Chapter 6
Cost-Volume-Profit Relationships
The Contribution Format
Used primarily for
external reporting.
Used primarily by
management.
Micro Wave Co.
Contribution Income Statement
For the Month of June
Total
Per Unit
Sales (500 ovens)
$ 250,000
$ 500
Less: variable expenses 150,000
300
Contribution margin
100,000
$ 200
Less: fixed expenses
80,000
Operating income
$ 20,000
Practice…
(a)
Per Unit
Selling
Price
(b)
Var. Cost
Per
Unit
$30
$10
(c)
Total
Units
Sold
(d)
Total
CM
(e)
Total
Fixed
Costs
120,000
$720,000
$640,000
$6
100,000
$9
80,000
$320,000
$160,000
$120,000
(f)
Operating
Income
Contribution-Margin Ratio
Sales revenue, variable expenses and contribution for Micro
Wave can be expressed as a percentage of sales
Total
Sales (500 ovens)
$ 250,000
Less: variable expenses
150,000
Contribution margin
$ 100,000
Less: fixed expenses
80,000
Operating Income
$ 20,000
Per Unit
$
500
300
$
200
Percent
100%
60%
40%
Pop Quiz
Tasty Bagel is a snack shop in a strip mall. The average
selling price of a bagel is $1.49 and the average variable
expense per bagel is $0.36. The average fixed expense per
month is $1,300. 2,100 bagels are sold each month on
average.
What is the CM Ratio for Tasty Bagel?
a. 1.319
b. 0.758
c. 0.242
d. 4.139
Contribution Margin Method to Determine Break-even
The contribution margin method is a variation of the equation method.
Break-even point
in units sold
=
Break-even point in
total sales dollars
=
Fixed expenses
Unit contribution margin
Fixed expenses
CM ratio
Pop Quiz
Tasty Bagel is a snack shop in a strip mall. The average selling
price of a bagel is $1.49 and the average variable expense per
bagel is $0.36. The average fixed expense per month is
$1,300. 2,100 bagels are sold each month on average.
What is the break-even sales in units?
a. 872 bagels
b. 3,611 bagels
c. 1,200 bagels
d. 1,150 bagels
Pop Quiz
Tasty Bagel is a snack shop in a strip mall. The average selling
price of a bagel is $1.49 and the average variable expense per
bagel is $0.36. The average fixed expense per month is
$1,300. 2,100 bagels are sold each month on average.
What is the break-even sales in dollars?
a. $1,300
b. $1,715
c. $1,788
d. $3,129
CVP Graph
450,000
400,000
Total Sales
350,000
300,000
Total Expenses
250,000
200,000
Fixed expenses
150,000
100,000
50,000
-
100
200
300
Units
400
500
600
700
800
CVP Graph
450,000
400,000
350,000
300,000
250,000
200,000
Break-even point
150,000
100,000
50,000
-
100
200
300
Units
400
500
600
700
800
Break-even Reduction
Micro is currently selling 500 ovens per month. Break-even
units are 400 per month under the current cost structure.
What would be the break-even units if fixed costs decrease to
$70,000?
What would be the break-even units if variable costs were
reduced to $250?
What would be the break-even units if selling price was
increased to $513.33?
Target Operating Profit - CM Approach
Original contribution margin formula:
Break Even Point in Units =
Fixed Expenses
Contribution Margin per Unit
Target operating profit modification:
Units Sold to Earn Target Profit = Fixed Expenses +Target Op. Profit
Unit Contribution Margin
Pop Quiz
Tasty Bagel is a snack shop in a strip mall. The average selling
price of a bagel is $1.49 and the average variable expense per
bagel is $0.36. The average fixed expense per month is
$1,300.
How many bagels would have to be sold to attain target
profits of $2,500 per month?
a. 3,363 bagels
b. 2,212 bagels
c. 1,150 bagels
d. 4,200 bagels
Sensitivity Analysis – Fixed Costs
Micro Wave Co. is currently selling 500 ovens per month
The sales manager believes that an increase of $10,000 in the
monthly advertising budget would increase sales of ovens to
540 per month
Should the increase in advertising be made?
Change in Variable Costs and Sales Volume
Micro Wave management is contemplating the use of higherquality components, which would increase variable costs by
$15 per oven. However, the sales manager predicts that the
overall higher quality would increase sales to 600 ovens per
month. Should the higher quality components be used?
