How to find the critical volume. Analysis of the ratio of costs, volume of production and profit (CVP-analysis). Critical production volume
To determine the break-even production of products consider the relationship between revenue, profit, variables and fixed costs.
Total cost of production divided by fixed(VOSTZ) and variable costs (PERZ), can be represented as an equation:
Or (3.6.)
Where p1 - variable costs per unit of product; K is the volume of production.
Sales revenue is determined by the ratio:
, (3.7.)
where C is the unit price of the product.
Then the relationship between profit, revenue, constant and variable costs is characterized by the ratio:
Or (3.8.)
Let us evaluate the impact of revenue and costs on profit based on the assumption that the profit of the enterprise should be non-negative, i.e. PRP > About
If the profit of the enterprise is equal to zero: PRP \u003d O, then in this case the revenue of the enterprise is equal to the costs, i.e. before acceptance has zero profit: VPP = O, V = ZAT.
The main indicators characterizing this situation are:
1. Specific contribution margin
2 . Critical production volume
3. Production safety margin, production strength range, production strength level
4. Marginal profit
5. Critical revenue
6. Margin of financial strength
7. Range of financial strength
8. Level of financial strength
Specific marginal profit.
Difference between unit price and variables for costs of its production is called marginal profit per unit of output or specific marginal profit
(3.9.)
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Critical production volume.
The volume of production and sales at which the enterprise has zero profit, is called critical - Kkr (break-even point).
The value of the critical production volume (Kcr) is determined is obtained from the ratio:
(3.10.)
With an increase in the critical volume, the profit decreases. acceptance. The main factors affecting the value of criti cal volume of production are:
An increase in fixed costs leading to an increase the critical volume of production, respectively, with a decrease in fixed costs, the critical volume of production decreases;
An increase in variable costs per unit of output when constant price, leading to an increase in the critical volume of production, respectively, with a decrease in variable costs per unit of production, the critical volume of production decreases stva;
increase in selling price with constant variables costs per unit of output, leading to a decrease in critical cal volume of production.
Obviously, the critical volume of production is decreasing if the growth rate of fixed costs is less than the growth rate increase in marginal income per unit of output.
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Production safety margin.
Difference between actual (Kfact) and critical volume production (Kcr) characterizes the margin of safety of production in in kind (ZPR):
(3.11.)
If Kfact > Kkr, then the enterprise makes a profit from the production and sale of products, if the ZPR value is negative, then the enterprise from the production and sale of these products has losses.
When Kfact > Kcr, you can set the range of production strength - DPP and the level of industrial safety U (ZPP):
(3.12.)
(3.13.)
The larger the value of Uprb, the more efficient production and sales this product.
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Marginal profit.
The difference between sales revenue and variable costs called marginal profit (MPR). This is the part of the gain ki from the sale of products that remain to cover the permanent fixed costs and profit generation:
(3.14.)
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Critical revenue.
Critical revenue (or profitability threshold) (Vcr),
1. Calculation of the critical volume of production.
The critical volume of production can be depicted in two more ways (Fig. 4.11. "a" and 4.12.)
Fig.4.11. "a" Critical production volume.
Marginal income is a function of Y1 of products sold:
Result (profit and loss)
Rice. 4.12 Critical production volume
The result represents the function Y2
Y2 = MD * q - Zc
2. Calculation of critical revenue
To calculate the critical volume of sales, subject to a decrease
the price of the product and maintaining the same value of marginal income, the following ratio is used:
MD0*Q0=MD1*Q1; Ql = MD0*Q0 /MD1
0 - indicators of the previous period;
1 - indicators of the reporting period.
3. Fixed cost critical level report:
Zc = N-Zvaz = p*q-Zv*q = q*(p-Zv) = q* MD
Zvaz = Total variable costs;
This formula allows you to determine the amount of fixed costs if the level of marginal income is set as a percentage of the price of the product, or as a percentage of the sales volume.
4. Calculation of the critical selling price
5. Calculation of the level of minimum marginal income (as a percentage of revenue):
6. Calculation of the planned volume for a given amount of expected profit:
Rpl. - planned profit.
In a market economy, direct costing provides information on the possibility of using dumping in the competition - selling goods at deliberately low prices, which is associated with the establishment of a lower price limit.
This technique is used during periods of temporary reduction in demand for products to conquer markets.
Thus, thanks to "direct costing", the analytical capabilities of accounting are expanding, and there is a process of close integration of accounting and analysis.
