Determination of the optimal volume of production. The optimal output of a firm in a perfectly competitive market

1. Determination of the optimal volume of production and sales of products by comparing gross indicators.

The company, as a rule, seeks to maximize profits.

Other things being equal greatest influence profit maximization is provided by the volume of production (sales) of products and the price of the goods produced. Having passed the production volume corresponding to the breakeven point, the enterprise will subsequently receive a certain profit with an increase in production volume. The optimization method is the method of comparing gross indicators.

Its use involves a number of assumptions:

1) the company produces and sells only one product;

2) the purpose of the enterprise is to maximize profits in the period under review;

3) only the price and volume of production are optimized.

The essence of this method, when the manufacturer does not have any influence on the formation of prices, is to determine the amount of goods that he can offer to buyers at the prevailing market price.

The method of comparing gross indicators involves the calculation of profit at different values ​​of the volume of production and sales of products by subtracting the amount of gross costs from gross revenue.

Gross costs are determined by multiplying the unit cost of production by its quantity. Gross revenue is calculated by multiplying the price by the same quantity.

2. Determining the optimal volume of production and sales of products by comparing marginal indicators.

Along with determining the optimal volume of production and sales of products by comparing gross indicators, the method of comparing marginal indicators is used for the same purposes.

When optimizing production volumes using this method, the concepts of "marginal revenue", "marginal cost" and "marginal profit" are used.

marginal revenue– average value decrease (increase) in revenue per unit of goods as a result of a change in the volume of production and sales of products by more than one unit. It is defined as the quotient of dividing the difference between subsequent and previous revenue by the corresponding difference in sales volumes in natural terms.

marginal cost- the average value of the cost of growth (reduction) per unit of output, which arose as a result of a change in the volume of production (sales) of products by more than one unit. They are determined by the ratio of the difference between subsequent and previous gross costs to the difference between the corresponding volumes of output.

marginal profit- the average value of the increase (decrease) in profit per unit of output, which arose as a result of a change in production volumes by more than one unit.

marginal profit is the difference between marginal revenue and marginal cost.

The starting point of the marginal comparison method is that an increase in output is profitable as long as the value of marginal revenue exceeds the value marginal cost.

In order to produce the volume of production, it is necessary to know the indicators of labor productivity of workers. Labor productivity characterizes the performance of an employee in a broad sense - this is the ability of a particular employee to produce products or provide services.

Labor productivity can be individual (for one worker, measured by the amount of material goods produced by one worker per unit time) and social (determined by the costs of not only living, but also materialized labor).

Labor efficiency indicators are used for various purposes - planning, comparison, standardization, etc. Therefore, they may have different shape measurement, which is determined by the purpose and purpose of determining the indicator.

Natural indicators characterize the production of products in kind per unit of working time and are expressed in kind, for example, tons, kilograms, liters, meters, etc.

They are absolute and have limited application. They are mainly used when comparing the performance indicators of brigades, links, workers, as well as in determining the production standards and the level of their implementation.

To analyze the actual costs of working time, determine the intensity of labor, a natural indicator of labor intensity of work is used (an indicator inversely proportional to output), which is defined as the ratio of the total amount of working time spent on the entire volume of work to the number of work performed (norm of time).

However, cost indicators of labor productivity are characterized by greater efficiency, expediency and ease of use. They have become more widespread in industrial enterprises, have great versatility.

Their application makes it possible to take into account and compare various types of work by bringing them to a single meter (cost).

Labor indicators characterize the ratio of standard costs to the actual costs of working time. Such indicators are used to determine the efficiency of using the labor of workers in comparison with the norms. It is convenient to use such indicators when setting labor standards and determining optimal labor standards for employees.

Depending on the purpose of planning, apply various methods measurement of labor productivity. After all, labor productivity has a great influence on the level of competitiveness of the enterprise and its financial result.

Any planning cannot do without taking into account the productivity of labor, both individual and social. Production planning is inseparable from the rationing of workers' labor and from accounting for their compliance with labor standards.

In practice, with general accounting, the main distribution was received by the cost indicators of accounting, since they are general and universal for the purposes of production planning. The enterprise should strive to increase labor productivity as a guarantee of future prosperity.

The optimal volume of production is such a volume that ensures the fulfillment of concluded contracts and obligations for the production of products on time with a minimum of costs and the highest possible efficiency.
The optimal production volume can be determined by two methods:

• the method of comparing gross indicators;
• the method of comparison of limit indicators.

The following assumptions apply when using these methods:
the company produces and sells only one product;

• the purpose of the enterprise is to maximize profits in the period under review;
• only the price and volume of production are optimized, since it is assumed that all other parameters of the enterprise's activity remain unchanged;
• the volume of production in the period under review is equal to the volume of sales.

