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 (calculation of it), 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 the cash flow (its value) that relates to periods in the future (that is, future earnings in this moment). 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. initial stage you need 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 project C is implemented, 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.

AT 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, 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. These costs include information about 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 the help of 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 the 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 practice, methods for calculating the discount rate of real options and cash flows.

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.

Also a 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 are artificially inflated by practitioners in project evaluation (up to 50%). 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.

The discount rate for equity can be calculated using the CAPM model or the cumulative build model. The rate of return for discounting debt-free cash flow is calculated using the WACC weighted average cost of capital model. The following is the content of these models and options for substantiating their main parameters in Russian practice. Much is unclear, do not know how to approach the discount rate? Especially for you, then the fifth question)

1. Types of discount rates in business valuation

To discount future cash flows in business valuation, it is necessary to calculate the discount rate, the type of which must correspond to . As shown in the following table, according to the four main types of cash flows in business valuation, there are four types of discount rates.

If the valuation is based on nominal cash flow, then nominal discount rate, which takes into account the effect of inflation. To discount the real cash flow, the real rate discount, which does not take into account inflation expectations.

Rates of return based on actual market data take into account the effect of inflation and are nominal. Therefore, in practice, it often becomes necessary to calculate the real discount rate based on the known nominal rate what can be used for Fisher formula:

2. Weighted average cost of capital (WACC) model

The WACC model involves determining the discount rate by summing the weighted rates of return on equity and borrowed funds, where the weights are the shares of equity and borrowed funds in the capital structure. Wherein we are talking on the structure of invested capital, which, in addition to equity capital, as a rule, includes only long-term borrowed funds.

The weighted average cost of capital is calculated using the following formula:

WACC = W 1 × Re + W 2 × R d ×(1 – h), where

• W 1 - the share of equity in the capital of the company;
• W 2 - the share of long-term debt in the capital of the company;
• R e - rate of return on equity;
• R d is the cost of borrowed capital (cost of debt);
• h is the effective income tax rate.

3. Capital Asset Pricing Model (CAPM)

The discount rate for equity can be justified using a Capital Assets Pricing Model (CAPM) or a cumulative build model.

Basic SARM Model is used to estimate the expected return of open companies based on the analysis of stock market information, has significant assumptions and a well-defined scope. The basic CAPM model is discussed in detail in educational literature in various financial and economic disciplines (primarily in financial management) and is presented in the following formula:

R e = R f + β ×(R m – R f), where

• Re– required (expected) rate of return on equity;
• Rf — risk free rate of return;
• Rm- the average market rate of return;
• (Rm-Rf) is the average market risk premium;
• β is the beta coefficient as a quantitative measure of systematic risk.

The basic CAPM model occupies an important place in portfolio theory and is based, in particular, on the assumption that a rational investor, by diversifying his investment portfolio, seeks to minimize the non-systematic risks associated with investing in a particular asset. For example, non-systematic risks of investing in a company's shares are due to the nature of its activities - in particular, the level of product diversification, management quality, etc., as well as the company's financial position - primarily, the degree of dependence on external sources financing.

In this regard, the expected return on the basic CAPM model includes a premium only for systematic risk, which is formed under the influence of macroeconomic factors (inflation, economic recession, etc.) and cannot be eliminated by diversifying the investment portfolio.

In the practice of business valuation, in the process of substantiating the rate of return on equity of the company being valued, modification of the basic CAPM model, according to which the basic CAPM model is supplemented (by adding) the following main premiums for the unsystematic risk of investing in the company being valued: From 1– premium for the risk of investing in a particular company; From 2– risk premium for investing in small business; From 3 is the country risk premium.

How to justify the parameters of the CAPM model in Russian practice?

risk free rate of return Rf corresponds effective rate yield to maturity of risk-free assets – i.e. assets that meet the following conditions:

• returns on them are determined and known in advance;
• the probability of loss of funds as a result of investments in the asset is minimal;
• the duration of the circulation period of the asset coincides or is close to the period of the projected period of ownership of the property being valued.

