Chapter 7: Cost-Volume-Profit
(Part 3 of 3)
Sections 1 and 2
Feb 8, 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
8 Feb 2013 Overview
• Last lecture …
– More break-even analysis
– Margin of Safety analysis
– Target operating profit analysis
• Today’s lecture …
– Cost Structure Choice and Leverage
– Indifference analysis
– Multi-product Settings
2
Cost structure choice
•
Company can choose a particular cost structure
(i.e., relative proportion of fixed and variable
costs)
Which cost structure is better (more fixed costs or
more variable costs)?
•
–
•
Depends on many factors
Concept of leverage plays a key role in the
analysis
3
“Give me a place to stand and with
a lever I will move the whole world”
Operating Leverage
CM
OI
Measure of the sensitivity of OI to % change in sales
Degree of Operating Leverage =
•
–
–
–
•
Acts as a multiplier
Higher leverage: small change in sales leads to larger shift
in OI
Differs at any level of sales (i.e. valid at given X only),
greatest at break-even point and decreases as sales
increases
Cost structure drives leverage
–
–
More FC rather than VC yields greater leverage
Drive to automation?
5
Leverage Graph: Cost Structure
Total Sales Revenue
$
High FC
Case A: Total
Expenses
Break-even Point
Case B: Total
Expenses
Lower FC results in a lower breakeven point (Fixed expenses/unit
CM), so less risk of losses when
sales decrease
Low FC
Activity
Leverage Graph: Cost Structure
$
Which has a greater degree
of operating leverage at point
X: A or B?
Total Sales Revenue
X
Case A: Total
Expenses
Case B: Total
Expenses
Higher FC (higher CM) results
in higher leverage (CM/OI), so
better upside potential in
profits when sales increases
High FC
Low FC
Activity
Operating Leverage Example 1
Degree of Operating Leverage =
Rev
VC
CM
FC
OI
Units
Degree of
Leverage
Per Unit
$100
$60
$40
Income
$100,000
$60,000
$40,000
$30,000
$10,000
Income
$110,000
$66,000
$44,000
$30,000
$14,000
1,000
1,100
CM
OI
Sales increase by 10%
OI increases by 4 times
(i.e., 40%)
4
8
Operating Leverage Example 2
Degree of Operating Leverage =
Rev
VC
CM
FC
OI
Units
Degree of
Leverage
Per Unit
$100
$30
$70
Income
$100,000
$30,000
$70,000
$60,000
$10,000
Income
$110,000
$33,000
$77,000
$60,000
$17,000
1,000
1,100
7
CM
OI
Same total sales
Same total expenses, but
greater proportion of FC
Sales increase by 10%
OI increases by 7 times
(i.e., 70%)
Higher FC (higher CM) results
in higher leverage (CM/OI), so
better upside potential in
profits when sales increases
9
The critical assumption about leverage
• As fixed cost increases, variable cost will come
down
– More roads and infrastructure, people are more
productive because they spend less time on the
travel
– Bigger class rooms, fewer instructors need to be
hired
It is Clicker Time!!
Feel Free to Work Together on Clicker Questions
Clicker Question #1
Green Company's variable expenses are 75% of sales. At
a sales level of $400,000, the company's degree of
operating leverage is 8. At this sales level, fixed expenses
equal which of the following?
A)
B)
C)
C)
D)
$87,500.
$100,000.
Dogbert
$12,500.
$75,000.
12
Clicker Question #1: Answer
Green Company's variable expenses are 75% of sales. At a sales
level of $400,000, the company's degree of operating leverage is 8.
At this sales level, fixed expenses equal which of the following?
Answer:
13
Clicker Question #2
If two companies produce the same product and have
the same total sales and same total expenses,
operating leverage will be lower in the company with a
higher proportion of fixed expenses in its cost
structure.
A. True
B. False
Leverage Graph: Cost Structure
$
Which has a greater degree
of operating leverage at point
X: A or B?
