After reading this chapter, you will know:

• o decursive and anticipatory methods;
• o taking into account the impact of inflation.

Calculation of the value of an enterprise (business), like most economic calculations, is based on the calculation of interest using a decursive or anticipatory (preliminary) method and the theory of annuities.

Interest- is income in various forms from the provision of financial resources (capital) in debt or investment.

Interest rate- an indicator characterizing the amount of income or the intensity of interest accrual.

Increment factor- a value showing the ratio of the accumulated initial capital.

Accrual period- the period of time after which interest is accrued (income is obtained). The accrual period can be divided into accrual intervals.

Accrual interval- the minimum period after which part of the interest is accrued. Interest can be calculated at the end of the accrual interval (decursive method) or at the beginning (anticipatory or preliminary method).

Decursive method

Decursive interest rate (loan interest) is the ratio of the amount of income accrued for a certain period to the amount available at the beginning of this period.

When, after accruing income for a period, this income is paid, and in the next period interest income is accrued on the original amount, then the accrual formula is used simple interest rates.

If you enter the notation:

i (%) - annual loan interest rate (income); i - relative value of the annual interest rate; I - the amount of interest money paid for the period (year);

P - the total amount of interest money for the entire accrual period;

R - the amount of the original amount of money (present value);

F- accrued amount (future value);

k n - growth factor;

P - number of accrual periods (years);

d- duration of the accrual period in days;

TO - length of year in days K = 365 (366), then the decursive interest rate (i):

Hence (6.1)

Then the increase factor:

If the growth interval is less than one period (year), then

Determining the amount of the accrued amount F (future value) is called compounding (compounding).

Example. Credit 25,000 rub. issued for 3 years at a simple rate of 12% per annum. Determine the accrued amount.

According to formula (6.1):

Example. Credit 25,000 rub. issued for 182 days, an ordinary year, at a simple interest rate of 12% per annum. Determine the accrued amount.

According to formula (6.2):

Sometimes there is a need to solve the inverse problem: determine the value of the initial (current, reduced) amount R (present value), knowing what the accumulated amount should be F (future value):

Determining the value of the initial (current, reduced) amount R (present value) is called discounting (discounting).

Example. After 3 years you need to have an amount of 16,500 rubles. What amount in this case should be deposited at a simple rate of 12% per annum.

By transforming formulas 6.1-6.3, we can get

Interest rates may vary from time to time.

If during different accrual periods P , P 2 ,..., n N , different interest rates are used i 1 , i 2 ,..., i N , Where N- the total number of accrual periods, then the amount of interest money at the end of the accrual periods at the interest rate i 1 :

Where n 1 - number of accrual periods at the interest rate i 1 at the end of the accrual periods at the interest rate, etc.

Then, during JV accrual periods, the accrued amount (N- number of the last period) for any:

where the growth factor: (6.5)

Example. Loan in the amount of 250,000 rubles. issued for 2.5 years at a simple interest rate. Interest rate for the first year i = 18%, and for each subsequent six months it decreases by 1.5%. Determine the accrual factor and the accrued amount.

According to formula (6.5): k n = 1 + 0,18 + 0,5 (0,165 + 0,15 + 0.135) = 1,405.

According to formula (6.4): F = 250,000 x 1,405 = 351,250 rubles.

Inverse problem:

If p to = 1, then , (6.7)

where is the growth factor:. (6.8)

Example. Loan in the amount of 250,000 rubles. issued for 5 years at a simple interest rate. Interest rate for the first year i

According to formula (6.8): k n = 1 + 0,18 + 0,165 + 0.15 + 0,135 + 0,12 = 1,75.

According to formula (6.7): F = 250,000 x 1.75 = 437,500 rub.

When, after accruing income for a period, this income is not paid, but is added to the amount of money available at the beginning of this period (to the amount that created this income), and in the next period interest income is accrued on this entire amount, then accrual formulas are used compound interest.

If we add to the presented notations:

i c - relative value of the annual compound interest rate;

k nc - compounding factor in case of compound interest;

j- the nominal rate of compound loan interest, at which the interval rate of compound loan interest is calculated, then for the accrual period equal to a year, the accrued amount will be: . For the second period (a year later): etc.

Through P years, the accumulated amount will be:

where is the growth factor k nc equal to:

Example. Credit 25,000 rub. issued for 3 years at a compound rate of 12% per annum. Determine the accrued amount.

According to formula (6.9)

Solving the inverse problem:

where is the discount factor.

The discount factor is the reciprocal of the compounding factor:

Example. After 3 years you need to have an amount of 16,500 rubles. What amount in this case needs to be deposited at a compound rate of 12% per annum.

Comparing the accumulation coefficients when calculating simple and compound interest, it is clear that when p> 1. The more accrual periods, the greater the difference in the amount of the accrued amount when calculating compound and simple interest.

