cost behavior: analysis and use uaa – acct 202 principles of managerial accounting dr. fred barbee
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Cost Behavior: Analysis and Use
UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee
$
Volume (Activity Base)
As the volume of activity goes up
How does the cost react?
Why do I need to know this
information?
Good question. Here are some examples of
when you would want to
know this.
$
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.
Knowledge of Cost Behavior
Setting Sales Prices
Entering new markets
Introducing new products
Buying/Replacing Equipment
Make-or-Buy decisions
Total Variable CostsTotal Variable Costs
$
Volume (Activity Base)
Per Unit Variable CostsPer Unit Variable Costs
$
Volume (Activity Base)
Variable Costs - ExampleVariable 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 Cost1 $30 $30
10 30 300100 30 3,000200 30 6,000
Linearity is assumed
Variable CostsVariable Costs
The equation for total VC:
TVC = VC x Activity BaseTVC = VC x Activity Base
Thus, a 50% increase in volume results in a 50% increase in total VC.
Step-Variable CostsStep-Variable Costs
But differentbetween rangesof activity
$
Volume (Activity Base)
Step Costs are constant withina range of activity.
Total Fixed CostsTotal Fixed Costs
$
Volume (Activity Base)
$
Volume (Activity Base)
Per-Unit Fixed CostsPer-Unit Fixed Costs
Fixed Costs - ExampleFixed 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
RelevantRange
Curvilinear Costs & the Relevant RangeCurvilinear Costs & the Relevant Range
$
Volume (Activity Base)
Accountant’s Straight-Line Approximation
Economist’s CurvilinearCost Function
Mixed CostsMixed Costs
$
Volume (Activity Base)
Variable costs
Fixed costs
Intercept Slope
This is probably how you learned this equation in
algebra.
Total Costs
VC Per Unit
(Slope)
Fixed Cost
(Intercept)
Level of Activity
Total Costs
VC Per Unit
(Slope)
Fixed Cost
(Intercept)
Level of Activity
Dependent Variable
Independent Variable
20
• Account Analysis
• Engineering Approach
• High-Low Method
• Scattergraph Plot
• Regression Analysis
Methods of Analysis
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.
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.
Plot the data points on a graph (total cost vs. activity).
Plot the data points on a graph (total cost vs. activity).
0 1 2 3 4
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To
tal
Co
st i
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000’
s o
f D
oll
ars
10
20
0
***
**
**
*
*
Activity, 1,000’s of Units Produced
X
Y
The Scattergraph Method
0 1 2 3 4
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To
tal
Co
st i
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000’
s o
f D
oll
ars
10
20
0
***
**
**
*
*
Activity, 1,000’s of Units Produced
X
Y
Quick-and-Dirty Method
Intercept is the estimated fixed cost = $10,000
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.
Draw a line through the data points with about anequal numbers of points above and below the line.
0 1 2 3 4
*
To
tal
Co
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000’
s o
f D
oll
ars
10
20
0
***
**
**
*
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Activity, 1,000’s of Units Produced
X
Y
Quick-and-Dirty Method
The slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units
The slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units
Vertical distance is the change in cost.
Vertical distance is the change in cost.
Horizontal distance is
the change in activity.
Horizontal distance is
the change in activity.
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?
Nonlinear Relationship
ActivityCost
0 Activity Output
**
* **
Upward Shift in Cost Relationship
ActivityCost
0 Activity Output
* **
**
*
Presence of Outliers
ActivityCost
0 Activity Output
* **
*
**
MonthActivity Level: Patient Days
Maintenance Cost Incurred
January 5,600 $7,900
February 7,100 8,500
March 5,000 7,400
April 6,500 8,200
May 7,300 9,100
June 8,000 9,800
July 6,200 7,800
Brentline Hospital Patient Data
Textbook Example
Brentline Hospital Patient Data
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2000
4000
6000
8000
10000
12000
0 2000 4000 6000 8000 10000
Patient-Days
Mai
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ost
Brentline Hospital Patient Data
y = 0.7589x + 3430.90
2000
4000
6000
8000
10000
12000
0 2000 4000 6000 8000 10000
Patient-Days
Mai
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ost
Brentline Hospital Patient Data
y = 0.7589x + 3430.90
2000
4000
6000
8000
10000
12000
0 2000 4000 6000 8000 10000
Patient-Days
Mai
nte
nan
ce C
ost
Brentline Hospital Patient Data
y = 0.7589x + 3430.9R2 = 0.8964
0
2000
4000
6000
8000
10000
12000
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Patient-Days
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From Algebra . . .
• If we know any two points on a line, we can determine the slope of that line.
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
High-Low Method
• Using these two points, we determine the equation for that line . . .
–The intercept; and
–The Slope parameters
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.
MonthActivity Level: Patient Days
Maintenance Cost Incurred
January 5,600 $7,900
February 7,100 8,500
March 5,000 7,400
April 6,500 8,200
May 7,300 9,100
June 8,000 9,800
July 6,200 7,800
Brentline Hospital Patient Data
Textbook Example
High/ Low
MonthPatient Days
Maint. Cost
High June 8,000 $9,800
Low March 5,000 7,400
Difference 3,000 $2,400
Change in Cost V = ------------------ Change in Activity
(Y2 - Y1) V = ------------ (X2 - X1)
High/ Low
MonthPatient Days
Maint. 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
Change in Cost V = ------------------ Change in Activity
$2,400 V = ------------ 3,000
= $0.80 Per Unit
Total Cost (TC) = FC + VC- FC = - TC + VC
FC = TC - VC
FC = $9,800 - (8,000 x $0.80) = $3,400
FC = $7,400 - (5,000 x $0.80) = $3,400
TC = $3,400 + $0.80X
MonthActivity Level: Patient Days
Maintenance Cost Incurred
January 5,600 $7,900
February 7,100 8,500
March 5,000 7,400
April 6,500 8,200
May 7,300 9,100
June 8,000 9,800
July 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.
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?
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
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.
Relevant Range
$
Volume (Activity Base)
Strengths of High-Low Method
• Simple to use
• Easy to understand
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).
.
. ... .. .. ...
..
Extreme values - not necessarily representative
Representative High/Low Values
.
Weaknesses of High-Low
• Other months may not yield the same formula.
FC = $8,500 - (7,100 x $0.80) = $2,820
FC = $7,800 - (6,200 x $0.80) = $2,840
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.
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).
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
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
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
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.
Where: a = Fixed cost b = Variable cost n = Number of observations X = Activity measure (Hours, etc.) Y = Total cost
2xbxaxy
xbnay
))(()(
))(())((2
2
YXXn
XYXXYa
))(()(
))(()(2 XXXn
YXXYnb
Fixed Costs
Variable Costs
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.
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.
MethodFixed Cost
Variable Cost
High-Low
Scattergraph
Regression
$3,400
$3,300
$3,431
$0.80
$0.79
$0.76
Coefficient of Determination
• R2 is the percentage of variability in the dependent variable that is explained by the independent variable.
Coefficient of Determination
• This is a measure of goodness-of-fit.
• The higher the R2, the better the fit.
Coefficient of Determination
• The higher the R2, the more variation (in the dependent variable) being explained by the independent variable.
Coefficient of Determination
• R2 ranges from 0 to 1.0• Good Vs. Bad R2s is relative.• There is no magic cutoff
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.
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.”
Machine Hours
Utility Costs
Machine Hours
Utility Costs
Hours of Safety
Training
Industrial Accidents
Industrial Accidents
Hours of Safety
Training
Hair Length
202 Grade
Hair Length
202 Grade
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