B313F Management and Cost Accounting

Lecture 6

Cost Estimation

By Charles Chiu, PhD, CFA

Introduction

Cost estimation

Process of determining cost behavior, often focusing on

historical

data.

Cost behavior

Relationship between cost and activity.

Cost prediction

Using knowledge of cost behavior to forecast level of cost at a particular activity. Focus is on the

future

.

2

Cost Terminology

  

Variable Costs

total in relation to some chosen activity or output – costs that change in

Fixed Costs

– costs that do not change in total in relation to some chosen activity or output

Mixed Costs

– costs that have both fixed and variable components; also called semivariable costs 3

Cost Behavior Patterns

Summary of Variable and Fixed Cost Behavior Cost In Total Variable Fixed Total variable cost is proportional to the activity level within the relevant range.

Total fixed cost remains the same even when the activity level changes within the relevant range.

Per Unit Variable cost per unit remains the same over wide ranges of activity.

Fixed cost per unit goes down as activity level goes up.

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Total Variable Cost Unit Variable Cost Total Fixed Cost Unit Fixed Cost

5

Examples of variable costs Merchandisers Cost of Goods Sold Service Organizations Supplies and travel Manufacturers Direct Material, Direct Labor, and Variable Manufacturing Overhead Merchandisers and Manufacturers Sales commissions and shipping costs Examples of fixed costs Merchandisers, manufacturers, and service organizations Real estate taxes, Insurance, Sales salaries Depreciation, Advertising

6

Types of Fixed Costs

Committed Long-term, cannot be reduced in the short term.

Examples Depreciation on Buildings and Equipment Discretionary May be altered in the short-term by current managerial decisions Examples Advertising and Research and Development

7

Trends in Cost Structure

A trend toward

more fixed costs

• Increased automation.

• Stable workforce .

because of

Implications Managers are more “locked-in” with fewer decision alternatives.

Planning becomes more crucial:

fixed costs are difficult to change with current operating decisions.

8

Cost Functions

 A cost function is a

mathematical representation

of how a cost changes with changes in the level of an activity relating to that cost (cost driver) 9

Identifying Cost Drivers

Cost Driver Examples Activity Machining operations Setup Production scheduling Inspection Purchasing Shop order handling Valve assembly support Cost Driver Machine hours Setup hours Manufacturing orders Pieces inspected Purchase orders Shop orders Customer requisitions

10

Criteria for Evaluating Alternative Cost Drivers

1.

2.

3.



Economic Plausibility

Economic significance

Goodness of Fit



Significance of the Independent Variable

Statistical significance 11

The Linear Cost Function

The Dependent Variable: The cost that is being predicted

y = a + bX

The Intercept: Fixed costs The Independent Variable: The cost driver The Slope of the Line: Variable cost per unit

12

Cost Y The total cost line can be expressed as an equation: Y = a + bX Where: Y a b X = the total mixed cost = the total fixed cost (the vertical intercept of the line) = the variable cost per unit of activity (the slope of the line) = the level of activity Variable Cost X Fixed Cost Number of Units Produced

13

1.

2.

The Linearity Assumption and the Relevant Range

Variations in the level of a

single activity

(the cost driver) explain the variations in the related total costs  Cost behavior is approximated by a

linear

cost function

within the relevant range

Graphically, the total cost versus the level of a single activity related to that cost is a straight line within the relevant rage 14

Relevant Range Economist’s Curvilinear Cost Function

A straight line closely approximates a curvilinear variable cost line within the relevant range.

Accountant’s Straight-Line Approximation (constant unit variable cost)

Activity

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Fixed Costs and Relevant Range

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

16

90 60 30 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.

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

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Criteria for Classifying Variable and Fixed Components of a Cost

1.

2.

3.

Choice of Cost Object

may result in different classification of the same cost – different objects

Time Horizon

– the longer the period, the more likely the cost will be variable

Relevant Range

– behavior is predictable only within this band of activity 18

Cause-and-Effect Relationship for Cost Drivers

   The most important issue in estimating a cost function is determining whether a cause-and-effect relationship exists between the level of an activity and the costs related to that level of activity.