Change in Fixed Cost, Sales Price, and Sales
Volume
To increase sales, the sales manager would like to cut the
selling price by $40 per oven and increase the advertising
budget by $30,000 per month. The sales manager believes
that if these two steps are taken, unit sales will increase by
60% to 800 ovens per month. Should the changes be made?
Change in Variable Cost, Fixed Cost, and
Sales Volume
The sales manager would like to place the sales staff on
commission basis of $40 per oven sold, rather than on flat
salaries that now total $10,000 per month. The sales manager
is confident that the change will increase monthly sales by
15% to 575 ovens per month. Should the change be made?
Change in Regular Sales Price
The company has an opportunity to make a bulk sale of 200
ovens to a wholesaler if an acceptable price can be worked
out. This sale would not have any effect on the company’s
regular sales. What price per oven should be quoted to the
wholesaler if Micro wants to increase its Operating profits by
$5,000?
The Margin of Safety
Excess of budgeted (or actual) sales over the break-even
volume of sales. The amount by which sales can drop before
losses begin to be incurred.
Margin of safety = Total sales - Break-even sales
Let’s calculate the margin of safety for Micro
The Margin of Safety
Micro has a break-even point of $200,000. If actual sales are $250,000,
the margin of safety is $50,000 or 100 ovens.
Break-even
sales
400 units
Sales
$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
$
-
Actual sales
500 units
$ 250,000
150,000
100,000
80,000
$
20,000
The Margin of Safety
The margin of safety can be expressed as 20% of sales.
($50,000 ÷ $250,000)
Break-even
sales
400 units
Sales
$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
$
-
Actual sales
500 units
$ 250,000
150,000
100,000
80,000
$
20,000
Pop Quiz
Tasty Bagel is a snack shop in a strip mall. The average selling
price of a bagel is $1.49 and the average variable expense per
bagel is $0.36. The average fixed expense per month is
$1,300. 2,100 bagels are sold each month on average.
What is the margin of safety?
a. 3,250 bagels
b. 950 bagels
c. 1,150 bagels
d. 2,100 bagels
Cost Structure and Profitability
Alpha
Beta
Gamma
Amount
%
Amount
%
Amount
%
Sales
$800,000
100%
$800,000
100%
$800,000
100%
Variable
Expenses
400,000
50%
300,000
37.5%
200,000
25%
Contribution
Margin
400,000
50%
500,000
62.5%
600,000
75%
Fixed
Expenses
300,000
400,000
500,000
Op. Income
$ 100,000
$ 100,000
$ 100,000
Effect on Profit of 10% Increase in Sales Revenue
Increase in
Sales
Revenue
Contribution
Margin Ratio
Alpha
$80,000
X
50%
Beta
$80,000
X
62.5%
Gamma
$80,000
X
75%
=
=
=
Increase in
Op.Income
$40,000
+40%
$50,000
+50%
$60,000
+60%
Break-Even Points
Contribution
Margin Ratio
Fixed Expenses
Break-Even
Sales Revenue
Alpha
$300,000
/
50%
=
$600,000
Beta
$400,000
/
62.5%
=
$640,000
Gamma
$500,000
/
75%
=
$666,667
Margin of Safety
Actual Sales
Revenue
Break-Even
Sales Revenue
Margin of
Safety
Alpha
$800,000
-
$600,000
=
$200,000
Beta
800,000
-
640,000
=
160,000
Gamma
800,000
-
666,667
=
133,333
Definition of Operating Leverage
 The relative mix of a firm’s fixed and variable costs determines its
operating leverage.
 At a given level of sales:
Degree of operating =
leverage
Contribution Margin
Operating Income
 The higher a firm’s fixed cost as compared to its variable cost, the
greater its operating leverage.
 Operating leverage acts like a multiplier. The greater the operating
leverage, the greater the change in operating income for a given change
in sales.
 Let’s calculate the operating leverage for each firm.
Application of Operating Leverage
 At a given level of sales, the operating leverage is a measure of how a
given percentage change in sales will affect operating profits.
 In fact, the operating profit will increase by the operating leverage
times the percentage change in sales.
 For a 10% increase in sales , Firm Alpha’s operating income increased
40% (4 times 10%).
