Short Term Decision Making
Cost-Volume-Profit Analysis
By:
Associate Professor Dr. GholamReza Zandi
zandi@segi.edu.my
Types of Cost Behavior Patterns
Cost Behavior
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
Fixed
The Activity Base
Units
produced
Machine
hours
A measure of what
causes the
incurrence of a
variable cost.
Miles
driven
Labor
hours
True Variable Cost Example
Total Long Distance
Telephone Bill
A variable cost is a cost whose total dollar
amount varies in direct proportion to changes
in the activity level.
Your total long distance
telephone bill is based
on how many minutes
you talk.
Minutes Talked
Types of Cost Behavior Patterns
Recall the summary of our cost
behavior discussion from Chapter 1.
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
Fixed
Variable Cost Per Unit Example
The per minute cost of
long distance calls is
constant, for example,
10¢ per minute.
Per Minute
Telephone Charge
A variable cost remains constant if
expressed on a per unit basis.
Minutes Talked
Extent of Variable Costs
The proportion of variable costs differs across
organizations. For example . . .
A public utility with
large investments in
equipment will tend
to have fewer
variable costs.
A manufacturing company
will often have many
variable costs.
A service company
will normally have a high
proportion of variable costs.
A merchandising company
usually will have a high
proportion of variable costs
like cost of sales.
Examples of Variable Costs
1. Merchandising companies – cost of goods sold.
2. Manufacturing companies – direct materials,
direct labor, and variable overhead.
3. Merchandising and manufacturing companies –
commissions, shipping costs, and clerical costs
such as invoicing.
4. Service companies – supplies, travel, and
clerical.
True Variable Cost
Cost
Direct materials is a true or proportionately variable
cost because the amount used during
a period will vary in direct proportion to the
level of production activity.
Volume
Step-Variable Costs
Cost
A resource that is obtainable only in large chunks
(such as maintenance workers) and whose costs
increase or decrease only in response to fairly wide
changes in activity.
Volume
Step-Variable Costs
Cost
Small changes in the level of production are not
likely to have any effect on the number of
maintenance workers employed.
Volume
Step-Variable Costs
Cost
Only fairly wide changes in the activity level will
cause a change in the number
of maintenance workers employed.
Volume
The Linearity Assumption
and the Relevant Range
Total Cost
Economist’s
Curvilinear Cost
Function
Relevant
Range
A straight line
closely
approximates a
curvilinear
variable cost line
within the
relevant range.
Accountant’s Straight-Line
Approximation (constant unit
variable cost)
Activity
Types of Cost Behavior Patterns
Let’s turn our attention to fixed cost behavior.
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
Fixed
Total Fixed Cost Example
A fixed cost is a cost whose total dollar amount
remains constant as the activity level changes.
Monthly Basic
Telephone Bill
Your monthly basic
telephone bill is probably
fixed and does not change
when you make more
local calls.
Number of Local Calls
Types of Cost Behavior Patterns
Recall the summary of our cost
behavior discussion from Chapter 1.
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
Fixed
Fixed Cost Per Unit Example
The fixed cost per
local call decreases as
more local calls are
made.
Monthly Basic Telephone Bill
per Local Call
Average fixed costs per unit decrease
as the activity level increases.
Number of Local Calls
Types of Fixed Costs
Committed
Discretionary
Long-term, cannot be
significantly reduced in
the short-term.
May be altered in the
short-term by current
managerial decisions
Examples
Examples
Depreciation on
Buildings and
Equipment and Real
Estate Taxes
Advertising and
Research and
Development
The Trend Toward Fixed Costs
The trend in many industries is toward greater
fixed costs relative to variable costs.
As machines take over
many mundane tasks
previously performed
by humans,
“knowledge workers”
are demanded for
their minds rather
than their muscles.
Knowledge workers
tend to be salaried,
highly-trained and
difficult to replace. The
cost to compensate
these valued employees
is relatively fixed
rather than variable.
Is Labor a Variable or a Fixed Cost?
The behavior of wage and salary costs can differ
across countries, depending on labor regulations,
labor contracts, and custom.
In France, Germany, China, and Japan,
management has little flexibility in adjusting
the size of the labor force.
Labor costs are more fixed in nature.
Most companies in the United States continue
to view direct labor as a variable cost.