However, despite the strict limits of the above assumptions, the use of these methods greatly increases the likelihood of accepting right decisions.
Consider the example of determining the optimal volume of production by the above methods.
In table. 7.1 shows the initial data for determining the optimal volume of production.
Table 7.1
The volume of sales of products and the costs of its production

Volume	Permanent	Variables	Gross
0	1200	0	1200
10	1200	200	1400
20	1200	360	1560
30	1200	490	1690
40	1200	610	1810
50	1200	760	1960
60	1200	960	2160
70	1200	1220	2420
80	1200	1550	2750
90	1200	1980	3180
100	1200	2560	3760

The application of the method of comparing gross indicators to determine the optimal volume of production involves the following sequence of actions:

• the value of the volume of production is determined, at which zero profit is achieved;
• the volume of production with maximum profit is established. Consider the volume of sales of products (Table 7.2)

Table 7.2
The volume of sales of products with maximum profit

Volume	Price,	Gross	Gross	Profit,
implementation, thousand pieces	rub-	revenue, thousand rubles	costs, thousand roubles.	thousand roubles.
0	-	0	1200	-1200
10	48	480	1400	-920
20	48	960	1560	-600
30	48	1440	1690	-250
40	48	1920	1810	110 440
50	48	2400	1960	720
60	48	2880	2160	940
70	48	3360	2420	1090
80	48	3840	2750	1140
90	48	4320	3180	1040
100	48	4800	3760

Based on the data in the table, we can draw the following conclusions:

• zero profit is achieved with the volume of production and sales in the range from 30 to 40 thousand pieces. products;
• the maximum amount of profit (1140 thousand rubles) is obtained with a volume of production and sales of 90 thousand pieces, which in this case is the optimal volume of production.

The method of comparing marginal indicators allows you to establish to what extent it is cost-effective to increase production and sales. It is based on a comparison of marginal cost and marginal revenue. In this case, the rule applies: if the value of marginal revenue per unit of output exceeds the value of marginal cost per unit of output, then the increase in production and sales will be profitable.
Before moving on to determining the optimal volume of production using the method of comparing marginal indicators, one should consider such a concept as marginal cost. When forming the production plan of an enterprise, it is important to establish the nature of the increase in production volumes when additional production variables are added to the already available fixed resources, and how, in this case, the total costs of production and sales will be formed. The answer to this question is the law of diminishing returns. Its essence lies in the fact that, starting from a certain moment, the sequential addition of units of a variable resource (for example, labor) to an unchanged fixed resource (for example, fixed assets) gives a decreasing additional, or marginal, product per each subsequent unit of the variable resource. Consider this statement with an example (Table 7.3).
Table 7.3.
Dynamics of performance indicators of the enterprise
The table shows that the more additional workers are involved, the more products are produced. However, each time the attraction of another additional worker gives an unequal increase in the increase in output. This increase is the marginal product of the labor of one worker. It is calculated by simply subtracting the level of production in question from the subsequent increase in output. In our example, the marginal product per additional worker raised increases to a third worker and then starts to fall. This change in the growth of marginal product is explained by the decrease in the growth of average labor productivity per worker. This is due to the fact that with an increase in the number of employees, fixed assets remain unchanged. Based on the situation considered, one should not make hasty conclusions about the cessation of the production of additional products, since a decrease in the value of the increase in production volumes for each one employee involved does not yet indicate that the production of additional units products are unprofitable. It all depends on whether profit increases when hiring another employee. For example, if the price of a product in the market is unchanged, then the business will receive income as a result of having more products to sell, provided that the value of the additional cost associated with hiring an additional worker will be less price goods.
From the above example, we can assume that the cost of a unit of production produced by attracting additional work force decreases to a certain point, and then starts to rise again. The fall or rise in the cost of each additional unit of output is called the marginal cost.
The concept of marginal cost is practical value, because it shows the costs that the company will have to incur in the event of an increase in production by one unit. However, at the same time, this concept shows the costs that the company will "save" in the event of a reduction in production by this last unit. Thus, the costs of production in the conditions of market relations should be considered not just as the costs incurred for the acquisition of everything necessary for the production of products and their manufacture, but also as the establishment of the best opportunity for their use, i.e., in other words, it is necessary to form such costs, which give the best result.
Let us return to the determination of the optimal volume of production by the method of comparing marginal indicators. The calculation of the optimal volume of production is presented in Table 7.4.
Table 7.4
Calculation of the optimal volume of production by the method of comparison of marginal indicators

Sales volume, thousand units	Marginal income, rub.	Marginal costs, rub.	Marginal profit, rub.
10	48	20	28
20	48	16	32
30	48	13	35
40	48	12	36
50	48	15	33
60	48	20	28
70	48	26	22
80	48	33	15
90	48	43	5
100	48	58	-10

In our case, the marginal revenue per unit of output is the market price of the unit. Marginal cost is the difference between the next total cost and the previous total cost (see Gross Comparison Method) divided by the output. Marginal profit is found as the difference between marginal revenue and marginal cost.
Thus, based on the data in the table, the following conclusions can be drawn:

• expansion of production volumes efficiently (profitably) up to 90 thousand units;
• any increase in production volumes over 90 thousand units. production at a constant price will lead to a decrease in gross profit, since the amount of additional costs will exceed the amount of additional income per unit of output.

One of the most important factors in the management of production and sales processes is the division of costs into variable and fixed. This division makes it possible to predict profit based on how costs change depending on the growth or decline in sales, to determine for each specific situation the volume of sales that ensures the break-even activity of the enterprise. This, in turn, avoids erroneous decisions made in the case of costing in the amount of full costs.

The key indicator in the sales profit management system is − marginal income, which is the difference between sales revenue and variable expenses. The economic value of marginal income is that it provides coverage fixed costs. Any excess of marginal income over fixed costs generates company profit.

Marginal income characterizes the contribution of each sold product to the profit of the enterprise. Thanks to this indicator, the company's management receives information on the profitability of each type of manufactured products in the overall financial result.