The choice of an asset for calculating the risk-free rate of return is also determined by the calculation currency - for example, to calculate the rate of return for discounting the ruble cash flow, it is reasonable to calculate the yield on a risk-free asset denominated in rubles.

Abroad, the rate of return on government securities is usually used as a risk-free rate. In domestic practice, along with this, as risk-free assets after the 1998 crisis. it was proposed to consider also deposits of the Savings Bank of the Russian Federation and banks of a high category of reliability. However, the use of bank deposit rates as a risk-free rate of return currently does not seem to be sufficiently justified, which is due to the higher risk of investing in bank deposits compared to government securities and short terms for accepting deposits (one to two years).

Government bonds of the Russian Federation are represented by ruble and foreign currency financial instruments. An example of ruble bonds is federal loan bonds (OFZ), the issuer of which is the Ministry of Finance of the Russian Federation. The owners of these bonds can be both legal entities and individuals, residents and non-residents; auctions and secondary trading are held on the MICEX.

The volume of the currency bond market is significantly higher than the level of the ruble bond market. Foreign currency bonds of the Russian Federation are represented by two types: bonds of an internal foreign currency loan (OVVZ) and Eurobonds of the Russian Federation. At the same time, the riskiness of investments in OVVZ is assessed by international rating agencies as higher compared to Eurobonds. In this regard, it is advisable to consider Eurobonds as a risk-free asset to justify a non-ruble (for example, dollar) risk-free rate.

Rationale average market rate of return R m associated with the calculation of the actual return of the market portfolio. In practice, portfolios formed on the basis of broad-based indices are considered as a market portfolio - for example, in the Russian Federation, it is possible to calculate the index of the stock market (Moscow Exchange), news agencies (AK&M), etc.

Coefficient beta (β) as a quantitative measure of systematic risk in the CAPM model, it is calculated using information on the dynamics of the return on shares as investment assets in the stock market according to the following formula:

βi = Cov(R i , R m)/Var(Rm) , where

• βi — measure of systematic risk i-th asset (portfolio) relative to the market;
• cov(R i, Rm) - return covariance i-th asset (portfolio) (R i) and average market returns (Rm) ;
• Var(Rm) – variation in the average market return (Rm).

Thus, the beta coefficient reflects the amplitude of fluctuations in the return of a particular asset (portfolio) compared to the overall return of the stock market as a whole.

The value of beta characterizes how much the risk of owning specific assets is greater or less than the risk of the market portfolio. An asset whose beta is greater than one is more sensitive to systematic risk than the stock market on average, and, accordingly, is characterized by a higher risk than the average market situation. Accordingly, assets with beta less than one are less risky compared to the market portfolio.

Thus, the higher the beta value of an asset, the higher the level of its systematic risk. The stock price of a company for which the beta coefficient is 1.2, with an increasing trend in the market, will grow on average 20% faster compared to the average market level. And, conversely, when depressed state market, the share price of this company will decrease by 20% faster than the market average. Therefore, if the share price in the stock market falls by 10%, we can expect that the share price of this company will fall by 12%.

Describing the parameters that were added to the basic CAPM model in the process of its adaptation for business valuation purposes, we note that a wide scope has non-systematic risk premium investing in a specific company (C 1).

Small business risk premium (S2) applies if the company being valued is a small business; the purpose of its introduction is to compensate for the additional instability of small business income.

Country risk premium (S 3) is introduced, for example, if the return on equity of a Russian company is estimated according to the parameters of the basic CAPM model, which are calculated based on data from foreign developed capital markets. In this case, the country risk premium is needed to compensate for the additional risks of investing in the Russian Federation compared to developed markets.

To account for country risk, it is necessary to identify the most important factors that determine the risk of investing in a country, as well as develop a method for quantifying risk for the country in question. Among the main factors of country risk, the risk of instability of legislation and the risk of unreliability of property rights are singled out. Under the influence of these factors, the following additional risks may arise: the risk associated with foreign currency conversion; the risk of loss of assets due to possible government actions of nationalization and expropriation; risk associated with restrictive measures on the movement of capital; risk associated with the possibility of state regulation of prices, etc.

