Capitalization rate discount rate growth rate. Discount and capitalization rates

(In preparation for the appraiser qualification exam)

Good day, dear reader!

Since this issue is discussed quite often, we decided to add our clarifications.

So, the first thing you need to know about the discount rate and capitalization rate is that in almost all the materials that we had to familiarize ourselves with, a purely mathematical platform is laid down for determining the discount rate and capitalization rate, which does not explain anything with economic point vision. If we take the history of the origin of the term, then the term capitalization rate was first heard in economics, more precisely, in the section of economic analysis, and even more precisely, in the section of financial analysis.

At the same time, let us recall that the purpose of financial analysis is to characterize the financial condition of an enterprise, company, or organization.

Objectives of financial analysis:

1. Analysis of assets (property).
2. Analysis of funding sources.
3. Analysis of solvency (liquidity).
4. Analysis of financial stability.
5. Analysis financial results and profitability.
6. Analysis of business activity (turnover).
7. Cash flow analysis.
8. Analysis of investments and capital investments.
9. Market value analysis.
10. Bankruptcy probability analysis.
11. Comprehensive assessment of financial condition.
12. Preparation of financial position forecasts.
13. Preparation of conclusions and recommendations.

First, let's remember what capitalization is:

Capitalization: transformation of funds (part of net profit or all profit, dividends, etc.) into additional capital, additional factors of production (such as means of labor, objects of labor, labor, etc.), resulting in an increase in the amount of equity capital . The value of a company is assessed on the basis of: annual profit received, its fixed and working capital, the market value of its shares and bonds.

A special case of capitalization is real estate capitalization:

Real estate capitalization, in short, is the value of real estate, which, under the influence of various factors, can rise or fall. The capitalization of real estate is significantly influenced by such characteristics as the location of the object, technical condition and functional purpose.

Real estate is a product that differs from others in its fundamentality and thoroughness. During its existence, real estate gradually wears out. It is the percentage of wear and tear that determines the technical condition of the object, and therefore directly affects its capitalization. And this is understandable, there is a decrease in the consumer properties of the building or structure, the object becomes less suitable for use under the given conditions. Accordingly, the initial cost of real estate is reduced.

Now let's move directly to the capitalization ratio:

Capitalization ratio is an indicator that compares the size of long-term accounts payable with total sources of long-term financing, including, in addition to long-term accounts payable, the organization's own capital. The capitalization ratio allows you to assess the adequacy of the organization's source of financing its activities in the form of equity capital.

The capitalization ratio is included in the group of financial leverage indicators - indicators characterizing the ratio of the organization's own and borrowed funds. This ratio allows you to assess business risk. The higher the value of the coefficient, the more the organization is dependent in its development on borrowed capital, the lower its financial stability. At the same time, a higher level of the ratio indicates a greater possible return on equity (higher return on equity). This ratio is considered as one of the most important indicators of the company’s performance, both from the position of an investor and from the position of a creditor. For valuation purposes, capitalization ratio is also one of the main calculation tools.

Calculation (formula)

The capitalization ratio is calculated as the ratio of long-term liabilities to the sum of long-term liabilities and the organization’s equity capital:

Capitalization ratio = Long-term liabilities / (Long-term liabilities + Equity)

The capitalization ratio is an important indicator of a company's financial leverage, reflecting the structure of long-term financing sources. In this case, the company's capitalization (not to be confused with market capitalization) is considered as a combination of the two most stable liabilities - long-term liabilities and equity.

Secondly, very often, there is confusion between the concepts of discount rate, capitalization ratio, financial leverage ratio, financial risk ratio, rate of return on capital, rate of return on investments, profitability of an alternative project (in all cases it must be clearly understood that this is not realized, but desired profitability !), there is also the formulation rate of return on capital, etc. So you need to understand that all these definitions are often used as synonyms. Why does this happen? Here is one example of such confusion:

The balance sheet and net profit of an enterprise can be determined by the rate of return on the selected profit. In turn, the rate of return is a parameter that characterizes the volume of profit of the company or the activity of its receipt on the balance sheet of the enterprise. If during the period of activity of the enterprise there is no growth or reduction in production, then the rate of return remains at the same level. Respectively, capitalization rate will be equal to the rate profitability. If the latter indicator changes, the capitalization parameter will also change.

If we try to explain the material meaning of the discount rate, it seems very simple, namely

There are typical situations in which it is necessary to find the change in the value of money over time, i.e., let’s say today we have 10 thousand rubles in reserve in our pocket, so to speak, and a year later this money has already depreciated a little and represents the equivalent of today’s 9 thousand rubles . Thus, we see that the value of our “stash” has decreased by 10%. So in this case, this 10% is the discount rate for our case (specifically for our case, since each case has its own discount rate, we must always remember that this is a calculated value). The opposite situation could have happened - our money was lying in our pocket for a whole year (in Japanese yens, for example), we took it out, and the exchange rate changed in relation to the Russian ruble by the same 10% upward, could this be? - easily. So we received instead of 10 thousand rubles. how much now? - correct - 11 thousand rubles. and in this case, what was the discount rate? - the same almost 10% (more precisely 9.09%) is true again, but now it would be called a rate or capitalization rate or rate of return on investment, etc. for the case of conversion from 10 thousand to 11 thousand, and for In case of conversion from 11 thousand to 10 thousand, the term discount rate would be used.

Thus, the economic understanding of capitalization and discount rates usually refers to rates of two types of changes in value, either upward or downward, of money or their equivalents (real estate, shares and any other types of securities and types of assets). In some cases relating to cases of real estate valuation using the income approach, namely cases of using direct capitalization methods, the capitalization rate is understood as the sum of the discount rate (return on investment, etc. (desired or acceptable!) and a certain amount that would be nice to return to the investor against the depreciation over time of the asset. In this situation, three scenarios are possible - the capitalization rate will be less than the discount rate, equal to it, or the capitalization rate will be greater than the discount rate. All this will depend on the economic situation in the country and in this sector of the economy. At the same time, in the case assessments land plot any category of land and with any purpose, the capitalization rate is also used, but in this case no return of capital needs to be taken into account (it will be returned in full upon sale, since land is a non-aging asset), therefore the capitalization rate will be equal to the rate of return on capital is another example of the emergence of synonymous definitions.

When using the capitalization method in the income approach, the capitalization rate is calculated. It, like the discount rate, reflects the desired or acceptable return on an investment and, depending on the object of evaluation, has different components. The essence of calculating the cost based on this rate is to find the multiple by which to multiply the net annual income. Those. if an acceptable return should be high, then this usually correlates with a high investment risk, or with a high rate of wear and tear of the asset (object of valuation), or with both at the same time, therefore the value of such an asset from the investor’s position should be lower, so we see , that according to the existing calculation methodology, dividing by the capitalization rate is nothing more than establishing an inversely proportional multiple, which as a result will allow the asset to be assessed as cheaper and vice versa.

