Cost Estimation

Chapter 6
 Learning Objectives
1) Differentiate between cost estimation and product costing.
2) Understand the concept of and needs for cost estimation.
3) Understand reasons for estimating fixed and variable costs.
4) Understand general types of cost estimates.
5) Estimate costs using account analysis.
6) Estimate costs using scatter-graph.
7) Estimated costs using high-low method.
8) Estimate costs using linear regression method.
9) Perform regression analysis using Excel® Solver software to fit regression line into
cost data.
10) Interpret the results of linear regression analysis.

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 Reasons for Cost Estimation
Decisions make may need to compare costs and benefits among alternative
actions.

Need to know:
What adds value to the firm?

Cost estimates can be crucial for managers make decisions.

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 Basic Cost Behavior Patterns
Understand the reasons for estimating fixed and variable costs.

Costs

Fixed costs Variable costs

Total fixed costs do not Total variable costs

change proportionately change proportionately
as activity changes as activity changes

Per unit fixed costs Per unit variable costs

change inversely as do not change as
activity changes activity changes

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 General Types of Cost Estimates
1) Order of Magnitude (ROM) estimate;

2) Budget estimate;

3) Definitive estimate.

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 General Types of Cost Estimates
Order of Magnitude (ROM):
 A rough or “ballpark” estimate of costs used at the very early stage of a
project, particularly during the planning stages.
 Provides an estimate based on the available information at the time, just to
have some idea about general and total expenditures instead of itemizing
costs based on the project activities.
 Has a range of variance from -25% (underestimate) all the way to +75%
(overestimate) [could become 50% underestimate to +100% overestimate
of actual cost.

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 General Types of Cost Estimates
Budget estimate (or top-down estimate):
 Is a preliminary cost estimate, which is more accurate than an order of magnitude
estimate.
 Provides a preliminary itemized list of expenses based on the main components of the
project.
 Starts at the top of the project (major components) and works through to the bottom of
it (details).
 Has a range of variance from 10% underestimate to 25% overestimate.
 Is done at the planning stage of the project using historical data of a related project or
obtainable data from the project plan, and the expected labor cost and costs of
required equipment and materials.

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 General Types of Cost Estimates
Definitive Estimate: (aka detailed cost estimate or bottom-up estimate)
 Is the most accurate estimate of the three types.
 Breaks down the whole project into its detailed compositions to prepare a
list of all requirements, to each of which an estimated cost is assigned .
 Has a range of variance from 5% underestimate to 15% overestimate.

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 General Types of Cost Estimates
 With any type of estimate, the estimator should provide the range of
variance in the costs and an explanation of how the estimate has been
made.
 Otherwise, the customer may take the quoted cost as a promised cost.

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 Assumptions in Cost Estimating Models
Three important assumptions to consider when using the cost estimating
methods presented in this lecture:
1) The variable costs per unit and total fixed costs are assumed will remain
constant at all the activity levels.
2) The estimated cost is assumed to have a linear relationship with the activity
level (units, labor hours, machine hours, etc.)
3) When costs are estimated for a planned activity level, it is assumed that the
activity level is within the relevant range.

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 Relevant Range
Relevant range is a normal range of activity levels in which the total fixed
costs will not change as the level of activity changes.
Analyze costs within the relevant range to have a valid cost estimate.
Relevant range for a projection is usually between the upper and lower limits
(bounds) of past activity levels for which data is available.

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 Methods of Estimating Cost Behavior
There are four common methods for estimating costs behavior:

1) Account analysis method

2) Scatter-Graph method

3) High-Low method

4) Least-Square or Regression method

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 Account Analysis Method
• Review each account comprising the total cost being analyzed.
• Determine each cost as either fixed or variable.

Cost
Cost

Fixed Variable
Activity Level Activity Level

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 Account Analysis Method--Example
A service shop incurred the following costs during a period that provided 400
hours of service to its customers. Its costs were analyzed and broken down
into fixed and variable costs as listed in the following table.

