1. Break-even point and CVP analysis
Developing Next Generation Leaders through Applied Know-How
Introduction to Business
Break-even point and CVP analysis
Metka Tekavčič, PhD
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

2. BREAK-EVEN POINT
The quantity of output where there is no profit or loss (assuming that everything produced is also sold).
The revenues are equal to total costs, profit is zero.
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

3. WHY COMPANIES NEED TO KNOW THEIR BREAK-EVEN POINT?
To know which level of activity (quantity of output) is needed to have profit.
To find out if they have enough capacities.
To find out if there is enough demand for the product in the market.
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

4. Two aspects of break-even point:
1. The total level of activity (total number of products)
Break-even point when revenues equal total costs: TR = TC.
2. One product
Break-even point when selling price equals cost per unit : P = cost price (AC)
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

5. TC=LC*Q TR=PC*Q QBE1 QBE2
Break-even with TR and TC (total level of activity, theoretical curve of TC)
TC=LC*Q
TR=PC*Q Q
TR, TC
LOSS TC>TR
LOSS TC>TR
QBE1
QBE2
PROFIT TR>TC

6. Break-even with P and AC (one product)Q
AC, PC
AC=LC PC
LOSS
QBE1
QBE2
LOSS
PROFIT

7. In this case only one break-even point.
Break even with TR and TC (total level of activity, proportional VC)
Proportional VC increase in the same proportion as output – AVC are constant. Frequent assumption in business practice.
In this case only one break-even point. Q
TR, TC TR TC FC
Break-even point
LOSS
PROFIT

8. Derivation of the formula:
Break-even point when VC are proportional
Derivation of the formula:
Condition: TR = TC
P*Q = FC + VC
P*Q = FC + AVC*Q
P*Q – AVC*Q = FC
Q*(P – AVC) = FC
AVC are constant
P – AVC is contribution margin per unit; this is used to cover FC and make profit (when the level of activity is above the break-even point)
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

9. EXERCISE 1
Fixed costs in a company producing just one type of product are EUR 160 million. The capacity of production facilities is 120,000 units of product. The product is sold at EUR 7,000 and variable cost per unit is EUR 5,000. Questions:
At what capacity usage the company breaks even?
Is the company having a loss or profit when 60,000 products are produced (and sold)? How much is it?
Is the company having a loss or profit when 90,000 products are produced (and sold)? How much is it?

10. TR = 420 mio EUR, TC = 460 mio EUR, Loss = 40 mio EUR
SOLUTION
Q(PT) = pr. St izk = 66,67%
TR = 420 mio EUR, TC = 460 mio EUR, Loss = 40 mio EUR
TR = 630 mio EUR, TC = 610 mio EUR, Profit = 20 mio EUR
Q(PT) = pr. St izk = 66,67%
TR = 420 mio EUR, TC = 460 mio EUR, Izguba = 40 mio EUR
TR = 630 mio EUR, TC = 610 mio EUR, Dobiček = 20 mio EUR

11. CVP ANALYSIS AND THE BREAK-EVEN POINT
CVP analysis looks at the relationship between selling prices, sales volumes, costs, and profits.
The break-even point (BEP) is where total revenue equal total costs.
Q (units)
TR, TC (EUR)
Total Revenue (TR)
BEP in
sales EUR
Total Costs (TC)
BEP in units
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

12. EXERCISE 2
A firm can produce a maximum of 90,000 units of product, the selling price of the product is 8.50 EUR, variable cost per unit is 7 EUR, fixed costs are 45,000 EUR.
a) If variable costs are proportional, at which utilization rate the company reaches its break-even point?
 b) Calculate the profit for the firm when it produces 60,000 units of product.
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

13. SOLUTION a)
Contribution margin per unit (CMunit) = P – VCunit = €8.50 – €7 = €1.50
BEP(units) = FC/CMunit = €45,000/€1.50 = 30,000 units
Utilization rate = 30,000 units / 90,000 units =  33.33%
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

14. SOLUTION b) Sales = 60,000 * €8.50 = €510,000
Costs = 60,000 * €7 + €45,000 = €465,000
Profit = €45,000
OR: Profit at 60,000units = (CMunit * 60,000) – FC =
= (€1.50 * 60,000) - €45,000 =
= €90,000 - €45,000 = €45,000
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

15. EXERCISE 3
Company ABC makes high quality cases for laptops that sell for 200 EUR. The variable costs per briefcase are 80 EUR, and the total fixed costs are 360,000 EUR.
Find the BEP in units and in sales EUR for this company.
Draw a CVP graph for Company ABC. What is the profit if the company sells 4,100 briefcases? If it sells 2,200 briefcases?
How many briefcases does Company ABC need to sell to reach a target profit of 240,000 EUR? What level of sales revenue is this?
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

16. SOLUTION
a) Contribution margin per unit (CMunit) = P – VCunit = €200 – €80 = €120 Contribution margin ratio (CM %) = CMunit/P = €120/€200 = 60% BEP(units) = FC/CMunit = €360,000/€120 = 3,000 briefcases BEP(sales) = FC/CM% = €360,000/0.6 = €600,000
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

17. Profit at 2,200 units = (€120 x 2,200) - €360,000
SOLUTION
b) Recall that P = €200, VCunit = €80, and FC = €360,000. TR
Profit at 4,100 units =
= (€120 x 4,100) - €360,000
€132,000
units
in 1000s € TC
600
Profit at 2,200 units = (€120 x 2,200) - €360,000
3,000
- €96,000
360
More easily: 4,100 units is 1,100 units past BEP, so profit = €120 x 1,100 units;
2,200 units is 800 units before BEP, so loss = €120 x 800 units.
2,200
4,100
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA

18. SOLUTION
c) Q = (FC + target profit) / CMunit = = (€360,000+€240,000)/€120 = €600,000 / €120 = 5,000 briefcases Sales = (FC + target profit) / CM % = = (€360,000+€240,000)/0.6 = €600,000 / 0.6 = €1,000,000
Developing Next Generation Leaders through Applied Know-How project number: MK01-KA