Rent Cost in Thousands of
Dollars
Fixed Costs and Relevant Range
90
Relevant
60
Range
30
0
0
Total cost doesn’t
change for a wide range
of activity, and then
jumps to a new higher
cost for the next higher
range of activity.
1,000
2,000
3,000
Rented Area (Square Feet)
Fixed Costs and Relevant Range
The relevant range of activity for a fixed cost is
the range of activity over which the graph of
the cost is flat.
Example: Office space is
available at a rental rate of
$30,000 per year in increments
of 1,000 square feet. As the
business grows, more space is
rented, increasing the total
cost.
Fixed Costs and Relevant Range
How does this type of
fixed cost differ from a
step-variable cost?
Step-variable costs can
be adjusted more
quickly and . . .
The width of the activity
steps is much wider for
the fixed cost.
Quick Check 
Which of the following statements about cost
behavior are true?
1. Fixed costs per unit vary with the level of activity.
2. Variable costs per unit are constant within the
relevant range.
3. Total fixed costs are constant within the relevant
range.
4. Total variable costs are constant within the
relevant range.
Quick Check 
Which of the following statements about cost
behavior are true?
1.
2.
3.
4.
Fixed costs per unit vary with the level of activity.
Variable costs per unit are constant within the
relevant range.
Total fixed costs are constant within the relevant
range.
Total variable costs are constant within the relevant
range.
Mixed Costs
A mixed cost has both fixed and variable
components. Consider your utility costs.
Total Utility Cost
Y
Variable
Cost per KW
Activity (Kilowatt Hours)
X
Fixed Monthly
Utility Charge
Mixed Costs
The total mixed cost line can be expressed
as an equation: Y = a + bX
Where:
Y = the total mixed cost
a = the total fixed cost (the
vertical intercept of the line)
b = the variable cost per unit of
activity (the slope of the line)
X = the level of activity
Total Utility Cost
Y
Variable
Cost per KW
Activity (Kilowatt Hours)
X
Fixed Monthly
Utility Charge
Mixed Costs Example
If your fixed monthly utility charge is $40, your
variable cost is $0.03 per kilowatt hour, and your
monthly activity level is 2,000 kilowatt hours, the
amount of your utility bill is:
Y = a + bX
Y = $40 + ($0.03 × 2,000)
Y = $100
Analysis of Mixed Costs
Account analysis
Each account is classified as either
variable or fixed based on the analyst’s
knowledge of how the account behaves.
Engineering Approach
Cost estimates are based on an evaluation
of production methods,
and material, labor and overhead
requirements.
The Scattergraph Method
Plot the data points on a graph (total
cost vs. activity).
Maintenance Cost
1,000’s of Dollars
Y
20
* *
* *
10
0
0
1
2
* ** *
**
3
4
Patient-days in 1,000’s
X
The Scattergraph Method
Maintenance Cost
1,000’s of Dollars
Y
20
* *
* *
10
0
0
1
2
* ** *
**
3
4
Patient-days in 1,000’s
X
Draw a line
through the
data points
with about an
equal number
of points
above and
below the
line.
The Scattergraph Method
Maintenance Cost
1,000’s of Dollars
Y Total maintenance cost = $11,000
20
* *
* *
10
* ** *
**
Intercept = Fixed cost: $10,000
0
0
1
2
3
4
Patient-days in 1,000’s
Patient days = 800
X
Use one
data point
to estimate
the total
level of
activity and
the total
cost.
The Scattergraph Method
Make a quick estimate of variable cost per
unit and determine the cost equation.
Total maintenance at 800 patients
Less: Fixed cost
Estimated total variable cost for 800 patients
Variable cost per unit =
$1,000
800
$ 11,000
10,000
$ 1,000
= $1.25/patient-day
Y = $10,000 + $1.25X
Total maintenance cost
Number of patient days
The High-Low Method
Assume the following hours of maintenance work
and the total maintenance costs for six months.
The High-Low Method
The variable cost per
hour of maintenance
is equal to the change
in cost divided by the
change in hours.