The organization of production accounting according to the "direct costing" system is associated with a number of problems that arise from the features inherent in this system.
1. Difficulties arise when dividing costs into fixed and variable, since there are not so many purely fixed or purely variable costs.
2. "Direct Costing" does not answer the questions, what is the total cost of the product. Therefore, an additional distribution is required
semi-fixed costs, when you need to know the full cost of the finished product.
To solve the first problem, you can use, for example, the correlation method or the least squares method.
When using the correlation method, data on output and costs are taken for the period under study. All points are plotted on the graph, the correlation field is filled. Then a line of total costs is visually drawn, which, intersecting with the y-axis, shows the amount of fixed costs in the total amount of costs (Fig. 4.13.).
Rice. 4.13. Correlation method.
The least squares method allows you to most accurately determine the composition of the total costs and the content of their constant and variable components.
The coefficients a and a0 are calculated in the direct control
y = a0 + a*x; such that the squared distances from all population points to the theoretical regression line are minimal.
a0 - shows the value of fixed costs, and the coefficient a - long variable costs per unit of output.
The second problem can also be solved by periodically calculating the full cost off-system (depending on the goals of management).
Thus, this system allows you to analyze the costs and results of activities, makes it possible to manage the amount of profit, which is the most important indicator of the activities of enterprises in a market economy.
4.1.5 Break-even analysis of production. Problems of break-even analysis
Break-even analysis is based on the relationship between sales revenue, costs and profits over a short period, when production is limited to certain production capacities, the increase or decrease of which in a short period of time is impossible. However, attracting additional labor or material resources within a short period of time is quite realistic.
The break-even analysis is based on the division of the total cost of supply, production and sales of products into fixed and variable.
Tasks of break-even analysis:
1. determination of the break-even point;
2. determination of the number of units of production that must be sold to obtain the planned profit;
3. setting the price of products to ensure demand and profit at the planned level;
4. selection of the most efficient production technologies;
5. adoption of the optimal production plan.
From this it is quite obvious that break-even analysis is one of the methods for analyzing demand in a market economy.
Consider the economic approach to break-even analysis.
To increase the volume of sold products, the company must reduce the price per unit of production. This is the reason why sales revenue does not increase in proportion to total sales. Moreover, at some point the positive effect of increased sales will be lower than the negative effect of lower prices. The economic model of the behavior of costs, production volume and profit graphically looks like this, then the line of total income (OE), increasing at the beginning, gradually slows down the rise, and then goes down, (Fig. 4.14)
Rice. 4.14. economic model of cost behavior and sales proceeds
AD - behavior of total costs;
AB - at the initial stage, production and total costs increase sharply. This is due to the "pressure" of a large mass of fixed costs on a small amount of production;
BC - the steepness of the line of total costs decreases, since fixed costs in the composition of total costs occupy a smaller share with an increase in production volume. During this period, the equipment is operated at the level of design capacity, the advantages of labor organization are used: continuous schedules of the main production, specialization, mass or serial production.
At point C and D, the total cost line rises steeply again. This is because when the equipment is operated above the design level, unforeseen conditions arise. At the same time, the work schedules of the main production are becoming more complicated, there are failures in material and technical supply and a lack of resources and, as a result of all this, crisis situations. As a result, unit costs per unit of output increase and the total cost line tends upward.
The AF line reflects the behavior of the total fixed costs of the enterprise.
Information on the work "Improving the profitability of products based on reducing variable costs in the stainless steel cold rolling shop of OAO MMZ "Sickle and Hammer""
(Q cr). Assess the situation in the company and suggest ways to change it. Display the critical volume of production (break-even point chart) on the coordinate field.
Given:
The volume of production - 14000 units.
For all options:
Labor productivity of a worker (PT slave) - 500 units. in year;
The share of "managers" - 15% in the total number of industrial and production personnel (N PPP) - 1 person;
The average monthly salary of a worker (avg. month RFP slave) - 30 thousand rubles;
The salary of "managers" is accepted independently - 20 thousand rubles;
The share of labor costs for all personnel with insurance premiums in the total cost of production - 25%.;
The rate of return is 14% (the average price (C cf) is 1.14 times the cost of a unit of production (C units));
The share of variable costs (Z lane) in the total cost is 53%.
Solution:
The critical (break-even) volume in physical terms is determined by the formula:
Qcr \u003d Zpost / (Csr - Itching. per.) \u003d 27 472 / (4 759.5 - 2 212.8) \u003d 10790 units.
