Average capitalization rates for various types of real estate. How is the discount rate different from the capitalization rate?

Theoretically, the capitalization ratio for current income should directly or indirectly take into account the following factors:

1. Compensation for risk-free, illiquid investments.

2. Compensation for risk.

3. Compensation for low liquidity.

4. Compensation for investment management.

5. Adjustment for the projected increase or decrease in property value

There are several methods for determining the coefficient (rate) of capitalization:

1. Market squeeze method;

2. Method of cumulative construction (summation);

3. Method of related investments of debt and equity capital;

4. The method of connected investment of land and building;

5. Method for determining the capitalization ratio, taking into account the reimbursement of capital costs.

6. Elwood method (method of capitalization of debt and equity capital).

1. Method of market squeeze.

It is the simplest, fastest and most accurate way to determine the value of any property using comparable sales data collected from competitive and open markets. The sales are similar in terms of their characteristics (investment motivation, socio-legal status, solvency, ways of financing, etc.) and the usefulness of the properties. Under the income approach, the capitalization rate (R) is calculated using the formula:

V is the cost of an analogue object;

I - CHOD of the evaluated object.

2. Method of cumulative construction (summation method).

This method of determining the capitalization rate divides it into its component parts. The two main components of the capitalization rate are: the interest rate and the capital recovery (return) rate.

The interest rate is divided into several components:

1. The risk-free rate.

2. Bet on additional risk.

3. Compensation for low liquidity.

4. Compensation for investment management.

5. Adjustment for the projected increase or decrease in the value of real estate.

Risk free rate. The risk-free rate is used as the base rate, to which the rest of the interest rate components are added. To determine the risk-free rate, you can use both the average European indicators for risk-free operations and domestic ones. In the case of using average European indicators, a risk premium is added to the risk-free rate for investing in this country, the so-called country risk. The risk-free rate determines the minimum compensation for invested capital, taking into account the time factor (investment period).

Additional risk rate. All investments, with the exception of investments in government securities, have a higher degree of risk, depending on the characteristics of the type of property being valued. The greater the risk, the higher the interest rate must be in order for the investor to take on the risk of any investment project.

Compensation for low liquidity. Liquidity measures how quickly real estate can be turned into cash. Real estate is low liquid compared to, for example, stocks and other securities. The Illiquidity Adjustment is a kind of long-term allowance for the sale of a property, or for the time it takes to find a new tenant in the event of bankruptcy or abandonment of an existing tenant.

Compensation for investment management. The more risky and complex the investments, the more competent management they require.

Capital recovery rate. The value equal to one divided by the number of years required to return the invested capital is based on the time interval during which the typical investor calculates that the capital invested in the property being valued will return.

The overall capitalization ratio under this method is calculated by summing the interest rate calculated using the cumulative method and the capital return rate.

3. The method of related investments of own and borrowed capital.

Since most properties are purchased with both debt and equity capital, the total capitalization rate must satisfy the market requirements for return on both parts of the investment.

Investments = debt capital + own capital.

The capitalization rate on borrowed funds is called the mortgage constant and is calculated as follows:

Rz = annual maintenance payments. debt / mortgage principal

If the loan is repaid more frequently, then R is calculated by multiplying the debt service payments by their frequency (monthly, quarterly) and then dividing by the total amount of the mortgage loan.

The mortgage constant is a function of the interest rate, the frequency of debt amortization, and the terms of the loan. When the terms of the loan are known, the mortgage constant can be determined from the financial tables: it will be the sum of the interest rate and the sinking fund ratio. The equity investor also seeks systematic cash returns.

The rate used to capitalize return on equity is called the capitalization rate on equity (Rc) and is defined as follows:

Rc= pre-tax cash receipts / own funds invested

Rc is not just a rate of return on capital, but combines a rate of return on capital and a return on invested capital.