Account Total Cost Variable Fixed

Supplies $9,000 $6,200 $2,800
Utilities 375 150 225
Labor wages 2,350 2,350 0
Administrative Expenses 7,450 6,200 1,250
Building Rent 1,750 0 1,750
Total 20,925 14,900 6,025
Variable Cost per hour $37.25

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 Account Analysis Method--Example
Cost estimation using account analysis method:
Fixed costs + (Variable cost/unit × No. of units) = Total cost

Cost at 400 service-hours:

$6,025 + ($37.25 × 400) = $20,925

Estimated cost at 500 service-hours:

$6,025 + ($37.25 × 500) = $24,650

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 Account Analysis Method
Advantages:
• Managers and accountants are familiar with the company operations and
how costs incur as the activity level changes.

Disadvantages:
• Managers and accountants may apply biased judgments.
• Decisions often have major economic consequences for the company.

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 Scatter-Graph Cost Estimation
The procedure requires the following four steps:
Step 1: Draw Scatter Graph
Step 2: Draw a Regression Line
Step 3: Find Total Fixed Cost (F)
Step 4: Compute Variable Cost Per Unit (V):
Use two points on the regression line:
(X1, Y1) and (X2, Y2)
Use the following formula
V = =

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 Scatter-Graph--Example
The following data represent the overhead cost of a small manufacturing company for
producing one of its product during a 12-month period. Estimate costs producing 450
units using a scatter-graph.
Month Production units Total Cost
1 200 $13,595
2 235 13,035
3 254 15,825
4 235 15,100
5 260 12,325
6 280 14,150
7 400 21,325
8 380 18,750
9 290 17,545
10 310 14,405
11 340 16,680
12 360 20,440

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 Scatter-Diagram--Example
The scatter-graph helps visualize the relationship between the production level
and the overhead cost.
$25,000
Total Overhead Cost $20,000

$15,000

$10,000

$5,000

$0
0 50 100 150 200 250 300 350 400
Production Level (units)

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 Scatter-Diagram--Example
We try to fit a line through the data points, which minimizes their overall
distances from the line, using “visual judgment”.

$25,000
Total Overhead Cost
$20,000

$15,000

$10,000

$5,000

$0
0 50 100 150 200 250 300 350 400
Production Level (units)

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 Scatter-Diagram--Example
Now, we approximate the values of the intercept, which the fixed cost, and
slope of the line, which will be the variable cost per unit (F  $5,900).

$25,000
Total Overhead Cost
$20,000

$15,000

$10,000

$5,000

$0
0 50 100 150 200 250 300 350 400
Production Level (units)

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 Scatter-Diagram--Example
Now, choose two point on the regression line. For example, (125, 10,000) and
(400, 20,000)

$25,000
Total Overhead Cost $20,000

$15,000

$10,000

$5,000

$0
0 50 100 150 200 250 300 350 400
Production Level (units)

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 Scatter-Diagram--Example
Compute the variable cost based on (125, 10,000) and (400, 20,000) points:

V = = = $36.36 per unit

Then, the model for estimating a future planned production will be:
C = $5,900 + $36.36Q
For example, the estimated cost of producing 450 units will be:
C = $5,900 + $36.36(450) = $22,262

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 Scatter-Diagram--Note
Advantage:
• Provides a quick view of the fitness of a predictive line.
• Can detect the existence or lack of unusual data point (outliers).
• Its approximation is rather rough due to visual judgment and opinion of
the analyst in line drawing and choosing the points on the line for
computing the slope (variable cost per unit) and finding the y-intercept
(fixed cost).

