Indian Institute of Management Rohtak

Management Accounting

Session 5
Cost-Volume-Profit Analysis
By
Prof Archana Patro
 Learning Objective 1

Explain how changes in activity affect

contribution margin and net operating income.
 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 behavior.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales (500 bicycles) $ 250,000
Less: Variable expenses 150,000
Contribution margin 100,000
Less: Fixed expenses 80,000
Net operating income $ 20,000

Contribution Margin (CM) is the amount remaining from

sales revenue after variable expenses have been deducted.
 Basics of Cost-Volume-Profit
Analysis
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales (500 bicycles) $ 250,000
Less: Variable expenses 150,000
Contribution margin 100,000
Less: Fixed expenses 80,000
Net operating income $ 20,000

CM is used first to cover fixed expenses. Any

remaining CM contributes to net operating income.
 The Contribution Approach
Sales, variable expenses, and contribution margin can
also be expressed on a per unit basis. If Racing sells
an additional bicycle, $200 additional CM will be
generated to cover fixed expenses and profit.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Total Per Unit
Sales (500 bicycles) $ 250,000 $ 500
Less: Variable expenses 150,000 300
Contribution margin 100,000 $ 200
Less: Fixed expenses 80,000
Net operating income $ 20,000
 The Contribution Approach
Each month, RBC must generate at least
$80,000 in total contribution margin to break-even
(which is the level of sales at which profit is zero).
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Total Per Unit
Sales (500 bicycles) $ 250,000 $ 500
Less: Variable expenses 150,000 300
Contribution margin 100,000 $ 200
Less: Fixed expenses 80,000
Net operating income $ 20,000
 The Contribution Approach
If RBC sells 400 units in a month, it will be
operating at the break-even point.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Total Per Unit
Sales (400 bicycles) $ 200,000 $ 500
Less: Variable expenses 120,000 300
Contribution margin 80,000 $ 200
Less: Fixed expenses 80,000
Net operating income $ -
The Contribution Approach
If RBC sells one more bike (401 bikes), net
operating income will increase by $200.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Total Per Unit
Sales (401 bicycles) $ 200,500 $ 500
Less: Variable expenses 120,300 300
Contribution margin 80,200 $ 200
Less: Fixed expenses 80,000
Net operating income $ 200
 The Contribution Approach
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 Racing sells 430

bikes, its net
operating income
will be $6,000.
CVP Relationships in Equation Form
The contribution format income statement can be
expressed in the following equation:

Profit = (Sales – Variable expenses) – Fixed expenses

Racing Bicycle Company
Contribution Income Statement
For the Month of June
Total Per Unit
Sales (401 bicycles) $ 200,500 $ 500
Less: Variable expenses 120,300 300
Contribution margin 80,200 $ 200
Less: Fixed expenses 80,000
Net operating income $ 200
 CVP Relationships in Equation
Form
This equation can be used to show the profit RBC
earns if it sells 401. Notice, the answer of $200 in our
earlier solution.
Profit = (Sales – Variable expenses) – Fixed expenses

401 units × $500 $80,000

401 units × $300

$200 = ($200,500 – $120,300)

Profit – $80,000
Variable expenses) – Fixed
Fixed expenses
 CVP Relationships in Equation
Form
When a company has only one product we can further
refine this equation as shown on this slide.
Profit = (Sales – Variable expenses) – Fixed expenses

Quantity sold (Q) Quantity sold (Q)

× Selling price per unit (P) × Variable expenses per unit (V)
= Sales (Q × P) = Variable expenses (Q × V)

Profit = (P × Q – V × Q) – Fixed expenses

 CVP Relationships in Equation
Form
This equation can also be used to show the $200
profit RBC earns if it sells 401 bikes.

Profit = (Sales – Variable expenses) – Fixed expenses

Profit = (P × Q – V × Q) – Fixed expenses

$200 = ($500 × 401 – $300 × 401) – $80,000
Profit
 CVP Relationships in Equation
Form
It is often useful to express the simple profit equation in
terms of the unit contribution margin (Unit CM) as follows:

Unit CM = Selling price per unit – Variable expenses per unit

Unit CM = P – V
Profit = (P × Q – V × Q) – Fixed expenses
Profit = (P – V) × Q – Fixed expenses
Profit = Unit CM × Q – Fixed expenses
 CVP Relationships in Equation
Form
Profit = (P × Q – V × Q) – Fixed expenses
Profit = (P – V) × Q – Fixed expenses
Profit = Unit CM × Q – Fixed expenses

