BREAK-EVEN POINT ANALYSIS

2. BREAK
EVEN
POINT
•the Break-Even Point (BEP) is the
point at which cost, or expenses
and revenue are equal : there is
no net loss or gain and one has
“broken even”
TOTAL COST = TOTAL REVENUE is
BEP

3. - used to determine how much sales
volume your business needs to start
making a profit.
-useful when you're developing a
pricing strategy, either as part of a
marketing or a business plan

4. TR(Total Revenue) is obtained by finding the product of
the selling price per unit by the number of units sold.
TC(Total Cost) is obtained by finding the sum of the fixed
cost (FC) and variable cost (VC).
FC(Fixed costs) are costs that don’t depend on the
production levels (mortgages, property taxes, rents,
salaries of front-office staff, utilities, etc.)
VC (Variable costs) are costs that don’t depend on
the production levels. (raw materials, machining costs,
the hourly wages,etc.)

5. What it can be used for?
 To see if your monthly income is more than your
expenses
 To determine minimum price product can be sold
for
 To determine optimum price product can be
sold for
 To calculate effects of marketing programs on
price

6. BREAK EVEN POINT (BEP) FORMULA
PROFIT = TR - TC
Where:
TR=selling price per unit times the number of units sold
TR=selling price per unit times the number of units sold
At break even point, TR=TC or TR – TC = 0 or Profit = 0

7. Simple Break-Even Point Application
Virgo company produces and sells quality pens. Its fixed costs
amount to Php 400,000 approximately, whereas each pen costs 12
pesos to be produced. The company sells its products at the price
of 20 pesos each.
Determine each of the following:
a. TR, TC, Profit Function
b. BEP quantity
c. Quantity Sold & Profit when sales is 1.6 million
a. Let X be the qty sold
P = TR – TC
P = 20x – (12x + 400,000)
P = 8x - 400,000
b.TR = TC
20x = 12x + 400,000
20x – 12x = 400,000
8x = 400,000
X = 50,000 pens BEP
c. TR = 1,600,000
20x = 1,600,000
20x = 1,600,000
20 20
X = 80,000
P = 8x – 400,000
P = 8(80,000) – 400,000
P = 640,000 – 400,000
P = 240,000
PROFIT (0) = TR – TC

