared.


11-37

Includes all data points, resulting in more thorough study of the relationship between the variables.

Generates statistical information that describes the relationship between variables.

Permits the use of more than one cost driver activity to explain cost behavior.

Includes all data points, resulting in more thorough study of the relationship between the variables.

Generates statistical information that describes the relationship between variables.

Permits the use of more than one cost driver activity to explain cost behavior.

Regression Analysis

11-38

Statistics courses deal with detailed regression computations using computer spreadsheet software.

Accountants and managers must be able to interpret and use regression estimates.

Let’s look at an example using Excel.

Statistics courses deal with detailed regression computations using computer spreadsheet software.

Accountants and managers must be able to interpret and use regression estimates.

Let’s look at an example using Excel.

Regression Analysis

11-39

Simple Regression Example

Eagle Enterprises wants to analyze the relationship between units

produced and total costs.

Using the data to the right, let’s see

how to do a regression using

Excel.

Eagle Enterprises wants to analyze the relationship between units

produced and total costs.

Using the data to the right, let’s see

how to do a regression using

Excel.

11-40

Simple Regression Using Excel

We will obtain three piecesof information from ourregression analysis:

1. Estimated Variable Cost per Unit (line slope)

2. Estimated Fixed Costs (line intercept)

3. Goodness of fit, or R2

We will obtain three piecesof information from ourregression 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

find the following Excel

functions: LINEST,

INTERCEPT and RSQ.

To get these three pieces of

information we will need to

find the following Excel

functions: LINEST,

INTERCEPT and RSQ.

11-41

After opening Excel and

entering your data, click on “Insert” and “Function”

After opening Excel and

entering your data, click on “Insert” and “Function”


11-42

When the function box opens, click

on “Statistical”,

then on “LINEST”

When the function box opens, click

on “Statistical”,

then on “LINEST”


11-43

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.


11-44

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.


11-45

Repeat the procedure

using “Intercept”, to estimate fixed cost.

Repeat the procedure

using “Intercept”, to estimate fixed cost.


11-46

As previously, enter the

appropriate cell ranges in their

appropriate places.



appropriate places.

The estimated fixed cost per unit is identified here.

The estimated fixed cost per unit is identified here.


11-47

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.


11-48



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.


11-49

Simple RegressionExample Summary

The objective of the regression method is a linear equation to estimate costs TC = F + VX

We found the following linear equation for Eagle:TC = $2,618.72 + $2.768 per unit

The high value for R2 tells us that approximately93.26 percent of the variation in total cost

is explained by the variation in the number ofunits produced.

11-50

For example, demand for a product may be affected by factors such as inflation, interest rates and

competitors’ prices.

For example, demand for a product may be affected by factors such as inflation, interest rates and

competitors’ prices.

Multiple Regression is a regression that has more than one independent (X) variable.

Can be very useful in situations where the dependent variable is impacted by several

different independent variables.

Can be very useful in situations where the dependent variable is impacted by several

different independent variables.

Multiple Regression Analysis

11-51

Terms in the equation have the samemeaning as in a simple regression.

Here there are two or more independentvariables instead of only one.

TC = F + V1X1 + V2X2

Multiple Regression Analysis

Each additional independent variable increases the proportion of explained variation (R2)

which is then adjusted for the number of

independent variables.

11-52

A logical relationship must

be established between

the variables. Entering data into the

analysis that have no

logical relationship will

result in meaningless

estimates.

Regression Analysis

Let me give you somepointers on

regression analysis.

11-53

Data points that vary significantly from the regression line (outliers) draw the regression line away from the majority of data points. The least squares

procedure minimizes the sum of squares of the distances from the data points to the line.

Regression Analysis



11-54

The intercept term should be used with caution to estimate fixed cost. The intercept is likely

to be outside the relevant range of observations as it occurs at an activity level of zero.

Regression Analysis



11-55

A regression equation may be a poor predictor of future costs if . . . . Cost-activity

relationships have changed.

Costs themselves have changed independently of changes in activity.

Regression Analysis



11-56

Attempting to fit a linear equation to nonlinear data

Failing to exclude outliers

Including variables that have apparent but spurious relationships

Regression Analysis – Utilization Problems

Regression results are questionable when:

11-57

Missing Data

Mismatched Time Periods

Allocated Costs

Inflation

Regression Analysis Data Problems

11-58


11-59

Objective: Relate costs and activity inthe form of the general cost equation:

TC = F + VX

Account Analysis

Cost estimates are based on areview of each activity account making up

the total cost being analyzed.

11-60

Identify cost drivers and the costs associated with each driver.

Sum the fixed costs (facility costs).

Sum the variable costs for each cost driver activity.