Sales growth leads to growth working capital and requires more funding sources. Therefore, any sales increase forecast requires predictive analysis. cash flows undertaking in which the risk of a shortage can be assessed Money(negative value of net cash from current activities).

Costs, production and sales volumes, profits are closely interconnected, and there are many questions related to these indicators. Many of them will be discussed in this article.

IMPACT OF SALES STRUCTURE

All expenses of the enterprise can be divided into two parts:

• variable costs - they change in proportion to the scale of the company's activities;
• fixed costs - remain unchanged when the scale of the enterprise changes.

to variable expenses includes direct material costs and wage production personnel with deductions ( piece-work payment). For fixed expenses usually include administrative and management costs, depreciation, and selling and general expenses.

The meaning of the division of costs into variable and fixed is that they behave differently in the process of managing the production of products at the enterprise.

It's believed that variable costs per unit of output are a constant, often referred to as specific variable costs or a variable cost rate. Variable costs rise almost in proportion to the growth in output.

Fixed costs per unit of output decrease as the number of products produced increases. Thus, total costs per unit of output decrease as production and sales increase.

Such an economic presentation of these costs simplifies the analysis of the influence of individual factors of production at the stage of preliminary aggregated calculations. First of all, this concerns the impact of the structure of production and sales on the company's profit. After all, most enterprises produce a wide range of products.

In this case, the question arises: how rational is the existing structure of sales of individual products? It is possible that the production and sale of products of the same names, but in different volumes and ratios, are more profitable for the company. Selection of a criterion for evaluating the optimal sales structure acquires paramount importance in these conditions.

EXAMPLE 1

The manufacturing business segment of the company produces three types of products - A, B and C (Table 1). The segment is currently operating at a loss. The amount of loss is 4 million rubles.

The current sales structure determined by the following data:

• product A - 10.87%;
• product B - 34.78%;
• product C - 54.35%.

If there is demand for products, the solution to the issue of improving the sales structure depends on the profitability of certain types of products (goods). By increasing the share of the most profitable products in total sales, you can increase the overall profitability of sales, increase the marginal income of the company.

Table 1. Manufacturing business segment of the company
No. p / p	Index	Product type			Total
	Sales volume, thousand units
	Fixed expenses, thousand rubles

Before proceeding with the calculations, we will analyze the profitability of all types of products presented in Table. one.

Products C have a maximum marginal income per unit of production - 500 rubles / unit. It is followed by product B - 300 rubles/unit, and product A closes the row - 80 rubles/unit.

It is a mistake to assume that product C is the most profitable in the sales structure, since the relative measure of profitability should not be marginal income per unit, but ratio of marginal revenue to price.

Then it turns out that the share of marginal income in the price of product C is minimal (20%), and the most profitable product from this point of view is product A (40%). Accordingly, product B occupies an intermediate position (37.5%).

Therefore, the level of marginal income for the company as a whole is the higher, the greater the share in the cost structure is occupied by types of products with the maximum ratio of marginal income to price (or the maximum value coefficient MD/C). It follows that an increase in the share of high-margin products (MD / C ratio) will lead to an increase in sales profit.

EXAMPLE 2

Suppose the management of the enterprise (example 1) raises the question of increasing the output of products A and B by reducing product C. The new and old sales structure are presented in Table. 2.

Let's evaluate how the change in the structure will affect the financial result of the company's activities.

Table 2. Old and new sales structure of the company
Product type	Marginal income per unit of production, rub.	MD/C coefficient	Sales structure, %
			former	new

First, let's solve the problem in general view. To do this, we calculate weighted average MD/C ratios for both sales structures by multiplying this factor by the sales structure (as a percentage).

Former structure:

• product A:

0.4 × 0.1087 = 0.04348;

• product B:

0.375 × 0.3478 = 0.13042;

• product C:

0.2 × 0.5435 = 0.1087.

Total MD/C ratio — 0,2826 .

New structure:

• product A:

0.4 × 0.30 = 0.12;

• product B:

0.375 × 0.45 = 0.16875;

• product C:

0.2 x 0.25 = 0.05.

Total MD/C ratio — 0,33875 .

As we see, the new sales structure led to an increase in the weighted average ratio(MD/C). This also means an increase in profits, since fixed costs have not changed.

Let's calculate the value of marginal income relative to revenue, taking into account the weighted average MD / C ratio. For the old sales structure, this would be:

RUB 92,000 thousand × 0.2826 = 26,000 thousand. rub.

The amount of loss for the old structure will be:

26,000 thousand rubles - 30,000 thousand rubles. = -4000 thousand rubles.

This completely coincides with the financial result from example 1 (see Table 1).

Marginal income for new structure sales:

RUB 92,000 thousand × 0.33875 = 31 165 thousand. rub.

With a constant value of fixed costs, the profit for the new structure will be:

RUB 31,165 thousand - 30,000 thousand rubles. = 1165 thousand. rub.

That this is so can also be shown by a full calculation economic indicators companies (Table 3).

