(this situation is typical for countries with developed market economies) they also use an approximate version of the Fisher formula.

What determines the Fisher formula

What value in the Fisher formula is called the inflationary premium

In what cases can you use an approximate version of the Fisher formula

Who is more profitable to use an approximate version of the Fisher formula in the contract for the lender or the borrower

Solution. To determine the desired interest rate, we use the Fisher formula (111) with r = 0.16 and h = OD

Note that when solving this example, formula (46) could also be used. Obviously, the Fisher formula also allows us to answer the questions of the example. In particular, substituting into it the values ​​of the interest rate and inflation of the first case (in the notation of the Fisher formula F = 0.45, /r = OD5), we obtain the equation 0.45 = r + OD5 + 0.15r, whence

Using the Fisher formula, determine the real profitability of a financial transaction if the interest rate on deposits for 12 months is 15%, and the annual inflation rate is 10%.

A more accurate relationship between interest rates and inflation is provided by Fisher's formula.

The results of such calculations can vary significantly. One of the methods for obtaining a single result is to construct a geometric mean of two territorial indices of the physical volume of production (Fischer's formula)

For task No. 8, we introduce the condition that the annual real interest rate was 80%, and the nominal one increased to 250%. Determine the inflation rate (to complete the task, find in the sources educational literature expression of the Fisher formula).

To avoid unreasonably high interest payments, it can be recommended when concluding loan agreements to provide for a revision of the interest rate depending on inflation. One of the possibilities of this kind is to fix in the loan agreement not a nominal, but a real interest rate (see Appendix 1), in order to increase it (according to the Fisher formula) in the calculation and payment of interest in accordance with the inflation that actually took place during this time .

Calculate the price and volume indices using the Fisher formula

Fisher did not find a perfect formula; there was not a single average that simultaneously met the proposed tests. However, this only confirmed his initial assumption that there is no ideal formula for the average index. The best was the formula, which is a combination of the Laspeyres and Paasche indices. It is called the ideal Fisher index.

What then lies main reason obtaining strange results when calculating according to different formulas, Fisher argued that the main errors accumulate at the stage of grouping goods into aggregated groups.

Fisher's formula is incorrect under the gold standard because it ignores the intrinsic value of money. However, when paper money is in circulation, which cannot be exchanged for gold, it acquires a certain meaning. Under these conditions, a change in the money supply affects the level of commodity prices, although, of course, I. Fischer idealized the price mechanism to a certain extent, since he assumed absolute elasticity of commodity prices. Fisher, like other neoclassicists, proceeded from perfect competition and extended his conclusions to a society in which monopolies dominated and prices had already largely lost their former elasticity.

The new equation of exchange is a variation of the quantity theory of money and therefore shares all its advantages and disadvantages. Of course, means of payment are an organic component of the modern money supply, however, it follows from the Fisher formula that they directly and directly affect commodity prices, which is not true.

M/P)° = /.(/, Y), since with an increase in income Y, the accumulated wealth of the individual W increases, and the Fisher formula / = r + jf tells us that with an increase in the inflation rate, nominal interest(opportunity cost of holding liquidity) and, accordingly, the demand for money falls.

Fisher's formula makes sense only with a gold coin standard; when switching to paper money circulation, it loses its meaning (yes).

Fisher's formula - the so-called ideal formula involves the calculation of the stock index using the geometric mean of the indices calculated on the basis of the Laspey-Rese and Paasche formulas.

West enjoy mathematical formula, proposed by the American economist I. Fisher, showing the dependence of the price level on the money supply MV = PQ, where M is the money supply V is the velocity of money P is the level of commodity prices Q is the number of circulating goods. In accordance with this formula, the level of commodity prices is determined by the formula / == Ml f/Q, i.e. the product of the mass of banknotes by the speed -Ax of circulation, divided by the number of goods, the volume of money mabs M = PQ / F. Based on this formula, Fisher concludes that the value of money is inversely proportional to its quantity. I. Fisher's equation of exchange MV = PQ expresses quantitative dependencies between the sum of commodity prices and the circulating money supply.

This formula more accurately reflects the effectiveness of investing funds in GKOs with their subsequent reinvestment over the entire 1 year, but only under conditions of a stable market and little changing prices for bonds of each issue. With inflation and fluctuations in interest rates, the real rate of return of a particular GKO issue can be calculated using the Fisher formula considered earlier

For understanding Fisher's concept, it is very important that the author formed it in order to find easy way and quick calculation of indices, and one of the informal requirements for the index formula, Fisher considered the following index to be simple and understandable for the uninitiated.