The practice of applying the CAPM model in a developed capital market, as a rule, involves the use of ready-made values ​​of the model parameters calculated by specialized companies. In emerging markets, the appraiser usually calculates the parameters of the CAPM model on his own.

Characterizing scope of the CAPM model, we note that the model is unambiguously applicable for estimating the expected return on equity of open companies listed on the stock market. You can also use this model to evaluate a company whose analogues are actively traded on the stock market.

4. Cumulative building model

The model of cumulative construction of the discount rate is used when evaluating closed companies, for which it is difficult to find comparable open companies-analogues and, accordingly, it is impossible to use the CAPM model.

When using this model, the risk-free rate is taken as the basis, to which the premium for the risk of investing in closed companies is added. The cumulative construction model best takes into account all types of risks associated with both factors general(macroeconomic factors and factors of the type of economic activity of the enterprise), and with the specifics of the enterprise being assessed.

The discount rate for the cumulative construction model is calculated using the following formula:

Re = Rf + From 1+ From 2+ From 3+ From 4+ From 5+ From 6+ From 7 , where

• R e– required (expected) rate of return on equity of the company being valued;
• Rf is the risk-free rate of return;
• From 1– risk premium associated with the size of the enterprise;
• From 2– premium for the risk of the financial structure (sources of financing of the enterprise);
• From 3– premium for product and territorial diversification risks;
• From 4– risk premium for customer diversification;
• From 5– risk premium for the level and predictability of profit;
• From 6– risk premium for management quality;
• From 7– premium for other risks.

The indicated risk premiums are set for the assessed enterprise in the range from 0% to 5% for each type of premium - with the maximum risk level, the highest premium is set.

The cumulative construction model has an almost unlimited scope. Its main disadvantage is the predominant use of subjective approaches to justify the values ​​of risk premiums. Meanwhile, at present, in separate publications, in the reports of large appraisal firms, methodological approaches are proposed to justify the values ​​of risk premiums in the cumulative construction model. The use of such approaches, while increasing the degree of objectivity and validity of determining the discount rate, at the same time requires significant information both on the enterprise being valued, and on similar companies, and on the market as a whole.

For example, during the assessment size risk premium , it should be taken into account that a large company often has advantages over small ones due to greater business stability, relatively easier access to financial markets if additional resources are required. At the same time, there are a number of industries where small businesses operate more efficiently: trade, catering, public service, production without the use of complex technological processes. Therefore, it is reasonable to estimate the value of the risk premium taking into account the trends prevailing in similar enterprises that are engaged in the same types of economic activity as the enterprise being assessed.

As a result, the risk premium associated with the size of the company can be determined by the following formula:

Xr= X max×(1 - N/ Nmax), where

• Xr- the desired level of risk premium associated with the size of the company;
• X max– maximum premium (5%);
• N- the value of the assets of the company being valued according to the balance sheet as of the date of evaluation;
• Nmax- the maximum value of assets among similar enterprises that are engaged in the same types of economic activity.

For example: to determine the risk premium associated with the size of the company for OAO “Subject of Assessment”, the value of total assets of which at the date of assessment was 46,462 million rubles. Information on the value of the assets of similar companies is known: “First analogue” 20,029 million rubles, “Second analogue” 22,760 million rubles, “Third analogue” 51,702 million rubles, “Fourth analogue” 61,859 million rubles .

Solution: The maximum amount of assets among similar enterprises is noted by the Fourth Analogue and amounts to 61,859 million rubles. Then the premium for the risk associated with the size of the company for JSC "Subject of Assessment" according to the presented formula will be

1,2% = 5% * (1- 46 462/ 61 859).

