Break - Even Point Analysis

ITTI `S EGG WHOLESALER AND

RETAILER STORE

BREAK - EVEN POINT ANALYSIS:LINEAR fUNCTIONS

BREAK – EVEN POINT (BEP) the simplest quantitative model

used by decision makers which concerned the interrelationship of cost, volume and profit

common point between the total revenue and total cost

total revenue equals the total cost

the company has no profit but has no loss also

also referred to as Cost – Volume Analysis

is the determination of the number of units that must be produced and add to equate sale with total cost

the point at which your product stops costing you money to produce and sell, and starts to generate a profit for your company.

BREAK-EVEN ANALYSIS DEPENDS ON THE FOLLOWING VARIABLES:Selling price per

Unit

Total Fixed Cost

Variable Unit Cost

Forecasted Net Profit

SELLING PRICE PER UNIT The amount of money charged to the

customer for each unit of a product or service.

TOTAL FIXED COST constant expenditures without regards

to the number of units produced like: rent expense, depreciation expense, factory supervisory salary. The sum of all costs required to produce the first unit of a product. This amount does not vary as production increases or decreases, until new capital expenditures are needed

VARIABLE COSTVariable Unit Cost Costs that vary directly with the

production of one additional unit. Examples of this are utilities, wages, raw materials, and packaging.

Total Variable Cost The product of expected unit sales and

variable unit cost, i.e., expected unit sales times the variable unit cost.

COMBINATION COST costs that are a combination of fixed and variable:

a certain minimum level will be incurred regardless of your sales levels, but the costs rise as your volume increases. (ex. phone bill)

Strictly speaking, these costs should be separated into their fixed and variable components, but that may be more trouble than it's worth for a small business. To simplify things, just decide which type of cost (fixed or variable) is the most important for the particular item, and then classify the whole item according to the more important characteristic. For example, in a telemarketing business, if your phone call volume charges are normally greater than your line access charges, you'd classify the entire bill as variable.

FORECASTED NET PROFIT Total revenue minus total cost

Total Revenue (TR)the product of the selling price per unit

and number of units sold

Total Cost (TC)sum of fixed cost (FC) and variable cost

(VC)

COMPONENT OF BREAK – EVEN ANALYSIS1. Volume level of production by a company, which is

expressed as the number of units (quantity) produced and sold

2. Profit the difference between total Sales and total cost

or the income generated by the sale of product3. Costs usual expenditures that must be taken into

account in order to determine profit

FORMULA

TR = Price per unit x units soldTC = FC + VC Profit = TR – TCTR = TC OR TR – TC = 0 ,

* Profit = 0 at break – even point

BEP GRAPH

MARKET EQUILIBRIUM GRAPH

EXERCISES1. Consider a firm that buys units for Php 10.00 and

sells them for Php 15.00. There are no other variable cost. Fixed costs are at Php 6000, Use the break-even formula to determine the following:

a)TR, TC and profit functionsb)Sales volume when profit is Php 8000c) Profit when sales are 500 unitsd)The break-even quantity and revenuee) The amount by which the variable cost per unit has to

be decreased in order to break even at 500 units. (selling price and FC remains)

f) The new fixed cost in order to break even at 800 units. Selling price cost remains constant.

g)The new selling price per unit, to break even at 500 units, if VC and TC are constant.

Given:

Variable Cost = 10 per unitSelling price = 15 per unitFixed Cost = 6000

a.TR = 15xTC = 10x + 6000 Profit = 15x –

(10x + 6000) = 15x –

10x – 6000 Profit = 5x – 6000

b.Profit = 8000Profit = 5x –

6000 8000 = 5x – 6000 -5x = -6000 –

8000 -5x/-5 = -14000/-

5 x = 2800

units

c.x = 500Profit = 5 (500) – 6000 = 2500 – 6000 = Php 3500 loss

d.TR = TC15x = 10x +

600015x-10x = 60005x/5 = 6000/5x = 1200 units

(BEP Quantity)

TR = 15x = 15 (1200) TR = Php 18000 BEP

revenue

e.Let y = new variable cost

VC = 500yOriginal TC = 10x

+ 6000 New TC = 500y +

6000

TR = TC15 (500) = 500y +

6000 7500 = 500y + 6000-500y = 6000 – 7500 -500y/-500 = -1500/-

500y = 3 new variable

cost per unit *Since the old VC is

10 per unit and the new VC is 3 so it decreases 7 per unit

f. Given:BEP quantity = 800let z = fixed cost

TR = TC15 (800) = 10 (800) +

z-z/-1 = (8000-12000)/-

1z = 4000 fixed cost

or

TC = TR10 (800) + z = 15

(800) 8000 + z = 12000z = 12000 – 8000z = 4000

g. Given: BEP quantity = 500 unitLet p = selling price

TR = TC 500p = 10 (500) + 6000 500p/500 = 11000/500 p = Php 22.00 selling price per unit

