Cost Behaviour: Part 2 of 2
Sections 1 and 2
Feb 1, 2013
Professor: Khim Kelly
Office: HH386B
Office Hours: Mon/Wed 11:30am – 12:30pm and Appointment
Email: kokelly@uwaterloo.ca
TA: Kun Huo
Email: khuo@uwaterloo.ca
1 Feb 2013 Overview
• Last lecture …
– Fixed costs, variable costs, step variable costs,
mixed costs
– How to use costs behaviour to predict costs
– Analyze mixed costs (High-Low Method)
• Major topics for today…
– Analyse mixed costs (Regression)
– Another example of High-Low method
– The contribution margin approach
2
Regression
• High-Low method uses only two data points
– Improve accuracy of results by considering more data points
• Regression analysis
– Uses all the available data points
– “Fits” a line to the data points while attempting to minimize
errors.
– Develops a similar looking equation to High-Low method
• Both assume linearity
– Need to be aware of potential differences in cost behaviour
outside of the relevant range
– When predicting costs, you might want to limit analysis to a
range around expected activity
The next slides plot data (from last lecture Clicker Question
#3) with activity on the X axis and the mixed cost on the
Y axis.
Last Lecture: Clicker Question #4: Answer
Month
Jan
Feb
March
April
May
June
July
Aug
Sept
Oct
Nov
Dec
Patient
Days
3,700
3,200
4,400
5,000
2,700
2,500
3,600
1,800
4,650
3,900
2,100
4,500
Mixed Cost
27,750
22,000
31,000
34,500
28,000
22,500
26,500
18,750
36,500
24,000
22,500
26,750
$34,500 - $18,750
=
5,000 - 1,800
$15,750
=
=
3,200
$4.92 per Patient-Day
Then:
$34,500
a
D.
=
=
a + ($4.92 * 5,000)
$9,891
Answer:
Y = $9,891 +$4.92X
Scattergram Plot
40,000
35,000
Mixed Cost
30,000
25,000
20,000
15,000
10,000
5,000
-
1,000
2,000
3,000
Patient days
4,000
5,000
6,000
High-Low Method
40,000
35,000
Mixed Cost
30,000
25,000
20,000
15,000
HL method: y = $4.92x + $9,891
10,000
5,000
-
1,000
2,000
3,000
Patient days
4,000
5,000
6,000
Least Squares Regression Method
40,000
35,000
Mixed Cost
30,000
25,000
20,000
15,000
HL method: y = $4.92x + $9,891
LSR method: y = 4.10x + $12,346
10,000
5,000
-
1,000
2,000
3,000
Patient days
4,000
5,000
6,000
Least Squares Regression Method
Outlier?
Nonlinear?
40,000
35,000
Mixed Cost
30,000
25,000
20,000
15,000
LSR method: y = 4.10x + $12,346 (with outlier)
10,000
5,000
-
1,000
2,000
3,000
Patient days
4,000
5,000
6,000
Least Squares Regression Method
Outlier?
Nonlinear?
40,000
35,000
Mixed Cost
30,000
25,000
20,000
15,000
LSR method: y = 4.10x + $12,346 (with outlier)
LSR method: y = 3.51x + $13,890 (without outlier)
10,000
5,000
-
1,000
2,000
3,000
Patient days
4,000
5,000
6,000
Example: High-Low Method and
Predicting Cost (P6-15)
Prince Company’s total OH costs at various levels of activity
are presented below:
Month
DL Hours
Total OH Cost
September
100,000
$388,000
October
80,000
$340,400
November
135,000
$485,600
December
140,000
$483,200
Example: High-Low and Predicting
Cost (P6-15)
Assume OH costs consists of utilities, supervisory salary,
depreciation, and maintenance. The breakdown for
October at 80,000 DL hour level of activity is:
OH
Type
OH Cost
Utilities
Variable
$104,000
Salaries & Depreciation
Fixed
$120,000
Maintenance
Mixed
$116,400
Total OH Cost
$340,400
The company wants the breakdown of costs into variable and
fixed cost elements. Answer the following required:
Example: High-Low and Predicting
Cost (P6-15)
1. Estimate how much of the $483,200 of OH cost in
December was maintenance cost
Example: High-Low and Predicting
Cost (P6-15)
OH
Type
OH Cost
December OH
Mixed
$483,200
December:
Salaries & Depreciation
Fixed
($120,000)
The company
wants the breakdown
of costs into variable
and
Utilities
Variable
($182,000)
fixed cost elements. Answer the following required:
Maintenance (Mixed Cost)
$181,200
Variable Cost = $104,000/80,000 * 140,000
It is Clicker Time!!