There are quite a few errors associated with the calculation of inflation. Shares, the most common of them, is the calculation of inflation not according to the Fisher formula, but according to the approximate formula K - N-I. Let's look at an example of what this leads to at various levels of inflation.

Mathematically, Fisher's Equation The equation looks like this:

real interest rate + inflation = nominal interest rate;

Here R is the real interest rate;
N is the nominal interest rate;
Pi - ;

The Greek letter Pi is commonly used to represent . It should not be confused with the pi constant used in geometry.

For example, if you put a certain amount of money in a bank at 10% per annum, with an inflation rate of 7%, then the nominal interest rate under such conditions will be 10%. Real rate will be only 3%.

Application of the Fisher Equation in Economics

If inflation is taken into account, then this is not a real interest rate, but a nominal rate that is adjusted or changes with inflation. The inflation rate used in evaluating the equation is the expected rate of inflation over the life of the loan. In Fisher's theory, the hypothesis was put forward that the count should be constant. The rate of inflation is taken into account differently when determining the interest rate of a loan within areas affected by current activities, technology and other world events that affect the real economy.

This equation can be applied both before the conclusion of the contract, and after the fact, that is, as a loan analysis. If the equation is used to evaluate credit ex post. For example, it can help determine purchasing power and calculate the cost of a loan. It is also used to help lenders determine what the interest rate should be. When using this formula, lenders can take into account the planned loss of purchasing power, and therefore set favorable interest rates.

The Fisher equation is commonly used in estimating investment amounts, bond yields, and ex post investment calculations.

Fisher also owns, which determines the dependence of the price and the amount of money in circulation. Many economic indicators depend on the amount of money. First of all, these are prices and rates on loans. Moreover, under conditions of stability economic development the amount of money supply regulates prices. In the case of structural imbalances, the primary change in prices is possible, and only then there is a change in the cash supply. It turns out that depending on changes in various conditions in the economy, political life countries, ecology prices can change, but vice versa can change due to an increase or decrease in prices. The formula looks like this:

Here M is the amount of money in circulation;
V is the rate of their turnover;
P - the price of the goods;
Q - volume, or quantity of goods

This formula is purely theoretical, since it does not contain a unique solution. However, we can conclude that the dependence of prices and money supply is mutual. In developed economies (a single country or a group of countries) with one currency, the amount of money in circulation must correspond to the level of the economy (production volume), the level of trade and income. Otherwise, it will be impossible to ensure price stability, which is the main condition for determining the amount of cash in circulation.

The interest rate characterizes the cost of using borrowed funds in the financial market. Rising interest rates mean that loans in the financial market will become more expensive and less accessible to potential borrowers. One of the reasons for the increase in interest rates is the increase in inflation. To describe the relationship between the interest rate and inflation, it is necessary to introduce the concepts of real and nominal interest rates.

The nominal interest rate (R) is the interest rate not adjusted for inflation.

The real interest rate (r) is the interest rate adjusted for the inflation rate.

With data on the inflation rate (π) and the nominal interest rate (R), the real interest rate (r) can be calculated using the Fisher formula:

If 0% ≤ π ≤ 10%, then the approximate formula can be used to calculate the real interest rate: r ≈ R – π

If we express the nominal rate from the approximate formula, that is, R ≈ r + π, then we get an effect called the Fisher effect. In accordance with this effect, two main components and, accordingly, two main reasons for the change can be distinguished. nominal rate percent: real interest and the rate of inflation. However, when a financial institution (bank) determines the nominal interest rate, it usually comes with some expectations about the future rate of inflation. Therefore, the formula can be formalized to the following form: R ≈ r+, where is the expected inflation rate.

Then, in accordance with the Fisher effect, the dynamics of the nominal interest rate is largely determined by the dynamics of the expected inflation rate.

nominal and real exchange rates.

The exchange rate of the national currency is the most important macroeconomic indicator.

The nominal exchange rate is the ratio of the values ​​of two currencies (in the exchange office we see exactly the nominal figures).

The real exchange rate is the ratio of the values ​​of goods produced in different countries, or the ratio in which the goods of one country can be exchanged for similar goods of another country.

= × , where is the real exchange rate, P* is the price of foreign goods (in dollars), P is the price of domestic goods (in rubles), is the nominal exchange rate of the dollar against the ruble.