8. X (VC+ FC) 20X 12X 8x - 400,000
UNIT SALES (PENS) FC TC TR/SALES VC PROFIT/LOSS
- 400,000 400,000 - - 400,000
-
10,000 400,000 520,000 200,000 120,000 320,000
-
20,000 400,000 640,000 400,000 240,000 240,000
-
30,000 400,000 760,000 600,000 360,000 160,000
-
40,000 400,000 880,000 800,000 480,000 80,000
-
50,000 400,000 1,000,000 1,000,000 600,000 -
60,000 400,000 1,120,000 1,200,000 720,000 80,000
70,000 400,000 1,240,000 1,400,000 840,000 160,000
80,000 400,000 1,360,000 1,600,000 960,000 240,000
X (VC+ FC) 20X 12X 8x - 400,000
UNIT SALES (PENS) FC TC TR/SALES VC PROFIT/LOSS
- 400,000 400,000 - - 400,000
-
10,000 400,000 520,000 200,000 120,000 320,000
-
20,000 400,000 640,000 400,000 240,000 240,000
-
30,000 400,000 760,000 600,000 360,000 160,000
-
40,000 400,000 880,000 800,000 480,000 80,000
-
50,000 400,000 1,000,000 1,000,000 600,000 -
60,000 400,000 1,120,000 1,200,000 720,000 80,000
70,000 400,000 1,240,000 1,400,000 840,000 160,000
80,000 400,000 1,360,000 1,600,000 960,000 240,000
(VC+ FC) 20X 12X 8x - 400,000
C TC TR/SALES VC PROFIT/LOSS
400,000 400,000 - - 400,000
-
400,000 520,000 200,000 120,000 320,000
-
400,000 640,000 400,000 240,000 240,000
-
400,000 760,000 600,000 360,000 160,000
-
400,000 880,000 800,000 480,000 80,000
-
400,000 1,000,000 1,000,000 600,000 -
400,000 1,120,000 1,200,000 720,000 80,000
400,000 1,240,000 1,400,000 840,000 160,000
400,000 1,360,000 1,600,000 960,000 240,000
X (VC+ FC) 20X 12X 8x - 400,000
UNIT SALES (PENS) FC TC TR/SALES VC PROFIT/LOSS
- 400,000 400,000 - - 400,000
-
10,000 400,000 520,000 200,000 120,000 320,000
-
20,000 400,000 640,000 400,000 240,000 240,000
-
30,000 400,000 760,000 600,000 360,000 160,000
-
40,000 400,000 880,000 800,000 480,000 80,000
-
50,000 400,000 1,000,000 1,000,000 600,000 -
60,000 400,000 1,120,000 1,200,000 720,000 80,000
70,000 400,000 1,240,000 1,400,000 840,000 160,000
80,000 400,000 1,360,000 1,600,000 960,000 240,000
X (VC+ FC) 20X
UNIT SALES (PENS) FC TC TR/SALES VC
- 400,000 400,000 -
10,000 400,000 520,000 200,000 1
20,000 400,000 640,000 400,000 2
30,000 400,000 760,000 600,000 3
40,000 400,000 880,000 800,000 4
50,000 400,000 1,000,000 1,000,000 6
60,000 400,000 1,120,000 1,200,000 7
70,000 400,000 1,240,000 1,400,000 8
80,000 400,000 1,360,000 1,600,000 9
X (VC+ FC) 20X 12X 8x - 400,000
UNIT SALES (PENS) FC TC TR/SALES VC PROFIT/LOSS
- 400,000 400,000 - - 400,000
-
10,000 400,000 520,000 200,000 120,000 320,000
-
20,000 400,000 640,000 400,000 240,000 240,000
-
30,000 400,000 760,000 600,000 360,000 160,000
-
40,000 400,000 880,000 800,000 480,000 80,000
-
50,000 400,000 1,000,000 1,000,000 600,000 -
60,000 400,000 1,120,000 1,200,000 720,000 80,000
70,000 400,000 1,240,000 1,400,000 840,000 160,000
80,000 400,000 1,360,000 1,600,000 960,000 240,000
X (VC+ FC) 20X 12X 8x - 400,000
UNIT SALES (PENS) FC TC TR/SALES VC PROFIT/LOSS
- 400,000 400,000 - - 400,000
-
10,000 400,000 520,000 200,000 120,000 320,000
-
20,000 400,000 640,000 400,000 240,000 240,000
-
30,000 400,000 760,000 600,000 360,000 160,000
-
40,000 400,000 880,000 800,000 480,000 80,000
-
50,000 400,000 1,000,000 1,000,000 600,000 -
60,000 400,000 1,120,000 1,200,000 720,000 80,000
70,000 400,000 1,240,000 1,400,000 840,000 160,000
80,000 400,000 1,360,000 1,600,000 960,000 240,000
(VC+ FC) 20X 12X 8x - 400,000
C TC TR/SALES VC PROFIT/LOSS
400,000 400,000 - - 400,000
-
400,000 520,000 200,000 120,000 320,000
-
400,000 640,000 400,000 240,000 240,000
-
400,000 760,000 600,000 360,000 160,000
-
400,000 880,000 800,000 480,000 80,000
-
400,000 1,000,000 1,000,000 600,000 -
400,000 1,120,000 1,200,000 720,000 80,000
400,000 1,240,000 1,400,000 840,000 160,000
400,000 1,360,000 1,600,000 960,000 240,000
X (VC+ FC) 20X
UNIT SALES (PENS) FC TC TR/SALES VC
- 400,000 400,000 -
10,000 400,000 520,000 200,000 1
20,000 400,000 640,000 400,000 2
30,000 400,000 760,000 600,000 3
40,000 400,000 880,000 800,000 4
50,000 400,000 1,000,000 1,000,000 6
60,000 400,000 1,120,000 1,200,000 7
70,000 400,000 1,240,000 1,400,000 8
80,000 400,000 1,360,000 1,600,000 9
X (VC+ FC) 20X 12X 8x - 400,000
UNIT SALES (PENS) FC TC TR/SALES VC PROFIT/LOSS
- 400,000 400,000 - - 400,000
-
10,000 400,000 520,000 200,000 120,000 320,000
-
20,000 400,000 640,000 400,000 240,000 240,000
-
30,000 400,000 760,000 600,000 360,000 160,000
-
40,000 400,000 880,000 800,000 480,000 80,000
-
50,000 400,000 1,000,000 1,000,000 600,000 -
60,000 400,000 1,120,000 1,200,000 720,000 80,000
70,000 400,000 1,240,000 1,400,000 840,000 160,000
80,000 400,000 1,360,000 1,600,000 960,000 240,000
X (VC+ FC) 20X 12X 8x - 400,000
UNIT SALES (PENS) FC TC TR/SALES VC PROFIT/LOSS
- 400,000 400,000 - - 400,000
-
10,000 400,000 520,000 200,000 120,000 320,000
-
20,000 400,000 640,000 400,000 240,000 240,000
-
30,000 400,000 760,000 600,000 360,000 160,000
-
40,000 400,000 880,000 800,000 480,000 80,000
-
50,000 400,000 1,000,000 1,000,000 600,000 -
60,000 400,000 1,120,000 1,200,000 720,000 80,000
70,000 400,000 1,240,000 1,400,000 840,000 160,000
80,000 400,000 1,360,000 1,600,000 960,000 240,000