5. How to understand the calculation of the discount rate

Perhaps you have read many textbooks and publications on business valuation and still do not understand the essence of the basic methods for calculating the discount rate. First of all, you are not alone! It is difficult for many to understand these methods, but not many admit it) Good news: knowledge and skills in calculating the discount rate have a very wide scope not only in business valuation, but also in financial management, in evaluating the effectiveness of investments. Therefore, by making efforts to study this issue, you will be rewarded with an increase in your qualifications and professional level)

According to my observations, difficulties in studying the methods of the discount rate calculation method may arise with a lack of knowledge in financial management, where the theoretical foundations of the CAPM and WACC models are considered in detail. Therefore, on this topic, I would suggest referring to the fundamental textbooks on financial management by Y. Brigham, Van Horn, and others. Interestingly and a lot has been written about the CAPM model in the book of one of its authors, W. Sharp, “Investments”.

, . .

Fisher formula

This formula allows you to express risk-free rate from the ruble of investments through the real rate without risk income r (it is also sometimes called the real interest rate without risk) and inflation expectations s:

R = r + s + rchs(7)

Rate s of expected inflation(averaged over the period n remaining until the end of the useful life of the business) can be determined by:

1) from the forecasts of research centers;

2) based on the official forecast of expected inflation;

3) by own forces of specialists in the development of a feasibility study.

The real risk-free lending rate can be evaluated:

1) taking for it the market rate of return on the shortest-term government bonds (in terms of the required longer period of the "step" t) - keeping in mind that for enough short term circulation of such bonds, inflation simply does not have time to have any significant effect;

2) equating it with the profitability of operations in the markets of those relatively risk-free (based on high demand) goods and services, where the domestic economy has already managed to integrate into the world markets for these goods and services (i.e., where a competitive domestic market open for them for imports combined with active export of the same goods and services abroad); the actual yield in these markets will then reflect how the real interest rate (at the level of 3-4%) has long stabilized in the industrialized countries of the world.

Determining the discount rate for discounting without debt cash flows

For discounting without debt cash flow, a discount rate calculated using the weighted average cost of capital (WACC) method is used.

Non-debt cash flow does not take into account the size and movement of the enterprise's future debt. And therefore, in order to reflect the share and cost of borrowed funds in such a future cash flow, discounting this non-debt cash flow is carried out at an income rate equal to the weighted average cost of borrowed and equity capital of the enterprise being valued, i.e. the interests of the creditor are taken into account in the process of forming not the cash flow, but the discount rate.

The current value of the discounted cash flow determined in this way (ie the value of the enterprise being valued at the date of valuation) characterizes the current value of all invested capital - both equity and debt.

The calculation without debt cash flow is similar to determining the cash flow for equity, except for the following:

· the decrease in debt is not taken into account;

· the increase in debt is not taken into account;

· cash payments on interest for debt servicing are not taken into account (not deducted from profit).

Calculation scheme without debt cash flow.

Without debt, the cash flow is equal to = Net profit (the cost of paying interest on loans in excess of the discount rate of the Central Bank is not deducted from profit, but only income tax is deducted) + Depreciation (full) + Decrease in own working capital - Increase in own working capital - Capital investments.

When implementing this algorithm for assessing an enterprise, in order to determine the value of the enterprise's own funds, it is necessary to subtract the cost of borrowed capital from the cost of all invested capital, i.e. amount of debt. If the profit is formed to a large extent by attracting borrowed funds for production, then it is more expedient to evaluate the enterprise on a non-debt cash flow (that is, without taking into account interest payments and changes in liabilities).

The main arguments for using one or another type of cash flow are the following judgments. If the profit (or cash flow) of an enterprise is formed mainly from its own funds without significant borrowing, then the cash flow to equity is used to value the enterprise.

FISHER EFFECT (fisher effect) - a concept that formally takes into account the impact of inflation on the interest rate on a loan or bond. In the equation proposed by Irwin Fisher (1867-1947), the nominal interest rate on a loan is expressed as the sum of the real interest rate and the inflation rate expected over the life of the loan: R = r + F, where R is the nominal interest rate, r is the real interest rate, and F is the annual inflation rate. 1 So if inflation is

6% per annum, and the real interest rate is 4%, then the nominal interest rate will be 10%. The inflation premium (6%), included in the nominal interest rate, makes it possible to compensate for the losses of creditors associated with the fall in the purchasing power of the money lent by the time they are returned by the borrowers.

