2. The Activity Base
A measure of what
causes the incurrence
of a variable cost
Units
produced
Miles
driven
Labour
hours
Machine
hours
2
3. Minutes Talked
Total
Long
Distance
Telephone
Bill
A variable cost is a cost whose total dollar
amount varies in direct proportion to changes in
the activity level. Your total long distance
telephone bill is based on how many minutes
you talk.
True Variable Cost Example
3
4. Summary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable Total variable cost is Variable cost per unit remains
proportional to the activity the same over wide ranges
level within the relevant range. of activity.
Total fixed cost remains the
same even when the activity Fixed cost per unit goes
Fixed level changes within the down as activity level goes up.
relevant range.
Types of Cost Behaviour Patterns
4
5. Minutes Talked
Per
Minute
Telephone
Charge
A variable cost remains constant if expressed on a
per unit basis. The cost per minute talked is
constant. For example, 10 cents per minute.
Variable Cost Per Unit Example
5
6. Volume
Cost
Direct materials is a true or proportionately
variable cost because the amount used during a
period will vary in direct proportion to the level of
production activity.
True Variable Cost
6
7. Relevant
Range
A straight line
closely
approximates a
curvilinear
variable cost line
within the
relevant range.
Activity
Total
Cost
Curvilinear Cost
Function
The Linearity Assumption and the
Relevant Range
7
8. Summary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable Total variable cost is Variable cost per unit remains
proportional to the activity the same over wide ranges
level within the relevant range. of activity.
Total fixed cost remains the
same even when the activity Fixed cost per unit goes
Fixed level changes within the down as activity level goes up.
relevant range.
Types of Cost Behaviour Patterns
8
9. Number of Local Calls
Monthly
Basic
Telephone
Bill
A fixed cost is a cost whose total dollar amount
remains constant as the activity level changes.
Your monthly basic telephone bill is probably fixed
and does not change when you make more local
calls.
Total Fixed Cost Example
9
10. Summary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable Total variable cost is Variable cost per unit remains
proportional to the activity the same over wide ranges
level within the relevant range. of activity.
Total fixed cost remains the
same even when the activity Fixed cost per unit goes
Fixed level changes within the down as activity level goes up.
relevant range.
Types of Cost Behaviour Patterns
10
11. Monthly
Basic
Telephone
Bill
per
Local
Call
Number of Local Calls
Average fixed costs per unit decrease as the
activity level increases. The fixed cost per local call
decreases as more local calls are made.
Fixed Cost Per Unit Example
11
12. Rent
Cost
in
Thousands
of
Dollars
0 1,000 2,000 3,000
Rented Area (Square Feet)
0
30
60
Fixed Costs and Relevant Range
90
Relevant
Range
Total cost doesn’t
change for a wide
range of activity, and
then jumps to a new
higher cost for the
next higher range of
activity.
12
13. • Marginal cost: the additional cost caused by
producing one more unit of output (activity).
– Incremental cost, avoidable cost
• Average cost: the average cost per unit of output
(activity).
– Unit cost
• Beware of unitized fixed costs
Marginal Cost vs. Average Cost
13
14. • January cellphone – texting plan (fixed cost) =
$30
Unitized Fixed Costs – Example
14
16. Fixed Monthly
Utility Charge
Variable
Cost per KW
Activity (Kilowatt Hours)
Total
Utility
Cost
•X
Y
Mixed Costs
The total mixed cost line can be expressed
as an equation: Y = a + bX
Where: Y = the total cost
a = the total fixed cost (the
vertical intercept of the line)
b = the variable cost per unit of
activity (the slope of the line)
X = the level of activity
16
17. If your fixed monthly utility charge is $40, your
variable cost is $0.03 per kilowatt hour, and your
monthly activity level is 2,000 kilowatt hours, what
is the amount of your utility bill?
Mixed Costs Example
Y = a + bX
Y = $40 + ($0.03 × 2,000)
Y = $100
17
18. • Methods for separating mixed costs into fixed
and variable components:
– Account-analysis method
– Scatterplot (or visual-fit) method
– High-low method
– Least-squares regression
– Single variable
– Multiple variables
Analysis of Mixed Costs
18
19. • Is reasonably accurate, cost-effective, and easy
to use, but is subjective
• Each account is classified as either variable or
fixed based on the analyst’s knowledge of how
the account behaves.
• Cost estimates are based on an evaluation of
production methods, and material, labour and
overhead requirements.
Analysis of Mixed Costs
Account Analysis
19
20. Plot the data points on a graph
(total cost vs. activity)
0 1 2 3 4
*
Maintenance
Cost
1,000’s
of
Dollars
10
20
0
*
*
*
*
*
*
*
*
*
Patient-days in 1,000’s
X
Y
Analysis of Mixed Costs
The Scattergraph Method
20
21. The Scattergraph Method
Draw a line through the data points with about an
equal numbers of points above and below the line.
0 1 2 3 4
*
Maintenance
Cost
1,000’s
of
Dollars
10
20
0
*
*
*
*
*
*
*
*
*
Patient-days in 1,000’s
X
Y
21
22. The Scattergraph Method
Use one data point to estimate the total level of activity and the
total cost.