Hours Total Cost
High
800 $ 9,800
Low
500
7,400
Change
300 $ 2,400
$2,400
300
= $8.00/hour
The High-Low Method
Total Fixed Cost = Total Cost – Total Variable Cost
Total Fixed Cost = $9,800 – ($8/hour × 800 hours)
Total Fixed Cost = $9,800 – $6,400
Total Fixed Cost = $3,400
The High-Low Method
The Cost Equation for Maintenance
Y = $3,400 + $8.00X
Quick Check 
Sales salaries and commissions are $10,000
when 80,000 units are sold, and $14,000
when 120,000 units are sold. Using the highlow method, what is the variable portion of
sales salaries and commission?
a. $0.08 per unit
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
Quick Check 
Sales salaries and commissions are $10,000 when
80,000 units are sold, and $14,000 when 120,000
units are sold. Using the high-low method, what is
the variable portion of sales salaries and
commission?
a. $0.08 per unit
Units
Cost
b. $0.10 per unit
High level
120,000
$ 14,000
c. $0.12 per unit
Low level
80,000
10,000
Change
40,000
$ 4,000
d. $0.125 per unit
$4,000 ÷ 40,000 units
= $0.10 per unit
Quick Check 
Sales salaries and commissions are $10,000
when 80,000 units are sold, and $14,000
when 120,000 units are sold. Using the highlow method, what is the fixed portion of
sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
Quick Check 
Sales salaries and commissions are $10,000 when
80,000 units are sold, and $14,000 when 120,000
units are sold. Using the high-low method, what is
the fixed portion of sales salaries and commissions?
a. $ 2,000
Total cost = Total fixed cost +
b. $ 4,000
Total variable cost
c. $10,000
$14,000 = Total fixed cost +
($0.10 × 120,000 units)
d. $12,000
Total fixed cost
= $14,000 - $12,000
Total fixed cost
= $2,000
The Contribution Format
Sales Revenue
Less: Variable costs
Contribution margin
Total
$ 100,000
60,000
$ 40,000
Less: Fixed costs
Net operating income
30,000
$ 10,000
Unit
$ 50
30
$ 20
The contribution margin format emphasizes cost
behavior, by separating costs into fixed and variable
categories. Contribution margin covers fixed costs
and provides for income.
Uses of the Contribution Format
The contribution income statement format is used
as an internal planning and decision making tool.
We will use this approach for:
1. Cost-volume-profit analysis.
2. Budgeting.
3. Special decisions such as pricing and make-orbuy analysis.
The Contribution Format
Used primarily for
external reporting.
Used primarily by
management.
Overview of Absorption
and Variable Costing
Absorption
Costing
Variable
Costing
Direct Materials
Product
Costs
Direct Labor
Product
Costs
Variable Manufacturing Overhead
Fixed Manufacturing Overhead
Period
Costs
Variable Selling and Administrative Expenses
Fixed Selling and Administrative Expenses
Period
Costs
Quick Check 
Which method will produce the highest values for
work in process and finished goods inventories?
a. Absorption costing.
b. Variable costing.
c. They produce the same values for these
inventories.
d. It depends.
Quick Check 
Which method will produce the highest values for
work in process and finished goods inventories?
a. Absorption costing.
b. Variable costing.
c. They produce the same values for these
inventories.
d. It depends.
Unit Cost Computations
Harvey Company produces a single product with
the following information available:
Unit Cost Computations
Unit product cost is determined as follows:
Selling and administrative expenses are
always treated as period expenses and deducted from
revenue as incurred.
Income Comparison of
Absorption and Variable Costing
Let’s assume the following additional
information for Harvey Company.
– 20,000 units were sold during the year at a price of
$30 each.
– There is no beginning inventory.
Now, let’s compute net operating
income using both absorption and
variable costing.
Absorption Costing
Variable Costing
Variable
manufacturing
costs only.
Variable Costing
Sales (20,000 × $30)
Less variable expenses:
Beginning inventory
$
Add COGM (25,000 × $10)
250,000
Goods available for sale
250,000
Less ending inventory (5,000 × $10)
50,000
Variable cost of goods sold
200,000
Variable selling & administrative
expenses (20,000 × $3)
60,000
Contribution margin
Less fixed expenses:
Manufacturing overhead
$ 150,000
Selling & administrative expenses 100,000
Net operating income
$ 600,000
All fixed
manufacturing
overhead is
expensed.
260,000
340,000
250,000
$ 90,000
Comparing Absorption and
Variable Costing
Let’s compare the methods.