Other parameters can be defined:

P is not an integer, then the increase coefficient can be represented in two forms:

Where P - not a multiple of an integer number of compounding periods;

Where P = p c + d- the total number of accrual periods (years), consisting of integer and non-integer accrual periods; p p d- number of days of non-integer (incomplete) accrual period; K = 365 (366) - number of days in a year; i c - relative value of the annual compound interest rate.

Both options are valid, but give different values ​​due to different calculation accuracy.

Example. Credit 25,000 rub. issued for 3 years 6 months at a compound rate of 12% per annum. Determine the accrued amount.

• 1) F= 25,000 (1 + 0.12) 3.5 = 25,000 x 1.4868 = 37,170 rubles;
• 2) F= 25,000 (1 + 0.12) 3 (1 + (180: 365) 0.12) = 25,000 x 1.4049 x 1.0592 = 37,201 rub.

The annual compound interest rate i 1 , i 2 ,..., i N may vary during different accrual periods n 1 , n 2 ,..., n N .

Then the accrued amount at the end of the first accrual period (year):

In the second period (a year later):

In the n-period (for P periods (years)):

Then the increase factor:

Example. Loan in the amount of 250,000 rubles. issued for 5 years at a compound interest rate. Interest rate for the first year i = 18%, and the following year it decreases by 1.5%. Determine the accrual factor and the accrued amount.

According to formula (6.14): k nc = (1 + 0,18)(1 + 0,165)(1 + 0,15)(1 + 0,135)(1 + 0,12) = 2,0096.

According to formula (6.13): F = 250,000 x 1.75 = 502,400 rub.

Inverse problem:

If compound interest is calculated at intervals, i.e. several times during the period, then the accrual formula for the interval

Where j = i - nominal rate of compound interest; T - number of accrual intervals in the period (quarterly, monthly, etc.).

The income for the interval is added to the amount of money available at the beginning of this interval.

Then the accrued amount during interval accrual for each period through P periods (years) will be

In addition, you can define other parameters:

Example. Credit 25,000 rub. issued on n = 3 years at a compound rate of 12% per annum, payment semi-annually t = 2. Determine the accrued amount.

According to the formula (6/16) .

If the number of compounding periods P is not an integer, then the increase coefficient can be represented as

Where p p - the number of whole (full) periods (years) of accrual; R - the number of whole (full) accrual intervals, but less than the total number of intervals in the period, i.e. R< m;d - the number of days of accrual, but less than the number of days in the accrual interval.

Example. Credit 25,000 rub. issued for and = 3 years 8 months, 12 days at a compound rate of 12% per annum, payment semi-annually T = = 2. Determine the accrued amount.

Essence and features of initial capital

Definition 1

The capital of an enterprise includes the amount of resources that are invested (advanced) in the economic activities of the entity and ensure its activities in the process of obtaining certain income.

The most common forms of initial capital are:

• monetary (financial) form,
• material and immaterial form.

The total amount of capital in monetary form is reflected on the liability side of the balance sheet; it determines the sources of financing of the enterprise.

The following features of capital exist:

• capital is a mandatory element that ensures the stable functioning and development of production;
• the amount of capital determines the market value of the company,
• initial capital reflects the volume of net assets that are formed from the company’s own funds, while borrowed funds are used to expand and modernize production.

Capital classification

Capital is classified according to certain criteria. In accordance with the form of ownership, there is equity capital (belongs to the company by right of ownership) and borrowed capital (raised to finance the company’s activities).

In accordance with the time of use, capital is divided into:

• short-term (for a period of up to a year),
• medium-term (from one to three years),
• long-term (more than three years).

According to the degree of liquidity there are:

• working capital in constant circulation.
• fixed (permanent) capital.

Sources of capital formation can be external and internal:

• Internal revenues can be generated in the process of enterprise activity (depreciation, profit, reserve funds, income from issue, etc.).
• External revenues can be generated as a result of raising borrowed funds by obtaining bank or commercial loans, as well as leasing or factoring.

Value of initial capital

Definition 2

Initial capital represents the funds that must be at the disposal of any business entity to start a business.

The presence of initial capital is a decisive condition for the creation of an enterprise, since it can provide financing for the necessary production elements. The structure and amount of initial capital largely depend on the specifics, goals and projected scale of the company's activities.

Note 1

Basically, the initial capital provides the minimum needs: the purchase of the necessary types of property, as well as the availability of funds, which should be sufficient to fulfill financial obligations.

Formation of initial capital

The formation of initial capital begins with the accumulation of own funds (savings of legal entities, existing fixed assets, other material assets, as well as current funds in bank accounts). Equity capital ensures the financial potential of the enterprise and is the main source of property financing.

The fundamental factor in starting any enterprise is a sufficient amount of initial capital. Initial capital is a fundamental factor in financial independence.

