Task 1. The company produces furniture. Variable costs are CU100. per unit, fixed costs - CU 50,000. in a year. Sales price - CU 200 for a unit.

Determine the critical production volume.

Solution:

In monetary units

those. To reach the break-even threshold, the company needs to sell 500 units. furniture and have revenue in the amount of CU 100,000.

Analysis of values ​​at the critical point, adjusted for the profit factor, can be used as a basis for assessing the profitability of an organization. For various alternative production plans, it is possible to calculate the corresponding amount of possible profit, as well as the production volumes that ensure the desired (given) profit.

Task 2. The company plans to make a profit of CU 20,000 next year. Variable, fixed costs and price are accepted according to the conditions of task 1.

What volume of production must be produced to obtain a given amount of profit?

Solution".

In order to answer this question, we transform the basic expression (31.5) as follows:

For the conditions of our example, the required volume of product sales will be

To check the correctness of the calculations, we use expression (31.4):
Task 3. Initial data of tasks 1, 2.

The company plans to increase sales volume to 800 units. Calculate the amount of profit planned to be received.

Solution:

Using expression (31.4) we determine

Optimizing profit under different production options

When choosing different technology options, prices, cost structures, etc., there is a need to select the most optimal one, i.e. giving maximum profit, while the number of options does not matter.

The algebraic solution to the problem is contained in the following expression (analysis of two options):

Where N- sales volume, ensuring an equal amount of profit for various options, in natural units; M a 1, 2 - absolute marginal income per unit of production for various options; Post 3, 2 - fixed costs for various options.

From here we determine the critical expression for the quantity of production:

If, under different options, the price of the final product remains unchanged, i.e. is a constant value, then, as a rule, they analyze options not through profit (marginal income), but through cost, and proceed from the expression

From here we determine the critical expression for the quantity of production:

Having determined the value of the critical production volume (N Kp), you need to compare it with the planned release of this product Nn and choose the most effective option. The option with lower fixed costs and higher variable costs is more profitable when Nn N Kp. When yV n > N Kp the more profitable option is with higher fixed costs for post and lower variable costs for post.

A graphical solution to this problem is also possible.

In Fig. 31.7 Roman numerals indicate the lines of dependence of profit on sales volume for the first (I) and second (II) production options.

Rice. 31.7.

At the point of intersection of the lines, their values ​​are equal, therefore, this point is the threshold value for choosing one or another option. However, this point should not be confused with the break-even point. By projecting it onto the x-axis, we get a certain amount of production at which the methods of its production have equal profit. This means that the constructed graphs make it possible to calculate the critical amount of production at which it is economically feasible to use certain options.

Task 4. The enterprise has two technological processes for obtaining the finished product:

• 1) by machining and welding;
• 2) by casting followed by mechanical processing.

The first option allows you to quickly begin production without significant preparation of production, the second option requires more time and initial funds. However, the consumer properties and price are higher in the second option (Table 31.1).

Table 31.1

Initial data

Choose the most profitable production option.

Solution:

1. Determine the absolute marginal income per unit of production:

M a 1 = 100 - 70 = 30 units;

M a 2 = 120 - 30 = 90 units

2. Determine the critical point of production volume:

Thus, we determine that for an order size of up to 150 pcs. it is necessary to use the technology of option 1. Since the planned sales volume is 200 units, we choose option 2 of production.

In this case we get the following profit:

Pr = 90,200 -10,000 = 8,000 CU Let's display the solution on the graph (Fig. 31.8).

Rice. 31.8.

Task 5. An enterprise can perform a technological operation using one of three options:

• 1) on a universal milling machine;
• 2) plasma cutting installation;
• 3) laser machine.

Data on fixed and variable costs for all three options (in units) are given in table. 31.2.

Data on fixed and variable costs

Table 31.2

The company produces 1,200 parts per year using laser cutting. It is necessary to make the optimal choice of machines depending on production volumes and determine the profitability of the option chosen by the enterprise.

Solution:

Let's create the total cost equations for each production option:

Let's find the output volumes corresponding to the critical cost point for two pairs of equipment: the first pair - milling and plasma cutting; the second pair is plasma cutting and laser cutting.

Let's create cost equations in which the costs of one option are equal to the costs of another. The critical volume for the first pair of machines (A cr 1), ensuring equality of costs,

20 N + 5000 = 5N+ 11 000.

N Kn= 400 pcs.

The critical volume for the second pair of machines (A cr 2) is determined similarly, ensuring equality of costs,

5N+ 11 000 = 1,2N+ 18 000.

A Kp 2 - 1842 pcs.

Consequently, with an annual production volume of up to 400 pcs. It is more profitable to use a milling machine for parts, with a production volume of 400 to 1815 pcs. - plasma cutting; and with a production volume of over 1842 pcs. It is advisable to use laser cutting.