The overall capitalization rate (R) must satisfy a certain level of mortgage constant for the lender and income inflow for the equity investor. It is determined by weighing its components in proportion to the size of debt and equity capital as part of investments. The ratio of the amount of borrowed capital to the value of the investment fund is called the credit share. The credit (debt) share in total investments in real estate is equal to:

Mredd. = amount of loan / cost of investment

Then the share of equity is: Msob. = 1 - Mkred., where the total capital is taken as 1.

When the mortgage constant (Rz) and the capitalization rate of income on equity are known, then the total capitalization rate will be equal to:

R \u003d Rz x Mkr. + Rc(1-Mkr.).

Typical terms and conditions for granting mortgage loans can be obtained by analyzing market data. Equity capitalization rates are derived from comparable sales data.

Example. Determine the value of the property, for the purchase of which you can get a loan of 1,000,000 at 12% per annum for 20 years with annual payments (annual debt service payment - 133880). The property is expected to sell for 1,200,000 after an 8-year holding period. The NPV is 180,000 and the investor expects to receive a 14% return on equity.

Solution. In accordance with the basic formula of mortgage investment analysis:

V=PV[(180000 - 133880), 8 years 14%] + PV[(1200000 - 829295), 8 years 14%] + 100000= 213944 + 129953 + 1000000=1343897.

4. Modified method of capitalization of debt and equity (Elwood's method). There is an opinion that the method of linked investments has some disadvantages, because. it does not take into account the duration of the period of planned investment, as well as the decrease or increase in the value of the property during this period. In 1959, a member of the Institute of Assessment (MAG) L.V. Elwood linked these factors with those already included in the linked investment method and proposed a formula that could be used to test or calculate the overall capitalization rate. In addition, tables have been developed to simplify the use of his method.

Elwood's formula, developed to calculate the total capitalization rate, is as follows:

R \u003d Rc - Mcr x C / Dep - app (SFF),

R - total capitalization rate;

Rc - the rate of return on equity - represents real income on the investment that the typical investor expects to receive over the period of ownership of the property. It includes losses or mostly profits from sales (because most investors plan to sell the acquired property for more than it was bought). The rate of return on equity is calculated on the basis of market data and depends on the specifics of a particular appraisal object.

Mcr - ratio of magnitude mortgage loan to cost (credit share in total capital);

С - mortgage coefficient;

Dep - decrease in the value of property for the forecast period;

app - increase in the value of property for the forecast period;

SFF is the sinking fund ratio at rate Y for the projected holding period.

The mortgage rate can be calculated using the formula:

C \u003d Y + P (SFF) - Rs,

where P is the part of the mortgage loan that will be amortized (repaid) during the forecast period;

Rs is the mortgage constant.

The mortgage rate can be found in the Elwood tables without having to calculate it yourself.

Example. Suppose you want to determine the value of a property based on the following data:

Solution. According to the Elwood method, the capitalization rate will be equal to:

R = / 1 + 0=0.12173.

Therefore, the value of the property is V=50000/0.12179=410745.

5. The method of connected investments of land and building.

The essence of this method is to determine the weighted capitalization rates for each structural element of the entire property complex - the land and the structure standing on it. Weighing the capitalization rates is carried out on the basis of the size of the shares of the components in the value of the property complex as a whole. The total capitalization rate is calculated using the formula:

R \u003d Cz x Kz + Czd x Kzd,

Sz - the cost of land as a percentage of the total share of the property complex;

Kz - capitalization rate for land;

Szd - the cost of the building as a percentage of the total property complex;

Kzd - capitalization rate for the building.

6. Accounting for reimbursement of capital costs in the capitalization ratio

As mentioned earlier, the capitalization ratio in relation to real estate includes return on capital and return on capital. Return on capital is the compensation that must be paid to an investor for the value of money, taking into account time, risk, and other factors associated with a particular investment. Return on capital is also called return. The return of capital means the repayment of the amount of the initial investment. The return of capital is called the return of capital.

Streams of income on investments, the receipt of which is expected to be equal in amounts over an unlimited period, and also, if no change in the cost of invested capital is forecasted, can be capitalized at the rate of interest (discount).