The following can be included in equity capital:

1. Authorized capital formed at the time of creation of the company and remaining at its disposal throughout its existence;
2. Reserve capital, which represents the company's insurance fund necessary to cover losses or payments;
3. Additional capital, which includes funds from special purpose funds, as well as targeted revenues and financing;
4. Retained earnings (uncovered losses) generated in the previous period and not used for consumption.

Sources of initial capital formation

Introduction

1. Characteristics and essence of capital

3. Sources of initial capital formation

Conclusion

Glossary

“The capital factor is presented in the balance sheet in a special way: in the liability side - as capital-property, which gives a certain idea about the owner of a given company, the structure of its capital (the ratio of equity and debt capital). Hence an important corollary: the structure of capital is the essence of the structure of power. This is an expression of the first role of capital as money that brings new value to its owners.”

The substantive side of the process of obtaining new value is expressed in an asset, where capital is represented in its second role: capital-function. It is she who gives a clear idea of ​​the company’s profile, its technological specifics and many other business characteristics that distinguish it from other companies. Two hypostases of capital make it possible to use the terms of capital and its components, characterizing it as property on the right side of the balance sheet (authorized, additional capital, etc.) and as a function on the left side of the balance sheet (fixed, working capital).

“Capital management is a system of principles and methods for developing and implementing management decisions related to its optimal formation from various sources, as well as ensuring its effective use in various types of economic activities of a trading enterprise.”

Enterprise capital management is aimed at generating a sufficient amount of capital to ensure the necessary pace of economic development of the enterprise. This task is implemented by determining the total capital requirement to finance the assets required by the enterprise, developing schemes for financing current and non-current assets, developing a system of measures to attract various forms of capital from the provided sources.

The level of efficiency of the enterprise's upcoming economic activities is largely determined by the targeted formation of its capital.

“The main goal of forming an enterprise’s capital is to attract a sufficient volume of capital to finance the acquisition of the necessary assets, as well as to optimize its structure from the standpoint of ensuring conditions for subsequent effective use.”

In the management system of capital formation of an enterprise, an important role belongs to the justification of the scheme and the choice of sources of its financing.

2. Features of the formation of initial capital

Forming initial capital for all business entities is a complex task and requires determining its optimal size, sources of financing, as well as the most profitable placement in terms of generating future income.

It should be emphasized that the volume and structure of initial capital largely depend on the specifics of the activity, its projected scale, and the intended goal. It is these and other features of the subject that influence the value of the property, its structure, and therefore the volume of financial resources. For example, for manufacturing enterprises, funds are necessary for the acquisition of fixed assets (machinery, equipment, structures), the creation of certain reserves of raw materials, materials and other valuables. For trading companies, the decisive share of funds is allocated to the purchase of necessary goods, vehicles, the creation of warehouse and retail premises or their rental.

“Therefore, there cannot be a single general approach to the formation of the initial capital of business units, but at the same time there are general rules, the main issues that must be observed and resolved when performing proper management actions.” These include:

1) a clear definition of the scope of activity of the new business unit, its size, and its purpose of operation;

2) justification of the optimal structure of initial capital and the main directions of its use, ensuring the start of economic activity;

3) identifying sources of initial capital formation, optimizing their structure, as well as creating a rational system for the accumulation and use of relevant resources.

All these actions are interconnected and must be carried out taking into account the real situation, specific opportunities, social needs, and the economic interests of the entrepreneur himself. At the same time, the possibility of accumulating an appropriate amount of initial capital limits the scale and sometimes the scope of a new business. There are many examples of business in all countries of the world, but in each specific case they depend on the availability of initial capital, its volume, structure, and possibilities for its expansion. In this case, part of the capital can be formed in the form of property, i.e. available to the owner of buildings, premises, related furniture, equipment, tools and other valuables that may be suitable for the proposed activity. If an entrepreneur does not have at his disposal the necessary fixed assets, as well as raw materials, materials, fuel for the production of products or other types of activities, then he must purchase (sometimes rent) them. In addition, already at the initial stage of formation, business organization also requires money to pay for a number of mandatory services. These include, first of all, notary, transport, utility services, advertising, and, if there are employees, remuneration.

“It should be remembered that the formation of initial capital is a responsible task, the first stage of effective management of a business entity. Its successful implementation requires not only simple arithmetic calculations, but also a reasonable justification of economic decisions to optimize the volume of necessary resources, the size and structure of the initial capital.”

Having calculated the volume of initial capital - the basis for creating and starting to operate a new business, it is necessary to solve no less complex problems, where to get these resources, i.e. find sources of funding.

The easiest way to solve the problem of forming initial capital is when the entrepreneur has his own funds: money, securities, property that can be used in production, sold or exchanged for the necessary resources. Cash can take the form of personal savings, deposits, various deposits in banks, financial companies, and joint ventures. Monetary resources also include securities, i.e. documents confirming the property rights of the owner or the relationship regarding the loan of funds.