Let's compare the costs associated with a volume of 1200 pieces. details:

• on a universal milling machine: 20 1200 + 5000 = 29,000;
• plasma cutting installation: CU 5,1200 + 11,000 = CU 17,000;
• laser machine: 1.2 1200 + 18,000 = 19,440 cu.

Thus, due to an unjustified technological solution for the production of parts, the enterprise suffers losses, the value of which is equal to the difference in costs on machines with plasma and laser cutting:

17,000-19,440 = -2440 cu.

According to the situation considered, it is clear that an increase in the technical level of production results, on the one hand, in a significant reduction in specific variable costs, and on the other, an increase in the total amount of fixed costs due to the higher cost of advanced equipment, tooling and technologies.

The final stage in calculating the main financial indicators and planning the organization’s activities is determining the break-even volume of production, that is, conducting a break-even analysis. The essence of this method is to determine the critical volume of product output - such a volume of product sales that allows the enterprise to cover all costs and reach a zero profit level.

The critical volume of output in natural units of measurement is determined by the formula:

where Z post – fixed costs for the entire volume of output, thousand rubles;

Z per ed – variable costs per unit of production, thousand rubles.

The amount of fixed costs as part of the total cost of marketable products was determined earlier in Table 7. Variable costs per unit of production and price are in Table 8.

The critical volume of output in monetary terms is determined by the formula:

, (27)

thousand roubles.

The difference between the actual and critical production volumes allows us to determine the margin of financial safety, which shows how much sales volume can be reduced before the company begins to incur losses:

, (28)

The difference between price and variable cost per unit is the contribution margin per unit, an important measure of cost structure. The marginal profit value shows what share of sales volume can be used to cover fixed costs and generate profit.

Marginal profit for the entire output is determined as the difference between sales revenue (net) and variable costs.

Pr margin = B – Se TP per = 255271.64 – 141813.15 = 113458.48 thousand rubles.

Based on marginal profit, one can quantify the sensitivity of profit to changes in sales volume using operating leverage:

Operating leverage shows by what percentage profit will change if revenue changes by 1%. Such leverage is associated with the level of entrepreneurial risk: the higher the leverage, the higher the risk.

%

The strength of the operating leverage depends on the cost structure of the cost of goods sold, that is, on the ratio of variable and fixed costs. A high level of operating leverage occurs with a high share of fixed costs and a low share of variable costs. With an inverse cost ratio, the level of operating leverage is lower.

In this work, a break-even analysis should be carried out and the impact of changes in the cost structure on the level of operating leverage and the margin of financial strength should be determined. 3 options for generating profit were considered: the first option is the planned values ​​of the main financial indicators, calculated during the course work; the second – with an increase in variable costs by 10%; the third – with a reduction in variable costs by 8%. The amount of revenue, total cost and profit remains at the level of planned values. The calculation results are shown in Table 13.

Table 13 – Break-even analysis and calculation of operating leverage

№	The name of indicators	Planned values	Values ​​for increasing variable costs by 10%	Values ​​when reducing variable costs by 8%
	Sales revenue, thousand rubles.	255271,64
	Variable costs, thousand rubles.	141813,15	155994,47	130468,10
	Marginal profit, thousand rubles.	113458,48	99277,17	124803,54
	Fixed costs, thousand rubles.	20802,22	6620,91	32147,28
	Total cost, thousand rubles.	162615,38
	Profit from sales, thousand rubles.	53716,52
	Critical output volume, nat. units	9,81	3,53	13,88
	Critical output volume, thousand rubles.	44788,20	16113,05	63369,23
	Operating leverage, %	2,11	1,85	2,32
	Margin of financial strength, %	82,45	93,69	75,18

This calculation shows that the enterprise in the planning period has a margin of financial strength equal to 82.45%. This means that the amount of revenue reduction to the break-even point will be 82.45% in the planning period. The value of operating leverage shows that if revenue changes by 1%, profit will change by 2.11%. When the share of variable costs in the cost structure increases by 10%, marginal profit and operating leverage decrease. With a decrease of 8% - PR margin and OP increase.

Critical sales volume (Break-evenSales) is the volume of products, the income from the sale of which exactly covers the total costs of its production and sale, thereby ensuring zero profit. In other words, the next unit of product sold in excess of the critical sales volume will bring profit to the company, while the sale of previous units was only to cover costs.

Determining the critical sales volume is of practical importance in cases where the price level for products does not provide the enterprise with a profit from sales, or when low demand for products does not make it possible to sell such a quantity that would be sufficient to exceed revenues over costs.

Total costs can be divided into two groups: conditionally constant (determined by the very fact of the company’s life and activities and practically do not depend on how large the volume of products produced.