 For a 10% increase in sales , Firm Beta’s operating income increased 50%
(5 times 10%).
 For a 10% increase in sales , Firm Gamma’s operating income increased
60% (6 times 10%).
Pop Quiz
Tasty Bagel is an snack shop in a strip mall. The average selling price of a
bagel is $1.49 and the average variable expense per bagel is $0.36. The
average fixed expense per month is $1,300. 2,100 bagels are sold each
month on average. What is the operating leverage?
a. 2.21
b. 0.45
c. 0.34
d. 2.92
Pop Quiz
At Tasty Bagel the average selling price of a bagel is $1.49, the average
variable expense per bagel is $0.36, and the average fixed expense per month
is $1,300. 2,100 bagels are sold each month on average.
If sales increase by 20%, by how much should operating income increase?
a. 30.0%
b. 20.0%
c. 22.1%
d. 44.2%
Break-even Analysis (in Units) with Multiple Products
Curl Company provides us with the following information:
Description
Surfboards
Sailboards
Total sold
Unit
Unit
Selling Variable Contribution
Price
Cost
Margin
$
20 $
14 $
6
30
18
12
Description
Surfboards
Sailboarads
Total sold
Unit
Sales
15,000
5,000
20,000
Unit
Sales
15,000
5,000
20,000
% of
Total
75.0%
25.0%
100.0%
Fixed cost is $120,000. What is the break-even point in units? What
are the sales of Surfboards and Sailboards at the break-even point?
POP QUIZ
Mark Corporation produces two models of calculators. The Business
model sells for $60, and the Math model sells for $40. The variable
expenses are given below:
Business
Math
Model
Model
Variable production costs per unit
$15
$16
Variable selling and administrative expenses per unit
$9
$6
The fixed expenses are $75,000 per month. The expected monthly sales of each
model are: Business, 1,000 units; Math, 500 units.
The break-even point for the expected sales mix is (round to nearest whole
unit):
A) 833 of each
B) 1,667 Business and 833 Math
C) 1,667 of each
D) 833 Business and 1,667 Math
Break-even Analysis (in Sales Dollars) with Multiple
Products
Curl’s Contribution Margin income statement is shown below:
Sales
$
Var. exp.
Contrib. margin $
Fixed exp.
Operating income
Sales mix
$
Surfboards
Sailboards
300,000 100% $ 150,000
210,000
70%
90,000
90,000
30% $
60,000
300,000
67% $
150,000
$150,000
$450,000
100%
60%
40%
33%
Total
$ 450,000
300,000
150,000
120,000
$ 30,000
$ 450,000
100.0%
66.7%
33.3%
100.0%
= 33.3%
What is the break-even point in Sales? What are the sales of Surfboards and
Sailboards at the break-even point?
Break-even Analysis (in Sales Dollars) with Multiple
Products
A Shift in Sales Mix
Sales
$
Var. exp.
Contrib. margin $
Fixed exp.
Operating income
Sales mix
$
Surfboards
Sailboards
150,000 100% $ 300,000
105,000
70%
180,000
45,000
30% $ 120,000
150,000
33% $
300,000
$165,000
$450,000
100%
60%
40%
67%
Total
$ 450,000
285,000
165,000
120,000
$ 45,000
$ 450,000
100.0%
63.3%
36.7%
100.0%
= 36.7%
What is the break-even point in Sales? How does it compare with the previous
amount?
Pop Quiz
Shirley’s Shoes sells two products.
information:
Sales Revenue
Variable Expenses
Contribution Margin
Fixed Expenses
Net Income
The controller provides you with the following
Low Heel
In Total
Per Unit
$120,000
$1.20
60,000
0.60
$60,000
$0.60
High Heel
In Total
Per Unit
$80,000
$0.80
60,000
0.60
$20,000
$0.20
What is Shirley’s Shoes breakeven point in dollars?
(a)
(b)
(c)
(d)
(e)
$66,667
$100,000
$125,000
$180,000
$300,000
Combined
$200,000
120,000
80.000
50,000
$30,000
Assumptions Underlying CVP Analysis
• Selling price is constant throughout the entire relevant range
• Costs are linear over the relevant range (costs can be divided
into variable and fixed)
• In multi-product companies, the sales mix is constant
• In manufacturing firms, inventories do not change (units
produced = units sold)