In this case, the recovery of investment costs occurs at the time of resale of the asset. The entire income stream is a return on investment.

If a change in the value of an asset (loss or growth) is predicted, then it becomes necessary to take into account the capitalization ratio in the capitalization ratio. There are three ways to recover invested capital:

· Straight-line return of capital (Ring's method) - for exhaustible assets;

· Return of capital by compensation fund and rate of return on investment (Inwood method) or annuity method - to value assets that generate constant streams of income;

· Return of capital on the compensation fund and the risk-free rate of interest (Hoskold method) - for highly profitable assets.

1. Straightforward return on capital (Ring's method). The Ring method assumes that the principal is repaid annually. equal parts. With a straight-line return on capital, annual total payments decrease. This indicates that straight-line capitalization corresponds to declining income streams and is not applicable to equal income streams, since leads to underestimation. The annual rate of return is calculated by dividing 100% of the asset's value by the remaining life:

Ry - rate of return on investment;

n - Remaining economic life.

Example. A loan was issued in the amount of $ 1,000 for a period of 4 years at 12% per annum. Determine the amount of return on the initially invested capital for investments.

Solution. Given that the loan is issued for a period of 4 years, the straight-line capitalization ratio will be equal to 25% (100% : 4 = 25%). Each year, 25% (1000$ / 4 = 250$) of the initial capital invested and 12% of the investment are reimbursed. Therefore, the overall capitalization ratio will be R= 25% + 12%= 37%.

2. Return of capital on the compensation fund and the rate of return on investment (Inwood's method). The rate of return on investment, as an integral part of the capitalization ratio, is equal to the compensation fund factor at the same interest rate as for investments:

R= Ry + SFF(n, Y),

SFF - compensation fund factor;

Y=Ry - rate of return on investment.

Part of the total income stream is the NOR, the remainder of the income stream provides capital recovery or return. In the event of a 100% loss of capital, the part of the income going to replace the capital, being reinvested at an interest rate, will grow to the original principal amount: thus, a full recovery of the capital occurs.

Example. A loan in the amount of $2,000 was issued for a period of 5 years at 10% per annum. It can be fully repaid subject to annual equal payments of $527.6 (based on the depreciation contribution). Construct uniformly annuity capitalization.

Solution. The bank's income will be $200 annually. The return of the principal amount in the first year will be $527.6 - 10% of $2000=$327.6. In the second year: $527.6 - 10% ($2000 - $327.6) = $360.36. Similarly, income is calculated for the next 3 years. The calculation results are shown in the table:

3. Return of capital on the compensation fund and the risk-free rate of interest (Hoskold's method). In some cases, the rate of return brought by the initial investment is somewhat high. This makes reinvestment at the same rate as the original investment unlikely. Therefore, for reinvested funds, it is expected to receive income at the risk-free interest rate:

R= Ry + SFF (n, Yb),

Yb - Risk-free interest rate.

Example. The investment project assumes an annual 10% return on capital for 5 years. For the first year, an income of $554 is expected. Return on investment amounts can be risk-free reinvested at a rate of only 6%. Determine the value of income.

Solution. According to the table "6 functions of compound interest", the five-year factor of the compensation fund at 10% is 0.1773964. The capitalization ratio will be equal to R= 0.1 + 0.1773964 ? 0.277. If the expected income for the first year is $554, then the value of the income is V= NOR / R= 554 / 0.277 = $2000.

After calculating the NPC and the capitalization ratio, the value of the property is calculated on their basis. The main stages of the capitalization valuation procedure:

1) determination of the expected annual (or average annual) income, as the income generated by the property at its best and most efficient use;

2) calculation of the capitalization rate based on comparable sales data collected on competitive and open markets;

3) determination of the value of the property based on net operating income and capitalization ratio by dividing the NPC by the capitalization ratio:

Example. Determine the value of the object based on the following data on the object of assessment:

1) PVD = 160000 c.u.

2) Debts - 5% of the PVD

3) Operating expenses - 45% of the PVD

4) The industry average capitalization ratio is 0.10.