When using the discounted cash flow method, the concept of a discount rate is used, with the help of which future cash flows can be calculated, i.e., show how much interest per year the cash flows of the next years should depreciate from the point of view of the market or a specific investor. There is a clear conflict of interest here and, as a consequence, a possible discrepancy in the calculation - from the position of a seller who wants to sell an asset at a higher price, the discount rate will be lowered as much as possible in order to increase the present value of future cash flows, which will ultimately lead to an increase in the value of the asset. From the position of a buyer who does not want to overpay (since over the years of expectations of future cash flows, he wants or could receive an acceptable or desired return for each year, which will also, depending on the type and quality of the asset, be different accordingly) depreciation of future cash flows will be more significant, as a result, a higher discount rate will lead to a decrease in the final value of the asset. Thus, the discount rate is a subjective value and depends on arguments that turn out to be more significant for specific purposes and for each specific case separately.

Now, having understood a little, you can become more familiar with the specific approaches and methods used in assessment:

INCOME APPROACH TO REAL ESTATE VALUATION

The income approach is based on the principle of expectation, which states that the value of an object of evaluation is determined by the amount of future benefits of its owner. Valuation using the income approach assumes that potential buyers consider the income-generating object of assessment from the point of view of investment attractiveness, that is, as an investment object with the aim of receiving corresponding income in the future.

The income approach includes two methods: the direct capitalization method and the discounted cash flow method. These methods differ in the way they transform income streams.

When using the income capitalization method, income for one time period is converted into the value of real estate if the income from the property is stable or changes at a constant growth rate. When using the discounted cash flow method, income from the proposed use of real estate is calculated over several forecast years and the proceeds from the resale of the property at the end of the forecast period are taken into account. This method is used when income varies from period to period, i.e. they are not stable.

• PVP (potential gross income);
• DVD (actual gross income);
• NOR (net operating income);
• DP (cash receipts) after interest payments on the loan.

Potential Gross Income (GPI) – the income that can be received from real estate, with its 100% use without taking into account all losses and expenses. PPV depends on the area of ​​the property being assessed and the established rental rate and is calculated using the formula:

PVD = S S a, (4.2)

where S is the area rented out, m2;

C a – rental rate per 1 m2.

The lease agreement is the main source of information about income-generating real estate. Lease is the provision of property to the lessee (tenant) for a fee for temporary possession and use. The right to lease property belongs to the owner of the property. Lessors can be persons authorized by law or the owner to rent out property. One of the main regulatory documents regulating rental relations is the Civil Code of the Russian Federation (Chapter 34).

In the process of work, the appraiser relies on the following provisions of the lease agreement:

• under a lease agreement for a building or structure, the tenant, simultaneously with the transfer of rights of ownership and use of such real estate, is transferred the rights to use that part of the land plot that is occupied by this real estate and necessary for its use, even in the case where the land plot on which the leased buildings or structures are located , sold to another person;
• if the lease term is not specified in the agreement, then the lease agreement is considered to be concluded for an indefinite period;
• the transfer of property for rent is not a basis for termination or cancellation of the rights of third parties to this property. When concluding a lease agreement, the lessor is obliged to warn the tenant about all the rights of third parties to the leased property (easement, right of lien, etc.). Otherwise, the tenant has the right to demand a reduction in rent or termination of the contract and compensation for losses.

Lease agreement for a building or structure:

• concluded in writing for a period of at least one year, subject to state registration and is considered concluded from the moment of such registration;
• provides for the terms and amounts of rent agreed upon by the parties, without which the lease agreement is considered not concluded;
• if the tenant has made, at his own expense and with the consent of the lessor, improvements to the leased property that are inseparable without harm to the property, then he has the right, after termination of the contract, to reimburse the cost of these improvements, unless otherwise provided by the lease agreement. The cost of inseparable improvements to the leased property made by the tenant without the consent of the lessor is not subject to compensation;
• The tenant has the right, with the consent of the lessor, to sublease the leased property, provide the leased property for free use, and also make it as a contribution to the authorized capital.

The rental rate, as a rule, depends on the location of the property, its physical condition, the availability of communications, the lease term, etc.

Rental rates are:

• contractual (defined by the lease agreement);
• market (typical for a given market segment in a given region).

Market rental rate represents the rate prevailing in the market for similar real estate, i.e. is the most likely rent that a typical landlord would agree to let and a typical tenant would agree to lease the property for, which is a hypothetical transaction. Market rent is used to value freehold ownership, where the property is essentially owned, operated and enjoyed by the owner himself (what would be the income stream if the property were rented out). The contract rental rate is used to value the lessor's partial property rights. In this case, it is advisable for the appraiser to analyze lease agreements from the point of view of the terms of their conclusion. All lease agreements are divided into three large groups:

• with a fixed rental rate (used in conditions of economic stability);
• with a variable rental rate (revision of rental rates during the contract period is carried out, as a rule, in conditions of inflation);
• with an interest rate (when a percentage of the income received by the tenant as a result of the use of the leased property is added to the fixed amount of rental payments).

Income capitalization method It is advisable to use in the case of concluding an agreement with a fixed rental rate; in other cases, it is more correct to use the discounted cash flow method.

Actual Gross Income (DVD) - this is the potential gross income minus losses from underutilization of space and from the collection of rent, with the addition of other income from the normal market use of the property:

DVD = PVD – Losses + Other income. (4.3)

Typically these losses are expressed as a percentage of potential gross income. Losses are calculated at a rate determined for the typical level of management in a given market, i.e. The market indicator is taken as a basis. But this is only possible if there is a significant information base on comparable objects. In the absence of such, to determine the coefficient of underutilization (underutilization), the appraiser first of all analyzes retrospective and current information on the object being assessed, i.e. existing lease agreements by duration, the frequency of their re-conclusion, the size of the periods between the expiration of one lease agreement and the conclusion of the next (the period during which units of the property are vacant) and on this basis calculates underutilization ratio(Knd) of the property:

K nd = (D p T s) / N a, (4.4)

D p – the share of real estate units for which contracts are renewed during the year;

T s – middle period during which the real estate unit is vacant;

N a – the number of rental periods per year.

The determination of the underutilization coefficient is carried out on the basis of retrospective and current information; therefore, in order to calculate the estimated ADV, the obtained coefficient must be adjusted taking into account the possible utilization of space in the future, which depends on the following factors:

• general economic situation;
• prospects for the development of the region;
• stages of the real estate market cycle;
• the relationship between supply and demand in the assessed regional segment of the real estate market.