Comparing Absorption and
Variable Costing
We can reconcile the difference between absorption
and variable net operating income as follows:
Variable costing net operating income
$ 90,000
Add: Fixed mfg. overhead costs
deferred in inventory
(5,000 units × $6 per unit)
30,000
Absorption costing net operating income $ 120,000
Fixed mfg. overhead
Units produced
$150,000
=
25,000 units
= $6.00 per unit
Extended Comparison of Income Data
Here is information about the operation
of Harvey Company for the second year.
Unit Cost Computations
Since there was no change in the variable costs
per unit, total fixed costs, or the number of
units produced, the unit costs remain unchanged.
Absorption Costing
Absorption Costing
Sales (30,000 × $30)
Less cost of goods sold:
Beg. inventory (5,000 × $16)
Add COGM (25,000 × $16)
Goods available for sale
Less ending inventory
Gross margin
Less selling & admin. exp.
Variable (30,000 × $3)
Fixed
Net operating income
$ 900,000
$ 80,000
400,000
480,000
-
$ 90,000
100,000
These are the 25,000 units
produced in the current period.
480,000
420,000
190,000
$ 230,000
Variable Costing
Variable
manufacturing
costs only.
All fixed
manufacturing
overhead is
expensed.
Comparing Absorption and
Variable Costing
We can reconcile the difference between absorption
and variable net operating income as follows:
Variable costing net operating income
$ 260,000
Deduct: Fixed manufacturing overhead
costs released from inventory
(5,000 units × $6 per unit)
30,000
Absorption costing net operating income $ 230,000
Fixed mfg. overhead
Units produced
$150,000
=
= $6.00 per unit
25,000 units
Comparing Absorption and
Variable Costing
Summary of Key Insights
NOI = net operating income
Basics of Cost-Volume-Profit Analysis
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales (500 bicycles)
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.
Basics of Cost-Volume-Profit Analysis
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales (500 bicycles)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
$ 250,000
150,000
100,000
80,000
$ 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 RBC sells an additional
bicycle, $200 more in contribution margin will be generated
to cover fixed expenses and profit.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales (500 bicycles)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Total
$ 250,000
150,000
100,000
80,000
$ 20,000
Per Unit
$ 500
300
$ 200
The Contribution Approach
To breakeven, RBC must generate $80,000
in total CM each month to cover fixed costs.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales (500 bicycles)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Total
$ 250,000
150,000
100,000
80,000
$ 20,000
Per Unit
$ 500
300
$ 200
The Contribution Approach
If RBC sells 400 units a month, it will
be operating at the break-even point.
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales (400 bicycles)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Total
$ 200,000
120,000
80,000
80,000
$
-
Per Unit
$ 500
300
$ 200
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
Sales (401 bicycles)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Total
$ 200,500
120,300
80,200
80,000
$
200
Per Unit
$ 500
300
$ 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 RBC sells 430
bikes, its net
operating income
will be $6,000.
CVP Relationships in Graphic Form
The relationship among revenue, cost, profit and volume
can be expressed graphically by preparing a CVP graph.
RBC developed contribution margin income statements
at 300, 400, and 500 units sold. We will use this
information to prepare the CVP graph.
Income
300 units
Sales
$ 150,000
Less: variable expenses
90,000
Contribution margin
$
60,000
Less: fixed expenses
80,000
Net operating income
$ (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
CVP Graph
450,000
400,000
350,000
300,000
In a CVP graph, unit volume is usually
represented on the horizontal (X) axis
and dollars on the vertical (Y) axis.
250,000
200,000
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
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
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
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
Break-even point
(400 units or $200,000 in sales)
400,000
350,000
300,000
250,000
200,000
150,000
100,000
50,000
-
100
200
300
Units
400
500
600
700
800
Contribution Margin Ratio
The contribution margin ratio is:
Total CM
CM Ratio =
Total sales
For Racing Bicycle Company the ratio is:
$80,000
= 40%
$200,000
Each $1.00 increase in sales results in a total
contribution margin increase of 40¢.
Contribution Margin Ratio
Or, in terms of units, the contribution margin ratio is:
CM Ratio =
Unit CM
Unit selling price
For Racing Bicycle Company the ratio is:
$200 = 40%
$500
Contribution Margin Ratio
400 Bikes
Sales
$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
$
-
500 Bikes
$ 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)
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. On average, 2,100 cups are sold
each month. 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. On average, 2,100 cups are sold
each month. What is the CM Ratio for Coffee
Klatch?
