Cost estimation - Cost behavior
What we really want to understand is how
spending will vary in a variety of decision
settings.
Cause-effect relations and costs drivers.
Capacity and capacity costs:
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Theoretical = 100,000
Practical = 90,000
Normal = 85,000
Budgeted = 80,000
Suppose fixed overhead is budgeted at
$1,000,000; variable overhead is $1 per unit;
direct material costs = $3; and direct labor =
$3. Overhead is applied based on units of
product.
Capacity and capacity costs:
What does a unit of product cost if overhead
is allocated based on theoretical capacity?
$17
Practical capacity? $18.11
Normal capacity?
$18.76
Budgeted capacity. $19.50
Which measure should the company use?
Capacity and capacity costs:
Suppose the company allocates overhead
based on practical capacity and actual
production is 70,000 units.
By how much is overhead underapplied?
About $222,300
What does that cost represent?
The cost of idle
or excess capacity.
Capacity and capacity costs
• Who should pay for excess capacity?
• Who should pay for idle capacity?
• How is capacity measured?
What is the scarcest resource?
• Idle capacity and opportunity costs.
Cost estimation: overhead
• When is it important to understand how overhead
behaves?
– When pricing, production, process and product
design decisions are made.
– When bids and make or buy decisions are made.
– When we need to answer “what if” questions.
Cost estimation: overhead costs
• First week’s product costing exercises:
applied overhead.
– Valuing inventories & costs of sales.
– Not for costing individual products
– Not for predicting costs
What methods are available?
• Engineering estimates
• Account analysis
• Scattergraph and high-low estimates
• Statistical methods (typically regression)
Cost behavior: linear function by
assumption.
TC = FC + VC*(level of cost driver)
where
TC =
FC =
VC =
total cost
fixed cost
variable cost per unit of the cost
driver,
and sometimes the cost driver is
represented by X.
Overhead Costs
Volume
A
B
C
D
Cost estimation: Account
analysis
• Review each account
• Identify it as fixed or variable (or mixed)
• Attempt to determine the relationship
between the activity of interest and the cost
– Cost of building occupancy
– Cost of quality inspections
– Cost of materials handling
Example
Suppose management believes that the monthly
overhead cost ($5000) in the factory is mixed. It is
believed to be 50% fixed and 50% variable. The
variable portion is believe to depend on machine
hours, which average 10,000 per month. How
would you show this as a linear equation?
TC = $2500 + $.25(machine hours)
Peterson Mfg. in Problem Set #1 will require account analysis.
Scattergraph
Suppose you have data on overhead costs and
machine hours for the past 15 months. Can
you easily determine whether the posited
relationship exists?
Yes, plot the data and look for a relationship.
Plot of overhead costs vs.
machine hours
Scattergram
4000.00
3500.00
3000.00
2500.00
2000.00
1500.00
1000.00
500.00
0.00
0.00
30.00
60.00
90.00
Machine Hours
120.00
150.00
High-Low cost estimation
Find the variable cost per unit of the cost
driver (VC):
Overhead at highest activity - Overhead at lowest activity
VC 
Highest activity - Lowest activity
High-Low method: Example
continued
$3,105 - $1,896
VC 
142 mhr - 50 mhr
$1,209
VC 
92 mhr
VC  $13.14/mhr
High-Low cost estimation
Fixed cost  $3,105 - ($13.14 * 142 mhr)
 $1,239
Estimate the total overhead cost during a
months when 115 machine hours will be used:
TC  FC  VC * 115 mhr
TC  $1,239  ($13.14 * 115 mhr)
TC  $2,750
Cost estimation using regression
• Y = the dependent variable (total O/H cost)
• X = the explanatory variables
Y = *X +
where X = machine hours and  = random error.
TC = FC + VC*X + .
Regression fits a line through
these data points:
Scattergram
4000.00
3500.00
3000.00
2500.00
2000.00
1500.00
1000.00
500.00
0.00
0.00
30.00
60.00
90.00
Machine Hours
120.00
150.00
Simple linear regression
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One explanatory variable
Cost estimation equation
Coefficient of correlation (R)
Coefficient of determination (R2)
– Goodness of fit
– Measure of importance
• F-statistic (hypothesis testing)
• p-value
Coefficient of determination
Measures the percentage of variation in the
dependent variable explained by the independent
variable.
When the predicted values exactly equal the
actual costs, R2 = 1.