Load factor depends on various types real estate (hotels, shops, apartment buildings, etc.). When operating real estate, it is desirable to maintain the load factor at a high level, since a significant part of operating costs is constant and does not depend on the load level.

K loading = 1 – K nd.

The appraiser makes an adjustment for losses when collecting payments, analyzing retrospective information on a specific object with subsequent forecasting of these dynamics for the future (depending on the development prospects of a specific segment of the real estate market in the region):

Based on historical and current information, the appraiser can calculate the rate of underutilization and losses in the collection of lease payments, followed by adjustments to predict the amount of actual gross income:

where K NDP is the coefficient of underutilization and losses when collecting rental payments;

P a – losses when collecting rent;

P nd – losses from underutilization of space;

PPV – potential gross income.

In addition to losses from underutilization, when collecting rental payments, it is necessary to take into account other income that can be linked to the normal use of this property for the purpose of servicing, in particular, tenants (for example, income from leasing a car park, warehouse, etc.), and not included in the rent.

Net operating income (NOI) – actual gross income minus operating expenses (OR) for the year (excluding depreciation):

CHOD = DVD – OR. (4.7)

Operating expenses are expenses necessary to ensure the normal functioning of the property and the reproduction of actual gross income.

Operating expenses are usually divided into:

• conditionally permanent;
• conditionally variable, or operational;
• replacement costs, or reserves.

Conditionally fixed expenses include expenses, the amount of which does not depend on the degree of operational workload of the facility and the level of services provided:

• property tax;
• land tax;
• insurance premiums (payments for property insurance);
• wages of service personnel (if they are fixed regardless of the load of the building) plus taxes on it.

Conditionally variable expenses include expenses, the amount of which depends on the degree of operational workload of the facility and the level of services provided:

• utilities;
• for the maintenance of the territory;
• for ongoing repair work;
• wages of service personnel;
• payroll taxes;
• security costs;
• management expenses (usually it is customary to determine the amount of management expenses as a percentage of actual gross income), etc.

Expenses not taken into account when assessing for tax purposes:

• economic and tax depreciation, which is considered in calculations by the income approach as compensation and is considered part of the capitalization rate, and not an operating expense;
• servicing the loan is a financing cost and not an operating expense, i.e. financing should not have an impact on the value of real estate (the assessment assumes typical financing for a given type of real estate, and the influence of atypical financing should be excluded);
• income tax is also not an operating expense (it is a tax on personal income, which may depend on factors (form of ownership, composition of property rights, tax status of the owner) not related to the real estate being valued);
• Additional capital structures typically increase revenue, overall cost, or extend economic life. The costs associated with them cannot be classified as operating;
• Business expenses of the property owner that do not lead to an increase in the income received from the property are also not considered operating expenses.

Replacement costs include the cost of periodically replacing wear-and-tear improvements (roofing, flooring, plumbing fixtures, electrical fixtures). Funds are supposed to be reserved in an account (although most property owners don't actually do this). The replacement reserve is calculated by the appraiser taking into account the value of depreciating assets, the length of their useful life, and also! interest accrued on funds accumulated in the account. If the replacement reserve is not taken into account, net operating income will be overstated.

In cases where real estate is purchased with borrowed funds, the appraiser uses this level of income in his calculations as cash receipts before taxes.

Pre-tax cash receipts equal annual net operating income minus annual debt service costs, i.e. reflect the cash receipts that the owner of the property receives annually from its operation.

Calculation of capitalization ratio.

There are several methods for determining the capitalization rate:

• taking into account the reimbursement of capital costs (adjusted for changes in the value of the asset);
• market squeeze method;
• linked investment method, or investment group technique.

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

• compensation for risk;
• compensation for investment management;
• adjustment for projected increases or decreases in the value of an asset.

Determination of the capitalization ratio taking into account the reimbursement of capital costs.

The capitalization ratio consists of two parts:

1) the rate of return on capital (rate of return on investment), which is the compensation that must be paid to the investor for the use of funds, taking into account the risk and other factors associated with a specific property;

2) capital return rates, i.e. repayment of the initial investment amount. Moreover, this element of the capitalization ratio applies only to the depreciable part of the assets.

R cap = R up cap + R normal return, (4.8)

where R cap is the capitalization ratio,

R income cap – rate of return on capital

R rate of return – rate of return of capital

– reduction in the value of real estate (depreciable part of assets).

Capital return rate ( R doh cap ) is most often constructed using the cumulative construction method:

Risk-free rate of return

Real estate risk premiums

Premiums for low real estate liquidity

Investment Management Awards.

Risk-free rate of return is the interest rate on highly liquid assets, i.e. This is a rate that reflects “the actual market opportunities for investing the funds of firms and individuals without any risk of non-return.”

The risk-free rate is used as a base rate, to which the remaining (previously listed) components are added - adjustments for various types of risk associated with the characteristics of the property being valued.

Risk-free rate requirements:

- return on the most liquid assets, which are characterized by a relatively low rate of return, but with a guarantee of return of capital;

- available to the investor as an alternative investment option.

To determine the risk-free rate, you can use both Russian and Western indicators for risk-free transactions. The risk-free rate according to Western methods is considered to be the rate of return on long-term (20 years) government bonds on the world market (USA, Germany, Japan, etc.). When using this risk-free rate, it is necessary to add a premium for the risk of investing in Russia (country risk). This calculation of the risk-free rate is accepted in modern valuation practice, but violates the principle of investor access to highly liquid assets, since Russian enterprises cannot seriously consider investing in long-term government bonds of the world market as an alternative. This risk-free rate was actively used in our country in the first stages of the development of valuation, since this period was characterized by uncritical replication of Western experience without taking into account Russian specifics. Nowadays, the yield on OFZ and VEB is often taken as a risk-free rate.

Country risk adjustment is usually calculated by rating agencies. But this information is not always available to appraisers. In this case, the appraiser can independently determine the country risk for Russia using the developed schemes, but the degree of subjectivity in the calculations increases significantly.

In the assessment process, it is necessary to take into account that nominal and real risk-free rates can be both ruble and foreign currency. When recalculating the nominal rate into the real one and vice versa, it is advisable to use the formula of the American economist and mathematician I. Fisher, which he derived back in the 30s of the 20th century:

R n = R r + J inf + R r J inf, (4.9)

where R n – nominal rate;

R р – real rate;

J inf – inflation index (annual inflation rate).

It is important to note that when using nominal income streams, the capitalization ratio and its components must be calculated in nominal terms, and when using real income streams - in real terms.