The change in the real exchange rate, based on the formula, is influenced by two factors: the nominal exchange rate and the ratio of prices abroad and in our country. In other words, an increase in the nominal exchange rate of the dollar (and, accordingly, a fall in the nominal exchange rate of the ruble) has a positive effect on the competitiveness of the domestic economy, while growth has a negative effect.

Approximate formula (for small changes): ∆% ≈ ∆% + - π

Purchasing power parity.

Purchasing power parity is the amount of one currency, expressed in units of another currency, required to purchase the same product or service in the markets of both countries.

= , - absolute PPP (prices for goods suitable for international exchange, when converted into one currency, should be the same)

∆% ≈ π - , ∆% = 0 - relative PPP (the nominal exchange rate is adjusted to compensate for the difference in inflation rates)

Question #10

Economic growth and cycle. Long- and short-term processes in the economy. What is a "recession" according to the NBER definition? Signs of an economic recession / recovery. Pro- and countercyclical indicators. Leading and lagging indicators. Recession and "overheating" - what is their danger? Economic growth and its possible sources. Decomposition of economic growth.

The economic growth is the long-term trend of increasing real GDP. To measure growth use:

1. Absolute growth or growth rate of real GDP;

2. Similar indicators per capita for a certain period of time.

IMPORTANT:

1) a trend, this means that real GDP should not necessarily increase every year, it only means the direction of the economy, the so-called "trend";
2) long-term, because the economic growth is an indicator characterizing the long-term period, and, therefore, we are talking about an increase in potential GDP (i.e., GDP at full employment of resources), about an increase in the production capabilities of the economy;
3) real GDP (rather than nominal, the growth of which can occur due to an increase in the price level, even with a reduction in real output). That's why important indicator economic growth is an indicator of the value of real GDP.

the main objective economic growth- the growth of well-being and the increase in national wealth.

A generally accepted quantitative measure of economic growth are indicators of absolute growth or growth rates of real output in general or per capita:

Business cycle- these are several periods of different activity to the economy (according to the US National Bureau of Economic Analysis).

Recession according to NBER (National Bureau of Economic Analysis)– a significant decline in economic activity that has spread throughout the economy, lasting more than several months and noticeable in the dynamics of production, employment, real income and other indicators.

The concept of the discount rate is used to bring the future value to the present value. The discount rate is the interest rate used to convert future cash flows into one present value.

The calculation of the discount rate coefficient is carried out different ways depending on the task at hand. And the heads of companies or individual departments in modern business are faced with completely different tasks:

• implementation of investment analysis;
• business planning;
• business valuation.

For all these areas, the basis is the discount rate (its calculation), since the definition of this indicator directly affects the decision-making regarding the investment of funds, the valuation of a company or certain types of business.

Discount rate from an economic point of view

Discounting determines cash flow(its value), which refers to periods in the future (that is, future earnings in currently). In order to correctly assess future income, it is necessary to have information about the forecasts of the following indicators:

• investments;
• expenses;
• revenue;
• capital structure;
• residual value of the property;
• discount rate.

The main purpose of the discount rate indicator is to evaluate the effectiveness of investments. This indicator implies the rate of return per 1 rub. invested capital.

The discount rate, the calculation of which determines the amount of investment required to generate future income, is a key indicator when choosing investment projects.

The discount rate reflects the value of money, taking into account time factors and risks. If we talk about the specifics, then this rate rather reflects an individual assessment.

An example of selecting investment projects using the discount rate factor

Two projects A and C are proposed for consideration. In both projects, at the initial stage, it is required to invest 1000 rubles, there is no need for other costs. If you invest in project A, then you can earn an income of 1000 rubles annually. If you implement project C, then at the end of the first and second years the income will be 600 rubles, and at the end of the third - 2200 rubles. It is necessary to select a project, 20% per annum is the estimated discount rate.

Calculation of NPV (current value of projects A and C) is carried out according to the formula.

Ct - cash flows for the period from the first to the T-th years;

Co - initial investment - 1000 rubles;

r - discount rate - 20%.

NPV A \u003d - 1000 \u003d 1106 rubles;

NPV C \u003d - 1000 \u003d 1190 rubles.

So, it turns out that it is more profitable for the investor to choose project C. However, if the current discount rate were 30%, then the cost of the projects would be almost the same - 816 and 818 rubles.