Intercept = Fixed cost: $?
0 1 2 3 4
*
Maintenance
Cost
1,000’s
of
Dollars
10
20
0
*
*
*
*
*
*
*
*
*
Patient-days in 1,000’s
X
Y
Patient days = ?
Total maintenance cost = $?
22
25. Example – Scattergraph Method
Draw a line through the data points with about an
equal numbers of points above and below the line.
25
26. Example – Scattergraph Method
We need to know where the line we drew crosses
the Y axis – this is the fixed costs
Let’s say this is 5.00 – just a guess
26
27. Example – Scattergraph Method
Use one data point to estimate the total
level of activity and the total cost.
Let’s choose this one: 40.20
27
28. Example – Scattergraph Method
As 40.20 is a Y data point, we know that the X is
16.00 (from the original data) and Y is 40.20
28
29. • So what do we have:
• Where the line crosses the Y axis is “5”. This is the fixed
cost – or in the equation Y=a + bX this is “a”.
• We have that Y = 40.2
• We have that X = 16
• We can now solve for “b”
– Y = a + bX
– 40.2 = 5 + 16b
– 40.2 – 5 = 16b
– 35.5 = 16b
– 2.21875 = b
• So our equation using the scattergraph method is
Y = 5 + 2.21875X
Example – Scattergraph Method
29
31. • Simplest method of quantitative analysis
• Uses only the highest and lowest observed
values
• Based on linear relationship
High-Low Method
y = a + bx
31
32. • Using the highest and lowest levels of activity,
compute:
– the variable cost per unit
– the fixed cost
– express the costs in equation form
Hi –Low Method Steps
y = a + bx
32
34. Choose the highest and
lowest levels of activity
(from the driver).
X Y
MH Overhead
High 20 $47
Low 2 $29
Example - High-Low Method
Note: Always choose the dependant variable that goes with the
corresponding driver value (i.e. Choose the high and low driver
and its corresponding overhead... Not $50 as the highest
overhead $)
34
35. Compute the Variable Cost per unit using MH as the
driver.
X Y
MH Overhead
High 20 $47
Low 2 $29
Difference 18 $18
Example - High-Low Method
Y / X = $18 / 18 = $1 per MH. The variable cost per unit
is $1. Or in the equation Y = a + bX, “b” is $1.
35
36. Compute the Compute the fixed cost: Use the equation Y = a + b
X, use the data used to calculate the variable cost, and the “b”
we already calculated.
Use ONE of the coordinates above – either the HIGH or the
LOW and sub into the equation with the b:
– Y = a + bX
– $47 = a + 1 * 20
– $47 – 20 = a
– $27 = a
Example - High-Low Method
X Y
MH Overhead
High 20 $47
Low 2 $29
36
37. Express the costs in equation form
• Y = a + bX
• Y = $27 + $1X or Y = $27 + X
Example - High-Low Method
37
39. A method used to analyze mixed costs if a
scattergraph plot reveals an approximately linear
relationship between the X and Y variables
Least-Squares Regression Method
This method uses all of the
data points to estimate
the fixed and variable
cost components of a
mixed cost.
The goal of this method is
to fit a straight line to the
data that minimizes the
sum of the squared errors.
39
40. • Regression analysis is a statistical method that
measures the average amount of change in the
dependent variable associated with a unit
change in one or more independent variables
• Is more accurate than the High-Low method
because the regression equation estimates
costs using information from all observations;
the High-Low method uses only two
observations
Regression Analysis
40
41. • Simple – estimates the relationship between the
dependent variable and one independent
variable
• Multiple – estimates the relationship between
the dependent variable and two or more
independent variables
Types of Regression
41
42. • Goodness of Fit - R2
– Indicates the strength of the relationship between the
cost driver and costs
– The higher the percentage, the better.
– the R2 test is a measure of the extent to which the
independent variable explains or accounts for the
variability of the of the dependent variable.
• Standard error
– The standard error of the estimate for regression
measures the amount of variability in the points
around the regression line. It is the standard deviation
of the data points as they are distributed around the
regression line.
– The standard error of the estimate can be used to
develop confidence intervals around a prediction.
Terminology
42
43. • T-statistic
– The t-statistic for the significance of the slope is
essentially a test to determine if the regression
model (equation) is usable. If the slope is
significantly different than zero, then we can use
the regression model to predict the dependent
variable for any value of the independent
variable.
– The larger the absolute value of t, the less likely
that the actual value of the parameter could be
zero.
– If the absolute value of t is less than two (2) the
regression model is not appropriate.
Terminology continued
43
45. Example – Regression Analysis
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.77
R Square 0.60
Adjusted R Square 0.56
Standard Error 5.86
Observations 12
Coefficients Standard Error t Stat
Intercept 16.95196252 4.824419266 3.513783
X Variable 1 1.36640295 0.355560276 3.8429573
45
47. Comparing Results from
the Three Methods
The three methods just discussed provide slightly
different estimates of the fixed and variable cost
components of the mixed cost.
This is to be expected because each method uses
differing amounts of the data points to provide
estimates.
Least-squares regression provides the most accurate
estimate because it uses all the data points.
47