Calculation of risk premiums:

• low liquidity premium . When calculating this component, the impossibility of immediate return of investments made in the property is taken into account, and it can be taken at the inflation rate as typical time exposure of objects similar to the one being valued on the market;
• real estate risk premium . In this case, the possibility of accidental loss of the consumer value of the object is taken into account, and the premium can be accepted in the amount of insurance contributions in insurance companies of the highest category of reliability;
• investment management bonus . The riskier and more complex the investment, the more competent management it requires. It is advisable to calculate the premium for investment management taking into account the coefficient of underload and losses when collecting rental payments.

The capitalization ratio includes the rate of return on an investment and the rate of return on capital. If the amount of capital invested in the property remains unchanged and will be returned upon resale, there is no need to calculate the rate of return.

If a change in the value of an asset is predicted, then it becomes necessary to take into account the return of the principal amount of capital in the capitalization ratio. The rate of return of capital shows the annual amount of reimbursement of funds invested in a property in the event that for some reason the loss of these funds (in whole or in part) during the period of ownership of the property is predicted. To recoup the initial investment, a portion of the net operating income is set aside in a recovery fund for recapitalization.

There are three ways to calculate the rate of return on capital ( R normal return ) :

• straight-line return of capital (Ring method);
• return of capital according to the replacement fund and the rate of return on the investment (Inwood method), it is sometimes called the annuity method;
• return of capital based on the compensation fund and the risk-free interest rate (Hoskold method).

Ring's method.

This method is appropriate to use when it is expected that the principal amount will be repaid in equal installments. The annual rate of return on capital is calculated by dividing 100% of the asset's value by its remaining useful life, i.e. It is the reciprocal of the asset's service life. The rate of return is the annual share of the original capital placed in the interest-free recovery fund:

R norm return = 100% / n, (4.11)

R cap = R dox cap + * 100 / n, (4.12)

where n is the remaining economic life, in years;

R return cap – rate of return on investment, %.

Example. Investment terms:

• term – 5 years;
• R income cap – rate of return on investment 18%;
• – 100%.

Solution. Ring's method. The annual straight-line rate of return on capital will be 20%, since in 5 years 100% of the asset will be written off (100: 5 = 20). In this case, the capitalization ratio will be 38% (18% + 20% = 38%).

Inwood method used if the capital return is reinvested at the rate of return on the investment. In this case, the rate of return as a component of the capitalization ratio is equal to the replacement fund factor at the same interest rate as for investments

R norm return = SFF(n, Y), (4.13)

R cap = R dox cap + * SFF(n, Y), (4.14)

Where SFF – compensation fund factor SFF = Y / ((1+ Y ) n – 1) ;

Y – rate of return on investment (R ex cap).

Example. Investment terms:

• term – 5 years;
• return on investment – ​​12%.
• – 100%.

Solution. The capitalization rate is calculated as the sum of the investment return rate of 0.12 and the compensation fund factor (for 12%, 5 years) of 0.1574097. Capitalization ratio is 0.2774097

Hoskold's method. Used when the rate of return on the initial investment is somewhat high, making reinvestment at the same rate unlikely. Reinvested funds are expected to receive income at a risk-free rate

R normal return = SFF (P, Y b), (4.15)

R cap = R dox cap + * SFF ( P, Y b). (4.16)

Where Y b — risk-free rate.

Example. The investment project provides for an annual 12% return on investment (capital) for 5 years. Return on investment amounts can be safely reinvested at a rate of 6%.

Solution. If the rate of return on capital is 0.1773964, which is the recovery factor for 6% over 5 years, then the capitalization rate is 0.2973964 (0.12 + 0.1773964).

The capitalization rate includes the rate of return on investment and the rate of return on capital taking into account the share of the depreciating part of the assets . If the amount of capital invested in real estate remains unchanged and is returned upon resale, then the share of the depreciable part of the assets is equal to 0. If the decrease in the value of the property is known, then we will build a compensation fund specifically to compensate for the depreciable portion of the assets. If, when investing in real estate, the investor expects that its price will increase in the future, then it becomes necessary to take into account the increase in the value of the investment in the capitalization rate.

Decrease in property value ( ), which will happen in P years, takes into account the cost of subsequent resale of the property in the capitalization ratio.

R cap = R up cap + * R normal return, (4.17)

0, if the value of the assessed object does not change,

The share by which the value of the valuation object is planned to be reduced if the value of the valuation object decreases,

= – the share by which the value of the valuation object is planned to increase if the value of the valuation object increases.

Example. It is predicted that the property will be sold in 5 years for 50% of its original price. The rate of return on investment is 12%.

Solution. According to the Ring method, the rate of return on capital is 20% (100% : 5 years) 1/2 = 10%. R cap = 0.1 (rate of return on capital) + 0.12 (rate of return on investment) = 0.22 (22%).

Under the Inwood method, the rate of return on capital is determined by multiplying the replacement fund factor by the percentage loss of the original price of the property.

50% loss 0.1574097 = 0.07887.

R cap = 0.07887 (rate of return on capital) + 0.12 (rate of return on investment) = 0.19887 (19.87%).

Example. The required rate of return on capital is 12%. It is predicted that the price increase after 5 years will be 40%.

Solution. If the value of the investment funds increases, the proceeds from the sale not only provide a return on the entire capital invested, but also provide part of the income necessary to obtain the 12% rate of return on the investment. Therefore, the capitalization ratio must be reduced to account for expected capital gains. Let's calculate deferred income: 0.4 0.1574 (compensation fund factor for 5 years at 12%) = 0.063. Deferred income is subtracted from the rate of return on investment on capital and, thus, the capitalization ratio is determined.

R cap = R y – share growth SFF (P, Y ),

R cap = 0.12 – 0,4 0,15474 = 0.0581 or 5.81%.

Calculation of the capitalization ratio using the market squeeze method

Based on market data on sales prices and NAV values ​​of comparable properties, the capitalization ratio can be calculated:

where CHODi is the net operating income of the i-th analogue object;

Сi is the selling price of the i-th analogue object.

where NORi is the net operating income of the i-th analogue object;

Сi – sale price of the i-th analogue object.

This method does not separately take into account return of capital and return on investment (Table 4.1).

Table 4.1.

Calculation of capitalization ratio ( R cap ) by market squeeze method

Despite all the apparent simplicity of application, this calculation method raises certain difficulties - information on NPV and sales prices falls into the category of “opaque” information.

Calculation of capitalization ratio using the linked investment method.

If a property is purchased using equity and borrowed capital, the capitalization ratio must meet the return requirements for both parts of the investment. The value of the ratio is determined by the related investment method, or investment group technique. The capitalization ratio for borrowed capital is called the mortgage constant and is calculated

R m = DO / K (4.19)

where R m is the mortgage constant;

DO – annual debt service payments;

K – mortgage loan amount.

The capitalization ratio for equity is calculated using the formula:

The overall capitalization ratio is determined as a weighted average:

R = M R m + (1 – M) R e (4.21)

where M is the mortgage debt ratio.

