Predicting Cost Behavior
Chapter 2, Appendix 2A
ACCTG 404
A2A-1
Build a model to predict life expectancy:
• What factors would you collect?
• How would you use data to build predictive
model?
A2A-2
Predictive Output
from Regression Models
Volunteer to use the model…
• Height / Weight
• Medical history
• Alcohol / Tobacco / Drug (!) use
A2A-3
Our Application of Predictive Models
There are many applications for predictive analysis
throughout accounting and finance.
In this course we will focus on using regression
analysis and other techniques to estimate future
(fixed and variable) costs.
– Pay attention to the basic principles
– Focus on understanding the outputs
A2A-4
Plot of Actual Observations
A2A-5
Which Line Best Estimates Total
Cost?
A2A-6
The High-Low Method
1) Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit
2) Fixed cost = Total cost – Total variable cost
Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)
Fixed cost = $9,800 – $6,400 = $3,400
3) Total cost = Fixed cost + Variable cost (Y = a + bX)
Y = $3,400 + $0.80X
A2A-7
Quick Check
Sales salaries and commissions are $10,000 when 80,000 units
are
aresold,
sold,and
and$14,000
$14,000when
when120,000
120,000units
unitsare
aresold.
sold. Using
Usingthe
the
high-low
high-lowmethod,
method,what
whatisisthe
thevariable
variableportion
portionof
ofsales
salessalaries
salaries
and
andcommission?
commission?
a.
a.
b.
b.
c.c.
d.
d.
$0.08
$0.08per
perunit
unit
$0.10
$0.10per
perunit
unit
$0.12
$0.12per
perunit
unit
$0.125
$0.125per
perunit
unit
$4,000 ÷ 40,000 units
= $0.10 per unit
A2A-8
Quick Check
Sales salaries and commissions are $10,000 when 80,000 units
are
aresold,
sold,and
and$14,000
$14,000when
when120,000
120,000units
unitsare
aresold.
sold. Using
Usingthe
the
high-low
high-lowmethod,
method,what
whatisisthe
thefixed
fixedportion
portionof
ofsales
salessalaries
salariesand
and
commissions?
commissions?
a.
a.
b.
b.
c.c.
d.
d.
$$ 2,000
2,000
$$ 4,000
4,000
$10,000
$10,000
$12,000
$12,000
A2A-9
Pitfalls to High-Low Method
• High level of activity may not coincide with
high level of cost and vice-versa
• Utilizes only two data points
• Unusually high or low levels of activity
(outliers) may produce inaccurate results
A2A-10
Regression Analysis
• Regression analysis is a statistical method that
measures the average amount of change in the
dependent variable (i.e., y variable) associated with a
unit change in one or more independent variables
(i.e., x variable or variables)
• It is more accurate than the High-Low method
because the regression equation estimates costs
using information from all observations; the HighLow method uses only two observations
A2A-11
Which Line Best Estimates Total
Cost?
High-Low Method
Regression Analysis
A2A-12
Simple Regression Analysis Example
Qdoba wants to know its
average fixed cost and
variable cost per unit.
Using the data to the
right, let’s see how to do
a regression using Excel.
A2A-13
Simple Regression Analysis Example
We will need three pieces of
information from your
regression analysis:
1. Estimated Variable Cost
per Unit (line slope)
2. Estimated Fixed Costs
(line intercept)
3. Goodness of fit, or R2
A2A-14
Mac Users: Data Analysis ToolPak
•
Mac users:
http://www.analystsoft.com/e
n/products/statplusmacle/dow
nload.phtml
• PC users:
http://technet.microsoft.com/e
n-us/magazine/ff969363.aspx
A2A-15
Regression Analysis in Excel
A2A-16
Regression Analysis in Excel
A2A-17
Regression Analysis in Excel
A2A-18
Regression Analysis in Excel: Intercept
Intercept (constant): amount of Y
when X is 0. In this regression it can
be interpreted as the fixed costs.