The most common securities that should be considered a source of financing initial capital include shares issued through joint stock companies. These securities are part of the total share capital, which is formed through contributions of cash and property of shareholders. Their total value must correspond to the total amount of share capital approved by the status of the company (in an amount not less than that established by law). Shares not only confirm the shareholder's ownership of part of the initial capital, but also provide them with broad rights in managing the enterprise. At the same time, responsibilities arise that arise from co-ownership of the property of a joint-stock company.

For limited liability companies (LLC), the initial capital is created mainly from the contributions of its partners. Each of them becomes a co-owner of the property of this company, recognized as its inseparable part. LLC participants are responsible before the law only for their contribution; debt on financial obligations is repaid from the common resources (property) of the entire limited liability company.

State enterprises and organizations form their initial capital at the expense of the budget, a special fund, as well as land plots, buildings, structures, equipment and other assets provided at their disposal free of charge. Thus, the own sources of financing for enterprises of different types of property are varied. In general they are presented in table. 2.

Table 2. Initial capital (own sources)

In a transformational economy, especially during the period of denationalization and decentralization of state-owned large enterprises, equity capital becomes the most important source of formation of initial capital. It is he, like the contributions (contributions) of voluntarily uniting individuals and legal entities to limited liability companies, cooperatives, joint ventures, that expands the real possibilities of increasing the size of the initial capital, extends responsibility for its effective use to all members of the organization.

This also applies to joint ventures in which a certain share of capital is formed from contributions (investments) of foreign partners. This form of activity is very promising for revitalizing the economy, expanding the possibility of modernizing production, and improving its technology. Essentially, it helps to increase the volume of initial capital through cash, know-how, sometimes modern equipment, advanced raw materials, and technologies.

“Own sources of financing the initial capital will include only that part of the deposits that is the property of domestic partners. The rest of the resources should be classified as borrowed funds, since the company (company) subsequently pays for their use with its foreign partners from general income.”

There are rare cases of gratuitous financial assistance from other enterprises and sponsors, whose funds can also be classified as their own sources of financing. In practice, such cases are very rare in domestic practice; isolated cases occur when creating enterprises for people with disabilities, student workshops or public organizations.

In many cases, there are not enough own resources to generate initial capital in the required amounts to start an activity. In such situations, entrepreneurs and firms are forced to buy additional resources from banks, financial companies or other organizations. In countries with developed market economies, these funds, as a rule, occupy a significant share in the formation of the initial capital of many economic entities. This is facilitated by stable rules for issuing and repaying loans, many credit institutions offering a variety of services for a reasonable fee, and the general economic situation in these countries.

During the period of formation of a market economy, the need of a significant group of entrepreneurs to acquire borrowed funds to create and operate their business increases. However, it is still very difficult to implement it. In most cases, loans are issued by banks for a short period of time at high interest rates and must be secured by significant collateral or a guarantee. The procedure for processing and issuing loans remains quite labor-intensive and expensive for the lender and the borrower.

Sources for the formation of initial capital of individual business entities can also be special funds that provide newly created units with part of their resources on preferential terms. They are distinguished by their great diversity, terms of provision of funds, and their targeted nature.

The most common are venture capital and investment funds that direct funds to create new venture firms, finance high-tech projects, and partially cover the risk of related operations. In many cases, special funds for the development and assistance of entrepreneurship at the macro- and microeconomic levels are also formed.

In recent years, a number of international funds have been created and actively used throughout the European Community, as well as throughout the world, which provide resources for the development of entrepreneurship free of charge or on preferential lending terms. For example, in Poland a special Polish-American Entrepreneurship Fund (PAEF) was created in 1990, which promotes the development of the private sector. This fund operates as a non-profit organization and has many companies that finance various investment projects and also provide loans to private entrepreneurs.

In most CIS republics, special funds for the development of entrepreneurship are formed (at the expense of budgetary funds, special allocations), which are also intended to provide financial support to newly created and developing small businesses. However, their size is still small, which largely reduces the chances of their widespread use to form the initial capital of new business units.

This largely applies to the formation of other special funds, as well as attracting investments from foreign partners. Only in conditions of stabilization of the economic situation in the relevant countries, the formation of a favorable financial policy that stimulates the expansion of entrepreneurial activity and investment, will there appear real conditions for expanding the sources of initial capital formation, and therefore the possibility of creating and successfully functioning of a large number of business entities.

Thus, when forming the capital structure of an enterprise, two main schemes for its financing are usually considered - full and mixed financing.

“Full self-financing provides for the formation of capital of the created trading enterprise exclusively at the expense of its own types, corresponding to the organizational and legal forms of the new business.”