Profit = ($500 – $300) × 401 – $80,000

Profit = $200 × 401 – $80,000
This equation
Profit = $80,200 – $80,000 can also be
Profit = $200 used to
compute RBC’s
$200 profit if it
sells 401 bikes.
 CVP Relationships and
the Income Statement
A. Traditional Format
ACCUTIME COMPANY
Income Statement
For the Year Ended December 31, 20x1

Sales $500,000
Less: 380,000
Gross margin $120,000
Less: Operating expenses:
Selling expenses $35,000
Administrative expenses 35,000 70,000
Net income $50,000

7-16
 CVP Relationships and
the Income Statement
B. Contribution Format
ACCUTIME COMPANY
Income Statement
For the Year Ended December 31, 20x1

Sales $500,000
Less: Variable expenses:
Variable manufacturing $280,000
Variable selling 15,000
Variable administrative 5,000 300,000
Contribution margin $200,000
Less: Fixed expenses:
Fixed manufacturing $100,000
Fixed selling 20,000
Fixed administrative 30,000 150,000
Net income $50,000

7-17
 Learning Objective 2

Prepare and interpret a cost-

volume-profit (CVP) graph and a
profit graph.
 CVP Relationships in Graphic
Form
The relationships among revenue, cost, profit and volume
can be expressed graphically by preparing a CVP graph.
Racing Bicycle developed contribution margin income
statements at 0, 200, 400, and 600 units sold. We will
use this information to prepare the CVP graph.
Units Sold
0 200 400 600
Sales $ - $ 100,000 $ 200,000 $ 300,000
Total variable expenses - 60,000 120,000 180,000
Contribution margin - 40,000 80,000 120,000
Fixed expenses 80,000 80,000 80,000 80,000
Net operating income (loss) $ (80,000) $ (40,000) $ - $ 40,000
 Preparing the CVP Graph
$3,50,000

$3,00,000

$2,50,000

$2,00,000

$1,50,000

$1,00,000
In a CVP graph, unit volume is usually
$50,000
represented on the horizontal (X) axis
and dollars on the vertical (Y) axis.
$0
0 100 200 300 400 500 600

Units
 Preparing the CVP Graph
$3,50,000

Draw a line parallel to the volume axis
$3,00,000
to represent total fixed expenses.
$2,50,000

$2,00,000

Fixed expenses
$1,50,000

$1,00,000

$50,000

$0
0 100 200 300 400 500 600

Units
 Preparing the CVP Graph

Choose some sales volume, say 400 units, and plot the point representing
total expenses (fixed and variable). Draw a line through the data point
back to where the fixed expenses line intersects the dollar axis.
$3,50,000

$3,00,000

$2,50,000

$2,00,000

Total expenses
$1,50,000 Fixed expenses

$1,00,000

$50,000

$0 Units
0 100 200 300 400 500 600
 Preparing the CVP Graph
$3,50,000 
Choose some sales volume, say 400 units, and plot the point representing
total sales.
$3,00,000
Draw a line through the data point back to the point of origin.

$2,50,000

$2,00,000
Sales
Total expenses
$1,50,000 Fixed expenses

$1,00,000

$50,000

$0
0 100 200 300 400 500 600

Units
 Preparing the CVP Graph
$3,50,000 Break-even point
(400 units or $200,000 in sales) Profit Area
$3,00,000

$2,50,000

$2,00,000
Sales
Total expenses
$1,50,000 Fixed expenses

$1,00,000

$50,000

$0
0 100 200 300 400 500 600
Loss Area Units
 Preparing the CVP Graph
Profit = Unit CM × Q – Fixed Costs
$ 60,000

$ 40,000

$ 20,000
Profit

$0

-$20,000 An even simpler form of

-$40,000 the CVP graph is called
the profit graph.
-$60,000

0 100 200 300 400 500 600

Number of bicycles sold
 Preparing the CVP Graph

$ 60,000 Break-even point, where

profit is zero , is 400
$ 40,000
units sold.
$ 20,000
Profit

$0

-$20,000

-$40,000

-$60,000

0 100 200 300 400 500 600

Number of bicycles sold
 Learning Objective 3
Use the contribution margin ratio (CM ratio) to
compute changes in contribution
margin and net operating income resulting from
changes in sales volume.
Contribution Margin Ratio (CM Ratio)
The CM ratio is calculated by dividing the total
contribution margin by total sales.

