Transcript OM-459 Financial Tools For Managers

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 Costs
$
Volume (Activity Base)
Per Unit Variable Costs
$
Volume (Activity Base)
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
1
10
100
200
Cost/Unit
Total Cost
$30
$30
30
300
30
3,000
30
6,000
Linearity is assumed
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.
Step-Variable Costs
Step Costs are constant within
a range of activity.
$
But different
between ranges
of activity
Volume (Activity Base)
Total Fixed Costs
$
Volume (Activity Base)
Per-Unit Fixed Costs
$
Volume (Activity Base)
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 Cost
1
$9,000
$9,000
10
9,000
900
100
9,000
90
200
9,000
45
Curvilinear Costs & the Relevant Range
Economist’s Curvilinear
Cost Function
$
Accountant’s
Straight-Line
Approximation
Relevant
Range
Volume (Activity Base)
Mixed Costs
$
Variable
costs
Volume (Activity Base)
Fixed
costs
Intercept
Slope
This is probably how
you learned this
equation in algebra.
Total Costs
Fixed Cost
(Intercept)
VC Per Unit
(Slope)
Level of
Activity
Dependent
Total Costs
Variable
Fixed Cost
(Intercept)
VC Per Unit
(Slope)
Independent
Level of
Variable
Activity
Methods of Analysis
• Account Analysis
• Engineering Approach
• High-Low Method
• Scattergraph Plot
• Regression Analysis
20
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.
The Scattergraph Method
Plot the data points on a
graph (total cost vs. activity).
Total Cost in
1,000’s of Dollars
Y
20
10
0
* *
* *
* ** *
**
X
0
1
2
3
4
Activity, 1,000’s of Units Produced
Quick-and-Dirty Method
Draw a line through the data points with about an
equal numbers of points above and below the line.
Total Cost in
1,000’s of Dollars
Y
20
10
* ** *
**
* *
*
* Intercept
is the estimated
fixed cost = $10,000
0
X
0
1
2
3
4
Activity, 1,000’s of Units Produced
Quick-and-Dirty Method
The slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units
Total Cost in
1,000’s of Dollars
Y
20
10
0
* *
*
*Horizontal
distance is
the change in
activity.
* ** *
**
Vertical distance is
the change in cost.
X
0
1
2
3
4
Activity, 1,000’s of Units Produced
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
Activity
Cost
*
*
0
*
*
*
Activity Output
Upward Shift in Cost Relationship
Activity
Cost
*
* *
0
*
*
*
Activity Output
Presence of Outliers
Activity
Cost
*
*
*
* *
0
*
Activity Output
Brentline Hospital Patient Data
Month
January
February
March
April
May
June
July
Activity Level:
Patient Days
5,600
7,100
5,000
6,500
7,300
8,000
6,200
Maintenance
Cost Incurred
$7,900
8,500
7,400
8,200
9,100
9,800
7,800
Textbook Example
Brentline Hospital Patient Data
12000
Maintenance Cost
10000
8000
6000
4000
2000
0
0
2000
4000
6000
Patient-Days
8000
10000
Brentline Hospital Patient Data
12000
Maintenance Cost
10000
8000
6000
4000
2000
y = 0.7589x + 3430.9
0
0
2000
4000
6000
Patient-Days
8000
10000
Brentline Hospital Patient Data
12000
Maintenance Cost
10000
8000
6000
4000
2000
y = 0.7589x + 3430.9
0
0
2000
4000
6000
Patient-Days
8000
10000
Brentline Hospital Patient Data
12000
Maintenance Cost
10000
8000
6000
4000
2
R = 0.8964
y = 0.7589x + 3430.9
2000
0
0
2000
4000
6000
Patient-Days
8000
10000
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.
Brentline Hospital Patient Data
Month
January
February
March
April
May
June
July
Activity Level:
Patient Days
5,600
7,100
5,000
6,500
7,300
8,000
6,200
Maintenance
Cost Incurred
$7,900
8,500
7,400
8,200
9,100
9,800
7,800
Textbook Example
High/
Low
Month
Patient
Days
Maint.
Cost
High
June
8,000
$9,800
Low
March
5,000
7,400
3,000
$2,400
Difference
Change in Cost
V = -----------------Change in Activity
(Y2 - Y1)
V = -----------(X2 - X1)
High/
Low
Month
High
June
Low
March
Divided by the
Difference
change in
activity
Patient
Days
Maint.
Cost
The
Change
8,000
$9,800
in Cost
5,000
7,400
3,000
$2,400
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
Activity Level:
Month
Patient Days
January
5,600
February
7,100
March
5,000
We have taken “Total
April
6,500
a
MayCosts” which is7,300
mixed cost and we
June
8,000
have separated it 6,200
into
July
its VC and FC
components.
Maintenance
Cost Incurred
$7,900
8,500
7,400
8,200
9,100
9,800
7,800
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 + bx
TC = $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).
Cost
Actual Y
Error
Estimated y
The objective is to find
values of a and b in the
equation y = a + bX that
minimize (Y  y) 2
Production
The equation for a linear
function (straight line) with
one independent variable is . . .
y = a + bX
Where:
y
a
b
X
=
=
=
=
The Dependent Variable
The Constant term (Intercept)
The Slope of the line
The Independent variable
The equation
for a linear
The
function
(straight line) with
Dependent
Variable
one independent
variable is . . .
y = a + bX
Where:
The
y = The Dependent Variable
Independent
a = The Constant term (Intercept)
Variable
b = The Slope of the
line
X = 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.
xy

a
x

b
x

 
y

na

b
x


Where: a
b
n
X
Y
=
=
=
=
=
Fixed cost
Variable cost
Number of observations
Activity measure (Hours, etc.)
Total cost
2
(Y )(X )  (X )(XY )
a
2
n(X )  (X )(Y )
2
n(XY )  (X )(Y )
b
2
n(X )  (X )(X )
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.
Method
Fixed
Cost
Variable
Cost
High-Low
$3,400
$0.80
Scattergraph
$3,300
$0.79
Regression
$3,431
$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-offit.
• 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
Hours of
Safety
Training
Industrial
Accidents
Hair
Length
202
Grade
Hair
Length
202
Grade