Example. Share of equity capital – 30%; interest rate on the loan – 12%; the loan was provided for 25 years; the rate of return on equity is 5%, then total rate capitalization is equal to:

a) permanent mortgage loan provided for 25 years at 12% per annum - 0.127500;

b) the total capitalization rate is calculated using formula 4.21:

R = 0,7 *0,127500 + 0,3 *0,05 = 0,08925 + 0,015 = 0,10425 (10,42%).

Thus, the specifics of the income capitalization method are as follows:

• NPV for one time period is converted into current value;
• the reversion price is not calculated;
• The capitalization rate is calculated for real estate using three methods:

- market squeeze method;

— the method of determining the capitalization ratio taking into account the reimbursement of capital costs;

— the method of related investments.

Advantages of the income capitalization method are that this method directly reflects market conditions, since when it is applied, as a rule, a large number of real estate transactions are analyzed from the point of view of the relationship between income and value, and also when calculating capitalized income, a hypothetical income statement is drawn up, the basic principle of construction which is an assumption about the market level of real estate exploitation.

Disadvantages of the income capitalization method are that

• its application is difficult when there is no information about market transactions;
• The method is not recommended for use if the object is unfinished, has not reached the level of stable income, or has been seriously damaged as a result of force majeure and requires serious reconstruction.

4.2. Discounted Cash Flow Method

The discounted cash flow (DCF) method is more complex, detailed and allows you to evaluate an object in case of receiving unstable cash flows from it, modeling the characteristic features of their receipt.

The DCF method is used when:

• it is expected that future cash flows will differ significantly from current ones;
• there is data to justify the size of future cash flows from real estate;
• income and expense flows are seasonal;
• The property being assessed is a large multifunctional commercial facility;
• the property is under construction or has just been built and commissioned: (or put into operation).

The discounted cash flow method is the most universal method for determining the present value of future cash flows. Cash flows may change arbitrarily, be uneven and have a high level of risk. This is due to the specifics of such a concept as real estate. Real estate is purchased by an investor primarily for certain future benefits. An investor views a property as a bundle of future benefits and evaluates its attractiveness in terms of how the monetary value of those future benefits compares to the price at which the property can be purchased.

The DCF method estimates the value of real estate based on the present value of income, consisting of projected cash flows and residual value.

Calculation algorithm for the DCF method.

1. Determination of the forecast period.

Determining the forecast period depends on the amount of information sufficient for long-term forecasts. A carefully executed forecast allows you to predict the nature of changes in cash flows for a longer period.

In international assessment practice, the average forecast period is 5-10 years; for Russia, the typical value will be a period of 3-5 years. This is a realistic period for which a reasonable forecast can be made.

1. Forecasting cash flows from a property for each forecast year.

Forecasting cash flow amounts, including reversion, requires:

— a thorough analysis based on financial statements submitted by the customer on income and expenses from the property in a retrospective period;

— studying the current state of the real estate market and the dynamics of changes in its main characteristics;

— forecast of income and expenses based on the reconstructed income statement.

When valuing real estate using the DCF method, several types of income from the property are calculated:

1) potential gross income;

2) actual gross income;

3) net operating income;

4) cash flow before taxes;

5) cash flow after taxes.

After-tax cash flow is the pre-tax cash flow minus the property owner's income tax payments.

In practice, Russian appraisers discount income instead of cash flows:

• CHOD (indicating that the property is accepted as not burdened with debt obligations),
• net cash flow less operating costs, land tax and reconstruction,
• taxable income.

Features of calculating cash flow when using the method.

• Property tax (real estate tax), which consists of land tax and property tax, must be deducted from actual gross income as part of operating expenses.
• Economic and tax depreciation is not a real cash payment, so taking depreciation into account when forecasting income is unnecessary.
• Capital investments must be subtracted from net operating income to obtain cash flow, since these are real cash payments that increase the life of the facility and the value of the reversion cost.
• Loan servicing payments (interest payments and debt repayments) must be deducted from net operating income if the investment value of the property (for a specific investor) is estimated. When assessing the market value of a property, it is not necessary to deduct loan servicing payments.
• Business expenses of the property owner must be deducted from actual gross income if they are aimed at maintaining the necessary characteristics of the property.

Thus:

DVD = PVD – Losses from vacancy and rent collection + Other income (4.22)

CHOD = DVD - OR - Business expenses of the property owner associated with real estate (4.23)

Cash flow before taxes = NPV – Capital investments – Loan servicing + Loan growth. (4.24)

After-Tax Cash Flow for Real Estate = Before-Tax Cash Flow – Property owner's income tax payments. (4.25)

1. Calculation of the cost of reversion.

Reversion is the residual value of an object when the income stream ceases.

The cost of reversion can be predicted using:

1) assigning a sales price based on an analysis of the current state of the market, monitoring the cost of similar objects and assumptions regarding the future state of the object;

2) making assumptions regarding changes in the value of real estate during the ownership period;

3) capitalization of income for the year following the year of the end of the forecast period, using an independently calculated capitalization rate.

1. Determining the discount rate.

“A discount rate is a rate of interest used to calculate the present value of a sum of money received or paid in the future.”

The discount rate reflects the risk-return relationship, as well as the various types of risk inherent in the property.

The capitalization rate is the rate used to reduce a stream of income to a single amount of value. However, in our opinion this definition gives an understanding of the mathematical essence of this indicator. From an economic point of view, the capitalization ratio reflects the investor's rate of return.

Theoretically, the discount rate for a property should directly or indirectly take into account the following factors:

• compensation for risk-free, liquid investments;
• compensation for risk;
• compensation for low liquidity;
• compensation for investment management.

The relationship between nominal and real rates is expressed by Fisher's formulas.

Cash flows and the discount rate must correspond to each other and be calculated in the same way. The results of calculating the present value of future cash flows in nominal and real terms are the same.

In Western practice, the following methods are used to calculate the discount rate:

1) cumulative construction method;

2) a method for comparing alternative investments;

3) isolation method;

4) monitoring method.

Cumulative construction method is based on the premise that the discount rate is a function of risk and is calculated as the sum of all risks inherent in each specific property.

Discount rate = Risk-free rate + Risk premium.

The risk premium is calculated by summing up the risk values ​​inherent in a given property.

The cumulative construction method is discussed in detail in Section 4.1. of this manual when calculating the rate of return on capital as part of the capitalization ratio by the method of reimbursement of capital costs.

Method for comparing alternative investments used most often when calculating the investment value of a property. The discount rate can be taken as follows:

— the return required by the investor (set by the investor);

— expected profitability of alternative projects and financial instruments available to the investor.

