2. Drill
If 𝒙𝟐 - 𝒚𝟐 = 0 and x.y ≠ 0,
which of the following must
be true?
• x = y
• 𝒙 = 𝒚
•
𝒙𝟐
𝒚𝟐 = 1
3. What is
Break
Even
Analysis?
The purpose of break-even analysis is to
determine the number of units of a
product (i.e., the volume) to sell or
produce that will equate total revenue
with total cost.
The point where total revenues equals
total cost is called the break-even point,
and at this point profit is zero.
The break-even point gives a manager a
point of reference in determining how
many units will be needed to ensure
profit.
5. Component of
Break-Even
Analysis
Volu
me
Cost
Volume is the level of sales or production
by a company. It can be expressed as the
number of units (i.e., quantity) produced
and sold, as the dollar volume of sales , or
as a percentage of total capacity available.
Fixed costs can include such items as rent
on plant and equipment, taxes, staff and
management salaries , insurance
,advertising, depreciation, heat and light ,
and plant maintenance.
Variable costs include items as raw
materials and resources, direct labor,
packaging, material handling and freight.
6. Revenue >Variable Cost + Fixed Cost
Revenue =VariableCost +Fixed Cost
Revenue <VariableCost +Fixed Cost
Loss
Profit
BEP
8. Assumptions
General relationship for determining the
break-even volume
This relationship enables us to see how the level of profit (and
loss) is directly affected by changes in volume
However, when we developed this, we assumed that our
parameters, fixed and variable costs and price, were constant
In reality such parameters are frequently uncertain and can rarely
be assumed to be assumed to be constant, and changes in any of
parameters can affect the model solution
1
2
3
4
9. Sensitivi
ty
Analysis
The study of changes on a management
science model is called sensitivity
analysis-that is, seeing how sensitive the
model is to changes.
Sensitivity analysis can be performed on
all management science models in one
form or another.
In fact, sometimes companies develop
models for the primary purpose of
experimentation to see how the model
will react to different changes the
company is contemplating or that
management might expect to occur in the
future.
10. Old Total
Revenue
New Total
Revenue
Total Cost
Fixed Cost
OLD BEP
New BEP
400 1000
600 1200
200 800 1400
10
40
0
30
50
20
Revenue,
Cost &
Profit
($ 1,000s)
Volume, V
IncreaseinPrice
11. Total
Revenue
Old Total
Cost
Fixed Cost
OLD BEP
New BEP
400 1000
600 1200
200 800 1400
10
40
0
30
50
20
Revenue,
Cost &
Profit
($ 1,000s)
Volume, V
New Total
Cost
IncreaseinVariableCost
12. Total
Revenue
Old Total
Cost
Old Fixed
Cost
OLD BEP
New BEP
400 1000
600 1200
200 800 1400
10
40
0
30
50
20
Revenue,
Cost &
Profit
($ 1,000s)
Volume, V
New Total
Cost
New Fixed
Cost
ChangeinFixedCost
13. As an example, consider Western Clothing
Company, which produces denim jeans. The
company incurs the following monthly cost to
produce denim jeans:
Fixed Cost = $10,000
Variable Cost = $8 per pair
Arbitrarily, let us assume monthly sales
volumes (v), equals to 400 pairs of denim
jeans .
So, what will be the total cost?
14. Now, a third component is added. Let us
assume, each denim jeans sell for $23 per
pair and the company sell 400 pairs of
denim jeans.
So, what will be total revenue?
15. So, Considering the previous information,
• Fixed Cost = $10,000
• Variable Cost = $8 per jeans
• Selling Price = $ 23 per jeans
• Total Sales = 400 pair of jeans
Calculate the total profit?
What will be the break even in this
scenario?
16. Now, if change in price
• Fixed Cost = $10,000
• Variable Cost = $8 per jeans
• Selling Price = $ 30 per jeans instead of $23
• Total Sales = 400 pair of jeans
What will be the break even in this scenario?
17. Now, if change in Fixed cost
Fixed Cost = $13,000 instead of $ 10,000
Variable Cost = $12 per jeans
Selling Price = $ 30 per jeans
Total Sales = 400 pair of jeans
What will be the break even in this scenario?
18. Fixed Cost = $13,000
Variable Cost = $12
per jeans
Selling Price = $ 30
per jeans
Total Sales = 400 pair
of jeans
Fixed Cost = $10,000
Variable Cost = $8 per
jeans
Selling Price = $ 23 per
jeans
Total Sales = 400 pair of
jeans
Before
After
21. DataforHerronCorporationareshownbelow:
PerUnit PerUnitofSales
Sellingprice $75 100%
Variableexpenses $45 60%
Contributionmargin $30 40%
Required:
The marketing manager believes that an $8,000 increase in the monthly advertising budget would
increasemonthlysalesby$15,000. Shouldtheadvertisingbudgetbeincreased?
Refer to the original data. Management is considering using higher-quality components that would
increase the variable cost by $3 per unit. The marketing manager believes that the higher-quality
productwouldincreasesalesby15%permonth. Shouldthehigher-qualitycomponentsbeused?
Fixed expenses are $75,000 per
month and the company is selling
3,000 unitspermonth.
22. Maxson Products distributes a single product, a woven basket whose selling price is
$8 and whose variable cost is $6 per unit. The company's monthly fixed expense is
$5,500.
Required:
1. Solve for the company's break-even point in unit sales using the equation
method.
2. Solve for the company's break-even point in sales dollars using the equation
methodandtheCMratio
3. Solve for the company's break-even point in unit sales using the formula
method.
4. So orthecompany'sbreak-evenpointinsalesdollarsusing
methodandtheCMratio.
23. Lucky Products markets two computer games: Predator and Runway. A
contribution format income statement for a recent month for the two games
appears below:
Predator Runway Total
Sales $100,000 $50,000 $150,000
Variableexpenses 25,000 5,000 30.000
Contributionmargin $75,000 $45,000 120,000
fixedexpenses 90,000
Netoperatingincome $30,000
Required:
l.Compute theoverall contribution margin (CM) ratio for thecompany.
2. Compute theoverall break-even pointfor thecompanyinsales dollars.
3. Verify the overall break-even point or the company by constructing a contribution format income
statementshowing theappropriate levelsof salesfor thetwo products.
