6
Cost Volume Profit Analysis
Chapter 6
INTRODUCTION
The Profit Function
Breakeven Analysis
Differential Cost Analysis
Slide 1
6
The Profit Equation
Operating
Profit
=
Total
Revenue
–
Total
Costs
Operating profit equals total revenue
less total costs.
Slide 2
6
The Profit Equation
Operating
Profit

Slide 3
=
=
Total
Revenue
–
Total
Costs
TR –
TC
6
The Profit Equation
Total
=
Revenue
TR
Slide 4
=
Average Selling
Units of
×
Price Per Unit
Output
P
×
X
6
Slide 5
The Profit Equation
Total
Costs
=
TC
=
Variable Costs
Units of
Fixed
×
+
Per Unit
Output
Costs
(V
×
X) + F
6

Slide 6
The Profit Equation
Now, we’ll expand our
original equation for profits!
=
(P × X) - [(V × X) + F]
6


Slide 7
The Profit Equation
Now, we’ll expand our
original equation for profits!
=
(P × X) - [(V × X) + F]
=
(P – V)X – F
6
Example
Here is the information from the Hap Bikes:
Total
Sales (500 bikes)
$ 250,000
Less: variable expenses
150,000
Contribution margin
$ 100,000
Less: fixed expenses
80,000
Net income
$ 20,000
Slide 8
Per Unit
$
500
300
$
200
Percent
100%
60%
40%
6
Example

Slide 9
=
(P – V)X – F
6
Finding Target Volumes
The formula to find a volume expressed in
units for a target profit is . . .
Target
Volume
(units)
Fixed costs + Target profit
=
Contribution margin per unit
How many bikes must Hap sell to
earn an annual profit of $100,000?
Slide 10
6
Finding Target Volumes
Target
Volume
(units)
Slide 11
Fixed costs + Target profit
=
Contribution margin per unit
6
Proof
If Hap sells 900 bikes, its operating profit
would be . . .

Slide 12
=
(P – V)X – F
6
Finding the Break-Even Point
The Break-Even Point is the volume level
where profits equal zero.
To find the break-even point in units, we use
the target volume in units equation and set
the profit to zero.
To find the break-even point in sales dollars,
we use the target volume in sales dollars
equation and set the profit to zero.
Slide 13
6
Break-Even in Units
Let’s use the Hap Bikes information again.
Total
Sales (500 bikes)
$ 250,000
Less: variable expenses
150,000
Contribution margin
$ 100,000
Less: fixed expenses
80,000
Net income
$ 20,000
Per Unit
$
500
300
$
200
Percent
100%
60%
40%
Contribution margin ratio
Slide 14
6
Break-Even in Units
Break-Even
=
Volume
(units)
Slide 15
Fixed costs + Target profit
Contribution margin per unit
6
Break-Even in Sales Dollars
Break-Even
=
Volume
(sales $)
=
Slide 16
Fixed costs + Target profit
Contribution margin ratio
$80,000 + $0
.40
6
Target Volume in Sales Dollars
We can calculate the target volume in sales
dollars using the contribution margin ratio.
Contribution margin per unit
Sales price per unit
Slide 17
6
Target Volume in Sales Dollars
The equation for finding the target volume in
sales dollars is . . .
Target
Volume =
(sales $)
Slide 18
Fixed costs + Target profit
Contribution margin ratio
6
Graphic Presentation
Consider the following information for Hap Bikes:
Income
300 units
Sales
$ 150,000
Less: variable expenses
90,000
Contribution margin
$
60,000
Less: fixed expenses
80,000
Net income (loss)
$ (20,000)
Slide 19
Income
400 units
$ 200,000
120,000
$
80,000
80,000
$
-
Income
500 units
$ 250,000
150,000
$ 100,000
80,000
$ 20,000
6
Graphic Presentation
450,000
400,000
350,000
300,000
250,000
200,000
150,000
100,000
50,000
-
Slide 20
100
200
300
400
500
600
Volume per period (X)
700
800
6
Graphic Presentation
450,000
400,000
350,000
300,000
250,000
200,000
Break-even point
150,000
100,000
50,000
Slide 21
100
200
300
400
500
600
Volume per period (X)
700
800
Using CVP to Analyze Different
Cost Structures
6
 Cost structure - The proportion of fixed and
variable to total costs of an organization.
 Operating leverage - The extent to which an
organization’s costs structure is made up of
fixed costs.
Let’s look at an example of different costs
structures for different companies.
Slide 22
6
Using CVP to Analyze Different
Cost Structures
High
Variable
Company
%
(50,000 units)
Sales
$
500,000 100%
Variable costs
400,000 80%
Contribution margin
100,000 20%
Fixed costs
40,000
8%
Operating profit
$
60,000 12%
Break-even units
Contribution margin
per unit
$
Slide 23
Hi Fixed
Company
%
(50,000 units)
$
500,000 100%
100,000 20%
400,000 80%
340,000 68%
$
60,000 12%
20,000
2.00
42,500
$
8.00
6
Using CVP to Analyze Different
Cost Structures
High
Variable
Company
%
(50,000 units)
Sales
$
500,000 100%
Variable costs
400,000 80%
Contribution margin
100,000 20%
Fixed costs
40,000
8%
Operating profit
$
60,000 12%
Break-even units
Contribution margin
per unit
$
Hi Fixed
Company
%
(50,000 units)
$
500,000 100%
100,000 20%
400,000 80%
340,000 68%
$
60,000 12%
20,000
2.00
42,500
$
8.00
Let’s see what happens when both companies
experience a 10% increase in sales.
Slide 24
6
Using CVP to Analyze Different
Cost Structures
High
Variable
Company
%
(55,000 units)
Sales
$
550,000 100%
Variable costs
440,000 80%
Contribution margin
110,000 20%
Fixed costs
40,000
7%
Operating profit
$
70,000 13%
Break-even units
Contribution margin
per unit
$
Slide 25
Hi Fixed
Company
%
(55,000 units)
$
550,000 100%
110,000 20%
440,000 80%
340,000 62%
$
100,000 18%
20,000
2.00
42,500
$
8.00
6
Margin of Safety
 Excess of projected (or actual) sales over
the break-even volume.
 The amount by which sales can fall before
the company is in the loss area of the
break-even graph.
Sales
Break-even
–
volume sales volume
Slide 26
= Margin of Safety
6
Margin of Safety
Hap is currently selling 500 bikes, and we
calculated the break-even to be 400 units
($80,000 fixed costs ÷ $200 contribution margin).
Slide 27