Solution. 1) Debts are equal to 5% of 160,000 = 8,000 c.u.

2) DVD = 160000 - 8000= 152000 c.u.

3) Operating expenses 45% of 160,000 = 72,000 c.u.

4) CHOD \u003d DVD - operating costs \u003d 152,000 - 72,000 \u003d 80,000 c.u.

5) cost V = I/R = 80,000 / 0.10 = 800,000 c.u.

The capitalization rate has great importance when planning financial or investment activities. At the same time, in Russia, the capitalization rate cannot always be determined with reliable accuracy. This is because information from various markets arrives incomplete. In addition, often it is not entirely true. What is the capitalization rate?

What is the capitalization rate?

This indicator is the ratio of the value of the property and the income that it can bring during the year. The capitalization rate allows the investor to assess the prospects of the investment Money to one asset or another. There are several types of this indicator. By analyzing each of them, you can better understand the characteristic features of capitalization rates.

Characteristics of the indicator

For example, the risk-free capitalization rate provides for the direction of investments in those assets for which at least a return on investment is guaranteed. As far as we know, there is practically no risk-free investment at all. In this case, we mean such investments for which the probability of unpleasant accidents is reduced to zero.

As an example of such investments, one can cite investments, the guarantor of which is the state or a reliable bank from Switzerland. At the same time, market risks are inextricably linked with financial instruments such as stocks, bonds and other securities. Income from such investments directly depends on the success of the company issuing them.

Investors are the first to feel the low profitability of the business for investing their own money in securities. But not only this type of financing is accompanied by risks. For example, real estate is a traditional and one of the most reliable ways to invest. However, this asset is also subject to such risks as low liquidity, depreciation during operation, as well as changes in legislation, including tax.

Capitalization rate calculation methods

What are the calculation methods for the capitalization rate? There are several of them:

• cumulative construction;
• related investments;
• market squeeze method;
• Inwood's method and others.

In practice, the most common method is the cumulative construction. What are the components of the capitalization rate? This method uses the principle of summing the risk-free rate, the market risk premium, and the risk premium associated with investing in a particular asset. What does it mean? In other words, in order to predict the likely return, it is necessary to take into account indicators such as the risk-free rate, the total level of market risks and the degree of risk relative to a particular asset.

Real estate capitalization rate

In the process of analyzing the likely return on investing in real estate, investors calculate the profit that they can receive in the course of its operation. This method allows you to predict the effect of investments and compare the cost of purchasing an object with revenue.

The capitalization rate for real estate is calculated using a formula that is derived from the following equation:

V = I/R where:

• V is the value of the real estate object;
• I is the expected profitability from the operation of the facility;
• R is the real estate capitalization rate.

Accordingly, the capitalization rate: R = I/V.

It should be noted that the income capitalization rate is sometimes also called the capitalization ratio, capitalization rate, or net rent multiplier. These terms are synonyms. The calculation of this indicator is quite effective and objective. This is due to the fixed value of real estate, which is set by the market and which can be found out from open sources. In addition, the price of renting real estate objects is also regulated by the market, which simplifies the task.

Principles for calculating the capitalization rate for real estate

It should be emphasized that when calculating the profitability of an object, mandatory expenses should be deducted from the total amount of revenue. These include:

• payment for electricity;
• payment for the protection of the object;
• salaries of various employees;
• other costs associated with the process of real estate operation.

In addition, the shortfall in profit due to the leasing of not all 100% of the building's area should be deducted from parameter I. Also, expenses that reduce the overall profitability include taxes, interest on loans and other fixed costs. And only after deducting all costs, we get net operating income, which is used in the formula for calculating the real estate capitalization rate.

Having received all the necessary data, we can calculate the required indicator using the already given formula. Consider an example. Suppose funds are invested in such a type of real estate as warehouses. The cost of the object is 50 million rubles. After deducting all costs, the investor determines that the net operating income will be 13 million rubles per year. To determine the capitalization rate for real estate, you must use the formula: 13 million / 50 million = 0.26. This value shows that every year the investor will receive 26% of his investment from the lease of warehouse space.

