Cost estimation - Cost behavior

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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.

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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 product.

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Capacity and capacity costs

• What does a unit of product cost if overhead is
  allocated based on theoretical capacity?

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Practical capacity?
18.11
Normal capacity?
18.76
Budgeted capacity.
19.50
Which measure should the company use?
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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?
About 222,300
What does that cost represent?
The cost of idleor 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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A
B
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.
  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.

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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
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High-Low cost estimation

• Find the variable cost per unit of the cost
  driver (VC)

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High-Low method Example continued
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High-Low cost estimation
Estimate the total overhead cost during amonths
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 ?????X ???
• where X machine hours and ? random error.
• TC FC VCX ?.

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Regression fits a line through these data points
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Simple linear regression

• 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

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Coefficient of correlation
Measures the correlation between the
independentand the dependent variables.
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Coefficient of determination
Measures the percentage of variation in
thedependent variable explained by the
independentvariable.
When the predicted values exactly equal
theactual costs, R2 1.
A goodness of fit test R2 gt .3
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The 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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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.

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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.

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Regression result interpretation
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Simple linear regression
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Results using DM
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Multiple regression
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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
• ? 1,333.96
• Coefficient for mhrs 4.359
• Coefficient for DM .258

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Predicted overhead
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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
• Inaccurate accounting cut-offs
• Arbitrarily allocated costs
• Missing data
• Inflation

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Thursday

• Cenex and Burd Fletcher Cases.
• Use Excel for regression computations
• We will discuss the problems in class and
• Work a handout problem in groups.