Cost Behavior: Analysis and Use

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Cost Behavior Analysis
and Use

• Chapter 4

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Graphically
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Why do I need to know this information?
Good question. Here are some examples of when
you would want to know this.
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Graphically

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Volume (Activity Base)
For decision making purposes, its important for
a manager to know the cost behavior pattern and
the relative proportion of each cost.
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Knowledge of Cost Behavior
Setting Sales Prices
Make-or-Buy decisions
Entering new markets
Introducing new products
Buying/Replacing Equipment
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Total Variable Costs
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Per Unit Variable Costs
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Variable Costs - Example
A company manufacturers microwave ovens. Each
oven requires a timing device that costs 30.
The per unit and total cost of the timing device
at various levels of activity would be
of Units
Cost/Unit
Total Cost
1
30
30
10
30
300
100
30
3,000
200
30
6,000
Linearity is assumed
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Variable Costs
The equation for total VC
TVC VC x Activity Base
Thus, a 50 increase in volume results in a 50
increase in total VC.
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Step-Variable Costs
Step Costs are constant within a range of
activity.

But different between ranges of activity
Volume (Activity Base)
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Total Fixed Costs
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Per-Unit Fixed Costs
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Fixed Costs - Example
A company manufacturers microwave ovens. The
company pays 9,000 per month for rental of its
factory building. The total and per unit cost of
the rent at various levels of activity would be
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Curvilinear Costs the Relevant Range
Economists Curvilinear Cost Function

Accountants Straight-Line Approximation
Volume (Activity Base)
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Mixed Costs
Variable costs
Fixed costs
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The Analysis of . . .
Mixed Costs
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Slope
Intercept
y a bX
This is probably how you learned this equation in
algebra.
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Total Costs
VC Per Unit (Slope)
y a bX
Fixed Cost (Intercept)
Level of Activity
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Total Costs
VC Per Unit (Slope)
Dependent Variable
y a bX
Fixed Cost (Intercept)
Level of Activity
Independent Variable
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Methods of Analysis

• Account Analysis
• Engineering Approach
• High-Low Method
• Scattergraph Plot

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Account Analysis

• Each account is classified as either
• variable or
• fixed
• based on the analysts prior knowledge of how the
  cost in the account behaves.

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Engineering Approach

• Detailed analysis of cost behavior based on an
  industrial engineers evaluation of required
  inputs for various activities and the cost of
  those inputs.

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The Scattergraph Method
Plot the data points on a graph (total cost vs.
activity).
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Quick-and-Dirty Method
Draw a line through the data points with about
anequal numbers of points above and below the
line.
Y
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Total Cost in1,000s of Dollars


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Intercept is the estimated fixed cost 10,000
0
X
0 1 2 3 4
Activity, 1,000s of Units Produced
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Quick-and-Dirty Method
The slope is the estimated variable cost per
unit. Slope Change in cost Change in units
Y
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Total Cost in1,000s of Dollars


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Horizontal distance is the change in activity.
Vertical distance is the change in cost.
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X
0 1 2 3 4
Activity, 1,000s of Units Produced
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Advantages

• One of the principal advantages of this method is
  that it lets us see the data.
• What are the advantages of seeing the data?

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Nonlinear Relationship
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Upward Shift in Cost Relationship
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Presence of Outliers
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Petro Dar Machine Data
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From Algebra . . .

• If we know any two points on a line, we can
  determine the slope of that line.

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High-Low Method

• A non-statistical method whereby we examine two
  points out of a set of data . . .
• The high point and
• The low point

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High-Low Method

• Using these two points, we determine the equation
  for that line . . .
• The intercept and
• The Slope parameters

y a bX
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High-Low Method

• To get the variable costs . . .
• We compare the difference in costs between the
  two periods to
• The difference in activity between the two
  periods.