A cause-and-effect relationship might arise as a result of:    A physical relationship between the level of activity and costs A contractual agreement Knowledge of operations Note: a high correlation (connection) between activities and costs does not necessarily mean causality 19

Question for Discussion 1

 Which of the following statements about cost behavior are true?

a

Fixed costs per unit vary with the level of activity.

b c

Variable costs per unit are constant within the relevant range.

Total fixed costs are constant within the relevant range.

d

Total variable costs are constant within the relevant range.

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Cost Estimation Methods

1.

2.

3.

4.

Industrial Engineering Method Conference Method Account Analysis Method

1.

2.

Quantitative Analysis Methods

High-Low Method Regression Analysis 21

Industrial Engineering Method

    Estimates cost functions by analyzing the relationship between inputs and outputs in physical terms Includes time-and-motion studies Very thorough and detailed, but also costly and time consuming Also called the Work-Measurement Method 22

Direct Labor Direct Material

•

Analyze the kind of work performed.

•

Estimate the time required for each labor skill for each unit.

•

Use local wage rates to obtain labor cost per unit.

•

Material required for each unit is obtained from engineering drawings and specification sheets.

•

Material prices are determined from vendor bids.

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1.

2.

3.

4.

5.

Nonlinear Cost Functions

Economies of Scale Quantity Discounts

Step Cost Functions – resources increase in “lot-sizes,” not individual units Learning Curves – labor hours consumed decrease as workers learn their jobs and become better at them Experience Curve – broader application of learning curve that includes downstream activities including marketing and distribution 24

Learning Curves

There is often a systematic relationship between experience in performing a task and the time required to do it.

The average time per task declines by a constant percentage each time the quantity of tasks done doubles.

25

Types of Learning Curves

 

Cumulative Average-Time Learning

Model – cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced doubles Incremental Unit-Time Learning Model – incremental unit declines time needed to produce the last by a constant percentage each time the cumulative quantity of units produced doubles 26

Effect of Learning on Cost Behavior

Berry Co. makes products requiring labor that follows an 80 percent learning rate. If the first unit of such a product requires 10 hours, what is the average time for 16 units of this product?

An 80 percent learning rate: the average time required to make 2 units is 80 percent of the time for 1 unit and the average time for 4 units is 80 percent of the time for 2 units, etc.

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Cumulative Average-Time Learning Model

Number of Units 1 2 4 8 16 Average Labor Time per Unit 1 × 10 = 10 .80 × 10 = 8 .80 × 8 = 6.4

.80 × 6.4 = 5.12 .80 × 5.12 = 4.096

Total Time: Average x Units 1 × 10 = 10 2 × 8 = 16 4 × 6.4 = 25.6

8 × 5.12 = 40.96

16 × 4.096 = 65.536

The graphic presentation of the learning phenomenon is called the learning curve.

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Learning Curve

Learning effects are large initially.

Learning effects become smaller, eventually reaching expected final time.

Cumulative Production Output

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This is used to help determine investment required.

This is used to estimate ongoing results.

Cumulative Production Output

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Learning Curve Formula

Cumulative average labor time per unit  DLH to produce unit 1   Cumulative no.

of units produced  learning factor Learning factor  ln  learning rate % in decimal form  ln 2 31

Question for Discussion 2

   Time to produce the first unit = 100 minutes Learning factor = ln(0.80)/ln2 = -0.32193

1.

2.

3.

What is the cumulative average time to produce 5 units?

What is the total time to produce 5 units?

What is the time it took to produce the 5 th unit?

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Incremental Unit-Time Learning Model

Using the example of Berry Co. and using the incremental unit-time learning model

Number of Units 1 2 3 4 5 Individual Unit Time for X-th Unit 1 × 10 = 10 0.80 × 10 = 8 7.02

0.80 × 8 = 6.40

5.96

Cumulative Total Time 10 10 + 8 = 18 18 + 7.02 = 25.02

25.02 + 6.40 = 31.42

31.42 + 5.96 = 37.38

Cum.