“Mixed financing involves the formation of an enterprise’s capital at the expense of both its own and borrowed types, attracted in various proportions.”

The choice of an organization’s financing scheme is inextricably linked with taking into account the peculiarities of using both equity and borrowed capital.

Own capital is characterized by the following main positive features:

1.Simplicity of attraction, since decisions related to increasing equity capital (especially through internal sources of its formation) are made by the owners and managers of the enterprise without the need to obtain the consent of other economic entities.

2. Higher ability to generate profits in all areas of trading activity, because when using it, payment of loan interest in all its forms is not required.

3. Ensuring the financial sustainability of the development of a trading enterprise, its solvency in the long term, and, accordingly, reducing the risk of bankruptcy.

However, it has the following disadvantages:

1.Limited volume of attraction, and therefore the possibility of significantly expanding the operating and investment activities of a trading enterprise during periods of favorable market conditions at certain stages of its life cycle.

2.High cost in comparison with alternative borrowed sources of capital formation.

An unused opportunity to increase the return on equity ratio by attracting borrowed funds, since without such attraction it is impossible to ensure that the financial profitability ratio of the enterprise's activities exceeds the economic one.

Borrowed capital is characterized by the following positive features:

1. Quite wide opportunities for attraction, especially with a high credit rating of the trading enterprise, the presence of collateral or a guarantor’s guarantee.

2. Ensuring the growth of the financial potential of a trading enterprise if it is necessary to significantly expand its assets and increase the growth rate of the volume of its commercial activity.

3. Lower cost in comparison with equity capital due to the provision of a “tax shield” effect (withdrawal of costs for its maintenance from the tax base when paying income tax).

4. The ability to generate an increase in financial profitability (return on equity ratio).

At the same time, the use of borrowed capital has the following disadvantages:

1. The use of this capital generates the most dangerous financial risks in the economic activities of a trading enterprise - the risk of reduced financial stability and loss of solvency. The level of these risks increases in proportion to the increase in the proportion of use of borrowed capital.

Assets formed from borrowed capital generate a lower (other things being equal) rate of return, which is reduced by the amount of loan interest paid in all its forms (interest for a bank loan; leasing rate; coupon interest on bonds; bill interest for a trade loan and etc.).

3. High dependence of the cost of borrowed capital on fluctuations in financial market conditions. In a number of cases, when the average lending interest rate in the market decreases, the use of previously obtained loans (especially on a long-term basis) becomes unprofitable for a trading enterprise due to the availability of cheaper alternative sources of credit resources.

4. The complexity of the attraction procedure (especially on a large scale), since the provision of credit resources depends on the decisions of other economic entities (creditors), requires in some cases appropriate third-party guarantees or collateral (in this case, guarantees from insurance companies, banks or other economic entities are provided, usually on a paid basis).

Conclusion

To summarize, it should be noted that the formation of initial capital for all business entities is a complex task and requires identifying sources of financing.

The easiest way to solve the problem of forming initial capital is when the entrepreneur has his own funds.

Own sources of financing of initial capital will include only that part of deposits that is the property of domestic partners. The rest of the resources should be classified as borrowed funds, since the company (company) subsequently pays for their use with its foreign partners from general income.

Thus, an enterprise that uses only its own capital has the highest financial stability (its autonomy coefficient is equal to one), but limits the pace of its development (since it cannot ensure the formation of the necessary additional volume of assets during periods of favorable market conditions) and does not use financial opportunities to increase profit on invested capital.

Thus, an enterprise using borrowed capital has a higher financial potential for its development (due to the formation of an additional volume of assets) and the possibility of increasing the financial profitability of its activities, but to a greater extent generates financial risk and the threat of bankruptcy (increasing as the share of borrowed funds increases in the total amount of capital employed).

Glossary

Capital is a stock of economic goods accumulated through savings in the form of cash and real capital goods, involved by its owners in the economic process as an investment resource and a factor of production in order to generate income.

Initial capital is associated with the funds that any business entity must have in order to start its business activity. It acts as a decisive condition for the creation and start of operation of an enterprise, since it ensures the formation of mandatory elements of production.

Full self-financing - provides for the formation of capital of the created trading enterprise exclusively at the expense of its own types, corresponding to the organizational and legal forms of the new business.

Mixed financing - provides for the formation of the enterprise’s capital at the expense of both its own and borrowed types, attracted in various proportions.

Capital management is a system of principles and methods for developing and implementing management decisions related to its optimal formation from various sources, as well as ensuring its effective use in various types of economic activities of a trading enterprise.

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The capabilities of the enterprise will be clear when they analyze the capital requirements necessary for the practical implementation of some entrepreneurial idea or project.