10. BEP

11. BREAK-EVEN ANALYSIS - LINEAR FUNCTION
Example:
A firm sells its products at Php 6 per unit. The
product has a variable cost of Php 3 per unit and the
company’s fixed cost is Php 9,000.
Determine each of the following:
1. TR, TC, and Profit Function
2. Sales Volume when profit is Php 9,000
3. Profit when sales are 600 units
4. The break-even quantity and revenue

12. A firm sells its products at Php 6 per unit. The
product has a variable cost of Php 3 per unit
and the company’s fixed cost is Php 9,000.
Determine each of the following:
1. TR, TC, and Profit Function
2. Sales Volume when profit is Php 9,000
3. Profit when sales are 600 units
4. The break-even quantity and revenue

13. BREAK-EVEN ANALYSIS - LINEAR FUNCTION continuation
Example:
A firm sells its products at Php 6 per unit. The product has a
variable cost of Php 3 per unit and the company’s fixed cost is
Php 9,000.
Determine each of the following: cont.
5. The amount by which the variable cost per unit has to be decreased or
increased for the firm to break even at 2,000 units. Assume that the selling price
and fixed cost remain constant.
6. The new selling price per unit in order to break even at 300 units, assuming the
FV and VC remain constant.
7. Number of units to sell to cover the fixed cost.

14. A firm sells its products at Php 6
per unit. The product has a
variable cost of Php 3 per unit
and the company’s fixed cost is
Php 9,000.
Determine each of the following:
5. The amount by which the variable
cost per unit has to be decreased or
increased for the firm to break even
at 2,000 units. Assume that the
selling price and fixed cost remain
constant.
6. The new selling price per unit in
order to break even at 300 units,
assuming the FV and VC remain
constant.
7. Number of units to sell to cover
the fixed cost.

15. BASIC RULES FOR DERIVATIVES
Common Functions
Function Derivative
Constant c 0
Line x 1
Multiplication by
constant
cf cf’
Power Rule xn nxn−1
Sum Rule f + g f’ + g’
Difference Rule f - g f’ − g’
Product Rule fg f g’ + f’ g
Quotient Rule f/g f’ g − g’ fg2
Reciprocal Rule 1/f −f’/f2

16. BASIC RULES FOR DERIVATIVES

17. BASIC RULES FOR DERIVATIVES

18. STEPS IN LOCATING CRITICAL POINTS
1. Find the derivative of the Function
2. Set the first derivative to zero and solve for x.
3. Substitute this value of x in the original function and solve for
y. These values of x and y are the coordinates in the maxima
or minima.
4. Test wheter the point is maxima or minima by finding the
second derivative Y-prime as y-double prime). If second
derivative is negative, the point is maxima. If the second
derivative is positive, the point is minima.

21. ANSWERS :
a. X = 200 Units for minimum cost
b. C = Php 300 Minimum Cost