Selection of the property with the highest capitalization rate

When choosing a real estate object for investment, preference should be given to those that have the highest capitalization rate. In addition, it should be noted that without taking into account such a coefficient, it is impossible to predict the effectiveness of investments and evaluate the object before purchasing it. It is also required to analyze the market and track important economic indicators based on the available data on investments in real estate.

In the process of full monitoring, the information received should be summarized. At the same time, it is necessary to evaluate various segments of the real estate market. Subsequently, this information will serve as a guideline and will allow for a correct assessment of the object. In addition, it makes it possible to carry out high-quality comparative analysis available calculated indicators and average figures for the market.

Tied investment method

Often, the sum of own and borrowed capital is used to purchase real estate. Therefore, for the correct calculation of the capitalization rate, it is necessary to take into account both sources of investment. How to calculate the indicator? In this case, the direct investment method, or, as it is also called, the investment group technique, is used to determine the capitalization ratio. In this case, the capitalization rate formula for credit funds is as follows:

Pm \u003d DO / IR, where:

• Рм is the coefficient of capitalization of borrowed funds, or the mortgage constant;
• TO - annual payments on borrowed funds;
• IC - the principal amount of the mortgage loan.

In this case, the capitalization rate for own funds is calculated according to the following formula:

Pe \u003d DP / K, where:

• Pe - the rate of return on equity;
• DP - cash flow for the year before all taxes;
• K - the amount of equity capital.

The total capitalization rate when using the direct investment method is determined by calculating the weighted average of the first two indicators: P = M x Pm + (1 - M) x Pe, where M is the part of the funds taken on credit in the total cost of the object.

Market squeeze method

This method involves using in the calculation of the capitalization rate an indicator of net operating income from the activities of a similar company or from its real estate, as well as from the cost of selling its assets. To determine the capitalization ratio using the market squeeze method, it is necessary to divide the net operating income by the value of a similar object or company.

What does it mean? In other words, to determine the capitalization rate of the company in question, the indicators of the basic capitalization ratio formula are used, but for another similar enterprise that occupies the same market segment and is comparable in size. characteristic feature This method of calculation is the lack of accounting for return on investment and return on investment.

This technique has both advantages and obvious disadvantages. To positive characteristics can be attributed to the relative simplicity of determining the capitalization ratio. The rate calculated in this way has its drawbacks. For example, the disadvantages include the lack of necessary data regarding the net operating income and cost of sales of the company, which is taken as the basis for the analysis. Therefore, it is not always possible to choose correct and suitable examples.

Inwood method

This method is used in cases where, according to the forecast, throughout the entire investment cycle, the income from investments will be equal in magnitude. In this case, part of the income is the proceeds from investments, and the other part is the return on invested capital. The capital recovery amount is reinvested. This takes into account the rate of return on investment. It is possible to determine the capitalization rate, provided that equal revenue is received, by obtaining the sum of the rate of return on investments and the return fund factor for the same percentage.

Capitalization rate(capitalization ratio) - an indicator that describes the ratio of the market value of an asset to net income for the year.

In property valuation, this indicator is calculated as follows: net profit per year / property value. Thus, the capitalization rate shows the investor the percentage of income that he will receive by purchasing this or that asset. This indicator is important for evaluating investments, but in Russia it is not always possible to accurately calculate it due to the lack of statistical information on the real estate market and other markets in the country.

If the income from the asset grows, the growth rate indicator is included in the formula. If income either grows or falls, instead of the capitalization rate, the DCF method (Discounted Cash flow(English) discounted cash flow).

A decrease in capitalization rates may indicate a recession in the market or even its stagnation. Most often this indicator is used in the real estate market.

Capitalization ratio must match the chosen level of income. The capitalization rate for an enterprise is usually derived from the discount rate by subtracting the expected average annual growth rate of income or cash flow (depending on which amount is capitalized). Respectively for the same enterprise, the capitalization rate is usually lower than the discount rate.