Selection method – discount rate, as a rate compound interest, is calculated based on data on completed transactions with similar objects on the real estate market. This method is quite labor-intensive. The calculation mechanism consists of reconstructing assumptions about the magnitude of future income and then comparing future cash flows with the initial investment (purchase price). In this case, the calculation will vary depending on the amount of initial information and the size of the rights being assessed.

The discount rate (as opposed to the capitalization rate) cannot be extracted directly from sales data, since it cannot be calculated without identifying the buyer's expectations regarding future cash flows.

The best option for calculating the discount rate using the allocation method is to interview the buyer (investor) and find out what rate was used to determine the sales price and how the forecast of future cash flows was built. If the appraiser has fully received the information he is interested in, then he can calculate the internal rate of return (final return) of a similar object. He will be guided by the resulting value when determining the discount rate.

Although each property is unique, under certain assumptions it is possible to obtain discrete discount rates that are consistent with the overall accuracy of the forecast for future periods. However, it must be taken into account that purchase and sale transactions of such comparable objects should be selected as similar ones, the existing use of which is the best and most effective.

The usual algorithm for calculating the discount rate using the allocation method is as follows:

• modeling for each analogue object over a certain period of time according to the scenario of the best and most effective use of income and expense streams;
• calculation of the rate of return on investment for an object;
• process the results obtained by any acceptable statistical or expert method in order to bring the characteristics of the analysis to the object being assessed.

Monitoring method is based on regular market monitoring, tracking the main economic indicators of real estate investment based on transaction data. Such information needs to be compiled across different market segments and published regularly. Such data serves as a guide for the appraiser and allows for a qualitative comparison of the obtained calculated indicators with the market average, checking the validity of various types of assumptions.

If it is necessary to take into account the impact of risk on the amount of income, adjustments should be made to the discount rate when valuing individual real estate objects. If income is generated from two main sources (for example, from basic rent and interest premiums), one of which (basic rent) can be considered guaranteed and reliable, then one rate of income is applied to it, and the other source is discounted at a higher rate (so, the size percentage allowances depend on the volume of the tenant’s turnover and are an uncertain value). This technique allows you to take into account different degrees of risk when generating income from one property. By analogy, one can take into account the different degrees of risk of obtaining income from a property over the years.

Russian appraisers most often calculate the discount rate using the cumulative method (formula). This is explained by the greatest simplicity of calculating the discount rate using the cumulative construction method in the current conditions of the real estate market.

The income approach is used to determine the best and most efficient use (BHEI). Let's consider the use of the income capitalization method when determining LNEI.

Example. Best and best use analysis required non-residential premises.

Best and best use analysis is performed by checking whether the considered use cases meet the following criteria:

• legislative permission;
• physical feasibility;
• financial feasibility;
• maximum efficiency.

The land plot is not owned by the owner of the property being assessed. The owner of a non-residential premises has the right to use part of the plot under the house where the non-residential premises are located, according to the area of ​​this premises in relation to the total area of ​​​​the premises located in the house.

Consequently, the current use of the land plot is the only legally permitted, and therefore the most effective.

Let's move on to analyzing the best and most effective use of non-residential premises.

Possible types of use of non-residential premises: office, restaurant or cafe, shop.

Physically feasible use: All options are physically feasible.

Financially feasible use: Considering the location and size of the non-residential premises, all three options may be economically feasible.

Maximum efficiency. The criterion for maximum efficiency is a positive return on invested capital, i.e. a return equal to or greater than the cost of compensation for maintenance costs, financial obligations and the return of the capital itself.

Table 4.2.

To a large extent, financial feasibility depends on supply and demand and location, which determine characteristics such as gross income, operating expenses, losses, etc. The net operating income of an eligible use case must meet the required rate of return.

Using non-residential premises as a store is more economically profitable and less risky. Since the repurposing of the premises, although it will lead to an increase in rental rates, it will entail underutilization of rental space during renovation, an increase in operating costs, an increased risk of underutilization of space and an increase in investments for the amount of reconstruction.

The best and most effective use of the subject matter: use as a store.

When calculating the market value of the assessed non-residential premises within the framework of the income approach, we will proceed from the use of the property being assessed as a store.

Let's consider the use of the discounted cash flow method as part of the income approach assessment of the market value of a real estate property.

The forecast period is 4 years, the assessment date is January 1, 2005. Cash flows will be calculated during the forecast period 2005-2008. and the first year of the post-forecast period (2009) to determine the value of future resale (reversion).

Table 4.3.

Capitalization rate must correspond to the selected income level. The capitalization rate for a business is usually derived from the discount rate by subtracting the expected average annual growth rate of earnings or cash flow (whichever is being capitalized). Respectively for the same enterprise, the capitalization rate is usually lower than the discount rate.

WITH mathematical position, the capitalization rate is a divisor used to convert the amount of income (profit or cash flow) over one period of time into a value indicator.

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

1. Capital asset valuation model;

2. Cumulative construction method;

3. Weighted average cost of capital model.

Given 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 cash flow).

2) The method of discounting future income - is based on forecasting future cash flows for the entire forecast period, as well as in the remaining 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 company being valued and the capitalization rate/return on 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 the basis for the assessment is selected; 2 the gross income, expenses and investments of the enterprise are analyzed and forecasted; 3 the discount rate is calculated; 4 cash flows are calculated for the forecast and post-forecast periods; 5 calculates the current 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 income rates in business valuation. OPTION 1

Most often, when calculating investment projects, the discount rate is determined as weighted average cost of capital (WACC), which takes into account the cost of equity (shareholder) capital and the cost of borrowed funds.

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

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

E is the market value of equity capital (share capital). Calculated as a product total number the company's common shares and the price per share;

D is the market value of borrowed capital. In practice, it is often determined by financial statements as the amount of the company's borrowings. If this 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 is the rate of return on the company's borrowed capital (the cost of raising borrowed capital). Such costs include interest on bank loans and corporate bonds of the company. In this case, 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 included in the cost of production, thereby reducing the tax base for income tax;

t c is the income tax rate.

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

The discount rate (rate of return) of equity capital (Re) is calculated using 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 a given market segment;

(Rm - Rf) - premium for market risk;

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

The rate of return on investments in risk-free assets (Rf). Government securities are usually considered as risk-free assets (that is, assets in which investments are characterized by zero risk).

Coefficient β. This coefficient reflects the sensitivity of the return on securities of a particular company to changes in market (systematic) risk. If β = 1, then the fluctuations in the price of 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 exceeded the rate of return on risk-free securities over an extended period of time. It is calculated based on statistical data on market premiums over a long period.