Ztot = (11 080 + 3532.8) ? 4 (25%) = 58,451,000 rubles.
Tsr \u003d 58,451,000.2 / 14,000 + 14% \u003d 4,759.5 rubles.
Zpost = 58451.2 ? 0.47 \u003d 27,472,000 rubles.
Zper = 58451.2? 0.53 \u003d 30,979,000 rubles.
Itchy lane \u003d 30979.1 / 14 \u003d 2,212.8 rubles.
where Z post - fixed costs; C - the price of a unit of production; Itchy lane - variable costs per unit of output.
The volume of sales in monetary terms corresponding to the break-even point is determined by multiplying Q kr on the price (C).
In this problem, to determine the total cost of production (3 total), it is necessary to know the amount of labor costs for all personnel with insurance premiums (the sum of the annual payroll fund (PAY) and insurance premiums (SV)), which can be determined based on What
FOT \u003d FOTrab + FOTau \u003d 10,080 + 960 \u003d 11,040 thousand rubles.
where FOT slave, FOT AU - wage fund for workers and "managers", respectively.
The rates of insurance premiums for compulsory social insurance (PFR, FSS RF, FFOMS) are applied in accordance with the legislation adopted and in force in the Russian Federation at the time of writing, and will amount to 11,040 ? 32% = 3532.8 thousand rubles
wherein:
A) FOTrab \u003d average year.ZPrab? Chrab = 360? 28 = 10,080 thousand rubles
where avg. year ZP slave - the average annual salary of one worker; H slave - the number of workers;
B) FOT AU \u003d average year. ZPau? Chow = 240 ? 4 = 960 thousand rubles;
C) Chrab \u003d Q / PTrab \u003d 14,000 / 500 \u003d 28 people.
Where Q- annual production volume; PT slave - the annual labor productivity of one worker;
D) Chpp \u003d Chrab + Chau \u003d 28 + 4 \u003d 32 people.
where N PPP - the number of industrial and production personnel.
Let's compare the level Qkr = 10790 units. with the achieved Qf = 14000 units. we can conclude that the company carries out its activities efficiently, tk. Qf is greater than Qkr, which provides the company with a sufficient level of profit for the development of the enterprise.
The margin of financial safety is: the ratio of the difference between the current sales volume and the sales volume at the break-even point to the current sales volume, expressed as a percentage.
DFP = ((14000 - 10790)/14000)*100% = 22.93%
Let's analyze the obtained results using the popular management model of CVP-analysis.
CVP analysis is an enterprise management system that integrates various subsystems and management methods and subordinates them to the achievement of a single goal. This discipline should have its own subject of study: in our opinion, these are the costs and results of the activity of the subject of market relations. To manage the process of optimizing performance results, CVP analysis should use methods from various disciplines: accounting, analysis, control, strategic and operational planning and management, enterprise economics, economic and mathematical methods, etc.
The CVP analysis model allows you to track and "play" the dependencies, ratios and dynamics of costs, results and sales volumes. It can help answer a number of important questions.
What is the price limit for a product when other parameters change? And we have it equal to 51,355,000 / 10790 = 4,760 rubles.
How much revenue is needed to provide a given profit? The amount of profit according to our schedule should not be less than 51,355,000 rubles.
Income, Revenue
Costs, thousand rubles
27472.1 Zpost
10790 14000 Q (unit).
Fig No. 2 Graph of critical production volume
An enterprise can make a profit when selling products in quantities exceeding the values of the critical break-even point Qcr. The point Qkr is called the critical point, at the transition through which all costs are paid off and the enterprise begins to make a profit.
Profit \u003d income - costs \u003d 66633 - 58451.3 \u003d 8181.7 thousand rubles.
Income = Tsr? Q = 4759.5? 14000 = 66,633,000
With an increase in prices for manufactured products, the minimum volume of production, which corresponds to the critical point, decreases, and with a decrease in prices, on the contrary, it increases.
With an increase in fixed costs, the minimum output corresponding to the break-even point increases.
Maintaining a break-even volume of production with an increase in variable costs is possible, other things being equal, by increasing the minimum volume of production.
The critical point of sales of products shows the volume of products that must be sold in order to start making real profits.
It can be calculated both in natural and in value terms. The critical point is found based on the main equation.
q cr \u003d S post / C unit. - S per unit.