FROM mathematical positions, the capitalization rate is a divisor used to convert the amount of income (profit or cash flow) for one period of time into a measure of value.

So, to determine the capitalization rate, you must first calculate the appropriate discount rate. Exist various methods determining the discount rate, the most common of them are:

1. Model for valuation of capital assets;

2. Method of cumulative construction;

3. Weighted average cost of capital model.

With a known discount rate, the capitalization rate in general view:

R to= R d– g, where R d- discount rate, g - long-term growth rate of income (profit or or cash flow).

2) The method of discounting future income - based on forecasting future cash flows for the entire forecast period, as well as in the residual period, which are then discounted at the appropriate discount rate. It is used in cases where it is assumed that the future income of the enterprise will be unstable over the years of the forecast period, as well as when attracting additional investments during the forecast period.

DP methods are used when it is possible to reasonably determine one or another type of future income of the enterprise being valued and the capitalization/return rate of the corresponding investments.

When determining the market value of an enterprise using the discounted cash flow method, as a rule, the following sequence of actions is observed:

1) the duration of the forecast period is determined, and the type of cash flow that will be used as a basis for the assessment is selected; 2 gross income, expenses and investments of the enterprise are analyzed and forecast; 3 the discount rate is calculated; 4 cash flows are calculated for the forecast and post-forecast periods; 5 calculates the present value of future cash flows in the forecast and post-forecast periods; 6final amendments are made and the cost is determined.

Methods for calculating capitalization ratios and rates of return in business valuation. OPTION 1

Most often in calculations investment projects the discount rate is defined as weighted average cost of capital (WACC), which takes into account the cost of own (share) capital and the cost of borrowed funds.

WACC= Re(E/V) + Rd(D/V)(1 - tc),

where Re is the rate of return on own (share) capital, calculated, as a rule, using the CAPM model;

E- market price own capital (share capital). It is calculated as the product of the total number of ordinary shares of the company and the price of one share;

D - market value of borrowed capital. In practice, it is often determined from financial statements as the amount of company loans. If these data cannot be obtained, then available information on the ratio of equity and debt capital of similar companies is used;

V = E + D - the total market value of the company's loans and its share capital;

R d - the rate of return on the borrowed capital of the company (the cost of raising borrowed capital). Interest on bank loans and corporate bonds of the company are considered as such costs. At the same time, the cost of borrowed capital is adjusted taking into account the income tax rate. The meaning of the adjustment is that interest on servicing loans and borrowings is charged to the cost of production, thereby reducing the tax base for income tax;

t c - income tax rate.

To determine the cost of equity capital is used capital assets pricing model (CAPM).

The discount rate (rate of return) of equity (Re) is calculated by the formula:

Re = Rf + β(Rm - Rf),

where Rf is the risk-free rate of return;

β is a coefficient that determines the change in the price of a company's shares compared to the change in share prices for all companies in this market segment;

(Rm - Rf) - market risk premium;

Rm - average market rates of return on the stock market.

Rate of return on investment in risk-free assets (Rf). As risk-free assets (that is, assets in which investments are characterized by zero risk), government securities are usually considered.

coefficient β. This ratio reflects the sensitivity of the returns on securities of a particular company to changes in market (systematic) risk. If β = 1, then the fluctuations in the prices of the shares of this company completely coincide with the fluctuations of the market as a whole. If β = 1.2, then we can expect that in the event of a general rise in the market, the value of the shares of this company will rise 20% faster than the market as a whole. Conversely, in the event of a general decline, the value of its shares will decline 20% faster than the market as a whole.

Market risk premium (Rm - Rf). This is the amount by which average market rates of return in the stock market have exceeded the rate of return on risk-free securities for a long time. It is calculated on the basis of statistical data on market premiums over an extended period.