Racing Bicycle Company

Contribution Income Statement
For the Month of June
Total Per Unit CM Ratio
Sales (500 bicycles) $ 250,000 $ 500 100%
Less: Variable expenses 150,000 300 60%
Contribution margin 100,000 $ 200 40%
Less: Fixed expenses 80,000
Net operating income $ 20,000

$100,000 ÷ $250,000 = 40%

Contribution Margin Ratio (CM ratio)
The contribution margin ratio at Racing Bicycle is:

CM per unit $200

CM Ratio = = = 40%
SP per unit $500

The CM ratio can also be calculated by

dividing the contribution margin per unit by
the selling price per unit.
 Contribution Margin Ratio (CM
Ratio)
If Racing Bicycle increases sales by $50,000, contribution
margin will increase by $20,000 ($50,000 × 40%).
Here is the proof:
400 Units 500 Units
Sales $ 200,000 $ 250,000
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net operating income $ - $ 20,000

A $50,000 increase in sales revenue results in a $20,000

increase in CM. ($50,000 × 40% = $20,000)
 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
 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 Unit contribution margin
CM Ratio =
b. 0.758 Unit selling price
c. 0.242 ($1.49-$0.36)
=
d. 4.139 $1.49
$1.13
= = 0.758
$1.49
Contribution Margin Ratio (CM Ratio)
The relationship between profit and the CM ratio
can be expressed using the following equation:
Profit = CM ratio × Sales – Fixed expenses
If Racing Bicycle increased its sales volume to 500
bikes, what would management expect profit or net
operating income to be?

Profit = 40% × $250,000 – $80,000

Profit = $100,000 – $80,000
Profit = $20,000
Learning Objective 4
Show the effects on
contribution margin of
changes in variable costs,
fixed costs, selling price, and
volume.
 The Variable Expense Ratio
The variable expense ratio is the ratio of variable
expenses to sales. It can be computed by dividing the
total variable expenses by the total sales, or in a single
product analysis, it can be computed by dividing the
variable expenses per unit by the unit selling price.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Total Per Unit CM Ratio
Sales (500 bicycles) $ 250,000 $ 500 100%
Less: Variable expenses 150,000 300 60%
Contribution margin 100,000 $ 200 40%
Less: Fixed expenses 80,000
Net operating income $ 20,000
Changes in Fixed Costs and Sales
Volume

What is the profit impact if Racing

Bicycle can increase unit sales from
500 to 540 by increasing the monthly
advertising budget by $10,000?
 Changes in Fixed Costs and Sales
Volume
$80,000 + $10,000 advertising = $90,000

500 units 540 units

Sales $ 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 operating income $ 20,000 $ 18,000

Sales increased by $20,000, but net operating

income decreased by $2,000.
Changes in Fixed Costs and Sales
Volume
A shortcut solution using incremental
analysis

Increase in CM (40 units X $200) $ 8,000

Increase in advertising expenses 10,000
Decrease in net operating income $ (2,000)
 Change in Variable Costs and
Sales Volume

What is the profit impact if Racing

Bicycle can use higher quality raw
materials, thus increasing variable costs
per unit by $10, to generate an increase
in unit sales from 500 to 580?
Change in Variable Costs and Sales
Volume
580 units × $310 variable cost/unit = $179,800

500 units 580 units

Sales $ 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 operating income $ 20,000 $ 30,200

Sales increase by $40,000, and net operating income

increases by $10,200.
 Change in Fixed Cost, Sales Price
and Volume

What is the profit impact if RBC: (1) cuts its

selling price $20 per unit, (2) increases its
advertising budget by $15,000 per month,
and (3) increases sales from 500 to 650
units per month?
 Change in Fixed Cost, Sales Price
and Volume
650 units × $480 = $312,000

500 units 650 units

Sales $ 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 operating income $ 20,000 $ 22,000

Sales increase by $62,000, fixed costs increase by

$15,000, and net operating income increases by $2,000.
 Change in Variable Cost, Fixed Cost
and Sales Volume

What is the profit impact if RBC: (1) pays a

$15 sales commission per bike sold instead
of paying salespersons flat salaries that
currently total $6,000 per month, and (2)
increases unit sales from 500 to 575 bikes?
 Change in Variable Cost, Fixed Cost
and Sales Volume
575 units × $315 = $181,125
500 units 575 units
Sales $ 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 operating income $ 20,000 $ 32,375

Sales increase by $37,500, fixed expenses decrease by

$6,000. Net operating income increases by $12,375.
Change in Regular Sales Price

If RBC has an opportunity to sell 150

bikes to a wholesaler without disturbing
sales to other customers or fixed
expenses, what price would it quote to
the wholesaler if it wants to increase
monthly profits by $3,000?
 Change in Regular Sales Price

