Learning Objectives Part 1
CHAPTER 4
1 Explain how changes in activity affect
contribution margin and operating income.
2 Prepare and interpret a cost–volume–profit
graph.
3 Calculate the contribution margin ratio and the
variable expense ratio. Use the contribution margin
ratio to compute changes in contribution margin
and operating income resulting from changes in
sales volume.
4-1
Learning Objectives Part 2
4 Show the effects on contribution margin of
changes in variable costs, fixed costs, selling price,
and volume.
5 Compute the break-even point in unit sales and
sales dollars.
6 Determine the level of sales needed to achieve a
desired target profit.
7 Compute the margin of safety and explain its
significance.
4-2
Learning Objectives Part 3
8 Explain cost structure, compute the degree of
operating leverage at a particular level of sales,
and explain how operating leverage can be used
to predict changes in operating income.
9 Compute the break-even point for a multiproduct company and explain the effects of
changes in the sales mix on the contribution
margin and the break-even point..
4-3
Cost-Volume-Profit Relationship
Interactions
•
Cost-volume-profit (CVP) analysis is a powerful
tool that managers use to help them understand
the interrelationship among cost, volume and
profit in an organization by focusing on
interactions among the following five elements:
1.prices of products
2.volume or level of activity
3.per unit variable costs
4.total fixed costs
5.mix of products sold
4-4
Basics of Cost-Volume-Profit
Analysis
The contribution income statement is helpful to managers
in judging the impact on profits of changes in selling price,
cost, or volume. The emphasis is on cost behaviour.
Example Company
Contribution Income Statement
For the Month of June
Sales (500 units)
$
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
$
250,000
150,000
100,000
80,000
20,000
Contribution Margin (CM) is the amount remaining from
sales revenue after variable expenses have been deducted.
4-5
Contribution Margin (CM)
Sales, variable expenses, and contribution margin can also
be expressed on a per unit basis. If an additional unit is
sold, $200 additional CM will be generated to cover fixed
expenses and profit.
Example Company
Contribution Income Statement
For the Month of June
Total
Per Unit
Sales (500 units)
$
250,000
$
500
Less: Variable expenses
150,000
300
Contribution margin
100,000
$
200
Less: Fixed expenses
80,000
Net operating income
$
20,000
% of Sales
100%
60%
40%
4-6
Contribution Margin Ratio
The CM ratio is calculated by dividing the total
contribution margin by total sales.
Example Company
Contribution Income Statement
For the Month of June
Total
Per Unit
Sales (500 units)
$
250,000
$
500
Less: Variable expenses
150,000
300
Contribution margin
100,000
$
200
Less: Fixed expenses
80,000
Net operating income
$
20,000
CM per unit
=
CM Ratio =
SP per unit
$200
$500
CM Ratio
100%
60%
40%
= 40%
4-7
The Contribution Approach 1
Each month, $80,000 in total CM must be
generated to break even.
Example Company
Contribution Income Statement
For the Month of June
Total
Per Unit
Sales (500 units)
$
250,000
$
500
Less: Variable expenses
150,000
300
Contribution margin
100,000
$
200
Less: Fixed expenses
80,000
Net operating income
$
20,000
CM Ratio
100%
60%
40%
4-8
The Contribution Approach 2
If 400 units are sold in a month, they will be
operating at the break-even point.
Example Company
Contribution Income Statement
For the Month of June
Total
Per Unit
Sales ( 400 units)
$ 200,000
$ 500
Less: Variable expenses
120,000
300
Contribution margin
80,000
$ 200
Less: Fixed expenses
80,000
Net operating income
$
-
CM Ratio
100%
60%
40%
4-9
The Contribution Approach 3
If one more unit is sold (401 units), net
operating income will increase by $200.