Divide the total variable costs for each cost driver activity by the total number of cost driver units to obtain variable cost per unit.

Divide the fixed costs by the numberof time periods in the data.

Objective: TC = F + VX

Identify cost drivers and the costs associated with each driver.

Sum the fixed costs (facility costs).

Sum the variable costs for each cost driver activity.

Divide the total variable costs for each cost driver activity by the total number of cost driver units to obtain variable cost per unit.

Divide the fixed costs by the numberof time periods in the data.

Objective: TC = F + VX

Account Analysis

11-61

Overhead Costs for 1,000 UnitsTotal Variable Fixed

Account Cost Cost CostIndirect Labor 450$ 450$ Indirect Material 700 700 Depreciation 1,000 1,000 Property Taxes 200 200 Insurance 300 300 Utilities 400 350 50 Maintenance 600 500 100 Totals 3,650$ 2,000$ 1,650$

V = $2,000 ÷ 1,000 units = $2 per unitTC = $1,650 + $2 per unit

Account Analysis - Example

11-62

Estimate the total overhead cost for 1,400 units using the cost relationship from the the preceding

example.

a. $3,300

b. $4,450

c. $3,650

d. $5,650


example.

a. $3,300

b. $4,450

c. $3,650

d. $5,650


11-63


example.

a. $3,300

b. $4,450

c. $3,650

d. $5,650


example.

a. $3,300

b. $4,450

c. $3,650

d. $5,650

TC = F + VXTC = $1,650 + ($2 × 1,400 units)TC = $1,650 + $2,800 = $4,450


11-64


11-65

Engineering Method

Past costs are not

taken into account.

Past costs are not

taken into account.

Engineering estimates of cost are made, based on:

• Measurement of work involved in the

activities that go into a product.

• Assigning a cost to each of the activities.

Engineering estimates of cost are made, based on:

• Measurement of work involved in the

activities that go into a product.

• Assigning a cost to each of the activities.

11-66

Direct Labor

•Material requiredfor each unit isobtained from

engineering drawings and specification sheets.

•Material prices are determined from

vendor bids.

•Analyze the kindof work performed.

•Estimate the time required for each labor

skill for each unit.

•Use local wage rates to obtain labor cost

per unit.

Direct Material

Engineering Method

11-67

Overhead costs are obtained in a similar manner – a detailed step-by-step analysis of the work involved.

Advantages of the engineering approach:Detailed analysis results in better knowledge of the

entire process.

The method is used to estimate costs of new activities. Data from prior activities are not required.

A disadvantage of the engineering approach is the high cost of detailed analysis.

Engineering Method

11-68

Choice of an Estimation Method

Regression and account

analysis rely on past data. The

engineering method relies

on present data.

Regression and account

analysis rely on past data. The

engineering method relies

on present data.

Each method will likely

yield a different estimate.

Each method will likely

yield a different estimate.

Cost/Benefit must be

considered in choosing a

method.

Cost/Benefit must be

considered in choosing a

method.

11-69

No single method is best for all situations.

Better results are often obtained by use of several of the methods. For example: Engineering estimates and account analysis may

lead to the establishment of logical, causal relationships between variables.

A scattergraph plot will lead to a better understanding of the relationship and may reveal outlier data points.

Regression provides a cost equation for the data points with statistical measures of fit.

No single method is best for all situations.

Better results are often obtained by use of several of the methods. For example: Engineering estimates and account analysis may

lead to the establishment of logical, causal relationships between variables.

A scattergraph plot will lead to a better understanding of the relationship and may reveal outlier data points.

Regression provides a cost equation for the data points with statistical measures of fit.

Choice of an Estimation Method

11-70

Use of the Results

Levels of demand under different prices Success of new products/services Adequacy of present production and office

facilities; feasibility of outsourcing Overall profitability under many cost and

price scenarios

Cost estimation provides important information for forecasting:

Just keep in mind the limitations of

these estimation techniques!

11-71


11-72

Issues in Using Regressions

This technique does not provide exact measurements. It yields good approxima-tions of the actual relationships between cost drivers and costs.

There is seldom 100% confidence about a relationship between dependent and independent variables.

It cannot be always assumed that the cost estimation errors are normally distributed, independent and with constant variation.

So-called independent variables may be in fact closely correlated.

11-73


11-74

Learning Curve

The learning phenomenon: as we gain in experience,

we take less time to perform a task.

For cost estimation:as cost driver activity increases,the learning phenomenon leads

to lower costs per unit andgreater profitability.

Time

Repeated tasks$

Output

Minimum profit

Incremental profit

11-75

End of Chapter 11

Cost Estimation

Documents

level of cost

cost projection

higher cost

cost driver activities

graph total cost

total cost steps

past cost behavior

multiple cost drivers