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Cost estimation - Cost behavior
What we really want to understand is howspending will vary in a variety of decision
settings.
Cause-effect relations and costs drivers.
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Capacity and capacity costs:
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
roduct.
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Capacity and capacity costs:
What does a unit of product cost if overhead
is allocated based on theoretical capacity?
Practical capacity?
Normal capacity?
Budgeted capacity.
Which measure should the company use?
$17
$18.11
$18.76
$19.50
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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?
What does that cost represent?About $222,300
The cost of idle
or excess capacity.
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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.
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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.
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Cost estimation: overhead costs
First weeks product costing exercises:
applied overhead.
Valuing inventories & costs of sales.
Not for costing individual products
Not for predicting costs
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What methods are available?
Engineering estimates
Account analysis
Scattergraph and high-low estimates
Statistical methods (typically regression)
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Cost behavior: linear function by
assumption.TC = FC + VC*(level of cost driver)
where
TC = total cost
FC = fixed cost
VC = variable cost per unit of the cost
driver,
and sometimes the cost driver is
represented by X.
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Volume
Overhead Costs
AB
C D
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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
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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. Thevariable 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.
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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.
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Plot of overhead costs vs.
machine hours
0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
4000.00
0.00 30.00 60.00 90.00 120.00 150.00
Machine Hours
Scattergram
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High-Low cost estimation
Find the variable cost per unit of the cost
driver (VC):
activityLowest-activityHighest
activitylowestatOverhead-activityhighestatOverheadVC!
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High-Low method: Example
continued
mhr50-mhr142
$1,896-$3,105VC !
mhr92
$1,209VC !
$13.14/mhrVC !
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High-Low cost estimation
$1,
mhr)142*($13.14-$3,105costFixed
!
!
$2,7T
r)*($13.14$1,239T
r115*FT
!
!
!
Estimate the total overhead cost during a
months when 115 machine hours will be used:
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Cost estimation using regression
Y = the dependent variable (total O/H cost)
X = the explanatory variables
Y = EFX +I
where X = machine hours and I = random error.
T
C =F
C + VC*X + I
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Regression fits a line through
these data points:
0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
4000.00
0.00 30.00 60.00 90.00 120.00 150.00
Machine Hours
Scattergram
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S
imple linear regression
One explanatory variable
Cost estimation equation
Coefficient of correlation (R)
Coefficient of determination (R2)
Goodness of fitMeasure of importance
F-statistic (hypothesis testing)
p-value
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Coefficient of correlation
Measures the correlation between the independent
and the dependent variables.
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Coefficient of determination
Measures the percentage of variation in the
dependent variable explained by the independentvariable.
When the predicted values exactly equal the
actual costs, R2 = 1.
A goodness of fit test: R2 > .3
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T
he F statistic
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
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T
he 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.
IfF is large, the hypothesis is rejected.
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Regression result interpretation
15
0
.896
.802
.787
182.244
Count
Num. Missing
R
R Squared
Adjusted R Squared
RMS Residual
Regression Summary
Overhead Costs vs. Machine Hours
1 1753772.049 1753772.049 52.804
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Simple linear regression
0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
4000.00
0.00 30.00 60.00 90.00 120.00 150.00
Machine HoursOverhead Costs = 1334.293 + 12.373 * Machine Hours; R^2 = .802
Scattergram
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R
esults using DM$15
0
.960
.921
.915
115.087
Count
Num. Miss ing
R
R Squared
Adjust ed R Squared
RMS Residual
Regression Su ary
Overhead osts vs. Direct Materials ost
1 2013351.144 2013351.144 152.007
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Multiple regression15
0
.976
.952
.944
93.658
Count
Num. Miss ing
R
RS ua e
juste RS ua e
RMS Resi ual
Regress n Summ ry
OverheadC s s vs. 2 Independen s
2 2080274.802 1040137.401 118.576
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Forecasting overhead Predict monthly overhead when machine
hours are expected to be 62 and direct
materials costs are expected to be $1,900.
Recall
E = $1,333.96
Coefficient for mhrs = $4.359
Coefficient for DM$ = $.258
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Predicted overhead
$2,094.42
00)$.258($1,9$4.359(62)$1,333.96Overhead
!
!
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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-time-
only job.
What if there is no idle capacity?
Would your bid change if there were
potential for repeated business?
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Problems with regression
Nonlinear relationships
Outliers Spurious relationships
Data problems
I
naccurate accounting cut-offsArbitrarily allocated costs
Missing data
Inflation
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Thursday
Cenex and Burd & Fletcher Cases.
U
seE
xcel for regression computations We will discuss the problems in class and
Work a handout problem in groups.
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