The approach described above for calculating the discount rate may not be used by all enterprises. Firstly, this approach is not applicable to companies that are not public joint stock companies, therefore, their shares are not traded on stock markets. Secondly, this method cannot be applied by firms that do not have sufficient statistics to calculate their β-coefficient, as well as those that do not have the opportunity to find a similar enterprise whose β-coefficient they could use in their own calculations. To determine the discount rate, such companies should use other calculation methods or improve the methodology to suit their needs. It should also be noted that the methodology for estimating the weighted average cost of capital does not take into account the share and value (usually 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 is the discount rate (nominal);

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

I - inflation rate;

r is a coefficient that takes into account the level of investment risk (risk premium).

As a rule, 30-year US government bonds are taken as the minimum real discount rate.

The main disadvantage of this calculation method is that it does not take into account the company's specific cost of capital. In essence, this indicator is replaced by inflation and a minimum yield comparable to long-term government bonds, which has nothing to do with the profitability of the company’s activities, the weighted average interest rate (on 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: Methodological recommendations for assessing the effectiveness of investment projects recommend taking into account three types of risk when using the cumulative method: country risk; the risk of unreliability of project participants; the risk of not receiving the income provided for by the project.

Country risk can be found out from various ratings compiled by rating agencies and consulting firms (for example, the German company BERI, which specializes in this). The size of the risk premium characterizing the unreliability of project participants, according to the Methodological Recommendations, should not be higher than 5%. It is recommended to set an adjustment for the risk of not receiving the income envisaged by the project depending on the purpose of the project. Many components of this methodology are assessed quite subjectively; there is no link between the risk premium and the specific risks of the project and taking into account the current activities of the company.

OPTION 2

Cumulative construction method involves the construction of an interest rate as a result of the summation of several quantities. The basis is the so-called risk-free rate. To the risk-free rate, adjustments are added for inflation (Fisher’s formula), for the risk associated with the characteristics of the property being valued, the industry, the country (the risk of objects leased to unreliable tenants; the risk of insufficient liquidity of the assets being valued; the risk of political instability, etc. ) All adjustments 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 rate is calculated. The basis for making amendments may be generally known data or the opinion of an expert appraiser based on his knowledge and experience.

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

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

Method according to the theory of capital assets CAPM (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 market average (industry average), multiplied by the variability of the company’s profitability:

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

The CAPM model provides the total value of the products of excess risk by the variability of returns of different 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 using 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 liquidity shortages.

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

The simplest way to adjust for inflation is revaluation of all balance sheet items based on changes in the ruble exchange rate relative to the exchange rate of another currency, such as the dollar or euro. The advantage of this method is its simplicity and the ability to work without a large amount of additional information. Disadvantages: adjustment by currency exchange rate gives inaccurate results, since the exchange rate ratios of the ruble and other currencies do not coincide with their real purchasing power.

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

The third method of inflation adjustment is based on taking into account 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 the varying degrees of change in the value of individual assets.

After inflation adjustment, the financial statements are normalized.

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

Control premium is considered as the percentage that the redemption price exceeds the market price of the shares.

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

The average control premium fluctuates between 30-40%, and the discount on 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 assessed package is reduced to reflect insufficient liquidity.

According to Sh. Pratt ( Pratt S.P. Business valuation. Discounts and bonuses/per. from English M.: Quinto-Management, 2005. P. 17.), the purpose of applying discounts and bonuses is the need to adjust the base cost, which will reflect the differences between characteristic features the assessed package (share) 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 a monetary expression of the advantage associated with owning a controlling interest.

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 quickly converting them into cash at minimal cost and at a price close to the market price.

However, with a more in-depth 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 acquiring the entire company (100% of the package)) is 20% of the value of the controlling stake;

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

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

– discount in connection with legal proceedings against the company being valued;

– a discount associated with the loss of a customer base or suppliers. Also considered as a replacement for the risk-related discount rate in the income approach or as an adjustment to multiples in the comparative approach;

– package discount – a value or percentage expression of an amount subtracted from the market price of shares in order to reflect a decrease in the value of a block of shares (per share) in the event that big size the package does not allow its implementation within the 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 drop in the price;

– “portfolio” discount (discount for heterogeneity of assets) – occurs in the case of the sale of multi-industry companies in whole or in large parts, combining several areas of activity, which reduces the attractiveness of the purchase (due to additional problems on the management of non-core assets and their further sale). The discount is determined from the amount of the cost of individual components companies.

To determine the appropriate capitalization rate, you must first calculate the appropriate discount rate. There are various methods for determining the discount rate, the most common of which are:

CAMP (Capital Asset Pricing Model)

WACC (Weighted Average Cost Model)

Cumulative construction

APT (Arbitrage Pricing Model)

With a known discount rate, the capitalization rate is determined in general form using the following formula: R = d - g

where R is the capitalization rate, d is the discount rate, g is the long-term growth rate of profit or cash flow

Income approach– a set of methods for assessing the value of a valuation object, based on determining the expected income from the valuation object and comparing them with current costs, taking into account time and risk factors.

Income approach involves the use of the capitalization method and the discounted cash flow method.

Advantages of the income approach to business valuation

Takes into account future changes in income and expenses.

Takes into account the level of risk (through the discount rate).

Takes into account the interests of the investor.

Disadvantages of the income approach to business valuation

Difficulty predicting future results and costs.

There may be multiple rates of return, making it difficult to make a decision.

Does not take into account market conditions.

The main advantage income capitalization method is that it reflects the potential profitability of the enterprise and allows taking into account the risks of the industry and the enterprise. However, this method is of little use for fast-growing companies.

Main advantage discounting method: most accurately determines the market value of the enterprise.

The main advantage of the DCF method is that it is the only known valuation method based on forecasts of future market development, and this is most in line with the interests of the investment process. The method is more applicable to income-generating enterprises that have a certain history of economic activity, with unstable streams of income and expenses. Its use is difficult due to the difficulty of making sufficiently accurate forecasts.

The profit capitalization method is used in business valuation of enterprises; this method is used quite rarely and mainly for small enterprises, due to significant fluctuations in profits or cash flows over the years, which is typical for most large and medium-sized enterprises.

Definitions

The terms “discount rate” and “capitalization rate” are often given ambiguous, unclear definitions in the financial press, textbooks, and conversations among financial analysts. Because of this ambiguity, many business people consider these terms to be identical and interchangeable. Meanwhile, although they are indeed closely related, they are far from the same thing. To understand both of these terms and their relationship, it is first necessary to define the discount rate.

Discount rate. In valuation theory, the discount rate represents the overall expected rate of return (as a percentage of the purchase price) that a buyer or investor can expect to receive when acquiring ownership of an asset (such as a U.S. Treasury bill), given the risk inherent in that ownership interest.