Example Company
Contribution Income Statement
For the Month of June
Total
Per Unit
Sales ( 401 units)
$ 200,500
$ 500
Less: Variable expenses
120,300
300
Contribution margin
80,200
$ 200
Less: Fixed expenses
80,000
Net operating income
$
200
© 2021 McGraw-Hill Limited
CM Ratio
100%
60%
40%
4-10
The Contribution Approach 4
• We do not need to prepare an income
statement to estimate profits at a particular
sales volume. Simply multiply the number
of units sold above break-even by the
contribution margin per unit.
• If 430 units are sold, the net operating
income will be $6,000
• 30 units above break-even: 30 x 200 =
$6,000
4-11
CVP Relationships in
Graphic Form
•
Relationships among revenue, cost, profit and volume
can be expressed graphically by preparing a CVP
graph. Below is a contribution margin income
statement at 300, 400, and 500 units sold. We will use
this information to prepare the CVP graph.
Sales
Less: variable expenses
Contribution margin
Less: fixed expenses
Net operating income
Income
300 units
$ 150,000
90,000
$
60,000
80,000
$ (20,000)
Income
400 units
$ 200,000
120,000
$ 80,000
80,000
$
-
Income
500 units
$ 250,000
150,000
$ 100,000
80,000
$ 20,000
4-12
CVP Graph 1
450,000
400,000
350,000
Dollars
300,000
250,000
In a CVP graph, unit volume is
usually represented on the
horizontal (X) axis and dollars on
the vertical (Y) axis.
200,000
150,000
100,000
50,000
-
100
200
300
400
500
600
700
800
Units
4-13
CVP Graph 2
450,000
400,000
Total Sales
350,000
Dollars
300,000
250,000
Total Expenses
200,000
Fixed Expenses
150,000
100,000
50,000
-
100
200
300
400
500
600
700
800
Units
4-14
CVP Graph 3
450,000
Break-even point
(400 units or $200,000 in sales)
400,000
350,000
Dollars
300,000
250,000
200,000
150,000
100,000
50,000
-
100
200
300
400
500
600
700
800
Units
4-15
Contribution Margin Ratio 1
•
The contribution margin ratio is:
Total CM
CM Ratio =
Total sales
•
For Example Company the ratio is:
$80,000
= 40%
$200,000
•
Each $1.00 increase in sales results in a
total contribution margin increase of 40¢.
4-16
Contribution Margin Ratio 2
•
Or, in terms of units, the contribution
margin ratio is:
Unit CM
CM Ratio =
Unit selling price
•
For Example Company the ratio is:
$200 = 40%
$500
4-17
Contribution Margin Ratio 3
If sales increase from 400 to 500 units
($50,000), contribution margin will increase by
$20,000 ($50,000 × 40%). Here is the proof:
Sales
Less: variable expenses
Contribution margin
Less: fixed expenses
Net operating income
400 Units
$ 200,000
120,000
80,000
80,000
$
-
500 Units
$ 250,000
150,000
100,000
80,000
$ 20,000
A $50,000 increase in sales revenue results in a $20,000
increase in CM ($50,000 × 40% = $20,000).
4-18
Contribution Margin Ratio 4
• The effect of a change in sales revenue on the
change in CM dollars can be expressed in
equation form as follows:
Change in CM dollars =
CM Ratio x Change in sales revenue
4-19
Quick Check 
Coffee Klatch is an espresso stand in a downtown office
building. The average selling price of a cup of coffee is $1.49
and the average variable expense per cup is $0.36. The
average fixed expense per month is $1,300. 2,100 cups are
sold each month on average. What is the CM Ratio for Coffee
Klatch?
a. 1.319
b. 0.758
c. 0.242
d. 4.139
4-20
Quick Check 
Coffee Klatch is an espresso stand in a downtown office
building. The average selling price of a cup of coffee is $1.49
and the average variable expense per cup is $0.36. The
average fixed expense per month is $1,300. 2,100 cups are
sold each month on average. What is the CM Ratio for Coffee
Klatch?