This example demonstrates that the investor's decision fully depends on the discount rate.

Various methods for calculating the discount rate are proposed for consideration. In this article, they will be considered objectively in descending order.

Weighted average cost of capital

Most often, when conducting an investment calculation, the discount rate is determined as the weighted average cost of capital, taking into account the cost indicators of equity (equity) capital and loans. This is the most objective way to calculate the discount rate for cash flows. Its only drawback is that not all companies can practically use it.

In order to conduct a valuation of equity capital, the Long-Term Assets Valuation Model (CAPM) is used.

At the end of the 20th century, American economists John Graham and Campbell Harvey surveyed 392 directors and finance managers of enterprises in various fields of activity to determine how they make decisions, what they pay attention to in the first place. As a result of the survey, it was revealed that the most used academic theory, or rather, most firms calculate their equity capital using the CAPM model.

Cost of equity (calculation formula)

When calculating the cost of equity, the discount rate is considered otherwise.

Re - the rate of return, or, in other words, the discount rate of equity, is calculated as follows:

Re = rf + ?(rm - rf).

Where are the discount rate components:

• rf is the risk-free rate of return;
• ? - a coefficient that determines how the price of a firm's shares changes in comparison with changes in stock prices for all firms in a given market segment;
• rm - average market rate of return on the stock market;
• (rm - rf) - market risk premium.

In different countries, different approaches are chosen to determine the components of the model. Much in the choice depends on the general state attitude to calculation. Each of these indicators is important to study and understand separately, in this way cash flow can be determined. Therefore, the elements of the model "Valuation of long-term assets" will be considered in more detail below. And also the objectivity of each component was assessed and the discount rate was assessed.

Constituent Models

The rf is the rate of return on investment in risk-free assets. Risk-free assets are those in which the risk is zero when invested. These mainly include government securities. The calculation of discount rate risks varies from country to country. For example, in the United States, for example, treasury bills are classified as risk-free assets. In our country, for example, such assets are Russia-30 (Russian Eurobonds), the maturity of which is 30 years. Information on the yield of these securities is presented in most economic and financial publications, such as the newspaper Vedomosti, Kommersant, The Moscow Times.

The coefficient with a question mark in the model means sensitivity to changes in the systematic market risk of the return on securities of a particular firm. So, if the indicator is equal to one, then changes in the value of the shares of this company completely coincide with changes in the market. If ?-coefficient = 1.3, then it is expected that with a general rise in the market, the price of the shares of this company will rise 30% faster than the market. And vice versa accordingly.

In countries where the stock market is developed, the ?-coefficient is considered by specialized information and analytical agencies, investment and consulting companies, and this information is published in specialized periodicals that analyze stock markets and financial directories.

Rm - rf, which is a market risk premium, is the amount by which the average market rate of return on the stock market has long exceeded the rate of return on risk-free securities. Its calculation is based on statistical data on market premiums over a long period.

Calculating the weighted average cost of capital

If, when financing a project, not only own, but also borrowed funds are involved, then the income received from this project must compensate not only the risks associated with investing its own funds, but also the funds spent on obtaining borrowed capital. To account for the cost of both equity and debt capital, the weighted average cost of capital is used, the calculation formula is below.

The CAPM model is used to calculate the discount rate. Re - rate of return on own (share) capital.

D is the market value of debt capital. Practically represents the amount of loans of the company according to the financial statements. If such data are not available, then the standard ratio of equity to debt of similar firms is used.

E - market value of share capital (own capital). Obtained by multiplying the total number of shares of a common firm by the price of one share.

Rd represents the firm's rate of return on debt capital. Such costs include information on bank interest on loans and bonds of a corporate type company. In addition, the valuation of borrowed capital is adjusted taking into account the income tax rate. Interest on credits and loans under tax legislation is attributed to the cost of goods, thus reducing the tax base.

Tc - income tax.

WACC Model: Calculation Example

The WACC model specifies a discount rate for Company X.

The calculation formula (its example was given when calculating the weighted average cost of capital) requires the following input indicators.

• Rf = 10%;
• ? = 0,90;
• (Rm - Rf) = 8.76%.

So, equity (its profitability) is equal to:

Re = 10% + 0.90 x 8.76% = 17.88%.

E / V = ​​80% - the share that the market value of equity capital takes in the total cost of capital of company X.

Rd = 12% - the weighted average level of costs for raising borrowed funds for company X.