The Fisher effect implies a direct relationship between inflation and nominal interest rates, when changes in the annual inflation rate lead to corresponding changes in nominal interest rates.

__________________

1 Here is a simplified version of the Fisher equation, which gives a good approximation for small interest rates and

the rate of inflation. Exact formula: R = r + F + rF. In the conditions of the example, the exact value of R = 0.06 + 0.04 + 0.06 0.04 = 0.1024, i.e. 10.24% per annum. (Ed. note)

Cm. Fisher Irving Fisher Irving (1867 - 1947), From Irving Fisher to Alexander Konyus (Economic School, lecture 19.2)

I.Fisher. The influence of monetary systems on the purchasing power of money ,

I.Fisher. The influence of the quantity of money and other factors on the purchasing power of money and on each other

QUANTITY THEORY OF MONEY (quantity theory of mo-ney)

NOMINAL INTEREST RATE (nominal interest rate) - the interest rate paid on a loan without adjusting for inflation.

Wed REAL INTEREST RATE .

REAL INTEREST RATE (real interest rate) - the interest rate paid on a loan, adjusted for inflation. If the borrower has to pay, say, 10% (nominal interest rate) on a loan during a year in which the inflation rate was 6%, then the real interest rate would be only 4%. Inflation reduces the real burden of interest payments on borrowers, while at the same time reducing the real remuneration of lenders.

See FISHER EFFECT.

INFLATION (inflation) - an increase in the general level of prices in the economy, continuing for a certain period of time. Annual price increases can be small and gradual (creeping inflation) or large and accelerating (hyperinflation). The rate of inflation can be measured, for example, by means of the consumer price index (see price index), which reflects annual percentage changes in the prices of consumer goods. See fig. 43. It should be noted that inflation reduces the purchasing power of money (see real values).

Rice. 42. Inflation gap ,

a.The aggregate supply schedule is drawn as a 45° line because firms will only plan for any level of output if they assume that total spending (aggregate demand) will be such that they will be able to sell all of their output. However, if the economy reaches a national income level corresponding to full employment ( O Y 1 ), then the volume of output cannot be increased, and at this level the aggregate supply line becomes vertical. If aggregate demand is at the level indicated by line AD, the economy will operate at full employment without inflation (point E). However, if aggregate demand is at a higher level, like AD 1 this excess aggregate demand will create an inflationary gap (equal to EG), pulling prices up,

b. In an alternative model where aggregate demand and aggregate supply are expressed in terms of real national income and the price level, the inflationary gap is expressed as the difference between the price level (RR) relative to the level of aggregate demand at full employment (AD) and the price level (RR 1 ) related to a higher level of aggregate demand (AD 1 ) at the level of real national income O Y 1 . See demand-pull inflation.

Overcoming inflation has long been one of the main goals of macroeconomic policy. Inflation is seen as undesirable: it adversely affects income distribution (inflation hurts people on a fixed income), lending and borrowing (creditors suffer losses, borrowers benefit), increases speculation (diversion of savings from production to speculation in goods and real estate), and worsens competitiveness in international trade (exports become relatively more expensive, while imports become cheaper). Hyperinflation is especially dangerous, as people lose confidence in money as a medium of exchange and the economic system falls into a state close to collapse.

There are two main explanations for the causes of inflation:

(a) the presence of excess demand at full employment, which pulls up prices (demand inflation);

(b) an increase in the cost of factors of production (labor and raw materials), which pushes up prices (cost inflation).

According to the concept of the monetarist school (see MONETARISM), demand-pull inflation is due to the creation of an excess amount of money. Monetarists propose to apply strict control over the money supply as a means of reducing excess aggregate spending (see monetary policy). The Keynesian school also promotes the policy of reducing aggregate spending as a way to contain excess demand, but proposes to implement this policy through tax increases and government spending cuts (see fiscal policy). Cost-push inflation is mainly due to an excess increase in monetary rates. wages(i.e., a wage rate higher than what can actually be paid for by increased productivity growth) and occasional commodity price hikes (a clear illustration of this is the increase in oil prices carried out by OPEC in 1973 and 1979). Cost inflation driven by demands for excessive wage increases can be curbed or eliminated either directly by imposing price and income controls (see price and income policy) or indirectly through "exhortations" and measures to reduce the monopoly power of unions.