Table 3. Manufacturing business segment of the company for the new sales structure
No. p / p	Index	Product type			Total
	Price per unit of production, rub.
	Variable costs per unit, rub.
	Marginal income per unit, rub. (p. 1 - p. 2)
	Marginal income to the price of products,% (p. 3 / p. 1)
	Sales volume, thousand units
	Revenue, thousand rubles (p. 1 × p. 5)
	Revenue for each type of product to total revenue, %
	Variable expenses, thousand rubles (p. 2 × p. 5)
	Fixed expenses, thousand rubles
	Financial result, thousand rubles (p. 6 - p. 8 - p. 9)

In table 3, the volume of sales in natural units is calculated by dividing the proceeds for each sales position (type of product) by the corresponding price per unit of production. The sales volume will be:

• for product A:

27 600 rub. / 200 rubles/piece = 138 thousand pieces;

• for product B:

RUB 41,400 / 800 rubles / piece = 51.75 thousand pieces;

• for product C:

23 000 rub. / 2500 rubles / piece = 9.2 thousand pieces.

As you can see, the financial results of the overall assessment and more complete calculations made in Table. 3 are in perfect agreement.

IT IS IMPORTANT

To ensure the receipt of the required (planned) profit, it is necessary to maintain a certain ratio of marginal income (contribution) to revenue.

Conclusion: if production conditions and demand allow, then the previous sales structure should be replaced by a new one, in which the share of high-margin products is much higher. At the same time, such factors as the occupied market share, the ability to offer customers the range of goods they need should be taken into account.

INFLUENCE OF THE PRODUCTION FACTOR

In real conditions, the considered opportunities for expanding the volume of production may be limited by the level of the company's existing production capacities and other production factors (lack of workers with the necessary qualifications, required materials, etc.).

If the demand for the product exceeds the production capacity of the enterprise, it is necessary to determine factors limiting its production. You can then analyze the relationships in the volume-cost-production chain and find an appropriate solution to overcome this limitation.

EXAMPLE 3

Let us introduce for the company under consideration, which produces three types of products, restrictive condition - throughput equipment. Table 4 presents all additional data subject to this limitation ( unit processing time).

Table 4. Manufacturing business segment of a resource constrained company
No. p / p	Index	Product type
	Price per unit of production, rub.
	Variable costs per unit, rub.
	Marginal income per unit, rub. (p. 1 - p. 2)
	Estimated demand, thousand units
	Marginal income per unit of the limiting factor, rub. (p. 3 / p. 5)

Suppose the technical capabilities of the equipment are limited 420 thousand machine-hours(we are talking about the output per month). To ensure the production of all products in a quantity corresponding to demand, more time will be required:

30 + 220 + 240 = 490 (thousand machine-hours).

Under these conditions, one can argue as follows. Product C generates the highest margin per unit, so it should be produced in the maximum possible quantity, that is, according to demand. Then you need to maximize the output of product B (the second most profitable type of product) and, if production capacity allows, produce product A.

Such a plan for the production of products of all three items is presented in Table. 5.

Table 5. Initial production plan with limited resources
No. p / p	Index	Product type			Total
	Price per unit of production, rub.
	Variable costs per unit, rub.
	Marginal income per unit, rub. (p. 1 - p. 2)
	Sales volume, thousand units
	Processing time for a unit of production, machine-hour
	Time required for release, thousand machine-hours (item 4 × item 5)
	Fixed expenses, thousand rubles

According to the calculation, it is possible to provide full demand only for products C in the amount 30 thousand. things. Moreover, its production required 240 thousand machine-hours of equipment operation. Therefore, 180,000 machine-hours (420 - 240) remain for the production of products A and B.

This machine time can be used to produce 45,000 pieces of product B (180,000 machine-hours / 4 machine-hours/unit). There are no opportunities for output A. Then the financial result from the sale of products of this structure will be negative (the loss will be RUB 1.5 million.).

We immediately note the viciousness of such a practice. This option did not take into account the labor intensity of the production of certain types of products in the sense of estimating income per unit of the limiting factor.

As can be seen from Table. 4, we have the largest marginal income (per unit of processing time) for product A (160 rubles), smallest value- for product C (62.5 rubles). This means that the order of choice of the quantity of manufactured products should be taken as follows: A → B → C.

Accordingly, it should be issued maximum amount products A (60 thousand. products). The time spent on its production will amount to 30 thousand machine-hours.

Maximum output B (55 thousand. things) will require 220 thousand machine-hours.

Remaining production time C will amount to 170 thousand machine-hours (420 - 30 - 220), which will allow to produce 21.25 thousand. units of this product (170 thousand machine hours / 8 machine hours / unit).

Estimated data on the new plan for the release of products are presented in table. 6.

Table 6. Final Production Plan with Resource Constraint
No. p / p	Index	Product type			Total
	Price per unit of production, rub.
	Variable costs per unit, rub.
	Marginal income per unit, rub. (p. 1 - p. 2)
	Sales volume, thousand units
	Processing time for a unit of production, machine-hour
	Time required for release, thousand machine-hours (item 4 × item 5)
	Marginal income for the entire issue, thousand rubles (p. 3 × p. 4)
	Fixed expenses, thousand rubles
	Financial result, thousand rubles (p. 7 - p. 8)

As you can see, the change in the sales structure allowed the company to get rid of losses. The financial result was positive 1925 thousand. rub. arrived.

IT IS IMPORTANT

The priority of the production of one or another type of product must be assessed based on the marginal income per unit of the limiting factor. AT this production this factor is unit processing time different kind products in machine hours.

Conclusion: to improve the sales structure and increase the profit of a company with limited resources, it is necessary to estimate the marginal income per unit of the limiting factor, and then establish the sequence (priority) of choosing the number of products manufactured by the company.