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 Hi-Low Method
This method estimates costs based on only two cost data point, the highest
and lowest activity levels.
It computes the variable cost (V) as:
V=

That is,

V=

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 Hi-Low Method
Then, we compute the fixed cost (F), the intercept, either using the highest activity level
data as:

F= –
or using the lowest activity level data as:

F= –

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 Hi-Low Method--Example
Estimate the cost of producing 450 units, using the High-Low method, based
on the data used in the scatter-graph example.
Month Production units Total Cost
1 200 $13,595
Lowest activity level 2 235 13,035
3 254 15,825
4 235 15,100
5 260 12,325
6 280 14,150
7 400 21,325
Highest activity level 8 380 18,750
9 290 17,545
10 310 14,405
11 340 16,680
12 360 20,440
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 Hi-Low Method--Example
Computing the variable cost (V) as:
V = = = $38.65

Computing the fixed cost (F) using the highest activity as:
F = $21,325 - $38.65(400) = $5,865

or using the lowest activity as:

F = $12,195 - $38.65(200) = $5,865
Now, we write the predictive model for estimating future costs:

TC = $5,865 + $38.65Q

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 Hi-Low Method--Example
We can, now, estimate the cost of manufacturing 450 units using the predictive
equation:

TC = $5,865 + $38.65Q

TC = $5,865 + $38.65(450) = $23,257.50

As this is an estimate, we can round the answer to $23,250.

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 Regression Analysis
Regression is a statistical procedure for establishing the relation between
variables.
It helps determine how well the estimated regression line equation describes
the relations between costs and the activity levels.
• Hi-Low method uses only two data points

• Regression uses all data points

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 Regression Analysis
In its simplest form, the general linear regression equation has the form:
Data = Model + Error
or
Y = (a + bX) + 
where:
a = intercept
b = slope
X = independent variable (or predictor)
Y = dependent variable
 = error of estimate

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 Regression Analysis
For cost estimation, the regression equation is written as:
Y = a + bX
or
C = F + VQ
where:
F = a = Fixed cost (intercept)
V = b = Variable cost per unit (slope)
Q = X = Activity level (independent variable)
C = Y = Predicted (estimated) cost (dependent variable)

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 Regression Method
Computing the intercept (a) and slope (b):
Step 1: List all n pairs of observed activity level and cost data points in two different
columns of a table.
Step 2: Sum up all observed activity levels (X) and divide the sum by the number
of observed data points (n) to find the average activity level ().
Step 3: Sum up all observed costs (Y) and divide the sum by the number of
observed data points (n) to find the average cost ().
Step 4: In a new column, multiply each observed activity level by its corresponding
cost (XY) and sum up all XY’s to find (XY).

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 Regression Method
Computing the intercept (a) and slope (b):
Step 5: In a new column, compute the squared value of each observed activity level
(X2) and sum up all X2’s to find (X2).
Step 6: Compute the slope (variable cost per unit) using the following equation:
b=
Step 7: Compute the intercept (a), the fixed cost using the following equation:
a= -b
This is solving the following equation for a:
=a+b

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 Regression Method--Example
Estimate the cost of producaing 450 units, using the regression method, based on the data used in
the scatter-graph and high-low examples.
Obs. X Y XY X2
1 200 $13,595 2,719,000 40,000
2 235 13,035 3,063,225 55,225
3 254 15,825 4,019,550 64,516
4 235 15,100 3,548,500 55,225
5 260 12,325 3,204,500 67,600
6 280 14,150 3,962,000 78,400
7 400 21,325 8,530,000 160,000
8 380 18,750 7,125,000 144,400
9 290 17,545 5,088,050 84,100
10 310 14,405 4,465,550 96,100
11 340 16,680 5,671,200 115,600
12 360 20,440 7,358,400 129,600
Sum 3,544 193,175 58,754,975 1,090,766

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 Regression Analysis--Example
From the bottom row of the table, we read the computed data as:
(X) = 3,544  = 3,544/12 = 295.33 units
(Y) = 193,175  = 193,175/12 = $16,098
(XY) = 58,754,975
(X2) = 1,090.766
Then, we compute the following
b= =
b = $38.6344 per unit
and using the = a + b relationship
a = - b = $16,098 - $38.6344(295.33) = $4,688

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 Regression Analysis
Now, we write the (regression) cost estimating model as:
Y = $4,688 + $38.63X
or
C = $4,688 + $38.63Q

The estimated cost of producing 450 units is:

C = $4,688 + $38.63(450) = $22,071.50
or $22,070.