D/V = 20% - the share of the company's borrowed funds in the total cost of capital.

tc = 25% - income tax indicator.

So WACC = 80% x 17.88% + 20% x 12% x (1 - 0.25) = 14.32%.

As noted above, certain methods for calculating the discount rate are not suitable for all companies. And this technique is exactly this case.

Firms are better off choosing other ways to calculate the discount rate if the company is not a public company and its shares are not traded on a stock exchange. Or if the company does not have enough statistics to determine the?-coefficient and it is impossible to find similar companies.

Cumulative assessment methodology

The most common and most often used method in practice is the cumulative method, with which the discount rate is also estimated. The calculation by this method assumes the following conclusions:

• if investments did not imply risk, then investors would require a risk-free return on their capital (the rate of return would correspond to the rate of return on investments in risk-free assets);
• The higher the risk of the project is assessed by the investor, the higher the requirements for its profitability.

Therefore, when calculating the discount rate, the so-called risk premium must be taken into account. Accordingly, the discount rate will be calculated as follows:

R = Rf + R1 + ... + Rt,

where R is the discount rate;

Rf - risk-free rate of return;

R1 + ... + Rt - risk premiums for different risk factors.

It is practically possible to determine one or another risk factor, as well as the value of each of the risk premiums, only by expert means.

When determining the effectiveness of investment projects, the cumulative method for calculating the discount rate recommends taking into account 3 types of risk:

• the risk resulting from the dishonesty of the project players;
• risk resulting from non-receipt of planned income;
• country risk.

The value of the country risk is indicated in various ratings, which are compiled by special rating firms and consulting companies (for example, BERI). The fact of the unreliability of the project participants is compensated by a risk premium, the recommended indicator is no more than 5%. The risk arising as a result of not receiving the planned income is determined in accordance with the objectives of the project. There is a special calculation table.

Discount rates estimated by this method are quite subjective (too dependent on expert risk assessment). They are also much less accurate than the calculation methodology based on the Long-Term Assets Valuation model.

Expert assessment and other calculation methods

The simplest way to calculate the discount rate and quite popular in real life is the installation of its expert method, with reference to the requirements of investors.

It is clear that for private investors, calculation based on formulas cannot be the only way to make a decision regarding the correctness of setting the discount rate for a project/business. Any mathematical models can only approximately estimate the reality of the situation. Investors, relying on their own knowledge and experience, are able to determine a sufficient return for the project and rely on it as a discount rate when making calculations. But for adequate sensations, an investor must be very well versed in the market, have extensive experience.

However, it must be assumed that the expert method is the least accurate and may well distort the results of business (project) evaluation. Therefore, it is recommended that when determining the discount rate by expert or cumulative methods, it is mandatory to analyze the sensitivity of the project to changes in the discount rate. In this case, investors will have the most accurate assessment.

Of course, there are alternative ways to calculate the discount rate. For example, the theory of arbitrage pricing, the model of dividend growth. But these theories are very difficult to understand and are rarely applied in practice.

Applying the discount rate in real life

In conclusion, I would like to note that most companies in the course of their activities need to determine the discount rate. It must be understood that the most accurate indicator can be obtained using the WACC methodology, while in other methods there is a significant error.

In work, it is not often necessary to calculate the discount rate. This is mainly due to the evaluation of large and significant projects. Their implementation entails a change in the capital structure, the company's share price. In such cases, the discount rate and method of its calculation are agreed with the investing bank. Focus mainly on the received risks in similar companies and markets.

The application of certain methods also depends on the project. In cases where industry standards, production technology, financing are understood and known, statistical data have been accumulated, the standard discount rate established by the enterprise is used. When evaluating small and medium projects, they refer to the calculation of payback periods, with an emphasis on the analysis of the structure and external competitive environment. In fact, methods for calculating the discount rate of real options and cash flows are combined.

You need to be aware that the discount rate is only an intermediate link in the evaluation of projects or assets. In fact, the assessment is always subjective, the main thing is that it be logical.

There is such a mistake - economic risks are taken into account twice. So, for example, two concepts are often confused - country risk and inflation. As a result, the discount rate is doubled, a contradiction appears.

It is not always necessary to count. There is a special table for calculating the discount rate, which is very easy to use.

Another good indicator is the cost of a loan for a particular borrower. The discount rate setting can be based on the actual lending rate and the level of yield of bonds that are available on the market. After all, the profitability of the project does not exist only within its own environment, it is also affected by the general economic situation on the market.