A2A-19
Regression Analysis in Excel: Slope
Slope (coefficient on independent
variable): the increase in Y (cost) for
each unit increase in X (cost driver).
so, expected monthly total costs = $2,618 + $2.76x
A2A-20
Regression Analysis in Excel: R2
“R-Square” measures the explanatory
power of the regression. It ranges
from 0 to 1.
More reliable (better fit) if closer to 1.
A2A-21
Regression Analysis in Excel: t-Stat
t-value (t-stat): Coefficient ÷ SE
Degree to which variable has a valid,
stable, long-term relationship with
the dependent variable. Generally
look for t-values > |2|.
A2A-22
Regression Analysis in Excel: p-value
p-value: risk that independent
variable has only a small chance of
relationship to dependent variable.
As a general guide p-values less than
.05 or .01 are generally representative
of a relationship.
A2A-23
Regression Analysis in Excel
In formal statistics, we would normally calculate the
desired CI from Z table for specific intervals. In this
course we concentrate on two approximations.
67% CI Z value ~ 1 then 67% C. I. = M ± (1 × SE)
95% CI Z value ~ 2 then 95% C. I. = M ± (2 × SE)
A2A-24
Regression Analysis in Excel
Confidence interval (CI): range around the regression
coefficient within which the user can be confident that the
predicted cost will fall.
Calculate 95% Confidence Interval for the variable cost per
meal.
95% C. I. = M ± (2 × SE)
95% C. I. = 2.768 ± (2 × .1988)
95% C. I. = 2.768 ± (.3976)
95% confidence that costs range from 2.3704 to 3.1656
A2A-25
Regression Analysis in Excel
Calculate 95% Confidence Interval for
the total cost assuming 1,500 meals.
2618.72+(1500×2.768) = 6770.72
95% C. I. = M ± (2 × SE)
95% C. I. = 6770.72 ± (2 × 588.307)
95% C. I. = 6770.72 ± (1,176.61)
95% confidence that costs range from
5,594.11 to 7,947.33
A2A-26
Types of Regression
• 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
A2A-27
The Ideal Database
1. The database should contain numerous
reliably-measured observations of the cost
driver and the costs
2. In relation to the cost driver, the database
should consider many values spanning a
wide range
A2A-28
Potential Data Issues
• The relationship between the cost driver and the cost is
not stationary
– Inflation has affected costs, the driver, or both
• Outliers in the data
– Hurricane Sandy in NJ/NY: you should exclude from national
Qdoba forecast
– Data errors
• Non-linearity
– Economies of Scale
– Quantity Discounts
– Step Cost Functions: resources increase in “lot-sizes,” not
individual units
A2A-29
In Class Problem
As part of his job as cost analyst, Max Thompson collected the following information
concerning the operations of the Machining Department:
Observation
Machine-hours
Total Operating Costs
January
4,000
$45,000
February
4,600
49,500
March
3,800
45,750
April
4,400
48,000
May
4,500
49,800
a. Use the high-low method to determine the estimating cost function with machinehours as the cost driver.
b. If June's estimated machine-hours total 4,200, what are the total estimated costs
of the Machining Department?
a. Slope coefficient = ($49,500 - $45,750)÷(4,600 - 3,800) = $4.6875 per machine-hour
Constant = $49,500 - ($4.6875 × 4,600) = $27,937.50
Estimating equation = $27,937.50 + $4.6875X
b. June's estimated costs = $27,937.50 + $4.6875 × 4,200 = $47,625
A2A-30
In Class Problem
a. What is linear regression estimate? Y = 1.355 + 0.0014X
b. What is the the predicted GPA for someone with a SAT_SCORE of
1200?
A2A-31
In Class Problem
c.
d.
What is the 95% confidence interval for the coefficient SAT_SCORE?
What is the 95% confidence interval around the predicted GPA for
someone with a SAT_SCORE of 1200?
A2A-32