Answer:
b. 0.758
4-21
Variable Expense Ratio
Variable expense ratio is the ratio of variable
expenses to sales:
Variable expense ratio = Variable expenses / Sales
This leads to a useful equation that relates the CM
ratio to the variable expense ratio as follows:
CM ratio = CM / Sales
CM ratio = (Sales – Variable expenses) / Sales
CM ratio = 1 – Variable expense ratio
4-22
Change in Fixed Cost and Sales
Volume 1
•
What is the profit impact if sales can
increase from 500 units to 540 units by
increasing the monthly advertising
budget by $10,000?
4-23
Change in Fixed Cost and Sales
Volume 2
$80,000 + $10,000 advertising = $90,000
Example Company
Contribution Income Statement
For the Month of June
Current Sales
(500 units)
Sales revenue
Projected Sales
(540 units)
$250,000
$270,000
Less: Variable expenses
150,000
162,000
Contribution Margin
100,000
108,000
Less: Fixed expenses
80,000
90,000
Net Income
20,000
18,000
Sales increased by $20,000, but net operating income
decreased by $2,000.
4-24
Change in Fixed Cost and Sales
Volume 3
The CM Solution:
Increase in CM (40 units x $200) $ 8,000
Increase in advertising expenses (10,000)
Decrease in net operating income (2,000)
4-25
Change in Variable Cost and
Sales Volume 1
• What is the profit impact if a higher
quality of raw materials is used, thus
increasing variable costs per unit by
$10, to generate an increase in unit
sales from 500 to 580?
4-26
Change in Variable Cost and
Sales Volume 2
580 units × $310 variable cost/unit = $179,800
Example Company
Contribution Income Statement
For the Month of June
Current Sales
(500 units)
Sales revenue
Projected Sales
(580 units)
$250,000
$290,000
Less: Variable expenses
150,000
179,800
Contribution Margin
100,000
110,200
Less: Fixed expenses
80,000
80,000
Net Income
20,000
30,200
Sales increase by $40,000, and net operating income
increases by $10,200.
4-27
Change in Variable Cost and
Sales Volume 3
The CM Solution:
Increase in VC of $10 x 500 units $ (5,000)
Increase in units sold:
80 units x 190 [200 – 10]
15,200
Decrease in net operating income 10,200
4-28
Change in Fixed Costs, Selling
Price and Sales Volume 1
• What is the profit impact if:
(1) selling price is cut by $20 per
unit,
(2) the advertising budget is
increased by $15,000 per month, and
(3) sales increase from 500 to 650
units per month?
4-29
Change in Fixed Costs, Selling
Price and Sales Volume 2
Example Company
Contribution Income Statement
For the Month of June
Current Sales
(500 units)
Sales revenue
Projected Sales
(650 units)
$250,000
$312,000
Less: Variable expenses
150,000
195,000
Contribution Margin
100,000
117,000
Less: Fixed expenses
80,000
95,000
Net Income
20,000
22,000
Sales increase by $62,000, fixed costs increase by
$15,000, and net operating income increases by $2,000.
4-30
Change in Fixed Costs, Selling
Price and Sales Volume 3
The CM Solution:
Decrease in Selling Price of
$20 x 500 units
$(10,000)
Increase in advertising by
$15,000/month
(15,000)
Increase in sales by
150 units x $180 [200-20]
27,000
Increase in net operating income
2,000
4-31
Change in Variable Cost, Fixed
Cost and Sales Volume 1
• What is the profit impact if:
(1) instead of paying
salespersons flat salaries that
currently total $6,000 per month,
a $15 sales commission per unit
sold is paid, and
(2) sales increase from 500 units
to 575 units?
4-32
Change in Variable Cost, Fixed
Cost and Sales Volume 2
Example Company
Contribution Income Statement
For the Month of June
Current Sales
(500 units)
Sales revenue
Projected Sales
(575 units)
$250,000
$287,500
Less: Variable expenses
150,000
181,125
Contribution Margin
100,000
106,375
Less: Fixed expenses
80,000
74,000
Net Income
20,000
32,375
Sales increase by $37,500, variable costs increase by
$31,125, but fixed expenses decrease by $6,000. Net
operating income increased by $12,375.