Unit contribution margin
CM Ratio =
a. 1.319
Unit selling price
b. 0.758
($1.49-$0.36)
=
$1.49
c. 0.242
d. 4.139
$1.13
=
$1.49
= 0.758
Changes in Fixed Costs
and Sales Volume
What is the profit impact if RBC 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
Racing Bicycle Company
Contribution Income Statement
For the Month of June
Sales revenue
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Current Sales
(500 bikes)
$
250,000
150,000
100,000
80,000
$
20,000
Projected Sales
(540 bikes)
$
270,000
162,000
108,000
90,000
$
18,000
Sales increased by $20,000, but net
operating income decreased by $2,000.
Changes in Fixed Costs
and Sales Volume
The Shortcut Solution
Increase in contribution margin
(40 units × $200)
Increase in advertising
Decrease in net operating income
$ 8,000
10,000
$ (2,000)
Changes in Variable Costs
and Sales Volume
What is the profit impact if RBC 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?
Changes in Variable Costs
and Sales Volume
580 units × $310 variable cost/unit = $179,800
Increase in contribution margin
(580 units × $190)
– (500 units × $200)
Racing Bicycle Company
Change in fixed
expenses
Contribution
Income Statement
For the Month
of June
Increase in net operating
income
Sales revenue
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Current Sales
(500 bikes)
$
250,000
150,000
100,000
80,000
$
20,000
$ 10,200
$ 10,200
Projected Sales
(580 bikes)
$
290,000
179,800
110,200
80,000
$
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 unit sales from 500
to 650 units per month?
Change in Fixed Cost,
Sales Price and Volume
Increase in contribution margin
(650 units × $180) – (500 units × $200)
Racing Bicycle Company
Increase in fixed costs
Statement
Increase in net Contribution
operatingIncome
income
For the Month of June
Sales revenue
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Current Sales
(500 bikes)
$
250,000
150,000
100,000
80,000
$
20,000
$ 17,000
15,000
$ 2,000
Projected Sales
(650 bikes)
$
312,000
195,000
117,000
95,000
$
22,000
Sales increase by $62,000, fixed costs increase by $15,000, and
net operating income increases by $2,000.
Change in Fixed Cost,
Sales Price and 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 Fixed Cost,
Sales Price and Volume
Increase in contribution margin
(575 units × $185) – (500 units × $200)
Racing Bicycle Company
Reduced fixed costs
Contribution Income Statement
Increase in net operating
income
For the Month
of June
Sales revenue
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net operating income
Current Sales
(500 bikes)
$
250,000
150,000
100,000
80,000
$
20,000
$ 6,375
6,000
$ 12,375
Projected Sales
(650 bikes)
$
287,500
181,125
106,375
74,000
$
32,375
Sales increase by $37,500, variable costs increase by $31,125,
but fixed expenses decrease by $6,000.
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 =
Variable cost per bike =
Selling price required =
$ 20 per bike
300 per bike
$ 320 per bike
150 bikes × $320 per bike
Total variable costs
Increase in net operating income
= $ 48,000
=
45,000
= $ 3,000
Break-Even Analysis
Break-even analysis can be approached
in two ways:
1. Equation method
2. Contribution margin method
Equation Method
Profits = (Sales – Variable expenses) – Fixed expenses
OR
Sales = Variable expenses + Fixed expenses + Profits
At the break-even point
profits equal zero
Break-Even Analysis
Here is the information from RBC:
Total
Sales (500 bikes)
$ 250,000
Less: variable expenses 150,000
Contribution margin
$ 100,000
Less: fixed expenses
80,000
Net operating income
$ 20,000
Per Unit
$
500
300
$
200
Percent
100%
60%
40%
Equation Method
We calculate the break-even point as follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
Where:
Q = Number of bikes sold
$500 = Unit selling price
$300 = Unit variable expense
$80,000 = Total fixed expense
Equation Method
We calculate the break-even point as follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
$200Q = $80,000
Q = $80,000 ÷ $200 per bike
Q = 400 bikes
Equation Method
The equation can be modified to calculate the
break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0
Where:
X = Total sales dollars
0.60 = Variable expenses as a % of sales
$80,000 = Total fixed expenses
Equation Method
The equation can be modified to calculate the
break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0
0.40X = $80,000
X = $80,000 ÷ 0.40
X = $200,000
Contribution Margin Method
The contribution margin method
has two key equations.