However, the obtained indicators also require significant adjustments related to the risk of the business (project) itself. Currently, the method of real options is quite often used, but it is very complicated from a methodological point of view.

In order to take into account such risk factors as the option of project suspension, changes in technology, market losses, discount rates (up to 50%) are artificially inflated by project appraisal practitioners. At the same time, there is no theory behind these figures. Similar results may well be obtained using complex calculations, in which, in any case, most of the predictive indicators would be determined subjectively.

Correctly determining the discount rate is a problem associated with the main requirement for the information content generated in financial reporting and accounting. In other words, if there is reason to doubt whether assets or liabilities are valued correctly, and not whether cash consideration is deferred, then discounting should be applied.

When choosing a discount rate, it is important to understand that it should be as close as possible to the rate received by the borrower of the lending bank on real terms in the existing environment.

So, the discount rate for certain assets (say, for fixed assets) is equated to the rate at which the firm would have to pay, raising funds to purchase similar property.

There are three methods of calculating the discount rate used to assess the value of a business:

• Capital Asset Pricing Model (CAPM).
• The method of cumulative construction.
• Weighted average cost of capital (WACC) method.

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The discount rate is used to bring the value of future cash flows to the present value (at the current point in time). This operation is called , it is the inverse of the calculation operation compound interest. Such an operation is necessary due to the fact that the amount of money available on this moment, is of greater value than the same amount that will be received in the future.

Cash flow discounting is used for business valuation purposes in the following cases:

• Within the forecast period.
• As part of the present value of individual assets and liabilities. For example, to calculate the cost of a loan debt, if it is assumed that repayment will occur over a long period of time.

The discount rate is calculated from capital asset pricing models (CAPM) or cumulative construction method if the total cash flow is discounted. Both of these methods of calculation include as initial stage calculation of the risk-free interest rate.

Risk free interest rate

The risk-free rate (also called the risk-free rate of return) is the percentage of return that can be earned by investing in zero-risk assets.

A zero-risk asset must meet the following conditions:

• The rate of return is known before the investment is made.
• The risk of capital loss is minimal even if force majeure occurs.
• The lifetime of the asset (circulation period) is commensurate with the residual life of the business being valued.

Usually such conditions are met by government bonds or deposits for an appropriate period in reliable banks. In this case, the value of the risk-free rate is about 4-5%. This so-called nominal risk-free rate, the value of which does not take into account the rate of inflation.

Real risk-free rate taking into account the inflation rate is calculated by the formula:

Rf = Rn + I + Rn*I, where

Rn - nominal risk-free rate
I - inflation rate

An example of calculating the real risk-free rate

Nominal risk-free rate Rn = 4%
Inflation rate I = 7%
Real risk-free rate:

Rf = 0.04 + 0.07 + 0.07*0.04 = 0.1128 = 11.28%

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Capital Asset Pricing Model (CAPM)

The discount rate calculated by this model takes into account the systematic risk, i.e. risk inherent in the entire market or market segment.

Calculation formula for the CAMP model:

R = Rf + β*(Rm-Rf), where

Rm- Average rate market returns
Rf - Real risk-free rate
β is a measure of the risk of the valued business in relation to the market (beta coefficient).

Sometimes the basic formula for calculating the CAPM model is supplemented with three additional terms (three standard risk premiums):

R \u003d Rf + β * (Rm-Rf) + Rmb + Rzk + Rst

Rmb - risk premium for investing in small business
Rзк - premium for the risk of investing in a closed company
Rst - country risk premium

Cumulative construction method

Takes into account the non-systematic risks inherent in the specific business being assessed.

The formula for calculating the discount rate using the cumulative construction method:

Rk = Rf + (R1 + R2 + ... + Rn) + (Rmb + Rbk + Rst), where

Rf - Real risk-free rate
R1, ..., Rn - one or more of the following risk factors:

• Key figure factor
• Leadership Quality Factor
• Funding source factor
• Factor of production diversification
• Customer diversification factor
• The resource constraint factor
• Other risk factors specific to the business or industry being assessed.

Rmb, Rzk, Rst - three standard bonuses.

Weighted average cost of capital (WACC) method

The discount rate is calculated using the WACC method - the weighted average cost of capital, if debt-free cash flow is discounted during business valuation. That is, the cash flow in which the receipt of a loan, the payment of a loan and the payment of interest on a loan are not taken into account.