4-33
Change in Variable Cost, Fixed
Cost and Sales Volume 3
The CM Solution:
Increase in VC of $15 x 500 units $(7,500)
Increase in CM of
$185 [200-15] x 75 units
13,875
Decrease (savings) in FC
6,000
Increase in net operating income 12,375
4-34
Break-Even Analysis 1
•
Break-even analysis is an aspect of
CVP analysis that is designed to
answer questions such as how far
sales could drop before the
company begins to lose money.
4-35
Break-Even Analysis 2
The contribution format income statement
can be stated in equation form:
Profits = (Sales – Variable expenses) – Fixed expenses
OR
Profits = [P x Q] – [V x Q] - Fixed expenses
Where P = selling price per unit, Q = number of
units sold; and VC = variable costs per unit.
4-36
Break-Even Analysis 3
Profits = [P x Q] – [V x Q] - Fixed expenses
We can simplify the above formula:
Profits = [CM x Q] – Fixed expenses
The Break-even point is when profits are
zero, therefore the equation becomes:
Break-even point in units sold =
Fixed expenses
Unit CM
4-37
Break-Even Analysis 4
Break-even point in units sold =
Fixed expenses
Unit CM
A variation of the break-even formula using
the CM ratio instead of the unit CM is
shown below. The result using this
formula is the break-even in total sales
dollars rather than in total units sold:
Break-even point in =
Total sales dollars
Fixed expenses
CM ratio
4-38
Break-Even Analysis 5
•
Here is the information from Example
Company:
Sales (500 units)
Less: variable expenses
Contribution margin
Less: fixed expenses
Net operating income
Total
$ 250,000
150,000
$ 100,000
$
Per Unit
$ 500
300
$ 200
Percent
100%
60%
40%
80,000
20,000
4-39
Break-Even Analysis 6
We calculate the break-even point as follows:
Break-even point in units sold = Fixed expenses
Unit CM
= $80,000 / 200
= 400 units
Break-even point in
total sales dollars
=
Fixed expenses
CM ratio
= $80,000 / 40%
= $200,000
4-40
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is $1.49 and the average
variable expense per cup is $0.36. The average
fixed expense per month is $1,300. 2,100 cups
are sold each month on average. What is the
break-even sales in units?
a. 872 cups
b. 3,611 cups
c. 1,200 cups
d. 1,150 cups
4-41
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is $1.49 and the average
variable expense per cup is $0.36. The average
fixed expense per month is $1,300. 2,100 cups
are sold each month on average. What is the
break-even sales in units?
Answer:
d. 1,150 cups
4-42
Quick Check 
Coffee Klatch is an espresso stand in a downtown
office building. The average selling price of a
cup of coffee is $1.49 and the average variable
expense per cup is $0.36. The average fixed
expense per month is $1,300. 2,100 cups 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
4-43
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is $1.49 and the average
variable expense per cup is $0.36. The average
fixed expense per month is $1,300. 2,100 cups
are sold each month on average. What is the
break-even sales in dollars?
Answer:
b. $1,715
4-44
Target Operating Profit Analysis 1
•
CVP formulas can also be used to
determine
•
•
•
the sales volume needed to achieve a target
operating profit.
The dollar sales needed to achieve a target
operating profit.
Suppose Example Company wants to know
how many units must be sold to earn a
profit of $100,000.
4-45
Target Operating Profit Analysis 2
Units sold to attain
Fixed expenses + Target operating profit
=
the target profit
Unit contribution margin
$80,000 + $100,000
= 900 units
$200/unit
4-46
Target Operating Profit Analysis 3
Dollar sales to
Fixed expenses + Target operating profit
=
attain target profit
CM Ratio
$80,000 + $100,000
= $450,000
40%
4-47
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is $1.49 and the average
variable expense per cup is $0.36. The average
fixed expense per month is $1,300. How many
cups of coffee would have to be sold to attain
target profits of $2,500 per month?
a. 3,363 cups
b. 2,212 cups
c. 1,150 cups
d. 4,200 cups
4-48
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is $1.49 and the average
variable expense per cup is $0.36. The average
fixed expense per month is $1,300. How many
cups of coffee would have to be sold to attain
target profits of $2,500 per month?