The approach described above for calculating the discount rate may not be used by all enterprises. First, this approach is not applicable to companies that are not public joint-stock companies therefore, their shares are not traded on the stock markets. Secondly, this method will not be able to be applied by firms that do not have sufficient statistics to calculate their β-coefficient, as well as those that are unable to find an analogue company whose β-coefficient they could use in their own calculations. To determine the discount rate, such companies should use other methods of calculation or improve the methodology to suit their needs. It should also be noted that the methodology for assessing the weighted average cost of capital does not take into account the share and cost (most often zero) of accounts payable in the structure of liabilities.

The cumulative method for estimating the discount rate is determined based on the following formula:

d = E min + I + r,

where d - discount rate (nominal);

E min - minimum real discount rate (risk-free rate);

I - inflation rate;

r - coefficient taking into account the level of investment risk (risk premium).

Usually for a minimum real rate discounting take 30-year US government bonds.

The main disadvantage of this calculation technique is that it does not take into account the specific cost of capital of the company. In fact, this indicator has been replaced by inflation and a minimum yield comparable to government long-term bonds, which has nothing to do with the profitability of the company, the weighted average interest rate (for loans and / or bonds) and the structure of its liabilities.

both methods involve the use of a risk premium. The risk premium can be determined different ways: Guidelines for evaluating the effectiveness of investment projects recommend taking into account three types of risk when using the cumulative method: country risk; risk of unreliability of project participants; risk of non-receipt of project revenues.

Country risk can be learned from various ratings compiled rating agencies and consulting firms(for example, by the German company BERI, which specializes in this). The amount of the risk premium characterizing the unreliability of project participants, according to methodological recommendations should not be higher than 5%. The adjustment for the risk of non-receipt of the income provided for by the project is recommended to be set depending on the purpose of the project. Many components of this methodology are assessed quite subjectively; there is no linkage of the risk premium to the specific risks of the project and taking into account the current activities of the company.

OPTION 2

Cumulative construction method provides for the construction of an interest rate as a result of the summation of several values. The basis is the so-called risk-free rate. The risk-free rate is adjusted for inflation (Fischer's formula), for the risk associated with the characteristics of the property being assessed and the industry, the country (the risk of objects leased to unreliable tenants; the risk of insufficient liquidity of the assets being evaluated; the risk of political instability, etc. ) All corrections are taken into account as a percentage. The sum of the risk-free rate and the adjustments made is the interest rate at which the capitalization ratio is calculated. The basis for making amendments may be well-known data, the opinion of an expert appraiser based on his knowledge and experience.

In general, the interest rate using the cumulative method can be represented as:

where Rr - interest rate (discount rate); i - risk-free interest rate; r - percentage of inflation; - systematic risks (of the economy as a whole); - non-systematic risks (inherent only in the enterprise).

Method according to the theory of capital assets САРМ (β-coefficient).

The Capital Asset Pricing Model (CAPM) was developed by W. Sharp. Its essence is that adjustments are added to the risk-free rate for the excess of the risk inherent in the company over the average market (average industry), multiplied by the volatility of the company's profitability:

where Rr is the rate of return determined by the capital asset valuation method; ir is the risk-free rate of return. Defined as the return on an asset known with absolute certainty over the time of analysis. It is calculated in two ways: 1) as the yield of government or especially reliable securities; 2) total profitability of interbank interest rates and profitability of stable, large banks. In both cases, the inflation component is taken into account. In state or especially reliable securities it is laid down immediately, an inflationary premium is added to the total return (Fisher's formula): R is the average market return in this industry; p - coefficient characterizing the variability of profitability shows a measure of relative systematic risk compared to the average value of risk in a given industry or the ratio of the change in the company's profitability to the change in the average market profitability in the industry, where δ com is the change in the company's profitability; δ neg - the amount of change in the average market profitability in the industry.

The CAPM model provides for the total value of the products of the excess of risk by the variability of the returns of various risk factors. But in practical conditions, when assessing the value of a business, the product is calculated only relative to the average market profitability in the industry, the remaining necessary amendments are added based on expert opinion according to the formula

17. Types of final adjustments and the process for making them. Premiums and discounts in the valuation of controlling and non-controlling stakes. Methods for making adjustments for lack of liquidity.