For example, if we are able to choose what to produce - furniture or children's toys made of wood - we can make one or the other decision depending on the amount of capital. If we have the opportunity to receive 1 million monetary units as initial capital, then we may decide to start producing furniture; If our capabilities are limited to only 50 thousand monetary units, then we will decide to start producing children's toys from wood.

The structure of the initial capital depends on the enterprise's needs for equipment, raw materials, etc., necessary to begin the normal production process. To create the necessary capital structure, an entrepreneur:

A) acquires all technical elements of production (buildings, structures, equipment, transport, etc.) (T/e);

B) purchases raw materials, tools (C);

C) creates a reserve of funds to pay wages during the first production cycle (from the start of production until the receipt of payments for sold products) (Salary);

D) creates a reserve fund (R/f).

At the same time, the manufacturer determines the size of the required initial capital: for T/e, 200 thousand monetary units are needed (100 thousand for the building, 50 thousand for equipment, 50 thousand for adapting the building to the specific needs of production), for C - 50 thousand monetary units, for salary. 25 thousand monetary units, total - 300 thousand monetary units.

Rice. 2.1 "Determining the amount of initial capital."

T/e. With salary R/f

200 thousand 50 thousand 25 thousand 25 thousand

Identification of the economic efficiency of future production.

Any investment in production is an advance investment. It is important for an entrepreneur to find the answer to the question of how, in what form and within what time frame the advance can be returned. The return of capital advanced into production is possible only through identifying the amount of profit received in the process of production and sale of products. An entrepreneur must know what the payback period of the project is.

However, the entrepreneur is interested not only in the return period of the invested capital, but also in the rate of capital increase, which is associated with the need to identify net profit. In order to determine the possible amount of net profit from the implementation of this idea, the entrepreneur carries out business calculations. Calculations are based on two immutable requirements:

1 accounting of all possible expenses;

2 accounting for income at the minimum acceptable level and accounting for expenses at the maximum acceptable level to reduce the degree of risk.

Of course, this approach should be based on taking into account the real situation. Calculations will include:

1 determination of possible income;

2 calculation of possible expenses;

3 identification of net income.

Each entrepreneur will use his own methodology when making calculations.

For example.

Figure 2.2 "Structure of possible income and expenses:"

A b c d e f h i j l m n o p

A - depreciation charges on the cost of all technical elements used in the production process

B - property tax (limit amount 0.5% of the book value of all property of the enterprise);

B - road tax (local tax levied in those regions whose local authorities have made such a decision; road tax in Moscow is 0.4% of the price of the purchased product);

D) cost of raw materials per one commodity unit;

D) road tax on purchased raw materials;

E) the planned wage fund per one commodity unit;

G) payroll tax (37% of the amount to be paid as wages;

3) payments to the employment fund (local tax, in Moscow - !% of the accrued wage fund;

I) VAT regarding the paid salary fund. together with all payments from this fund, i.e. 28% of the amount (e+f+h);

K) planned profit;

K) VAT regarding the planned profit (28% of K);

M) income tax (32% of the amount k + l);

H) additional profit;

O) VAT on additional profit (28% of n);

P) income tax in terms of additional profit (32% of the amount n + o).

The separate inclusion of planned profit and additional profit is methodically justified, because otherwise the entrepreneur will rely on the “residual principle” of identifying the profitability of production. In this case, he consciously plans the minimum acceptable level of profit for him, at which production will be considered expedient.

When thinking about the problem of establishing an enterprise, an entrepreneur first of all strives to predict the profitability of a future project. At the same time, the identified profit margin will allow the entrepreneur to come to the conclusion that the project is profitable. Typically, a new entrepreneur uses borrowed (not equity) capital. This means that when making calculations it is necessary to take into account the fee for using such borrowed funds (loan interest).

Tax problems

The tax pressure of the state and local authorities does not act as a stimulator, but quite often as a brake on the development of entrepreneurship. Entrepreneurs often seek to “evade taxes” in such a situation, taking advantage of the opportunities provided to them by current legislation or simply hiding their income. Many of these methods are known.

The burden of income tax can be eased in two ways: either take advantage of benefits, or try not to show profits in reporting. The possibilities of using the first method are limited due to the abolition of most benefits. There are quite a few tricks to hide profits. The most common is inflating costs, which include not only profits, but also consumer expenses of the owners and employees of the company. At the same time, this allows you to save on contributions to social insurance and the pension fund, as well as on income tax, since in this case there is “payment in kind”. The company maintains apartments for its managers (under the guise of “office premises”), company vehicles, buys furniture, consumer electronics, subscribes to newspapers, magazines, etc., etc. Some companies purchase “uniforms” for their employees (fur coats, sheepskin coats, leather jackets, suits, boots, etc.). As a result of all this, a thriving company may appear low-profitable or even unprofitable in its reporting.