IMPACT OF THE OPERATING LEVER

In the process of substantiating the decisions made about a particular innovation in the production process, it is necessary to observe relevance principle. The essence of the principle is that for the purposes of making any decision, only those incomes and expenses that are directly related to the solution of this problem are taken into account. Previous income and expenses on this issue are irrelevant and are not taken into account.

Let's consider this principle on the example of making a decision on an additional order in a situation with incomplete loading of production capacities.

EXAMPLE 4

According to the data on the main activity, the company's sales volume is 60 thousand pieces of products per month (the selling price is 100 rubles per unit).

An additional order was received for the production of the same products in the amount of 12 thousand pieces of products. Selling price is offered less - total 85 rub. for a unit ( option 1).

To fulfill the incoming order, additional one-time costs in the amount of 300 thousand. rub. This is due to the acquisition of the necessary special equipment for the implementation of customer requirements. In addition, on 10 % labor costs (including deductions) will increase, as employees will have to be paid extra for overtime work.

The question of the advisability of accepting an additional order can be resolved positively if the income from its implementation will cover the costs associated with it.

The management income statement for the main and additional orders (option 1) is shown in Table. 7.

Table 7. Assessment of the expediency of accepting an additional order
No. p / p	Index	Main order	Additional order
			option 1	option 2
	Sales volume, pcs.
	Sales price, rub./pc.
	Revenue, rub. (p. 1 × p. 2)
	Material costs, rub./piece
	Labor costs, rub./pc.
	General production expenses, rub./pc.
	Total variable costs, rub./pc. (p. 4 + p. 5 + p. 6)
	variable costs for the entire issue, rub. (p. 1 × p. 7)
	Fixed expenses, rub.
	Financial result, rub. (p. 3 - p. 8 - p. 9)

Let us evaluate the economic feasibility of accepting an additional order.

The production capacity is not fully loaded, so it can be assumed that the acceptance of an additional order will not increase fixed costs (with the exception of one-time costs associated with the order - 300 thousand rubles). Therefore, a reasonable assessment of such a situation requires that only the income and expenses associated with an additional order be taken into account.

As can be seen from the calculations, due to the lower selling price and additional one-time costs, the acceptance of such an order gives a negative financial result. Loss - 18 thousand. rub. Naturally, this option, in principle, cannot suit a manufacturing company.

The situation can be changed by applying Effect operating lever . It is based on the mechanism of varying degrees of influence of sales volume on the revenue and variable costs of the enterprise.

With the linear nature of the dependences of these indicators on the volume of revenue, everything is determined by the ratio selling prices (C pr) and unit cost of variable costs(From lane). Therefore, revenue is growing at a faster rate than variable costs. Inevitably, there comes a time when marginal income begins to exceed fixed costs.

To determine critical break-even point for a business, you can use a formula that equates marginal profit and fixed costs of the enterprise. This critical point can be found as follows:

Q cr = F/ (C pr - C lane),

where Q cr is the critical volume of sales in natural units;

F- fixed costs.

After substituting the relevant data, we get:

Q cr = 300,000 / (85 - 61.5) = 12 766 pcs.

After reaching this sales volume, the positive effect of the operating leverage effect will begin to appear.

To more tangibly represent the impact of operating leverage on earnings growth, double sales volume, up to 24 thousand. products (option 2). At the same time, we assume that labor costs (including deductions) will increase by 20 % compared with the data for the main order (see Table 7).

According to calculations, the acceptance of such an order provides additional profit in the amount of 228 thousand. rub. (despite the fact that the price offered by the buyer was lower than the price at which the company sold its products under the main order). The source of its formation is savings on the general fixed costs of the company.

As you can see, with an increase in sales volume, the value of sales volume (revenue) increases at a faster pace than the growth of variable costs in accordance with their price ratio. So, for option 2, this ratio will be:

C pr / S lane \u003d 85 rubles. / 63 rub. = 1,349 .

With the growth of sales in the same proportion, the change in the growth rate of marginal income remains. That is, with an increase in sales in option 2, for example, by 10%, there is an increase in marginal income also by 10%.

It is easy to check this by multiplying the volume of sales increased by 10% in natural units (pieces) by the difference in price and unit cost of variable costs. Then the new value of marginal income will be:

MD \u003d (85 - 63) × 24,000 × 1.1 \u003d 580,800 (rubles).

From here relative growth in marginal income in percents:

∆MD = (580,800 - 528,000) / 528,000 × 100% = 52,800 / 528,000 × 100% = 10 % .

Which was required to be proved due to the linear dependence of marginal income on the value of sales volume.

Conclusion: the acceptance by the company of an additional order depends on the influence of the effect of operating leverage, that is, on the ratio of variable and fixed costs associated with the implementation of the order. If the marginal income covers the fixed costs associated with the order, then the additional order can be accepted by the company for execution.

SALES PLANNING TO COVER CASH EXPENSES

The above does not exhaust the analytical possibilities of the economic grouping of expenditures into fixed and variable features. In particular, when predicting the possibility of covering all current expenses of an enterprise in cash, the above formula for determining the critical volume of sales can be used.

In this case, in the formula fixed costs should exclude expenses that are not accompanied by an outflow of cash primarily depreciation charges. The formula will take the following form:

Q cr = ( F - D) / (C pr - C lane),

where D- non-monetary expenses.