Situation 1. The company manufactures small retail products. Variable costs per unit of production (S per unit) - 200 rubles, the amount of fixed costs (S constant) - 100,000 rubles, the price of a unit of production (C unit) - 400 rubles. Determine the critical point of sales of products.
q cr \u003d 100,000 / 400 - 200 \u003d 500 units; In terms of value, this will be:
N cr \u003d C * q cr \u003d 500 * 400 \u003d 200,000 rubles.
Thus, in order to break even, the enterprise must sell 500 units of production and receive revenue in the amount of 200 thousand rubles.
The analysis of indicators at the critical point of sale, taking into account the profit factor, can be used as a basis for assessing the profitability of the company's activities.
Situation 2. Using the initial information (situation 1), determine what the volume of production should be so that the enterprise can make a profit of 40,000 rubles.
It is known that at the critical point the profit is by definition equal to zero, therefore, by transforming the basic formula, we obtain the following expression:
q \u003d S post + R / C - S lane. units
Thus, the required volume of sales of products for our conditions will be:
q = 100,000 + 40,000 / 400 - 200 = 700 units
You can check the correctness of the calculations based on the expression:
P \u003d C * q - S before * q - S post \u003d 400 * 700 - 200 * 700 - 100,000 \u003d 40,000 rubles.
Situation 3. Using the data of situations 1 and 2, determine the amount of profit if the company increases sales to 1600 units. products.
Transforming the expression to check the correctness of the calculations for situation 2, we get:
P \u003d (C - S trans. unit) * q - S post \u003d 1600 (400 - 200) - 100,000 \u003d 220,000 rubles.
Situation 4. Using the original data table. 5.6.1. determine the volume of production required to obtain the planned profit.
Table 5.6.1.
For calculations, we use the expression:
P \u003d (C - S per ed) * q - S post i.e. 10,000 = (200 - 100) * q - 20,000
Transforming the expression, we get:
q cr \u003d 10,000 + 20,000 / 200 - 100 \u003d 300 units.
Thus, in order to make a profit of 10,000 rubles, the enterprise must sell 300 units. products.
5.6.2. Profit optimization with different production technology options.
To obtain maximum profit, it is necessary to choose the best option for production technology, product prices, cost structure, etc., while the number of options may be different.
When considering two options, we can use the calculation formula, the development of which proceeded from the fact that for different options the price of the final product is unchanged, therefore, the options are analyzed not through marginal profit, but through the cost.
S lane 1 x q + S post 1 = S lane 2 x q + S post 2
From here we determine the critical volume of production:
q cr = (S post 2 - S post 1) / (S lane 1 - S lane 2)
Having determined the critical volume of production (q kr), we compare it with the release of this product according to the plan (q p) and choose the most effective option. Variant with lower fixed (S post) and higher variable unit costs (S ln)
more profitable for q p< q кр. При q п >q kr is more profitable option with large fixed costs and smaller variables.
Situation 5. The company can use two options for production technology:
Complex-mechanized line for forming and knocking out sections
Automated line for forming and knocking out sections.
Using the first option, you can quickly start production without significant pre-production; the second option requires additional investments, but provides higher consumer properties and product prices (Table 5.6.2.1.)
It is necessary to choose the most profitable production option.
Table 5.6.2.1.
1. First of all, let's determine the marginal profit per 1 unit. products (marginal profit rate):
M unit 1 \u003d 200 - 140 \u003d 60 rubles.
M unit 2 \u003d 240 - 60 \u003d 180 rubles.
2. Based on the equation of the critical point of production volume (clause 1.10 *)
q cr \u003d 20,000 - 2,000 / 180 - 60 \u003d 150 units.
Thus, with an order size of up to 150 units. you need to use the technology of the first option. Since the planned sales volume is 250 units. production, then we choose the second production option.
This will allow you to get the following profit:
P \u003d 180 x 250 - 20,000 \u003d 25,000 rubles.
Situation 6. An enterprise can perform a technological operation using one of three machine options:
semi-automatic;
Auto;
With software control.
In table. 5.6.2.2. data on fixed and variable costs for three equipment options are given.
Table 5.6.2.2.
The company produces 1800 parts per year on a CNC machine. It is necessary to choose the best option for machines depending on the volume of production and determine the profit from the selected option.
Consideration of this situation includes several stages.
