Cost Behavior: Analysis and Use
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Cost Behavior: Analysis and Use
UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee
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$
Volume (Activity Base)
As the volume of activity goes up
How does the cost react?
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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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$
Volume (Activity Base)
For decision making purposes, it’s 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
Entering new markets
Introducing new products
Buying/Replacing Equipment
Make-or-Buy decisions
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Total Variable Costs
$
Volume (Activity Base)
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Per Unit Variable Costs
$
Volume (Activity Base)
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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 $3010 30 300
100 30 3,000200 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
But differentbetween rangesof activity
$
Volume (Activity Base)
Step Costs are constant withina range of activity.
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Total Fixed Costs
$
Volume (Activity Base)
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$
Volume (Activity Base)
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:
# of Units Monthly Cost Average Cost1 $9,000 $9,000
10 9,000 900100 9,000 90200 9,000 45
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RelevantRange
Curvilinear Costs & the Relevant Range
$
Volume (Activity Base)
Accountant’s Straight-Line Approximation
Economist’s CurvilinearCost Function
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Mixed Costs
$
Volume (Activity Base)
Variable costs
Fixed costs
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Intercept Slope
This is probably how you learned this equation in
algebra.
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Total Costs
VC Per Unit
(Slope)
Fixed Cost
(Intercept)
Level of Activity
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Total Costs
VC Per Unit
(Slope)
Fixed Cost
(Intercept)
Level of Activity
Dependent Variable
Independent Variable
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20
• Account Analysis
• Engineering Approach
• High-Low Method
• Scattergraph Plot
• Regression Analysis
Methods of Analysis
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Account Analysis
Each account is classified as either – variable or – fixed
based on the analyst’s 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 engineer’s evaluation of required inputs for various activities and the cost of those inputs.
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Plot the data points on a graph (total cost vs. activity).
0 1 2 3 4
*
Tota
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t in
1,00
0’s
of D
olla
rs
10
20
0
***
**
* **
*
Activity, 1,000’s of Units Produced
X
Y
The Scattergraph Method
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0 1 2 3 4
*
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1,00
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olla
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10
20
0
***
**
* **
*
Activity, 1,000’s of Units Produced
X
Y
Quick-and-Dirty Method
Intercept is the estimated fixed cost = $10,000
Draw a line through the data points with about anequal numbers of points above and below the line.
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0 1 2 3 4
*
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1,00
0’s
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***
**
* **
*
Activity, 1,000’s of Units Produced
X
Y
Quick-and-Dirty MethodThe slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units
Vertical distance is the change in cost.
Horizontal distance is
the change in activity.
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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
ActivityCost
0 Activity Output
**
* **
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Upward Shift in Cost Relationship
ActivityCost
0 Activity Output
* * *
***
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Presence of Outliers
ActivityCost
0 Activity Output
* * *
*
* *
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Month Activity Level: Patient Days
Maintenance Cost Incurred
January 5,600 $7,900February 7,100 8,500March 5,000 7,400April 6,500 8,200May 7,300 9,100June 8,000 9,800July 6,200 7,800
Brentline Hospital Patient Data
Textbook Example
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Brentline Hospital Patient Data
0
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Patient-Days
Mai
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Brentline Hospital Patient Data
y = 0.7589x + 3430.90
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Brentline Hospital Patient Data
y = 0.7589x + 3430.90
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Patient-Days
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Brentline Hospital Patient Data
y = 0.7589x + 3430.9R2 = 0.8964
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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
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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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Month Activity Level: Patient Days
Maintenance Cost Incurred
January 5,600 $7,900February 7,100 8,500March 5,000 7,400April 6,500 8,200May 7,300 9,100June 8,000 9,800July 6,200 7,800
Brentline Hospital Patient Data
Textbook Example
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High/ Low Month Patient
DaysMaint. Cost
High June 8,000 $9,800
Low March 5,000 7,400
Difference 3,000 $2,400
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Change in Cost V = ------------------ Change in Activity
(Y2 - Y1) V = ------------ (X2 - X1)
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High/ Low Month Patient
DaysMaint. Cost
High June 8,000 $9,800
Low March 5,000 7,400
Difference 3,000 $2,400
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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Total Cost (TC) = FC + VC- FC = - TC + VC
FC = TC - VC
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FC = $9,800 - (8,000 x $0.80) = $3,400
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FC = $7,400 - (5,000 x $0.80) = $3,400
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TC = $3,400 + $0.80X
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Month Activity Level: Patient Days
Maintenance Cost Incurred
January 5,600 $7,900February 7,100 8,500March 5,000 7,400April 6,500 8,200May 7,300 9,100June 8,000 9,800July 6,200 7,800
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 + bxTC = $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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Relevant Range
$
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
Representative High/Low Values
.
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Weaknesses of High-Low
• Other months may not yield the same formula.
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FC = $8,500 - (7,100 x $0.80) = $2,820
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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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Production
Cost
Actual Y
Estimated yError
2)( yY
The objective is to find values of a and b in the equation y = a + bX that minimize
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y = a + bX
The equation for a linear function (straight line) with one independent variable is . . .
Where:
y = The Dependent Variable a = The Constant term (Intercept)
b = The Slope of the line X = The Independent variable
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y = a + bX
The equation for a linear function (straight line) with one independent variable is . . .
Where:
y = The Dependent Variable a = The Constant term (Intercept)
b = The Slope of the line X = The Independent variable
The Dependent 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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Where: a = Fixed cost b = Variable cost n = Number of observations X = Activity measure (Hours, etc.) Y = Total cost
2xbxaxy
xbnay
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))(()())(())((
2
2
YXXnXYXXYa
))(()())(()(
2 XXXnYXXYnb
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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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Method Fixed Cost
Variable Cost
High-Low
Scattergraph
Regression
$3,400
$3,300
$3,431
$0.80
$0.79
$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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Machine Hours
Utility Costs
Machine Hours
Utility Costs
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Hours of Safety
Training
Industrial Accidents
Industrial Accidents
Hours of Safety
Training
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Hair Length
202 Grade
Hair Length
202 Grade
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