Cost Estimation Question

Cost Estimation

Lecture 12

Chapter 5

Methods to Estimate Cost Behavior

Account analysis

Engineering estimates

Statistical methods

Recap of what we covered last class

Engineering Estimates

Cost estimates are based on measuring and then pricing the work involved in a task.

Identify the activities involved

Estimate the time and cost for each activity.

Labor

Rent

Insurance

Recap of what we covered last class

Account Analysis

Review each

account comprising

the total cost being

analyzed.

Identify each cost as either fixed or variable.

Activity level

Costs

($)

Fixed

Variable

Cost

($)

Activity level

Recap of what we covered last class

Statistical Cost Estimation

The limits within which a cost estimate may be valid.

Relevant range for a projection is usually between

the upper and lower limits (bounds)of past activity

levels for which data is available.

Analyze costs within a relevant range.

Relevant range?

Recap of what we covered last class

Statistical Cost Estimation

Statistical procedure to determine the relationship between variables.

High-Low Method

Regression

Uses two data points.

Uses all the data points.

3C Overhead

Example: Overhead Costs for 3C

The following information is used throughout this chapter:

Month Overhead Costs Repair-Hours

1 9,891 248

2 9,244 248

3 13,200 480

4 10,555 284

5 9,054 200

6 10,662 380

7 12,883 568

8 10,345 344

9 11,217 448

10 13,269 544

11 10,830 340

12 12,607 412

13 10,871 384

14 12,816 404

15 8,464 212

High-Low Cost Estimation

3C Overhead

Repair-Hours

A method to estimate costs based on two cost observations, usually at the highest and lowest activity level.

Choose two data

points.

Use the two points to

determine the line

representing the cost-

activity relation.

Draw a total cost line.

The highest and lowest activity.

Recap of what we covered last class

Highest

Activity

Level

Lowest

Activity

Level

Ɵ

Slop = tan Ɵ

M

N

Slop = M

N

Δ Total Cost

Δ Activity Slop =

Cost

Activity

Level

High-Low Cost Estimation

TC = VC(X) + FC

Recap of what we covered last class

Example: High-Low Cost Estimation, Contd .

A method to

estimate cost based

on two cost

observations, the

highest and lowest

activity level.

Month Overhead Costs Repair-Hours

1 9,891 248

2 9,244 248

3 13,200 480

4 10,555 284

5 9,054 200

6 10,662 380

7 12,883 568

8 10,345 344

9 11,217 448

10 13,269 544

11 10,830 340

12 12,607 412

13 10,871 384

14 12,816 404

15 8,464 212

Example: High-Low Cost Estimation, Contd .

A method to estimate cost based on two cost

observations, the highest and lowest activity level.

Month

OH Cost

Repair-

Hours

High 12,883 568

Low 9,054 200

Change 3,829 368

By definition, the change in cost due to a

change in activity is variable cost. So, to

calculate unit variable cost:

Δ Total Cost

Δ Activity =

3,829

368 =

10.40

VC per unit

TC = VC(X) + FC

9,054 = VC(200) + FC

9,054 = 10.40(200) + FC

9,054 = 2,080 + FC

FC = 6,974

TC = 10.40(X) + 6,974

Recap of what we covered last class

Statistical Cost Estimation

Statistical procedure to determine the relationship between variables.

High-Low Method

Regression

Uses two data points.

Uses all the data points.

3C Overhead

Independent variable Dependent variable

The X term, or predictor.

The activity that predicts

(causes) the change in

costs.

The Y term. The

dependent variable. The

cost to be estimated.

Repair-hours (X)

Overhead costs (Y)

The relationship between activities and costs

Costs

Activities

Y = a + b X

Statistical Cost Estimation Using Regression Analysis

Regression, Continued. . .

Y = a + b X

Y Intercept Slope X

Repair-hours OH Fixed costs V

The Regression Equation

= +

= +

Regression, Continued. . .