EXERCISES2. A business firm produces and sells a particular

product. Variable cost is Php 30.00 per unit. Selling price is Php 40.00 per unit. Fixed cost is Php 60000. Determine the following:

a) Profit when sales are 10000 units.b)The break-even point quantity and revenue.c) Sales when profits are at Php 9000.d)The amount by which fixed cost will have to be

decreased or increased, to allow the firm to break even at sales volume of 500 units. VC and selling price per unit remain constant.

e) The volume of sales to cover the fixed cost.f) Suppose that the firm wants to break even at a

lower number of units, assuming that FC and VC remain constant, how is the selling price affected?

g)Find the TC when sales are 500 units.

Given:

VC = Php 30.00 per unitSP = Php 40.00 per unit TC = Php 60000

a. x = 10000 units

Profit = 10x – 60000 = 10 (10000) –

60000 Profit = 40000

Functions:TC = 30x + 60000TR = 40x Profit = 40x – (30x + 60000) = 40x – 30x – 60000Profit = 10x – 60000

b. TR = TC 40x = 30x +

60000 10x/10 = 60000/10 x = 6000 (BEP

quantity )

TR = 40 (6000) TR = Php 240000

BEP revenue

c.Given: Profit = 9000

Profit = 10x – 600009000 = 10x – 60000 -10x = -60000 – 9000 -10x/-10 = -69000/-10x = 6900 units sold

TR = 40 (6900)TR = 276000 for

6900 units sold

d. Given: BEP quantity = 500 units Let y= fixed cost

Solution: TC=TR30(500) + y = 40(500)15000 + y = 20000y = 20000 - 15000y = 5000 new fixed cost.

*Since the old FC is 60000,and the new FC is 5000 so there is a decrease of 55000.

e. TR=FC40x = 6000040x/40 =

60000/40x = 1500 units

of sale to cover the fixed cost

f. If the firm wants to break even at a lower number of units, but the FC and VC remain constant. The selling price should be increased.

TR = TCSP x X = FC + VC

3. A factory sells a particular product at Php 0.80 per unit. The variable cost is Php 0.60 per unit. The total fixed cost is Php 12000. Determine the following:

a)The break-even point in units of sales.b)Profit when sales are 10000 units.c) TC when sales are 5000 units.d)The amount by which the selling price will have

to increase or decrease for the firm to break even at 4000 units. Assume all costs remain the constant.

e)The amount by which the fixed cost will have to decrease in order for the firm to break even at a sales volume of 4000 units. Assume selling price and variable cost remain the same.

Given:

SP = Php .80 per unitVC = Php .60 per unitFC = Php 12000

A. BEPTR = TC.80x = .60x +

12000.80x - .60x =

12000.20x/.20 =

12000/.20x = 60000 BEP

quantity

TR = .80x = .80

(60000)TR = 48000

BEP revenue

b. Given: Unit sold

10000

Profit = .20x - 12000

= .20 (10000) - 12000

= 10000 loss

c. Given: Unit sold 5000

TC = .60x + 12000 = .60(5000) +

12000TC = 15000

d. Given: BEP quantity = 4000let S = selling price

TR = TC4000S = .60(4000) + 120004000S = 2400 + 120004000S/4000 = 14400/4000S = 3.60 new selling price to break even of

4000

e. Given: BEP quantity = 4000

unitslet z = fixed cost

TC = TR.60x + z = .80x.60(4000) + z = .80(4000)2400 + z = 3200z = 3200 - 2400z = 800 new fixed cost to

break even of 4000 units

* Since the old FC is 12000,therefore there should be a decrease of 11200 to have a break even quantity of 4000.

4. A manufacturer sells his product at Php 10.00 per unit.

a) Find the total revenue if the volume sales is 1800.

b) If fixed cost is Php 3000, represent the total cost when the variable cost per unit is Php 5.00

c)Supposed that the variable cost per unit is 70% of the selling price. Represent the total cost when fixed cost is Php 5000.

d) If variable cost is 20% of the selling price and the fixed cost is Php 1000, find the break-even point.

Given: SP = Php 10 per unit

Solution: a. Given: Unit Sold

= 1800Solution: TR = 10x = 10 (1800) = 18000

b. Given: FC = 3000

VC = 5 per unit

Solution:TC = 5x + 3000

c. Given: FC = 5000 VC = 70% of SP = 70% (10) = 7Solution: TC = 7x + 5000

d. Given: VC = 20% of SP = 20% (10) = 2 per unit FC = 1000

Solution: TR = TC10x = 2x + 100010x - 2x = 10008x/8 = 1000/8x = 125

TR = 10x = 10 (125) = 1250 BEP

revenue if BEP quantity of 125 where VC is 20% of SP and FC is equal to 1000