Total Sales Revenue
X
A - Total Expenses
B - Total Expenses
High FC
Indifference Point
(indifferent wrt profit
between high FC vs.
low FC)
Low FC
Activity
Indifference Point (P7-31)
1) Find equations for both cost lines
2) Set the two equations equal to each other and solve for X
Item
DM per unit
DL per unit
Variable OH per unit
Cost 1
$9.00
1.2 DLH @
$14/DLH
0.75 of DL costs
Cost 2
$7.50
0.75 DLH @
$18/DLH
0.60 of DL costs
Fixed Man. Costs
Fixed S&A
Selling Price per unit
$1,108,000
$1,685,000
$60.00
$1,494,000
$1,685,000
$60.00
Variable Selling Cost per unit
$4.00
$4.00
16
Cost 1 Equation …
Item
Cost 1
DM per unit
DL per unit
Variable OH per unit
$9.00
1.2 DLH @
$14/DLH
0.75 of DL costs
Fixed Man. Costs
$1,108,000
Fixed S&A
$1,685,000
Selling Price per unit
$60.00
Variable Selling Cost per $4.00
unit
VC per Unit:
= $9 + ($14*1.2) +
($14*1.2*0.75) + $4
= $42.40 per unit
Fixed Costs:
= ($1,108,000 +$1,685,000)
= $2,793,000
Cost 1 Equation
Y = $2,793,000 + $42.40X
17
Cost 2 Equation …
Item
DM per unit
DL per unit
Variable OH per unit
Cost 2
$7.50
0.75 DLH @
$18/DLH
0.60 of DL costs
Fixed Man. Costs
Fixed S&A
Selling Price per unit
$1,494,000
$1,685,000
$60.00
Variable Selling Cost per
unit
$4.00
VC per Unit:
= $7.50 + ($18*0.75) +
($18*0.75*0.60) + $4
= $33.10 per unit
(Lower VC per unit)
Fixed Costs:
= ($1,494,000 +$1,685,000)
= $3,179,000
(Higher Total FC)
Cost 2 Equation
Y = $3,179,000 + $33.10X
18
Cost 1 = Cost 2
Set Cost 1 equation equal to Cost 2 equation to
determine the point of indifference:
Cost 1 = Cost 2
$2,793,000 + $42.40X = $3,179,000 + $33.10X
$9.30X = $386,000
X = 41,505 (rounded) units
The point of indifference in cost structure occurs when
41,505 units are produced and sold.
It is Clicker Time!!
Feel Free to Work Together on Clicker Questions
Clicker Question #3
Company Y is considering two production technologies for
producing its new product. The cost structures of the two
technologies are as follows:
Selling Price / Unit
Variable Production Costs / Unit
Total Fixed Production Costs
Bronze
Platinum
$
150 $
150
$
120 $
50
$300,000 $1,210,000
Q: At what sales volume in units (rounded to the nearest
whole unit) would Company Y be indifferent in
technologies?
21
Clicker Question #3
Q: At what sales volume in units (rounded to the nearest
whole unit) would Company Y be indifferent in
technologies?
A)
B)
C)
D)
E)
10,000 units.
12,100 units.
13,000 units.
Infinite number of units
Cannot be determined without additional
information.
22
Sales Mix
• Overall sales volume is very important to an
organization
• The mix of sales also matters
– Low CM products? High CM products?
• Relative proportions of product sales
– Expressed as a % of Total Sales
• Sum across products
– Revenue
– Variable Cost
• Fixed cost comes last
23
Budgeted Sales Mix (P7-20)
% of Total
Sales
VC
CM
FC
OI
CMR
Sinks
48%
$240,000
Mirrors
20%
$100,000
Vanities
32%
$160,000
Total
100%
$500,000
72,000
$168,000
80,000
$20,000
88,000
$72,000
240,000
$260,000
223,600
70%
20%
45%
$36,400
52%
Q: What is Break-Even Sales Point given actual
sales mix?
It is Clicker Time!!
Feel Free to Work Together on Clicker Questions
Clicker Question #4
Sinks
Mirrors
Vanities
Total
% of Total
Sales
VC
CM
FC
OI
CMR
223,600
70%
20%
45%
Q: Actual sales mix: Sinks: $160,000; Mirrors:
$200,000; Vanities: $140,000. What is breakeven
sales?
Clicker Question #4
Q: Actual sales mix: Sinks: $160,000; Mirrors:
$200,000; Vanities: $140,000. What is breakeven
sales?
A.
B.
C.
D.
E.
That is a good question
$520,000
$550,000
$580,000
$610,000
Important points
• Leverage:
– Beyond the break even point, higher leverage means
that you receive higher profit per unit sold.
– Higher leverage likely means higher fixed costs, so the
break even point is harder (more units) to reach
• Indifference means given two cost structures, the
profits are equal at some activity level
• In the real world, you would use a computer for
multi-product analysis because sales mixes will
not remain equal
Summary
• Today’s lecture …
– Cost Structure Choice and Leverage
– Indifference analysis
– Multi-product Settings
• Next lecture …
– Prof Kelly returns to lecture (Hooray!!)
– Introduction to Variable Costing (Chapter 8)