$ 3,000 ÷ 150 bikes = $ 20 per bike

Variable cost per bike = 300 per bike
Selling price required = $ 320 per bike

150 bikes × $320 per bike = $ 48,000

Total variable costs = 45,000
Increase in net operating income = $ 3,000
 Learning Objective 5

Determine the level of sales needed

to attain a target profit.
 Target Profit Analysis
We can compute the number of units
that must be sold to attain a target
profit using either:

1. Equation method
2. Formula method.
 Equation Method
Profit = Unit CM × Q – Fixed expenses

Our goal is to solve for the unknown “Q” which

represents the quantity of units that must be sold
to attain the target profit.
 Target Profit Analysis
Suppose Racing Bicycle management wants to know
how many bikes must be sold to earn a target profit
of $100,000.

Profit = Unit CM × Q – Fixed expenses

$100,000 = $200 × Q – $80,000
$200 × Q = $100,000 – $80,000
Q = ($100,000 + $80,000) ÷ $200
Q = 900
 The Formula Method

The formula uses the following equation.

Unit sales to attain Target profit + Fixed expenses

=
the target profit CM per unit
 Target Profit Analysis in Terms of
Unit Sales
Suppose Racing Bicycle Company wants to
know how many bikes must be sold to
earn a profit of $100,000.
Unit sales to attain Target profit + Fixed expenses
=
the target profit CM per unit

$100,000 + $80,000
Unit sales =
$200
Unit sales = 900
 Target Profit Analysis
We can also compute the target profit in terms of
sales dollars using either the equation method or
the formula method.

Equation OR Formula
Method Method
 Equation Method
Profit = CM ratio × Sales – Fixed expenses
Our goal is to solve for the unknown “Sales” which
represents the dollar amount of sales that must be
sold to attain the target profit.
Suppose RBC management wants to know the sales
volume that must be generated to earn a target
profit of $100,000.
$100,000 = 40% × Sales – $80,000
40% × Sales = $100,000 + $80,000
Sales = ($100,000 + $80,000) ÷ 40%
Sales = $450,000
 Formula Method
We can calculate the dollar sales needed to
attain a target profit (net operating profit) of
$100,000 at Racing Bicycle.
Dollar sales to attain Target profit + Fixed expenses
=
the target profit CM ratio

$100,000 + $80,000
Dollar sales =
40%
Dollar sales = $450,000
 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. Use the
formula method to determine 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
 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 Unit salesfixed expense per month is $1,300.
average Target profit + Fixed expenses
to attain
Use the formula method= to determineUnithowCM
many cups of
target
coffee would profit
have to be sold to attain target profits of
$2,500 per month. $2,500 + $1,300
= $1.49 - $0.36
a. 3,363 cups
b. 2,212 cups $3,800
=
c. 1,150 cups $1.13
d. 4,200 cups = 3,363 cups
 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. Use the
formula method to determine the sales dollars
that must be generated to attain target profits of
$2,500 per month.
a. $2,550
b. $5,011
c. $8,458
d. $10,555
 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.
Use the formula method
Sales $ to determine the sales dollars
Target profit + Fixed expenses
that must be to
generated
attain = to attain target profits of $2,500
CM ratio
per month. target profit
a. $2,550 $2,500 + $1,300
=
b. $5,011 ($1.49 – 0.36) ÷ $1.49
c. $8,458 $3,800
=
d. $10,555 0.758
= $5,011
 Learning Objective 6

Determine the break-even point.

 Break-even Analysis
The equation and formula methods can be used to
determine the unit sales and dollar sales needed to
achieve a target profit of zero. Let’s us the RBC
information to complete the break-even analysis.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Total Per Unit CM Ratio
Sales (500 bicycles) $ 250,000 $ 500 100%
Less: Variable expenses 150,000 300 60%
Contribution margin 100,000 $ 200 40%
Less: Fixed expenses 80,000
Net operating income $ 20,000
 Break-even in Unit Sales:
Equation Method
Profits = Unit CM × Q – Fixed expenses
Suppose RBC wants to know how many
bikes must be sold to break-even
(earn a target profit of $0).

$0 = $200 × Q + $80,000

Profits are zero at the break-even point.

 Break-even in Unit Sales:
Equation Method
Profits = Unit CM × Q – Fixed expenses
$0 = $200 × Q + $80,000

$200 × Q = $80,000

Q = 400 bikes
 Break-even in Unit Sales:
Formula Method
Let’s apply the formula method to solve for
the break-even point.