Goals inflation adjustment documentation are: bringing retrospective information for past periods to a comparable form; taking inflationary price changes into account when making cash flow forecasts and discount rates.

The simplest way inflation adjustment - revaluation of all balance sheet items based on changes in the exchange rate of the ruble relative to the exchange rate of another currency, such as the dollar or the euro. Dignity this method– simplicity and the ability to work without a large volume additional information. Disadvantages: Adjustment for the exchange rate gives inaccurate results, since the exchange rates of the ruble and other currencies do not match their real purchasing power.

The second method of inflation adjustment– revaluation of assets and liabilities of the balance according to fluctuations in the levels of commodity prices. Here you can focus both on the mass of goods as a whole, and on each specific product or product group. This is a more accurate way of inflation adjustment.

The third way of inflation adjustment based on accounting for changes in the general price level: various items of financial statements are calculated in monetary units of the same purchasing power (in rubles of the base or current period as of the reporting date); for recalculations, the index of dynamics of the gross national product or the index of consumer or wholesale prices is used. The method increases the realism of the analysis, but does not take into account varying degrees changes in the value of individual assets.

After inflation adjustment, the financial statements are normalized.

Normalization of financial statements- this is an adjustment of reporting based on the determination of income and expenses that are characteristic of a normally operating business.

Control Bonus considered as a percentage of the redemption price exceeding the market price of shares.

Discount for the non-controlling nature of the package is the derivative of the control premium. This trend is based on empirical data. The allowance for non-controlling nature (minority interest) as a percentage is calculated using the following formula:

The average control premium fluctuates between 30-40%, and the discount from the cost for a smaller share fluctuates around 23%.

discount for insufficient liquidity is defined as the amount or percentage by which the value of the package being evaluated is reduced to reflect insufficient liquidity.

According to Sh. Pratt ( Pratt Sh.P. Business valuation. Discounts and premiums/per. from English. M.: Kvinto-Management, 2005. S. 17.), the purpose of applying discounts and premiums is to adjust the underlying cost to reflect differences between characteristic features the package (share) being assessed and the group of companies on the basis of which the estimated cost was calculated. All data on premiums and discounts are calculated empirically.

The control premium is the value of the advantage associated with owning a controlling stake.

Discount for non-controlling nature - the amount by which the value of shares in the package being evaluated is reduced, taking into account its non-controlling nature.

The discount for insufficient liquidity arises due to the lack of liquidity of the shares, i.e. the possibility of their rapid conversion into cash at minimal cost and at a price close to the market.

However, with a deeper study of the problem, carried out in the specified manual by S. Pratt, a number of discounts and bonuses are considered:

– the premium for the strategic nature of the acquisition (the premium for taking over the entire company (100% of the stake)) is 20% of the cost of the controlling stake;

– discount associated with the change of key figure (considered as substitutions a risk premium associated with a key person in the management of the company, which can be reflected in the income approach as part of the calculation of the discount rate and when calculating multiples in the comparative approach);

– discount due to actual or potential security obligations environment. Also considered as a replacement for the final adjustment in the income and comparative approaches;

– discount due to litigation against the company being valued;

– a discount associated with the loss of a customer base or suppliers. It is also considered as a substitute for the corresponding risk in the discount rate in the income approach or adjustment to multiples in the comparative;

- block discount - a value or percentage expression of the value deducted from the market price of shares in order to reflect a decrease in the value of a block of shares (per share) in the case when big size package does not allow its implementation within a period of time characteristic of the normal volume of the package. This circumstance is due to the fact that there will be an excess supply of such shares on the market, which will lead to a fall in the rate;

- "portfolio" discount (discount for the heterogeneity of assets) - occurs in the event of the sale of diversified companies as a whole or in large parts, combining several lines of activity, which reduces the attractiveness of the purchase (due to additional problems in the management of non-core assets and their further sale). The discount is determined from the sum of the cost of individual constituent parts companies.