Answer:
a. 3,363 cups
4-49
After-Tax Analysis 1
•
For-profit organizations are required to
pay corporate income taxes.
•
In general, operating profit after taxes
can be computed as a fixed percentage
of income before taxes.
4-50
After-Tax Analysis 2
Profit after taxes = Before-tax profit – Taxes
= B – t(B)
= B(1-t)
Rearranged to calculate before-tax profit (B):
B = Profit after taxes / (1-t)
4-51
The Margin of Safety 1
The margin of safety is the excess of
budgeted (or actual) sales over the breakeven volume of sales.
Margin of safety = Total sales – Break-even sales
Margin of safety percentage =
Margin of safety in $
Total budgeted (or actual) sales
Let’s look at Example Company and
determine the margin of safety.
4-52
The Margin of Safety 2
If we assume that actual sales are $250,000, given
that we have already determined the breakeven sales to be $200,000, the margin of safety
is $50,000 as shown.
Sales
Less: variable expenses
Contribution margin
Less: fixed expenses
Net operating income
Breakeven sales
400 units
$ 200,000
120,000
80,000
80,000
$
-
Actual
sales
500 units
$ 250,000
150,000
100,000
80,000
$ 20,000
4-53
The Margin of Safety 3
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
4-54
The Margin of Safety 4
The margin of safety can be expressed in
terms of the number of units sold. The
margin of safety is $50,000, and each unit
sells for $500.
4-55
Quick Check 
Coffee Klatch is an espresso stand in a downtown
office building. The average selling price of a
cup of coffee is $1.49 and the average variable
expense per cup is $0.36. The average fixed
expense per month is $1,300. 2,100 cups are sold
each month on average. What is the margin of
safety?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
d. 2,100 cups
4-56
Quick Check 
Coffee Klatch is an espresso stand in a downtown
office building. The average selling price of a cup
of coffee is $1.49 and the average variable
expense per cup is $0.36. The average fixed
expense per month is $1,300. 2,100 cups are sold
each month on average. What is the margin of
safety?
Answer:
b. 950 cups
4-57
Cost Structure and Profit
Stability 1
• Cost structure refers to the relative
proportion of fixed and variable costs
in an organization. Managers often
have some latitude in determining
their organization’s cost structure.
4-58
Cost Structure and Profit
Stability 2
There are advantages and disadvantages to high fixed
cost (or low variable cost) and low fixed cost (or high
variable cost) structures.
An advantage of a high fixed
cost structure is that income
will be higher in good years
compared to companies
with lower proportion of
fixed costs.
A disadvantage of a high fixed
cost structure is that income
will be lower in bad years
compared to companies
with lower proportion of
fixed costs.
Companies with low fixed cost structures enjoy greater
stability in income across good and bad years.
4-59
Operating Leverage 1
A measure of how sensitive net operating income
is to percentage changes in sales.
Degree of
=
operating leverage
Contribution margin
Operating income
% change in
=
operating income
Degree of Op. Leverage x % change in sales
4-60
Operating Leverage 2
Example Company, the degree of operating
leverage is 5:
Sales
Less: variable expenses
Contribution margin
Less: fixed expenses
Net income
$100,000
$20,000
Actual sales
500 Units
$
250,000
150,000
100,000
80,000
$
20,000
= 5
4-61
Operating Leverage 3
With an operating leverage of 5, if sales are
increased by 10%, net operating income would
increase by 50%.
Percent increase in sales
Degree of operating leverage
Percent increase in profits
×
10%
5
50%
Here’s the verification!
4-62
Operating Leverage 4
Sales
Less variable expenses
Contribution margin
Less fixed expenses
Net operating income
Actual
sales
$ 250,000
150,000
100,000
80,000
$ 20,000
Increased
sales (550)
$ 275,000
165,000
110,000
80,000
$ 30,000
10% increase in sales from
$250,000 to $275,000 . . .
