Example 1

The analysis of costs necessary for the production and sale of one bottle of mineral water shows
that its unit variable costs amount to CZK 11 and the total monthly fixed costs of production and
sales amount to CZK 350 000. Based on the market research, it was found that the selling prices for
which it is possible to realize one bottle are CZK 18 CZK 22 and CZK 24. At a price of CZK 18, it
is possible to expect the sale of 200,000 bottles. Price elasticity of demand is estimated at 1.2.

What price should a company set if its goal is to maximize profits?

Solution:

Price elasticity of demand =


Expected sales at a price of 22 CZK:

1,2 =  =

X = 0,2666 = 26,7 % … reduction in quantity sold by 26,7 %

New quantity after reduction = (100% - 26,7 %) z 200 000 ks = 146 600 pcs

Or 73,3 % z 200 000 pcs = 146 600 pcs

or  26,7 % z 200 000 pcs = 53 400 pcs

200 000 pcs – 53 400 pcs = 146 600 pcs


Expected sales at a price of 24 CZK:

1,2 =  =

X = 0,4 = 40 % … reduction in quantity sold by o 40 %

New quantity after reduction = (100% - 40 %) z 200 000 ks = 120 000 pcs

or 60 % z 200 000 pcs = 120 000 pcs

or 40 % z 200 000 pcs = 80 000 pcs

200 000 pcs – 80 000 pcs = 120 000 pcs

Sales price (CZK / bottle)

Number of bottles sold

Total sales (CZK)

Total costs (CZK) = VC + FC

Profit (CZK)






18

200 000

18*200 000 = 3 600 000

(11*200 000) + 350 000 = 2 550 000

3 600 000 – 2 550 000 = 1 050 000

22

146 600

22*146 600 = 3 225 200

(11*146 600) + 350 000 = 1 962 600

3 225 200 – 1 962 600 = 1 262 600

24

120 000

24*120 000 = 2 880 000

(11*120 000) + 350 000 = 1 670 000

2 880 000 – 1 670 000 = 1 210 000


The company achieves the highest profit at a price of CZK 22.



Example 2

The company produces two types of irons: iron A requires a unit variable cost of CZK 270 and sells
for CZK 500. Iron B requires a unit variable cost of 380 CZK and sells for 650 CZK.

a) Which of these products should the company currently focus on as a priority, if both are equally
laborious and demanding in terms of machinery capacity?

b) Which of the products should the company focus on if the "bottleneck" of the business process is
the capacity of the machinery on which iron B spends twice as much time as iron A?

Solution:

Ad a)

Iron margin  = selling price - variable costs

Iron margin A =  500 – 270 = 230 Kč

Iron margin B =  650 – 380 = 270 Kč

The company should prefer to focus on iron B, as its product margin is higher than that of iron A.


Ad b)

The company should focus on iron A, because there is a limit per unit

230: 1 = 230 CZK margin

Iron B, on the other hand, will bring only the same for the same period

270: 2 = 135 CZK margin

For example, I make A in an hour and B in 2 hours. So I make half B in an hour.


Example 3

The company produces two types of irons: iron A requires a unit variable cost of CZK 270 and sells
for CZK 500. Iron B requires a unit variable cost of 380 CZK and sells for 650 CZK. Both products
are equally demanding in terms of capacity and the company decided to produce and sell a more
advantageous product B (higher margins) in the period under review. Fixed costs, fixed for capacity
utilization in the range of 900 - 2,500 products, amount to CZK 250 000.

Tasks:

1. How many products need to be produced and sold

a) To reach the turning point?

b) To achieve a profit of CZK 370,000?

2. What is the company's safety margin?

3. Budget for irons B

Solution:

Ad 1 a)

Q = Fixed costs / (price-variable costs) = 250 000 / (650-380) = 926 products B

Ad 1 b)

Q = (Fixed costs + profit) / (price-variable costs) = (250 000 + 370 000) / (650-380) = 2 297
products B


Ad 2)

SM = (2 500 – 2 297) / 2 500 = 0,0812 = 8,12 %


Ad 3)

Items

               Calculation

                                  CZK

Sales

               2 500 * 650

                                  1 625 000

-variable costs

               2 500 * 380

                                  950 000

Margin

               1 625 000 – 950 000

                                  675 000

-fixed costs

               250 000 (ze zadání)

                                  250 000

Profit

               675 000 – 250 000

                                  425 000









               March

                    April

                         May

                            June

Soap sales plan

               500

                    650

                         480

                            520


Example 4

From the economic point of view, the municipal authority assesses various variants of the
construction of a kindergarten. One of these variants has the following parameters:

• The expected service life is 32 years

• Capital expenditures amount to CZK 20 million

• The average annual operating costs are CZK 3 million.

Express the average annual cost of this investment option, assuming that the cost of capital has
been estimated at 10 % taking into account all construction conditions.

Solution:

AAC = I *  + OP

AAC = average annual cost

I = total cost of investment

1 + i = indexed amount of the discount rate

n = estimated life of the investment

OP = average annual cost of operating the investment


AAC = 20 mil. Kč *  + 3 mil. Kč

AAC = 20 *  + 3

AAC = 5,0994 CZK million

The average annual cost of the considered variant is approximately CZK 5.1 million.