There is another method of concealing profits from taxation: the client pays for the goods in the form of a targeted payment to your development fund (i.e. to already distributed profits). However, since 1992, tax inspectors have counted these amounts as sales revenue, and therefore targeted payments have to be sent somewhere else (for example, to create some kind of charitable organization - a self-help fund), but this is much more complicated.

From progressive income tax and salary fund. you can also dodge. There are proven techniques for avoiding taxes on excess profitability. The most common of them are: “side contract”, when a front company, usually owned by the same owners as the main enterprise, is involved as a co-executor of the work. For the main enterprise, payment for the services of a co-executor of the contract is included in the costs, which reduces profitability to the required level. In a similar way, it is possible to avoid taxes on excess of the standard amount of funds for wages: the same person receives a salary for the same work at several enterprises. A more complex version is called "Russian nesting doll". Its essence is that the same product or service on its way to the consumer passes through several colluding enterprises. Each of them increases its costs and artificially reduces the level of profitability to the level taxed at the minimum tax rate.

And finally, the most radical way of tax evasion is to conceal income and expenses from any accounting at all during cash transactions. The procedure for turning non-cash money into cash, and unaccounted for it, is called “cashing out.” In order to have unaccounted cash, it is necessary to collect it from the buyer and show it as expenses.

Under strong pressure from the existing tax system, a special structure of domestic business is being formed - a small business group consisting of several firms connected with each other not only by permanent partnerships, but also by a unique system of participation: their co-owners, as a rule, are the same persons. The key figure in a business group is often the informal president of one of the firms, and the person in charge of financial operations (financial director or chief accountant). The enterprises included in the group have inflated production costs, enormous inventories and fixed assets. Most of the personnel work for them under contract contracts, often holding their main jobs in the public sector of the economy. The bulk of wages and business income is paid in kind or through cash.

Basic concepts and definitions of financial mathematics:

Interest– income from the provision of capital in debt in various forms (loans, credits, etc.), or from investments of an industrial or financial nature.

The initial amount of money (present, modern, current, reduced) is the amount of capital available at the initial point in time (or the amount of capital invested in the operation in question).

Interest rate– a value characterizing the intensity of interest accrual.

Extension (compounding)– an increase in the original amount of money by adding accrued interest.

Accrued (future) amount of money– the original amount of money plus accrued interest.

Discounting– determination of the current financial equivalent of a future monetary amount (bringing a future monetary amount to the present time).

Increment factor– a value showing how many times the initial capital has grown.

Accrual period– the period of time during which interest is calculated. It can be expressed in days or years, and can be either an integer or a non-integer.

Accrual interval– the minimum period of time after which interest is calculated. An accrual period can consist of one or more equal accrual intervals.

Time base for calculating interest T - the number of days in a year used to calculate interest. Depending on the method of determining the duration of a financial transaction, either exact or ordinary interest is calculated.

The following options are possible:

There are several ways to calculate interest and, accordingly, several types of interest rates. Depending on the accrual method used, financial results can vary quite significantly. In this case, the difference will be greater, the greater the invested capital, the applied interest rate and the duration of the accrual period.

The following diagram gives a general idea of ​​the different methods of calculating interest:

Interest calculation methods

Decursive

Antisipative

Simple p/s

Complex p/s

Simple p/s

Complex p/s

Accrualn times a year

Continuous Interest

The most common is decursive method of calculating interest. With this method the interest I accrued at the end of each accrual interval. Their value is determined based on the amount of capital provided P. Decursive interest rate (loan interest) i represents the ratio, expressed as a percentage, of the income accrued for a given interval (percentage) to the amount available at the beginning of this interval. The interest rate characterizes the intensity of interest accrual.

This incremental operation corresponds to the following mathematical expression:

S = P + I = P + iP = P (1 + i)

The inverse of this operation is the operation discounting, i.e. determining the current value P equivalent to the future amount S:

P = S / (1 + i)

From the point of view of the concept of time value of money, for a given interest rate, the amount P And S are equivalent, we can also say that the sum P is current financial equivalent future amount S.

At antiseptic(preliminary) method, interest is calculated at the beginning of each accrual interval. The amount of interest money is determined based on the amount of future money. Anticipatory interest rate (discount rate) d there will be a percentage ratio of the amount of accrued income to the future amount of money.

In this case, the formula for determining the amount of the accrued amount is as follows:

S = P + I = P / (1 - d)

Accordingly, for the discounting operation, called in this case bank accounting:

P = S (1 - d)

In practice, anticipatory interest rates are usually used when discounting bills of exchange. The interest income received in this case is called a discount - a discount on the future amount.

With both calculation methods, interest rates may be simple, if they apply to the same initial monetary amount throughout the accrual period, and complex, if after each interval they are applied to the amount of the initial capital and interest accrued for the previous intervals.