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Brentline Hospital Patient Data
Low
High
Textbook Example
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Change in Cost V ------------------
Change in Activity
(Y2 - Y1) V ------------
(X2 - X1)
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Calculate the Variable Rate
The Change in Cost
Divided by the change in activity
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Change in Cost V ------------------
Change in Activity
2,400 V ------------
3,000
0.80 Per Unit
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Calculate Fixed Costs
Total Cost (TC) FC VC - FC - TC VC FC
TC - VC
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Calculate Fixed Costs
Using June
FC TC - VC
FC 9,800 - (8,000 x 0.80) 3,400
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Calculate Fixed Costs
Using March
FC TC - VC
FC 7,400 - (5,000 x 0.80) 3,400
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The Cost Formula
y a bx
TC 3,400 0.80X
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We have taken Total Costs which is a mixed cost
and we have separated it into its VC and FC
components.
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So what? You say! Thank you for asking! Now I
can use this formula for planning purposes. For
example, what if I believe my activity level will
be 6,325 patient days in February. What would I
expect my total maintenance cost to be?
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What is the estimated total cost if the activity
level for February is expected to be 6,325
patient days?
Y a bx TC 3,400 6,325 x 0.80 TC 8,460
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Some Important Considerations

• We have used historical cost to arrive at the
  cost equation.
• Therefore, we have to be careful in how we use
  the formula.
• Never forget the relevant range.

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8,000
5,000

5,000 to 8,000 activity level
Volume (Activity Base)
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Strengths of High-Low Method

• Simple to use
• Easy to understand

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Weaknesses of High-Low

• Only two data points are used in the analysis.
• Can be problematic if either (or both) high or
  low are extreme (i.e., Outliers).

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Extreme values - not necessarily representative
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Representative High/Low Values
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Weaknesses of High-Low

• Other months may not yield the same formula.

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Calculate Fixed Costs
Using February
FC TC - VC
FC 8,500 - (7,100 x 0.80) 2,820
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Calculate Fixed Costs
Using July
FC TC - VC
FC 7,800 - (6,200 x 0.80) 2,840
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Regression Analysis

• A statistical technique used to separate mixed
  costs into fixed and variable components.
• All observations are used to fit a regression
  line which represents the average of all data
  points.

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Regression Analysis

• Requires the simultaneous solution of two linear
  equations
• So that the squared deviations from the
  regression line of each of the plotted points
  cancel out (are equal to zero).

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Cost
Actual Y
Error
Estimated y
The objective is to find values of a and b in the
equation y a bX that minimize
Production
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The equation for a linear function (straight
line) with one independent variable is . . .
y a bX
Where y The Dependent Variable
a The Constant term (Intercept)
b The Slope of the line
X The Independent variable
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The equation for a linear function (straight
line) with one independent variable is . . .
The Dependent Variable
y a bX
Where y The Dependent Variable
a The Constant term (Intercept)
b The Slope of the line
X The Independent variable
The Independent Variable
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Regression Analysis

• With this equation and given a set of data.
• Two simultaneous linear equations can be
  developed that will fit a regression line to the
  data.

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Least-Squares Equations
Where a Fixed cost
b Variable cost
n Number of
observations
X Activity measure (Hours, etc.)
Y Total cost
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Estimating the Regression Line
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Fixed Costs
Variable Costs
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R2, the Coefficient of Determination is the
percentage of variability in the dependent
variable being explained by the independent
variable.
This is referred to as a goodness of fit
measure.
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R, the Coefficient of Correlation is square root
of R2. Can range from -1 to 1. Positive
correlation means the variables move together.
Negative correlation means they move in opposite
directions.
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Comparison of Methods
Method
Fixed Cost
Variable Cost
High-Low
3,400
0.80
Scattergraph
3,300
0.79
Regression
3,431
0.76
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Coefficient of Determination

• R2 is the percentage of variability in the
  dependent variable that is explained by the
  independent variable.

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Coefficient of Determination

• This is a measure of goodness-of-fit.
• The higher the R2, the better the fit.

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Coefficient of Determination

• The higher the R2, the more variation (in the
  dependent variable) being explained by the
  independent variable.

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Coefficient of Determination

• R2 ranges from 0 to 1.0
• Good Vs. Bad R2s is relative.
• There is no magic cutoff

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Coefficient of Correlation

• The relationship between two variables can be
  described by a correlation coefficient.
• The coefficient of correlation is the square root
  of the coefficient of determination.

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Coefficient of Correlation

• Provides a measure of strength of association
  between two variables.
• The correlation provides an index of how closely
  two variables go together.

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Positive Correlation
Machine Hours
Utility Costs
Machine Hours
Utility Costs
r approaches 1
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r approaches 1
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r Equals 1
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Negative Correlation
Hours of Safety Training
Industrial Accidents
Industrial Accidents
Hours of Safety Training
r approaches -1
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r approaches -1
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r Equals -1
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No Correlation
Hair Length
202 Grade
Hair Length
202 Grade
r 0
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