1. Let's make the equation of total costs for each variant of production.
S p / a \u003d 40 x q + 10,000
S a \u003d 10 x q + 20,000
S p / y \u003d 2.5 x q + 30,000
2. Let's determine the production volumes corresponding to the critical cost point for two pairs of machines: the first pair is semi-automatic and automatic; the second pair is automatic and with program control. Let's make cost equations in which the costs of one option are equated to the costs of another. The critical volume for the first pair of machines (q cr 1), ensuring the equality of costs:
40 q + 10,000 \u003d 10 q + 25,000, therefore q cr 1 \u003d 500 units.
Similarly, the critical volume for the second pair of machines (q kr2) is determined, which ensures the equality of costs:
10 q + 25,000 = 2.5q + 41,000, therefore q cr2 = 2133 units.
Thus, with an annual production of up to 500 units. products, it is more profitable to use a semi-automatic machine, with an output volume of 500 to 2133 units. – automatic; and with a production volume of more than 2133 units. it is advisable to use a machine with program control.
3. Compare the costs associated with the output of 1800 units. products:
On a semi-automatic machine: 40 x 1800 + 10,000 = 82,000 rubles;
On an automatic machine: 10 x 1800 + 25,000 = 43,000 rubles.
On a machine with program control: 2.5 x 1800 + 41,000 = 45,500 rubles.
Consequently, an unreasonable technological decision related to the production of products will bring to the enterprise losses, the amount of which is equal to the difference in the costs of production on an automatic machine and a machine with program control:
43,000 - 45,500 = - 2500 rubles.
Thus, the increase in production technology leads, on the one hand, to a significant reduction in variable costs per unit of output, on the other hand, to an increase in the total amount of fixed costs associated with the higher cost of modern equipment and technologies.
Volume of production at the break-even point (the critical volume of production) is the volume at which the company does not make a profit, but does not incur losses.
The critical volume (Qcr) is expressed in physical units (pieces).
Critical revenue (S cr) is the value expression of the critical volume.
Using the analysis of values in the break-even point, you can determine the critical value that shows when revenue covers the total costs of the enterprise. Analysis of break-even points provides managers at all levels with information for better decision making in the future. With the help of this analysis, you can better assess the opportunities for profit. Graphical interpretation of the break-even model Break-even chart:
FS - fixed costs; VC - variable costs; FC+VC - total costs; S - revenue; Qxp - critical volume; Q - volume of production in physical terms Calculation of revenue at the break-even point Analytical representation of the model under consideration is based on the following basic formula:
S = FC + VC + GI, where GI is profit. Since there is a relationship between the cost and natural volumes, expressed by the ratio S = p Q, where p is the price per unit of production, the above formula can be represented as follows: p Q = FC + v Q + GI,
where v - variable costs per unit of output.
Transforming the formula, we get Q ¦ (p - v) \u003d FC + GI
To find the critical volume, we set the condition GI = 0. Based on this, we obtain the formula: Qkp = FC / (р - v)
The denominator of the fraction (p - v) is called the specific coverage amount, and accordingly, S - VC, will be called the coverage amount. The critical revenue, taking into account the relationship between S and Q, can be found by the formula: Skp = p
Critical revenue can also be found using another formula, which is advisable to use if the price of the product is unknown in the condition: Skp = FC /
Break-even (critical) volume can be calculated in several ways.
1. The minimum volume of output in physical terms:
Qmin = CF / p - CV
2. To calculate the volume of output in value terms, the left and right parts of the expression are multiplied by the price (rubles).
p*Q=CF+CV*Q
where Q * p \u003d N - sales proceeds (taken without VAT).
3. Critical sales volume can be calculated using marginal revenue. Marginal income MD is defined as the difference between revenue and variable costs:
Then Nmin = CF / MD
The calculation of the break-even point is not difficult, provided that the company produces one product. If the company produces only one product, then this eliminates the need to allocate fixed costs to many manufactured products.
The given graphical dependence of costs, profits and sales volume allows us to draw important conclusions for the enterprise:
1. An enterprise can make a profit (revenue minus fixed and variable costs) only if it sells products of a larger volume than the critical point A.
2. Point A , , is called the critical point, at the transition through which all costs are paid off and the enterprise begins to make a profit.
3. The point of intersection of the curve of fixed costs and the marginal income curve shows the volume of production, after the passage of which the payback of fixed costs occurs.
4. With an increase in prices for manufactured products, the minimum volume of production, which corresponds to the critical point, decreases, and with a decrease in price, it increases.
5. With an increase in fixed costs, the minimum production volume corresponding to the break-even point increases.
6. Maintaining a break-even volume of production with an increase in variable costs is possible, other things being equal, by increasing the minimum volume of production.