Formulas for determining the future amount of money for various options for calculating interest for a period n years:

S = P (1 + ni) - for the occasion simple decursive interest

S = P (1 + i) n - for the occasion compound decursive interest

S = P / (1 - nd) - for the occasion simple anticipatory interest

S = P / (1 - d) n - for the occasion compound anticipatory interest

If the accrual period is expressed in days, the simple interest formulas will take the form:

S = P (1 + t/T i)

S = P / (1 – t/T d),

where t is the duration of the accrual period.

Multipliers showing how many times the future amount of money is greater than the amount of initial capital are called accumulation factors. The inverse of the accumulation factors are discount factors, which make it possible to determine the current financial equivalent of a future monetary amount.

In some cases, when analyzing the performance of various financial transactions, it may be useful to determine equivalent interest rates. Equivalent interest rates– these are interest rates of different types, the application of which under the same initial conditions gives the same financial results. In this case, the same initial conditions mean the same amount of initial capital and equal periods for accrual of income. Based on this, one can draw up equivalence equation and derive the ratio for the rates in question.

For example, for simple lending and discount rates such ratios will look like this:

d = i / (1 + ni); i = d / (1 - nd).

The lending rate equivalent to the discount rate reflects the profitability of the corresponding accounting transaction and is useful in comparing the profitability and efficiency of various financial instruments.

Accounting for inflation in financial calculations

Inflation is characterized by a decrease in the purchasing power of the national currency and a general increase in prices. The inflation process affects different participants in a financial transaction differently. Thus, if a lender or investor may lose part of the planned income due to depreciation of funds, then the borrower has the opportunity to repay the debt with money of reduced purchasing power.

In order to avoid errors and losses, inflationary effects must be taken into account when planning financial transactions.

Let us denote by S a the amount whose purchasing power, taking into account inflation, is equal to the purchasing power of the amount S in the absence of inflation. Inflation rate a is the relationship between the inflationary change of a certain value for a certain period and its initial value, expressed as a percentage (a relative indicator is used in calculations):

a= (Sa- S) / S 100%

From here: Sa = S (1 +a)

This means that at an inflation rate of a, prices rise over the period by (1 + a) times. The multiplier (1 + a) is called the inflation index I a.

If the period under consideration consists of several intervals, at each of which the inflation rate is a value, prices as a whole will increase by a factor of (1 + a) n. The overall result is expressed by the following ratio:

Sa= S (1 + a) n

This leads to the first important conclusion regarding the inflation process:

Inflationary growth is similar to the increase in initial capital according to the rule of compound interest. Only in this case we do not receive income, but lose it.

Another useful consideration is calculating the rate of return that could offset inflationary losses and provide capital gains.

Let a be the annual inflation rate,

i – desired profitability of a financial transaction (cleared of the influence of inflation)

i a - rate of return compensating for inflation.

Then for the increased amount S, which under inflation conditions will turn into the amount S a, we can write the following expression:

S a = P (1 + i) (1 + a)

The same result can be obtained in another way:

S a = P (1 + i a)

Equating the right-hand sides of the written equalities, we obtain an expression for calculating i a:

ia = i + a + ia

This is the well-known formula of I. Fisher, in which the quantity (a + i a) is "inflation premium" - a necessary addition to compensate for the impact of inflation.

Now we can formulate the second important conclusion:

To calculate the interest rate that compensates for inflation, to to the required rate of return it is necessary to add not only the value of the level inflation, but also the productia.

In real practice, a modification of this formula often turns out to be useful, allowing one to find the real profitability of an operation in conditions of inflationary price increases:

i = (ia - a) / (1 + a)

Most transactions related to capital investment imply in the future not a lump sum receipt of an increased amount, but a whole cash flow of income over a certain period. The main parameters of interest to the investor or lender in this case are the current (present) value of the cash flow, its future (increased) value, as well as the profitability of the financial transaction.

We will use the following notation:

P – the amount of invested capital,

CF k – value of the k-th element of cash flow,

i – discount rate (usually a compound interest rate),

A – present value (cost) of cash flow,

S – future value of cash flow,

n – number of cash flow elements.

Present value cash flow is the sum of all its elements reduced (discounted) to the present time:

A = CF 1 / (1 + i) + CF 2 / (1 + i)? + … + CF n / (1 + i) n

Likewise, future value cash flow is the sum of its accrued elements at the time of the last payment:

S = CF 1 (1 + i) n-1 + CF 2 (1 + i) n- ? + … + CF n

Profitability of a financial transaction This is called a decursive interest rate, when discounted at which the present value of the cash flow of income coincides with the amount of invested capital: P = A. To find such a rate, in the general case, you have to solve an equation of the nth degree.

The values ​​of the accumulation and discounting factors in the case of using complex decursive rates can be found in the special tables given in the appendix.

To determine the profitability of a short-term financial transaction (less than one year), a simple interest rate is usually used; for a long-term transaction, a complex one is used.