Y = a + b X

The Regression Equation

Where

Month Overhead Costs (y) Repair-Hours (x)

1 9,891 248

2 9,244 248

3 13,200 480

4 10,555 284

5 9,054 200

6 10,662 380

7 12,883 568

8 10,345 344

9 11,217 448

10 13,269 544

11 10,830 340

12 12,607 412

13 10,871 384

14 12,816 404

15 8,464 212

Excel

Regression, Continued. . .

Month Overhead Costs Repair-Hours

1 9,891 248

2 9,244 248

3 13,200 480

4 10,555 284

5 9,054 200

6 10,662 380

7 12,883 568

8 10,345 344

9 11,217 448

10 13,269 544

11 10,830 340

12 12,607 412

13 10,871 384

14 12,816 404

15 8,464 212

Regression Using Excel. . .

Excel

Interpreting Regression

Y = Intercept Slope X

Y = F + V X

Learning Objectives:

1. Understand the reasons for estimating fixed and variable costs.

3. Estimate costs using account analysis.

2. Estimate costs using engineering estimates.

4. Estimate costs using statistical analysis.

5. Interpret the results of regression output.

6. Identify potential problems with regression data.

7. Evaluate the advantages and disadvantages of alternative

cost estimates.

Interpreting Regression, Continued. . .

Correlation

coefficient

“R” measures the linear relationship between

variables. The closer R is to 1.0 the closer the

points are to the regression line. The closer R is to

zero, the poorer the regression line.

Coefficient of

determination

“R2” The square of the correlation coefficient. The

proportion of the variation in the dependent

variable (Y) explained by the independent

variable(s)(X).

T-Statistic The t-statistic is the value of the estimated coefficient divided by its standard error.

Generally, if it is over 2, then it is considered

significant. If significant, the cost is NOT totally

fixed.

Interpreting Regression, Continued. . .

Correlation Coefficient Coefficient of Determination

A linear relationship does exist between repair hours and overhead costs.

82.8% of the changes in overhead costs can be explained by changes in repair-hours.

.91

.828

Both have t-statistics that are greater than 2, so the cost is not totally fixed.

10.7 & 7.9

T-Statistic

Example: Regression

X

Estimate 3C’s overhead with 520 repair hours.

TC = 6,472 + 12.52

TC = F + V X

Multiple Regression

Multiple Regression: When more than one predictor (x)

is in the model.

Is repair-hours the only activity that drives

overhead costs at 3C?

Predictors: X1: Repair-hours

X2: Parts Cost

Equation: TC = V1 (X1) + V2 (X2) + FC

Multiple Regression, Continued. . .

Month OH Costs Repair-Hours (X1) Parts (X2)

1 9,891 248 1,065

2 9,244 248 1,452

3 13,200 480 3,500

4 10,555 284 1,568

5 9,054 200 1,544

6 10,662 380 1,222

7 12,883 568 2,986

8 10,345 344 1,841

9 11,217 448 1,654

10 13,269 544 2,100

11 10,830 340 1,245

12 12,607 412 2,700

13 10,871 384 2,200

14 12,816 404 3,110

15 8,464 212 752

3C Cost Information

Multiple Regression Output

Correlation coefficient squared and adjusted for the number of

independent variables used to make the estimate.

.89

Adjusted Correlation Coefficient

89% of the changes in overhead costs can be explained by

changes in repair-hours and parts costs.

Adjusted R Square

Multiple Regression Output, Continued. . .

3,500 520

TC = F + V1

= 6,416 + 8.61

+

0.77 +

= 13,588

X1 V2 X2

TC

TC

Can you use this regression output to estimate overhead costs for 520 repair-hours and 3,500 cost of parts?

Statistical Cost Estimation

Advantages

Reliance on historical data is relatively inexpensive.

Computational tools allow for more data to be used

than for non-statistical methods.

Disadvantages

Reliance on historical data may be the only cost-

effective basis for estimating costs.

Choosing an Estimation Method

High-Low

Estimated manufacturing overhead with 520 repair-hours.

Regression

12,384

12,982

Multiple Regression

Account Analysis 12,586

13,588*

520 repair-hours and 3,500 parts costs

* The more sophisticated methods yield more

accurate cost estimates than the simple methods.