Proceeds from the sale of the next unit of production, relatively speaking, go towards covering variable costs, i.e. costs directly associated with this unit, and part of the semi-fixed costs, and therefore it is clear that the greater the relative value of the semi-fixed costs in the total cost, the larger the volume of products must be produced. The value of the critical sales volume largely depends on the cost structure, i.e., ceteris paribus, an increase in the technical equipment of the company, an increase in the number and equipment of the management apparatus, an increase in advertising and sales costs, the emergence of additional non-production costs, etc. entail growth of critical sales volume.

This shows that any changes in the company’s activities that are costly in nature should be analyzed from the perspective of their impact on the value of the critical sales volume, at least in terms of whether it is possible to increase production volumes or new costs will be covered by the existing marginal profit (a kind of accumulated “ fat"). The famous accountant I. Scher (Johann F. Schar, 1846-1924) proposed calling the critical sales volume a “dead point”; the meaning of such a name is obvious.

There are three interrelated methods for calculating the break-even point - analytical, graphical, and calculation of specific gross margin.

Analytical method. The name of the method is arbitrary, and it is based on an obvious dependence

S=VC+FC+ EBIT (5)

S- sales in value terms;

V.C.- variable production costs;

F.C.- semi-fixed production costs;

EBIT- Operating profit.

Turning to natural units, formula (5) can be transformed as follows:

pQ = vQ + F.C. + EBIT (6)

Q- sales volume in physical terms;

R- unit price;

v- variable production costs per unit of production.

At the break-even point, by definition, profit is zero, i.e. EBIT= 0, therefore, from formula (6) one can find the corresponding sales volume (in natural units), called critical (Qc).

Qc = F.C. / p – v , (7)

The given formula is one of the basic ones in the system of intra-company analysis and can be used both in retrospective analysis and in planned analytical work. When planning, setting the values ​​of the initial factors (price, semi-fixed and variable costs), it is possible to calculate the minimum volume of production required to cover costs, i.e., ensuring break-even of financial and economic activities.

The graphical method is convenient for illustrating the relationship between the indicators involved in calculating the break-even point using the analytical method. A graphical representation of the model, characterizing the logic of the relationship between the indicators that form the value of the critical sales volume, is shown in the figure.

Calculation of specific gross margin. This method is a corollary of the analytical method. The denominator of the fraction in formula (14.3), called specific gross margin, or contribution(in English literature - contribution), characterizes the amount of profit before depreciation, amortization, interest and taxes (EBITDA) per unit of production (in rare situations, the marginal profit indicator can be used instead of EBITDA). Another interpretation of this indicator can be given, which is widespread in management accounting and financial management and explains its name “contribution”: it quantifies the contribution of an additional unit of production to the generated gross margin (EBITDA), or marginal profit. As production volume increases, the total contribution should fully cover semi-fixed costs and ensure the generation of profit.

Thus, the economic meaning of the “dead point” is extremely simple: it characterizes the number of units of production, the sale of which will provide a gross margin (or marginal profit) exactly equal to the amount of semi-fixed costs.

So, having studied the main methods for calculating the critical sales volume, we can conclude that these methods are interrelated and complement each other.

Critical volume - is the volume of production during an accounting period at which the total costs for the two alternatives are equally large.

When the production volume exceeds the critical one, a technological process with high fixed costs is more profitable than one with low ones. In this case, only those fixed and variable costs that influence the choice of process are taken into account. The critical volume can be determined:

• graphical method
• calculation method.

Graphical method for determining critical production volume

Figure 2 determines the critical volume of both technological processes, the fixed and variable costs of which were calculated in Figure 1. In this case, the costs of each technological process are presented as follows. First, a horizontal straight line of fixed costs is drawn, then a straight line of total costs.

Fig. 1: Comparative cost calculation scheme

Thus, process 1 is more profitable than process 2 until the output reaches M kr at 5,200 pieces per year.

Calculation method for determining the critical volume

We will proceed from the following equation (formula):

K = K f + k v * M, where K is the total costs in euros/year

K f - fixed costs in euros/year

k v - variable costs in euros/pcs.

M - production volume in pcs./year

M kr - critical volume in pcs./year.

At a critical volume M kr, the total costs of technological process 1 are equal to the total costs of process 2. Thus, we have the following formula:

K = K f 1 + k v 1 * Mkr = K f 2 + k v 2 * Mkr

Using the table values ​​in Fig. 12, we obtain the following critical volume of processes 1 and 2:

Production volume 3,000 pcs.: M kr =	2.702 euros/year - 908 euros/year					= 5.185 pcs./year
		4.200 euro/year		3,162.50 euro/year
		3,000 pcs/year		3,000 pcs/year

Production volume 6,000 pcs.: M kr =	2.702 euros/year - 908 euros/year					= 5.185 pcs./year
		8.200 euro/year		6.325 euros/year
		6,000 pcs/year		6,000 pcs/year

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