Depending on the specific conditions of the enterprise, this formula can be significantly changed. For example, when changing in the balance sheet items of the enterprise's working capital. The fact is that the volume of production is not always equal to the volume of sales, and the company has leftovers finished products in stock. The change in balances is also manifested in other items. current assets:

• productive reserves;
• work in progress, etc.

In this regard, the question arises: what should be the planned sales volume in order to compensate for unplanned expenses in cash?

In this case, an increase in net current assets requires an increase in sales volume in order to compensate not only current expenses associated with production and sales, but also funds diverted into inventories, settlements with buyers, etc. The acquisition of long-term assets also requires an increase in sales volume, except for cases their acquisition with borrowed capital.

Calculation formula the volume of sales required to cover current and capital costs in cash, will look like this:

Q cr = ( F - D ± N + I) / (C pr - C lane),

where N- change in net current assets (increase - "+", decrease - "-");

I— investments in long-term assets.

Using this formula, it is possible to determine at what volume of sales in natural units the company will be able to cover current expenses in cash and make a profit sufficient to increase net current assets and planned long-term investments.

To illustrate what has been said, consider an example.

EXAMPLE 5

We use the data from the previous example for the main order. Assume that the net current assets of the company are expected to grow by RUB 1.5 million. (due to an increase in stocks of raw materials and finished products). Accrued depreciation of the company's main equipment (in fixed costs) is 500 thousand rubles.

In this case, the known sales volume (60,000 units) turns out to be clearly insufficient. That this is indeed the case, we can check using the last formula:

Q kr \u003d (2,000,000 - 500,000 + 1,500,000) / (100 - 60) \u003d 3,000,000 / 40 \u003d 75,000 pieces of products.

It follows from this: if a cumulative increase in inventory balances by 1.5 million rubles is expected, then the company will have to sell not 60 thousand pieces, but all 75 thousand pieces of products. And all in order to ensure an inflow of funds sufficient to cover current expenses (in cash) and finance an increase in current assets.

SUMMING UP

1. The greater the share in the cost structure is occupied by high-margin products (products with the maximum ratio of marginal income to price), the higher the level of marginal income in the whole company. Structural adjustment in favor of increasing the share of high-margin products contributes to the growth of sales profits.

2. To improve the sales structure and increase the profits of a company with limited resources, the priority of production of one or another type of product must be assessed based on the marginal income per unit of the limiting factor (for example, by processing time per unit of production in machine hours).

3. The acceptance by the company of an additional order depends on the influence of the effect of operating leverage, that is, on the ratio of variable and fixed costs. The influence can be positive and negative.

The positive impact of the effect of operating leverage is manifested only after reaching a sales volume at which fixed costs are covered. This covers the critical volume of sales in the company.

4. To quantify the coverage of all current cash costs of the enterprise due to sales growth, you can use a formula similar to that used to determine the critical volume of sales. In this case, fixed costs exclude expenses that are not accompanied by an outflow of cash, primarily depreciation. This formula should take into account changes in the composition of current assets (inventory) and investments in long-term assets.

When planning production, the enterprise is faced with the task of determining the volume of production, which will ensure maximum profit.

For this, two methods of optimizing the volume of production are used:

· method of comparison of gross indicators (gross income and gross costs);

· method of comparison of marginal indicators (marginal income and marginal costs).

Gross comparison method based on the calculation of profit from the sale of products at different volumes of production. Profit is defined as the difference between gross income and gross costs (Table 10.1).

Table 10.1 presents an example of calculating gross and marginal indicators for an enterprise producing a certain type of product.

Table 10.1.

Production figures

Sales volume, thousand units	Price, thousand rubles	Sales proceeds, thousand rubles	Gross indicators, thousand rubles	Limit
fixed costs, thousand roubles.	variable costs, thousand roubles.	Total costs, thousand rubles	Profit, thousand rubles	Income, thousand rubles	Costs, thousand rubles	Profit, thousand rubles
						-18
						-13
						-6

The table shows that in order to obtain the maximum gross profit, the enterprise needs to produce 7,000 products, which will make it possible to make a profit of 32,000 rubles.

You can also determine the optimal production volume graphically. To do this, we will build a graph of gross costs and gross profit (Figure 10.4).

Rice. 10.4. The optimal volume of production according to the method of comparing gross indicators.

The graph shows that when selling products in the amount of up to 2,500 pcs. production is unprofitable, since gross costs are greater than sales revenue, since the cost curve in this segment is located above the revenue curve.

When selling products in the amount of 2,500 pcs. the curve of gross costs and revenues intersect. The point of intersection of these two curves is called the "point of zero profit". When selling products in the amount of more than 2,500 pcs. the company begins to make a profit, i.e. gross costs are less than sales proceeds.

According to the method of comparing gross indicators, the optimal production volume will be achieved when selling 7,000 units. products, at which the revenue indicator reaches its maximum value of 140 thousand rubles.

Limit Comparison Method based on a comparison of marginal costs and profits. This method gives an answer to the question: what additional income will the company receive with an increase in production per unit of output? After all, the enterprise will expand production until a faster growth of income compared to the growth of costs is ensured.

To determine the optimal volume of production according to the second method, we construct a graph of marginal costs and marginal profits according to the data in Table. 10.1.