Unit sales to Fixed expenses

=
break even CM per unit

$80,000
Unit sales =
$200
Unit sales = 400
 Break-even in Dollar Sales:
Equation Method
Suppose Racing Bicycle wants to compute
the sales dollars required to break-even (earn
a target profit of $0). Let’s use the equation
method to solve this problem.
Profit = CM ratio × Sales – Fixed expenses

Solve for the unknown “Sales.”

 Break-even in Dollar Sales:
Equation Method
Profit = CM ratio × Sales – Fixed expenses
$ 0 = 40% × Sales – $80,000

40% × Sales = $80,000

Sales = $80,000 ÷ 40%

Sales = $200,000
 Break-even in Dollar Sales:
Formula Method
Now, let’s use the formula method to calculate the
dollar sales at the break-even point.

Dollar sales to Fixed expenses

=
break even CM ratio

$80,000
Dollar sales =
40%
Dollar sales = $200,000
 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 dollars?
a. $1,300
b. $1,715
c. $1,788
d. $3,129
 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 dollars?
a. $1,300 Break-even Fixed expenses
b. $1,715 =
sales CM Ratio
c. $1,788 $1,300
=
0.758
d. $3,129
= $1,715
 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
 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 Fixedonexpenses
month average.
Break-even =
What is the break-even sales in units? CM per Unit
a. 872 cups $1,300
=
$1.49/cup - $0.36/cup
b. 3,611 cups
c. 1,200 cups $1,300
=
$1.13/cup
d. 1,150 cups
= 1,150 cups
Learning Objective 7

Compute the margin of

safety and explain its
significance.
 The Margin of Safety in Dollars
The margin of safety in dollars is the
excess of budgeted (or actual) sales over
the break-even volume of sales.
Margin of safety in dollars = Total sales - Break-even sales

Let’s look at Racing Bicycle Company and

determine the margin of safety.
The Margin of Safety in Dollars
If we assume that RBC has actual sales of
$250,000, given that we have already determined
the break-even sales to be $200,000, the
margin of safety is $50,000 as shown.
Break-even
sales Actual sales
400 units 500 units
Sales $ 200,000 $ 250,000
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net operating income $ - $ 20,000
The Margin of Safety Percentage
RBC’s margin of safety can be expressed as
20% of sales.
($50,000 ÷ $250,000)
Break-even
sales Actual sales
400 units 500 units
Sales $ 200,000 $ 250,000
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net operating income $ - $ 20,000
 The Margin of Safety
The margin of safety can be expressed in terms of
the number of units sold. The margin of safety at
RBC is $50,000, and each bike sells for $500;
hence, RBC’s margin of safety is 100 bikes.

Margin of $50,000
= = 100 bikes
Safety in units $500
 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
expressed in cups?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
d. 2,100 cups
 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 expressed in cups?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
Margin of safety = Total sales – Break-even sales
d. 2,100 cups = 2,100 cups – 1,150 cups
= 950 cups
 Learning Objective 8

Compute the break-even point for a

multiproduct company and explain the
effects of shifts in the sales mix on
contribution margin and the break-even
point.
 The Concept of 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.
• When a company sells more than one product,
break-even analysis becomes more complex
as the following example illustrates.

Let’s assume Racing Bicycle Company sells

bikes and carts and that the sales mix between
the two products remains the same.
 Multi-Product Break-Even Analysis
Bikes comprise 45% of RBC’s total sales revenue and the
carts comprise the remaining 55%. RBC provides the
following information:
Bicycle Carts Total
Sales $ 250,000 100% $ 300,000 100% $ 550,000 100.0%
Variable expenses 150,000 60% 135,000 45% 285,000 51.8%
Contribution margin 100,000 40.0% 165,000 55% 265,000 48.2%
Fixed expenses 170,000
Net operating income $ 95,000

Sales mix $ 250,000 45% $ 300,000 55% $ 550,000 100%

$265,000
= 48.2% (rounded)
$550,000
 Multi-Product Break-Even Analysis
Dollar sales to Fixed expenses
=
break even CM ratio

Dollar sales to $170,000

= = $352,697
break even 48.2%

Bicycle Carts Total

Sales $ 158,714 100% $ 193,983 100% $ 352,697 100.0%
Variable expenses 95,228 60% 87,293 45% 182,521 51.8%
Contribution margin 63,485 40% 106,691 55% 170,176 48.2%
Fixed expenses 170,000
Net operating income Rounding error $ 176

Sales mix $ 158,714 45% $ 193,983 55% $ 352,697 100.0%

 Key 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.
• In multiproduct companies, the sales mix is
constant.
• In manufacturing companies, inventories
do not change (units produced = units sold).