Feel Free to Work Together on Clicker Questions
Clicker Question #1 (P6-15)
LOW (October): 80,000 DL
hours @ $116,400
HIGH (December): 140,000
DL hours @ $181,200
Q: Use the high-low
method to develop the
cost formula for
maintenance cost
(select option that is
closest to your answer).
A.
B.
C.
D.
E.
Y = $15,000 + $23.80X
Eggs + Plants = Eggplant
Y = $30,000 + $3.12X
Y = $30,000 + $1.08X
Y = $15,000 + $2.38X
Clicker Question #1
LOW (October): 80,000 DL
hours @ $116,400
HIGH (December): 140,000
DL hours @ $181,200
$181,200 - $116,400
=
140,000 – 80,000
$64,800
=
60,000
=
D.
Answer:
Y = $30,000+$1.08X
$1.08 per DL hour
Then:
$116,400 = a + ($1.08 * 80,000)
a
=
$30,000
Example: High-Low and Predicting
Cost (P6-15)
3. Express the company’s total OH cost in the formula Y = a+
bX:
Variable Costs:
Utilities ($104,000/80,000 DL)
$1.30/DL hour
Maintenance
$1.08/DL hour
Total Variable
$2.38/DL hour
Fixed Costs:
Salaries and depreciation
$120,000
Maintenance
$30,000
Total Fixed
$150,000
Example: High-Low and Predicting
Cost (P6-15)
3. Express the company’s total OH cost in the formula Y = a+
bX:
Total Variable
$2.38/DL hour
Total Fixed
$150,000
Y = $150,000 + $2.38X
The Contribution Format
• Utilizes our ability to analyze cost behavior
– An income statement format that separates expenses into
fixed costs and variable costs
– Differs from traditional presentation of COGS and operating
expenses
– Total cost is the same under both methods but only subtotals
vary
• Contribution margin
– The amount remaining from sales after all variable costs have
been deducted
Contribution Income Statement
To Do: Analyze expense behaviour of the following and
develop a contribution income statement:
Cost
Number of units sold
Cost Formula
21,000
Sales revenue
COGS
Advertising Expense
1,050,000
$20 / unit
$170,000
Sales Commissions
Administrative Salaries
Shipping Expense
5% of Sales revenue
$80,000
$40,000 plus $7.50 / unit
Depreciation
$50,000
Contribution Income Statement
Income Statement
Revenue
COGS ($20/unit * 21,000)
Variable shipping expense ($7.50/unit * 21,000)
Commission (5% of sales revenue)
$1,050,00
0
$420,000
157,500
52,500
Total Variable Costs
$630,000
Contribution Margin
$420,000
Contribution Margin per Unit
$20
Contribution Income Statement
Income Statement
Contribution Margin
Fixed Shipping expense
Advertising expense
$420,000
40,000
170,000
Administrative salaries
80,000
Depreciation expense
50,000
Total Fixed Costs
$340,000
Operating Income
$80,000
It is Clicker Time!
Feel Free to Work Together on Clicker Questions
Clicker Question #2
Q: Contribution margin equals revenues
minus _______?
A.
B.
C.
D.
E.
Product costs
Period costs
Variable costs
Fixed costs
9 little monkeys jumping on the bed
Clicker Question #2: Answer
Q: Contribution margin equals revenues
minus _______?
Answer:
C. Variable costs
Clicker Question #3
Q: What is the contribution margin?
Cost
Sales
Fixed Manufacturing Overhead
Direct Labour
Fixed Selling Expenses
Variable Manufacturing Overhead
Variable Administrative Expenses
Direct Materials
Fixed Administrative Expenses
Variable Selling Expenses
Amount
$300,000
$ 55,000
$ 72,500
$ 46,250
$ 41,000
$ 48,000
$ 51,500
$ 44,500
$ 49,750
Clicker Question #3
Q: What is the contribution margin?
A.
B.
C.
D.
E.
$37,250
$100,000,000.23
$ 87,000
$176,000
$262,750
Clicker Question #3 - Solution
Amount
Sales
$300,000
Direct Labour
($72,500)
Direct Materials
($51,500)
Variable Manufacturing
Overhead
Variable Administrative
Expenses
Variable Selling Expenses
($41,000)
Total Variable Costs
Contribution Margin
($48,000)
($49,750)
($262,750)
($262,750)
$37,250
Clicker Question #3: Answer
Q: What is the contribution margin?
Answer:
A. $37,250
UW …
• UW is one of Canada’s leading research
institution
• The School of Accounting and Finance has
one of the country’s premier PhD programs
• Every year, I train PhD students in teaching.
• So, the next 3 classes (Cost-Volume-Profit
Relationships) will be taught by Kun Huo,
one of our PhD students.
• I will sit in the class as an observer.
Summary
• Major topics for today…
– Another example of High-Low Method
– Contribution margin approach
• Next class …
– Chapter 7 (Cost-Volume-Profit Relationships)