Rice. 10.5. Optimal production volume according to the method of comparison of marginal indicators.

The point of intersection of the curves of marginal revenue and marginal cost determines the optimal level of production. For our example, the optimal production volume is 7,000 pieces.

Thus, using one of the above methods, the company can determine the optimal production volume.

Test questions.

1. What factors of production are distinguished by modern economists?

2. Build a graph of a two-factor production function and give its characteristics.

3. What is the essence of the Cobb-Douglas function and what parameters determine its value?

4. What is common to all production functions?

5. Describe the relationship between the total product and the factors of production.

6. What is the average, marginal product and what is their relationship with the factors of production.

7. What is the method of comparing gross indicators based on and how is it implemented?

8. What is the basis for and how is the method of comparing marginal indicators implemented?

Literature.

1. Zaitsev N.L. Economics, organization and enterprise management. Tutorial. – M.: INFRA-M, 2008.

2. Kaverina O.D. Management accounting: systems, methods, procedures. - M.: Finance and statistics, 2004. - 352 p.

3. Sulyarenko V.K., Prudnikov V.M. Enterprise economy. Textbook, - M .: Infra-M, 2006

4. Enterprise Economics: Textbook / V.M. Semenov, I.A. baev, S.A. Terekhova and others; Ed. V.M. Semenov. 2nd ed., rev. M., 2000.

5. Economics of the enterprise: Expenses and incomes of the enterprise; Ecological and economic efficiency; Enterprise financing, etc.: Textbook for universities: Textbook / Pod. ed. Vyvarets A.D. – M.: Unity-dana, 2007.

Chapter 11. Production program and capacity of the enterprise

Manufacturing program

Manufacturing program presents a plan for the production and sale of products and determines the required volume of production in the planned period, corresponding in terms of nomenclature, assortment and quality to the requirements of the sales plan.

The production program is developed as a whole for the enterprise and for the main workshops, broken down by months, quarters, and, if necessary, determined by the content of contracts with customers, with the establishment of specific deadlines for fulfilling orders.

The guarantee of the implementation of the production program is ensured by its comprehensive justification, primarily in three areas:

§ the availability of production facilities necessary to ensure the envisaged production volume, the implementation of all production processes, technological operations;

§ presence material resources that fully meet the needs of production, or contracts with reliable suppliers-enterprises or intermediary organizations;

§ the availability of qualified specialists of all levels, and, if necessary, contracts with third parties for the performance of certain works and services.

The production program is developed at all enterprises that manufacture products for sale to consumers or perform certain types of work and services. Production volume in in kind characterized by the range and range of products

Nomenclature are called the totality various kinds goods and services. The economic entity at this stage predicts the production of various types of products.

Range - this is the composition of the types of goods produced, subdivided by types, types, varieties, etc.

The efficiency and competitiveness of the entire enterprise depend on the volume of the production program, its structure, since the production program forms the basis of the economic activity of the entity.

It is advisable to present the development of a production program as a sequence of the following stages:

1. The nomenclature and assortment of products, the volume of their deliveries in kind according to the sales plan are determined.

2. A plan and schedule for the supply of products to consumers is drawn up.

3. The volume and schedule of production of each product in physical terms is determined.

4. The volume of production is substantiated by calculations of balances of production capacities.

5. Cost indicators are calculated.

6. A program is drawn up for the shops and services of the enterprise.

The structure of the production program allows the enterprise to determine the number of necessary economic resources, to reserve capacity, to give production a systematic character.

When developing a production program, a number of indicators are used:

§ natural- the volume of output of products in physical terms - meters, tons, pieces. Based on the unit of production, technological norms for the consumption of raw materials, energy, working time are established, and the cost price is calculated. Natural meters serve to determine the need for production capacity, most correctly characterize the growth of labor productivity, but are applicable only to homogeneous products.

§ labor- the labor intensity of a unit of production and the production program in standard hours, man-hours, machine-hours.

§ cost- measurement of production and sales volumes of product groups in monetary units. This indicator is generalizing, it can be used to determine the total volume of products produced by the enterprise. In terms of value, such indicators as the volume of marketable, sold products, sales volume, etc. are planned.

A general indicator of the production program of the enterprise is the volume of sales or products sold.

Volume of sales- is the cost of goods and services produced and sold by the enterprise for a certain period of time.

Volume of products sold is one of the main indicators by which the results of the production and economic activities of the enterprise are evaluated. It is calculated by the formula:

Where - the volume of marketable products for a certain period (month, quarter, year);

The value of the balance of unsold products at the beginning and end of the same period, respectively.

Marketable products(TP) - products manufactured at the enterprise and intended for sale. Marketable products include the cost of: planned for release finished products, semi-finished products, components.

The planned volume of marketable output is calculated by the formula:

Where - the plan for the release of the i-th type of product in physical terms;

The current price of the i-th type of product;

n is the number of types of marketable products;

The volume of services and works of the j-th type;

m - the number of types of services and works of an industrial nature.

Marketable products characterize the volume of finished products produced and are used to calculate production costs, financial results, profitability and other performance indicators. This is the main indicator of the production plan and serves as the basis for calculating gross and sold products.

Gross output is the cost of the overall result production activities enterprises for a certain period of time. Gross output includes the value of all manufactured products and work performed, including work in progress. It differs from marketable output by the amount of change in the balance of work in progress at the beginning and end of the planning period.