Pyotr Ilyich Grebennikov.

COST INFLATION (cost-push inflation) is a general increase in prices caused by an increase in the cost of production factors. The cost of factors of production, on the other hand, may rise due to an increase in the cost of raw materials and energy due to their shortage on a global scale, or as a result of the action of cartels (for example, oil), or the fall in the country's exchange rate (see), or because wage rates in economy is growing faster than output per capita (). In the latter case, institutional factors such as the use of wage comparability and differentiation arguments in collective bargaining negotiations, and the persistence of restrictive labor practices can help raise wages and limit opportunities for productivity growth. Faced with rising factor costs, manufacturers try to pass on the increased costs by charging higher prices. To keep the unit gross margin unchanged, producers need to fully offset the increased costs by inflating prices, but whether or not they are able to do so depends on the price elasticity of demand for their products.

COMPARABILITY (comparability) - an approach to determining wages, consisting in the fact that in the course of negotiations on a collective agreement, the level or rate of increase in the wages of any particular group of workers or industry is associated with the level or rate of increase in wages of persons in other professions or industries.

Comparability can lead to

INFLATION OF DEMAND (demand-pull inflation) - an increase in the general price level as a result of an excess of aggregate demand compared to potential supply in the economy. At the level of output corresponding to full employment (potential gross national product), excess demand drives up prices while real output remains unchanged (see inflationary gap). According to the concept of monetarism, excess demand arises from too much rapid growth money offers.

GNP DEFLATOR (GNP deflator) - a price index used to adjust the gross national product (GNP) in order to obtain real GNP (see). Real GNP is important because it reflects the physical output of goods and services, and not the sum of their monetary terms. Sometimes it seems that the production of goods and services in the economy has increased () because monetary GNP has increased, but this may be the result of price increases (), which is not behind the increase in the physical volume of production. The GNP deflator is designed to remove the effect of price changes and only take into account real changes.

DEFLATION (deflation) - a decrease in the level of national income and output, usually accompanied by a fall in the general price level (disinflation).

Authorities often deliberately induce deflation in order to reduce inflation and improve the balance of payments by reducing demand for imports. Deflationary policy uses fiscal measures (such as raising taxes) and monetary measures (such as raising interest rates).

Cm. ,

INTERNATIONAL FISHER EFFECT (international Fisher effect) - a situation in which the difference in nominal interest rates in different countries reflects the expected rate of change in the exchange rate of their currencies.

For example, if British investors assume that the US dollar will appreciate, say, by 5% per year against the pound sterling, then in order to create currency parity between the two countries, they are ready to allow interest rates dollar-denominated securities would be approximately 5% less than the annual interest rates on sterling-denominated securities. From the borrower's point of view, under the Fisher effect, the cost of equivalent loans in these alternative currencies will be the same, despite the difference in interest rates.

The international Fisher effect can be compared to the internal Fisher effect, when nominal interest rates reflect expected real interest rates and the expected rate of price change (inflation). The international equivalent of inflation is

COMPOUND INTEREST(compound interest) - interest on a loan, which is charged not only on the original loan amount, but also on the interest that has increased before. This means that interest payments grow exponentially over time; For example, on a loan of 100l. Art. co compound interest, equal to 10% per year, will accumulate debt by the end of the first year at 110l. Art., by the end of the second year - by 121 f. Art. etc. according to the following formula:

(simple interest) - interest on a loan, which is charged only on the initial loan amount. This means that over time, the amount of interest increases linearly. For example, a loan of £100 Art. with a simple interest of 10% per annum rises to £110. Art. by the end of the first year, up to 120l. Art. by the end of the second year, etc.

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