Math related to cost volume profit analysis

1. WELCOME

2. COST-VOLUME-PROFIT

3. Profit = Sales – Costs
= Sales – (Variable Costs + Fixed Costs)
= Sales – Variable Costs – Fixed Costs
Profit + Fixed Costs = Sales – Variable Costs
Profit + Fixed Costs
= Units Sold X (Unit Sales Price – Unit Variable
Cost)
The Basic Profit Equation

4. The Problem
Delgado Food Services Company operates and services soft
drink vending machines located in:
• Restaurants
• Gas stations
• Factories
The machines are rented from the manufacturer.
Delgado also rent the space occupied by its machines.

5. The Problem
Elements of Cost Total
Machine rental: 40 machines @ $ 43.50 $ 1,740
Space rental: 40 location @ $ 28.80 1,152
Part-time wages to service the additional 40
machines
1,908
Other fixed costs 200
Total monthly fixed costs $ 5,000
Fixed Monthly Expenses

6. The Problem
Other Data
Elements of Cost Per Unit Per $ 100 of Sales
Selling price $ 1.00 100%
Cost of snack 0.80 80%
Contribution margin $ 0.20 20%

7. The Problem
Requirement
1. What is the monthly break-even point in number of
units and in dollar sales?
2. If 36,000 units were sold, what would be the
company’s net income?
3. If the space rental cost were doubled, what would
be the monthly break-even point in number of units and in
dollar sales?

8. The Problem
Requirement
4. If, in addition to the fixed rent, Delgado Food
Services Company paid the vending machine manufacturer
2 cent per unit sold, what would be the monthly break-
even point in number of units and in dollar sales? Refer to
the original data.
5. If, in addition to the fixed rent, Delgado paid the
machine manufacturer 4 cent for each unit sold in excess
of the break-even point, what would the new net income
be if 36,000 units were sold? Refer to the original data.

9. The Solution
Contribution Margin (CM)
Unit CM = Sales – Variable Expenses
= $ 1.00 - $ 0.80
= $ 0.20
 In the case of Delgado Food and Services Company, the
CM can be computed as follows:

10. The Solution
Contribution Margin (CM) Ratio
CM Ratio =
Total CM
Total Sales
=
$7,200
$36,000
= 20%
 For, Delgado Food and Services Company, the
computations are:

11. The Solution
 If 36,000 units were sold, what would be the company’s
net income?
Elements of Cost Total Per Unit Percent of Sales
Sales (36,000 units) @ $
1.00
$ 36,000.00 $ 1.00 100%
Variable expenses (cost of
snack) @ $ 0.80
28,800.00 0.80 80%
CM 7,200.00 $ 0.20 20%
Fixed expenses 5,000.00
Net operating income $ 2,200.00

12. The Solution
 What is the monthly break-even point in number of
units in sales?
Unit sales to break-even =
Fixed expenses
Unit CM
=
$ 5,000.00
$ 0.20
= 25,000
 In the case of Delgado Food and Services Company, the
break-even point can be computed as follows:

13. The Solution
 What is the monthly break-even point in dollar sales?
 In the case of Delgado Food and Services Company, the
break-even point can be computed as follows:
Dollar sales to break-even =
Fixed expenses
CM Ratio
=
$ 5,000.00
0.20
= $ 25,000

14. The Solution
 If the space rental cost were doubled, what would be
the monthly break-even point in number of units in
sales?
Elements of Cost Total
Machine rental: 40 machines @ $ 43.50 $ 1,740
Space rental: 40 location @ $ (28.80 X 2) = $ 57.60 2,304
Part-time wages to service the additional 40 machines 1,908
Other fixed costs 200
Total monthly fixed costs $ 6,152
If the space rental cost were doubled, fixed monthly
expenses of Delgado Food and Services Company would
be as follows:

15. The Solution
Unit sales to break-even =
Fixed expenses
Unit CM
=
$ 6,152.00
$ 0.20
= 30,760
In that case the break-even point of Delgado Food and
Services Company can be computed as follows:

16. The Solution
 If the space rental cost were doubled, what would be
the monthly break-even point in dollar sales?
Dollar sales to break-even =
Fixed expenses
CM Ratio
=
$ 6,152.00
0.20
= $ 30,760
In that case the break-even point of Delgado Food and
Services Company can be computed as follows:

17. The Solution
 If, in addition to the fixed rent, Delgado Food Services Company
paid the vending machine manufacturer 2 cent per unit sold,
what would be the monthly break-even point in number of units
in sales? Refer to the original data.
New Unit CM = Sales – Variable Expenses
= Sales – (Cost of Snacks @ $ 0.80 + Payment
to Manufacturer @ $ 0.02)
= $ 1 - $ 0.82
= $ 0.18
 If, Delgado Food Services Company paid the vending machine
manufacturer 2 cent per unit sold, the new CM would be:

18. The Solution
Unit sales to break-even =
Fixed expenses
Unit CM
=
$ 5,000.00
$ 0.18
= 27,778
 In that case the new break-even point of Delgado Food and
Services Company can be computed as follows:

19. The Solution
 If, in addition to the fixed rent, Delgado Food Services
Company paid the vending machine manufacturer 2
cent per unit sold, what would be the monthly break-
even point in dollar sales? Refer to the original data.
CM Ratio =
Unit CM
Unit selling price
=
$0.18
$1
= 18%
If, Delgado Food Services Company paid the vending
machine manufacturer 2 cent per unit sold, the new CM
Ratio would be:

20. The Solution
Dollar sales to break-even =
Fixed expenses
Unit CM
=
$ 5,000.00
0.18
= $ 27,778
 In that case the break-even point of Delgado Food and
Services Company can be computed as follows:

21. The Solution
 If, in addition to the fixed rent, Delgado paid the machine
manufacturer 4 cent for each unit sold in excess of the break-even
point, what would the new net income be if 36,000 units were sold?
Refer to the original data.
Variable expenses = Cost of snack @ $0.80 for 36,000 units + Payment
to Manufacturer @ $ 0.04 for (36,000 – 25,000)
units
= Cost of snack @ $0.80 for 36,000 units + Payment
to Manufacturer @ $ 0.04 for 11,000 units
= $ (28,800.00 + 440)
= $ 29,240
If, in addition to the fixed rent, Delgado paid the machine manufacturer
4 cent for each unit sold in excess of the break-even point, the new
variable expenses would be:

22. The Solution
Elements of Cost Total
Sales (36,000 units) @ $ 1.00 $ 36,000.00
Variable expenses (cost of snack @ $0.80
for 36,000 units + Payment to
Manufacturer @ $ 0.04 for 11,000 units)
29,240.00
CM 6,760.00
Fixed expenses 5,000.00
Net operating income $ 1,760.00
Therefore the new contribution income statement of
Delgado Food and Services Company for selling 36,000
units of soft drinks would be:

23. END