Gross output is calculated in two ways.

First way:

Gross turnover;

Internal turnover.

Gross turnover- this is the cost of the total volume of products produced for a certain period by all departments of the enterprise, regardless of whether this product internally for further processing or was sold.

Internal turnover- this is the value of products produced by one and consumed by other shops during the same period of time.

Second way:

Where and - the value of the balance of work in progress at the beginning and end of this period.

According to the second method, gross output is defined as the sum of marketable output and the difference between the balances of work in progress (tools, fixtures) at the beginning and end of the planning period.

Unfinished production- unfinished products: parts, blanks, semi-finished products that are at work, control, transportation, in workshop storerooms in the form of stocks, as well as products not accepted by the technical control department and not handed over to the warehouse of finished products.

Work in progress is accounted for at cost. The expected balances of work in progress at the beginning of the planned year in the shops are determined from the reporting data based on the inventory.

At the end of the planning year, the standard for balances of work in progress () is calculated by the formula:

Where N days- daily output in physical terms;

FROM- cost of production, rub.;

T and - duration of the production cycle, days;

K G - work in progress readiness factor.

Gross output is calculated in current comparable prices, i.e., constant prices of the enterprise on a certain date. With the help of this indicator, the dynamics of the total volume of production, capital productivity and other indicators of production efficiency are determined.

Sold products- products that entered the market in this period and are subject to payment by consumers. The cost of goods sold is determined as the cost of finished products, semi-finished products intended for delivery and payable in the planned period. own production and works of an industrial nature intended for sale to a third party (including overhaul equipment and Vehicle enterprise, performed by industrial and production personnel), as well as the cost of selling products and performing work for its own capital construction and other non-industrial facilities on the balance sheet of the enterprise. Cash receipts associated with the disposal of fixed assets, tangible current and intangible assets, the sale value of foreign exchange values, securities are not included in the proceeds from the sale of products, but are considered as income or losses and are taken into account when determining the total (balance sheet) profit.

The volume of sold products is calculated on the basis of current prices without value added tax, excises, trade and marketing discounts (for exported products - without export tariffs). Sold products for works and services of an industrial nature, semi-finished products of own production are determined on the basis of factory contract prices and tariffs.

The volume of products sold (RP) according to the plan is determined by the formula:

Where TP is the volume of marketable products according to the plan;

He and OK- balances of unsold products at the beginning and end of the planning period.

The balance of unsold products at the beginning of the year includes:

§ finished products in the warehouse (including shipped goods, documents for which have not been submitted to the bank);

§ shipped goods, the payment deadline for which has not yet arrived;

§ shipped goods not paid for on time by the buyer;

§ the goods are in safe custody with the buyer.

At the end of the year, the balance of unsold products is taken into account only for finished products in the warehouse and shipped goods, the payment deadline for which has not yet come.

All components of sold products are calculated at selling prices: balances at the beginning of the year - at current prices of the period preceding the planned one; marketable products and balances of unsold products at the end of the period - in the prices of the planned year.

The optimal volume of production is understood as such a volume that ensures the fulfillment of concluded contracts and obligations for the production of products (performance of work) on time with a minimum of costs and the highest possible efficiency.

The most common methods for determining the optimal production volume include:

method of comparing gross indicators;

limit comparison method.

The following assumptions apply when using these methods:

The enterprise produces and sells only one product;

The purpose of the enterprise is to maximize profits in the period under review;

Only the price and volume of production are optimized (it is assumed that all other parameters of the enterprise's activity remain unchanged);

The volume of production in the period under review is equal to the volume of sales.

The above assumptions may seem rather "tough", but if we take into account that it is the price of the product and the volume of its production and sale, as a rule, that have the greatest impact on the economy of the enterprise, the use of these methods greatly increases the likelihood that right decisions.

Let us consider the essence of the proposed methods using the example of a hypothetical enterprise operating in the free competition market (the initial data are given in Table 3.3).

Table 3.3.

The volume of sales of products and the costs of its production

Sales volume, thousand pieces	Costs, thousand rubles
	permanent	variables

The method of compiling gross indicators involves calculating the profit of an enterprise with various volumes of production and sales. The calculation sequence is as follows:

the value of the volume of production is determined, at which zero profit is achieved;

the volume of production with maximum profit is determined (Table 3.4).

Table 3.4.

The volume of sales of products with maximum profit

Sales volume, thousand pieces	Price, rub.	Gross revenue, thousand rubles	Gross costs, thousand rubles	Profit, thousand rubles

In our example, zero profit is achieved with a volume of production and sales in the range of 30-40 thousand pieces. products, which corresponds to the value of gross revenue and costs, respectively, in the intervals of 1440-1920 and 1690-1810 thousand rubles. On fig. 3.1 is a graphic representation of this method.

L the BB line shows the change in gross revenue, and the VI curve shows the corresponding gross costs. Rice. 3.1 shows that sales of products in the amount of up to 37 thousand pieces. for the enterprise is unprofitable, since the curve of gross costs is located above the line of gross revenue. At the point where production is 37 thousand units, profit is zero, and gross revenue is approximately 1850 thousand rubles. With an increase in production volumes after 37 thousand pieces. gross revenue begins to exceed costs and profit (AC) appears, the maximum value of which is 1140 thousand rubles. achieved with a volume of production and sales of products in 90 thousand pieces. This is the optimal production volume in this case.