A goodness of fit test: R2 > .3
The F statistic
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Goodness of fit hypothesis testing
Compute a statistic for regression results
Compute the associated p-value, or
Look up a critical F-value and compare
– 1 numerator degree of freedom
– (n-2) denominator degrees of freedom
– alpha = .05
The F test:
• The hypothesis is: The slope coefficient is
zero.
• The F-statistic measures the loss of fit that
results when we impose the restriction that
the slope coefficient is zero.
• If F is large, the hypothesis is rejected.
The p-value
• This is the probability that the statistic we
computed could have come from the
population implied by our null hypothesis.
• Suppose we hypothesize that the slope
coefficient is zero.
• If the p-value associated with the F-statistic
is small, chances are the slope coefficient is
not zero.
Regression result interpretation
Re gre ssion Summary
Ove rhe ad Costs vs. Machine Hours
Count
15
Num. Missing
0
R
. 896
R Squared
. 802
Adjusted R Squared
. 787
RMS Residual
182. 244
ANOVA Table
Ove rhe ad Costs vs. Machine Hours
DF
Sum of Squares
1
1753772. 049
Residual
13
431765.285
Total
14
2185537. 333
Regression
Mean Square
1753772. 049
F-Value
P-Value
52.804
<. 0001
33212. 714
Re gre ssion Coeff icients
Ove rhe ad Costs vs. Machine Hours
Interc ept
Mac hine Hours
Coeffic ient
Std. Er ror
1334.293
162. 913
12.373
1. 703
Std. Coeff .
1334.293
. 896
t-Value
P-Value
8. 190
<. 0001
7. 267
<. 0001
Simple linear regression
Scattergram
4000.00
3500.00
3000.00
2500.00
2000.00
1500.00
1000.00
500.00
0.00
0.00
30.00
60.00
90.00
Machine Hours
120.00
150.00
Overhead Costs = 1334.293 + 12.373 * Machine Hours; R^2 = .802
Results using DM$
Regression Summary
Ove rhe ad Cost s vs. Direct Materials Cost
Count
15
Num. Missing
0
R
.960
R S quared
.921
Adjusted R Squar ed
.915
RMS Residual
115.087
ANO VA Table
Ove rhe ad Cost s vs. Direct Materials Cost
DF
Sum of Squar es
1
2013351.144
Residual
13
172186.189
Total
14
2185537.333
Regr ession
Mean Square
2013351.144
F-Value
152.007
P-Value
<.0001
13245.091
Regression Coe fficie nts
Ove rhe ad Cost s vs. Direct Materials Cost
Inter cept
Dir ect Materials Cost
Coef ficient
Std. Error
1456.586
87.225
.356
.029
Std. Coeff.
t-Value
P-Value
1456.586
16.699
<.0001
12.329
<.0001
.960
Multiple regression
Regression Summary
Overhe ad Costs vs. 2 Inde pe nde nts
Count
15
Num . Missing
0
R
.976
R Squared
.952
Adjusted R Squared
.944
RMS Residual
93.658
ANOVA Table
Overhe ad Costs vs. 2 Inde pe nde nts
DF
Sum of S quares
2
2080274.802
Residual
12
105262.531
Total
14
2185537.333
Regression
Mean Square
1040137.401
F- Value
118.576
P- Value
<.0001
8771.878
Regression Coef ficie nt s
Overhe ad Costs vs. 2 Inde pe nde nts
Intercept
Mac hine Hours
Direct Mater ials Cost
Coeffic ient
Std. Err or
1333.960
83.724
Std. Coef f.
t-Value
P- Value
1333.960
15.933
<.0001
4.359
1.578
.316
2.762
.0172
.258
.042
.697
6.101
<.0001
Forecasting overhead
• Predict monthly overhead when machine
hours are expected to be 62 and direct
materials costs are expected to be $1,900.
• Recall
  = $1,333.96
– Coefficient for mhrs = $4.359
– Coefficient for DM$ = $.258
Predicted overhead
Overhead  $1,333.96  $4.359(62)  $.258($1,900)
 $2,094.42
Putting together a bid
• Calculate a minimum bid for a contract that
would use 22 machine hours and $900 in
direct materials. This would be a one-timeonly job.
• What if there is no idle capacity?
• Would your bid change if there were
potential for repeated business?
Problems with regression
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Nonlinear relationships
Outliers
Spurious relationships
Data problems
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Inaccurate accounting cut-offs
Arbitrarily allocated costs
Missing data
Inflation
Thursday
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Cenex and Burd & Fletcher Cases.
Use Excel for regression computations
We will discuss the problems in class and
Work a handout problem in groups.