Break-even point
in units sold
=
Break-even point in
total sales dollars
=
Fixed expenses
CM per unit
Fixed expenses
CM ratio
Contribution Margin Method
The contribution margin method can
be illustrated using data from RBC.
Break-even point
in units sold
$80,000
$200 per bike
=
= 400 bikes to breakeven
Break-even point in
total sales dollars
$80,000
40%
Fixed expenses
CM per unit
=
Fixed expenses
CM ratio
= $200,000 break-even sales
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. On average 2,100 cups are sold each month.
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. On average 2,100 cups are sold each month.
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 
Break-even =
=
Fixed expenses
Unit CM
$1,300
$1.49/cup - $0.36/cup
$1,300
=
$1.13/cup
= 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.
On average 2,100 cups are sold each month. What is
the break-even sales in 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.
On average 2,100 cups are sold each month. What is
the break-even sales in dollars?
a. $1,300
b. $1,715
c. $1,788
d. $3,129
Break-even
sales
=
=
Fixed expenses
CM Ratio
$1,300
0.758
= $1,715
Target Profit Analysis
The equation and contribution margin methods
can be used to determine the sales volume
needed to achieve a target profit.
Suppose Racing Bicycle Company wants to know
how many bikes must be sold to earn a profit of
$100,000.
The CVP Equation Method
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $100,000
$200Q = $180,000
Q = 900 bikes
The Contribution Margin Approach
The contribution margin method can be used
to determine that 900 bikes must be sold to
earn the target profit of $100,000.
Unit sales to attain
the target profit
=
Fixed expenses + Target profit
Unit contribution margin
$80,000 + $100,000
$200/bike
= 900 bikes
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
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
Quick Check 
Unit sales
to attain =
target profit
Fixed expenses + Target profit
Unit CM
=
$1,300 + $2,500
$1.49 - $0.36
=
$3,800
$1.13
= 3,363 cups
The Margin of Safety
The margin of safety is the excess of
budgeted (or actual) sales over the
break-even volume of sales.
Margin of safety = Total sales - Break-even sales
Let’s look at RBC and determine
the margin of safety.
The Margin of Safety
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
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
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.
Margin of
Safety in units
=
$50,000
= 100 bikes
$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. On average 2,100 cups are sold
each month. What is the margin of safety?
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. On average 2,100 cups are sold
each month. What is the margin of safety?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
d. 2,100 cups
Quick Check 
Margin of safety = Total sales – Break-even sales
= 2,100 cups – 1,150 cups
= 950 cups
or
Margin of safety
=
percentage
950 cups
2,100 cups = 45%
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.
Let’s assume RBC sells bikes and carts and
that the sales mix between the two
products remains the same.
Multi-product Break-even Analysis
RBC provides the following information:
Racing Bicycle Company
Contribution Income Statement
Sales revenue
Variable expenses
Contribution margin
Fixed expenses
Net operating income
Sales mix
Bicycles
$ 250,000
100%
150,000
60%
$ 100,000
40%
Carts
$ 300,000
100%
135,000
45%
$ 165,000
55%
Total
$ 550,000
100.0%
285,000
51.8%
265,000
48.2%
170,000
$ 95,000
$ 250,000
$ 300,000
$ 550,000
45%
$265,000
$550,000
55%
100%
= 48.2% (rounded)
Multi-product Break-even Analysis
Break-even
sales
Fixed expenses
=
CM Ratio
$170,000
=
48.2%
= $352,697
Racing Bicycle Company
Contribution Income Statement
Sales revenue
Variable expenses
Contribution margin
Fixed expenses
Net operating income
Sales mix
Bicycles
$ 158,714
100%
95,228
60%
$ 63,485
40%
Carts
$ 193,983
100%
87,293
45%
$ 106,691
55%
Rounding Error
$ 158,714
45%
$ 193,983
55%
Total
$ 352,697
100.0%
182,521
51.8%
170,176
48.2%
170,000
$
176
$ 352,697
100%
Key Assumptions of CVP Analysis
Selling price is constant.
Costs are linear.
In multi-product companies, the sales
mix is constant.
In manufacturing companies,
inventories do not change (units
produced = units sold).
The End