Ave. Time Per Unit 10 9 8.34

7.86

7.48

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Conference Method

   Estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of a company Pools

expert knowledge

Reliance on opinions still makes this method subjective 34

Account Analysis Method

  Estimates cost functions by classifying various cost accounts as variable, fixed, or mixed with respect to the identified level of activity Is reasonably accurate, cost-effective, and easy to use, but is subjective 35

Example

Account Indirect Labor Indirect Material Depreciation Property Taxes Insurance Utilities Maintenance Totals Overhead Costs for 1,000 Units Total Variable Fixed Cost $ 450 700 Cost $ 450 700 Cost 1,000 200 300 400 600 $ 3,650 $ 350 500 2,000 1,000 $ 200 300 50 100 1,650

Total Cost = $2 per unit + $1,650

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

Problems

    what is the proper cost driver what is truly fixed changes in price is a history available 37

Quantitative Analysis

  Uses a formal mathematical method to fit cost functions to past data observations Advantage: results are objective 38

1.

2.

3.

4.

5.

6.

Steps in Estimating a Cost Function Using Quantitative Analysis

Choose the dependent variable (the cost to be predicted) Identify the independent variable or cost driver Collect data on the dependent variable and the cost driver Plot the data Estimate the cost function using the High Low Method or Regression Analysis Evaluate the cost driver of the estimated cost function 39

The High-Low Method

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

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

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. 40

The High-Low Method

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

 

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

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Question for Discussion 3

 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 42

Question for Discussion 4

 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 43

Regression Analysis

  Regression analysis is a statistical method that measures the average amount of change in the dependent variable associated with a unit change in one or more independent variables Is

more accurate

than the High-Low method because the regression equation estimates costs using information from observations; the High-Low method uses only

two

observations

all

44

Types of Regression

 

Simple

the dependent variable and variable – estimates the relationship between

one

independent

Multiple

– estimates the relationship between the dependent variable and

more

independent variables

two or

45

Terminology

 

Goodness of Fit

– indicates the strength of the relationship between the cost driver and costs

Residual Term

– measures the distance between actual cost and estimated cost for each observation 46

The simple cost model is actually a regression model: TC = F + V

X

This model will only be useful within a relevant range of activity.

Caution: Before doing the analysis, take time to determine if a logical relationship between the variables exists.

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Simple 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 R 2 , that is a measure of the goodness of fit of the regression line to the data points.

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R 2 is the percentage of the variation in total cost explained by the activity.

Y 20 10 * * * * * * * * * * R 2 for this relationship is near 100% since the data points are very close to the regression line.

0 0 1 2 3 4 Activity X

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Multiple Regression

Multiple regression includes two or more independent variables:

TC = FC + V 1 X 1 + V 2 X 2

Terms in the equation have the same meaning as in simple regression with only one independent variable.

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Data Problems

    The

time period

for measuring the dependent variable does not match the period for measuring the cost driver Fixed costs are allocated as if they are variable Some data may be uniformly reliable

missing

or are not

Extreme values

of observations occur from errors in recording costs 51

   There is pool.

no homogeneous relationship

between the cost driver and the individual cost items in the dependent variable-cost The relationship between the cost driver and the cost is

not stationary

(not stable)

Inflation

both has affected costs, the driver, or 52

Data Adjustment

   Corresponding numbers should be

causally related

(i.e., if relating supplies to production units, the figures should be per some number of units of production NOT supplies purchased usage of supplies in the same period).

Consider outliers carefully

future.

: the object is to find the relationship that will hold in the Remember that cost relationships can change over time (a “

nonstationary

” relationship).

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The Ideal Database

1.

2.

The database should contain numerous costs

reliably measured

observations of the cost driver and the In relation to the cost driver, the database should consider many values spanning a

wide range

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