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 Regression Analysis Output
Using the Excel Solver:
 Make sure (Excel) Solver is added on;
 Click “Data Analysis;
 Choose “Regression” from scroll down window and click OK button;
 Follow the program instruction.

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 Regression Analysis Output
Using the Excel Solver, we get the following output:
Regression Statistics
Multiple R 0.8402
R Square 0.70594
Adjusted R Square 0.67653
Standard Error 1655.98
Observations 12
ANOVA
df SS MS F Signif F
Regression 1 65831446 65831446 24.006 0.000624
Residual 10 27422676 2742268
Total 11 93254123
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 4,687.884 2,377.32 1.97192 0.0769 -609.12 9984.89
X Variable 1 38.63442 7.8852 4.89961 0.0006 21.07 56.20

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 Regression Analysis: Interpretation
Correlation coefficient (R):
This is a measure of the linear relationship between variables.
• The value of R will be between -1.0 and +1.0.
• The closer R is to 1.0, the stronger correlation between the variables; and the closer the
data points are to the regression line.
• The closer R is to zero, the weaker correlation between the variables; the poorer the fit of
the regression line to the data points.

Coefficient of determination (R2):

This is the square of the correlation coefficient.
It is the proportion of the variation in the dependent variable (Y) explained by the
independent variable(s) (X).

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 Regression Analysis: Interpretation
t-statistic:
This is the value of the estimated coefficient, b, divided by its estimated
standard error (SEb).

Generally, if the t-statistic of b (tb) is greater than 2, then it is considered

significant. If significant, the cost is NOT totally fixed.

For the data used in our example, the t-statistics for b and a:

ta = a ÷ SEb = 4,687.884 ÷ 2,377.32 = 1.97192

tb = b ÷ SEa = 38.63442 ÷ 7.8852 = 4.89961

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 Regression Analysis: Interpretation
t-statistic:
An 0.84 correlation coefficient indicates that a linear relationship does
exists between the activity level (production quantity) and the costs.
An 0.70594 coefficient of determination means that 70.6% of the
changes in the costs can be due to changes in the activity level.

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 Regression Analysis: Interpretation
p-value:
The p-value of 0.000624 for the regression, which is less than 0.05, indicates that there is a
strong evidence to reject the null hypothesis that there is no correlation between the
independent variable (activity level) and the dependent variable (costs).
However, the p-value of 0.0769 for the intercept is greater than 0.05, which indicates that
there is no a strong evidence to believe the fixed cost is about $4,688 as its 95%
confidence indicates it ranges from -$609 to $9,985. This may have been caused by some
other factors, such seasonal factors, unusual expenditure, etc.

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 Practical Implementation Issues
Potential issues:
• Existence of outliers. Unusual situation may have occurred over the data
collection period.
• Attempting to fit a linear model to a set of nonlinear data.
• Non-linearity may occur near full-capacity.
Possible solutions:
• Define a more limited relevant range (e.g., 25-75% capacity).
• Try a multiple regression or a nonlinear regression model.

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 Practical Implementation Issues
Possible solutions:
• Review and analyze the scatter-graph and eliminate highly unusual
observations before running the regression.
• Collect more data.
• Define a more limited relevant range (e.g., 25-75% range of capacity).
• Try a multiple regression or a nonlinear regression model.

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 Data Problems
• Outliers
• Mismatched time periods
• Allocated and discretionary costs
• Inflation
• Missing data

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End of Chapter 6

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