. . . results in a 50% increase in
income from $20,000 to $30,000.
4-63
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is $1.49 and the
average variable expense per cup is $0.36.
The average fixed expense per month is
$1,300. 2,100 cups are sold each month on
average. What is the operating leverage?
a. 2.21
b. 0.45
c. 0.34
d. 2.92
4-64
Quick Check 
Actual sales
Coffee Klatch is an espresso stand in
a cups
2,100
downtown office
building. The average 3,129
selling
Sales
price of a cupLess:
of coffee
is $1.49
and the 756
Variable
expenses
average variable
expense
per cup is $0.36.
Contribution
margin
2,373
The average fixed
expense
per month is
Less: Fixed
expenses
1,300
$1,300. 2,100 Net
cups
are sold
each month1,073
on
operating
income
average. What is the operating leverage?
Answer:
a. 2.21
4-65
Quick Check 
At Coffee Klatch the average selling price of a cup
of coffee is $1.49, the average variable expense
per cup is $0.36, the average fixed expense per
month is $1,300 and an average of 2,100 cups are
sold each month.
If sales increase by 20%, by how much should net
operating income increase?
a. 30.0%
b. 20.0%
c. 22.1%
d. 44.2%
4-66
Quick Check 
At Coffee Klatch the average selling price of a cup
of coffee is $1.49, the average variable expense
per cup is $0.36, the average fixed expense per
month is $1,300 and an average of 2,100 cups are
sold each month.
If sales increase by 20%, by how much should net
operating income increase?
Answer:
d. 44.2%
Percent increase in sales
× Degree of operating leverage
Percent increase in profit
20.0%
2.21
44.20%
4-67
Verify Increase in Profit
Actual
sales
2,100 cups
Sales
$ 3,129
Less: Variable expenses
756
Contribution margin
2,373
Less: Fixed expenses
1,300
Net operating income
$ 1,073
% change in sales
% change in net operating income
Increased
sales
2,520 cups
$
3,755
907
2,848
1,300
$
1,548
20.0%
44.2%
4-68
Sales Mix
•
•
•
Sales mix is the relative proportion in
which a company’s products are sold.
Different products have different selling
prices, cost structures, and contribution
margins.
Let’s assume Example Company sells
bikes and carts and that the sales mix
between the two products remains the
same.
4-69
Sales Mix & Break-Even Analysis 1
Example Co. information:
$265,000
= 48.2% (rounded)
$550,000
4-70
Sales Mix & Break-Even Analysis 2
4-71
Assumptions of CVP Analysis
•
Selling price is constant.
•
Costs are linear and can be accurately divided into
variable (constant per unit) and fixed (constant in
total) elements.
•
Variable costs per unit are constant, and fixed costs
are constant in total over the entire relevant range.
•
In multiproduct companies, the sales mix is
constant.
•
In manufacturing companies, inventories do not
change (units produced = units sold).
4-72
End of Chapter Summary Part 1
•
Cost–volume–profit (CVP) analysis is based on a
simple model of how contribution margin (CM)
and operating income respond to changes in
selling prices, costs, and volume.
•
A CVP graph depicts the relationships between
sales volume in units and fixed expenses,
variable expenses, total expenses, total sales,
and profits.
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End of Chapter Summary Part 2
•
The CM ratio is the ratio of the total CM to total
sales. This ratio can be used to estimate the
effect of a change in total sales on operating
income.
•
The break-even point is the level of sales (in
units or in dollars) at which the company
generates zero profits.
•
The margin of safety is the amount by which the
company’s current sales exceed break-even
sales.
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End of Chapter Summary Part 3
•
The degree of operating leverage measures the
effect of a percentage change in sales on the
company’s operating income. The higher the
degree of operating leverage, the more sensitive
operating income will be to a change in sales.
•
The profits of a multi-product company are
affected by its sales mix.
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