Unlike a capitalization ratio, a company's discount rate is not used directly as a divisor or multiplier to determine a company's value. On the contrary, the discount rate is used to bring income (expenses) of a future period to the present time. A valuation method that applies a discount rate is more appropriate when a company's future performance is expected to be materially different from today's or past performance. Therefore, in order to calculate the coefficients for bringing income (expenses) of the future period to the present time for a certain discount rate, it is necessary to prepare a forecast of the company’s future activities, including the terminal year of calculation (which is often the first year after achieving a stable growth rate in the forecast period).

Capitalization rate. A company's capitalization ratio is usually calculated based on its discount rate. Consequently, a company's capitalization ratio is usually lower than its discount rate.

As a mathematical tool, the capitalization ratio is used as a divisor or multiplier to calculate the value of a stream of benefits over a given period. Note that the capitalization rate can be set as either a divisor or a multiplier. To determine value, net earnings (or cash flows) are divided by the capitalization ratio, expressed as a percentage. The same coefficient can also serve as a multiplier - by dividing one by the percentage of the capitalization ratio. The resulting number is then used as a multiplier of net income (or cash flow) in determining value. To illustrate, let's assume that the company's net income capitalization ratio is 20%. The same coefficient as a multiplier will be equal to 1/20%, or 5. If the company's net income level was $ 30,000, then its value is determined as follows.

In short, a company's capitalization ratio is often a derivative of the discount rate and is usually less than the latter. It is directly used in calculating the value of a company as either a divisor or a multiplier and is applied to one year's income stream (often to net income). This one-year income stream shows what can be expected from the company in the future based on historical normalized net earnings (or cash flow).

general characteristics comparative approach. Selecting a similar enterprise for comparison. Contents of the cost approach.

The comparative approach is a set of valuation methods based on obtaining the value of the valued object by comparing the valued object with analogous objects. The use of comparative valuation is widely practiced. Most equity research reports and many acquisition valuations are based on multiples such as price/sales and value/EBITDA, as well as a group of comparable firms.

Profit multipliers. One of the most understandable ways to think about the value of an asset is to look at the earnings multiplier generated by that asset. When a share is purchased, the price paid is usually looked at as a multiple of the company's earnings per share. This indicator - the price/earnings multiple - can be estimated using current earnings per share. In this case, it is called the current PE (price-earning ratio), and when referring to the expected earnings per share for the next year - forward PE. When purchasing a business itself, as opposed to purchasing just the shares in it, it is common to examine the value of the firm by looking at the multiple of operating income or earnings before interest, taxes, depreciation and amortization (EBITDA). Of course, for a buyer of a stock or firm, a low multiple is better than a high one. But it should be remembered that their value is complexly influenced by the growth potential and risk of the acquired business.

Book value and replacement cost multiples. While markets provide one valuation of a business, accountants often value it completely differently. The accounting treatment of book value is determined by the rules accounting and is highly dependent on the original price paid for the assets, as well as various accounting adjustments (such as depreciation) made thereafter. Investors often look at the relationship between the price they pay for a stock and its book value of equity (or net worth) as a measure of how overvalued or undervalued a stock is. The resulting price/book value (PBV) multiple can vary greatly across industries, depending on each industry's growth potential and investment quality. When a business is valued and this multiple is determined, the value of the firm and the book value of all capital (not just the shareholder portion) are used. For those who do not consider book value good indicator the true cost of the assets, an alternative is to use the replacement cost of the assets. The relationship between firm value and replacement cost is called the Tobin multiplier.

Revenue multipliers. Both earnings and book value are accounting measures that are determined by accounting rules and principles. An alternative, much less reliant on “accounting mix,” is to use the ratio of the cost of an asset to the revenue it generates. For investors who have invested money in shares, this indicator is the price-sales ratio-PS, which is calculated as the quotient of the market value of equity capital divided by revenue. When evaluating a company, this indicator can be modified as a value-sales ratio (VS) multiplier, then the numerator becomes the total value of the company. Again, this multiple varies widely across industries, especially as a function of profit margins within each industry. However, the advantage of using revenue multiples is that, with different accounting systems in place, it makes it much easier to compare firms in different markets rather than comparing revenue multiples or book value.

Specific sector multiples. Earnings, book value and revenue multiples can be calculated for firms in any sector and for an entire market, but there are some multiples that are specific to a particular sector. For example, when Internet firms first came to market in the late 1990s, they had negative earnings and negligible revenues and book values. Analysts looking for a valuation multiple for these firms divided the market value of each of these firms by the number of visits to that firm's website. Firms with a low market value per client visit were interpreted as more undervalued. More recently, retail firms doing business on the Internet have been valued by their market value of equity per customer.

Cost-effective approach- a set of methods for assessing the value of a valuation object, based on determining the costs necessary to restore or replace the valuation object, taking into account its wear and tear. Actual cost is based on comparative analysis, which allows you to determine the costs necessary to recreate a property that represents exact copy the object being evaluated or replacing it for its intended purpose. The calculated costs are adjusted for the actual service life, condition and usefulness of the assessed object.

Scope and advantages of the cost approach:

• gives the best result when assessing real estate with recently constructed buildings that have little wear and tear and meet the NEI of the site;
• used when there is sufficient data for separate assessment of land plots and buildings;
• used to determine the market value of construction projects, incl. when assessing unfinished construction projects;
• applicable for a more or less reliable assessment of real estate in an inactive market;
• a specific area of ​​application is the assessment of unique objects, especially non-profit purposes (hospitals, museums, libraries, music schools, etc.);
• applicable in the insurance industry;
• it can be used in conditions of lack of information to apply other approaches to assessment.

The property approach is based on determining the market value of all types of enterprise property minus debt obligations. The book value of an enterprise's assets as a result of inflation, changes in market conditions, accounting methods used and other factors deviates from the market value, therefore the appraiser needs to recalculate the book value of assets into the market value on the valuation date.

The property approach includes two methods:

· Net asset value method (asset accumulation method).

· Liquidation value method.

The net asset method is used in the following cases:

· The company being assessed has significant tangible assets.

· The company being assessed does not have historical data on profits or is unable to predict future profits.

· A new enterprise or unfinished construction is being assessed.

· The company being assessed is heavily dependent on contracts or does not have a regular clientele.

· A holding or investment company that does not make a profit from its own production is being assessed.

The information base of the net asset method is the balance sheet of the enterprise. The appraiser analyzes and adjusts all items of the quarterly balance sheet as of the last reporting date to determine the market value of existing assets.

Enterprise value = Market value of assets - debt obligations.

The procedure for assessing the market value of an enterprise using the net asset method:

1. The market value of the enterprise’s real estate is assessed.

2. The value of movable property of enterprises is determined.

3. Intangible assets are identified and assessed.

4. The market value of short-term and long-term financial investments is determined.

5. The market value of inventories is determined.

6. Accounts receivable are assessed.

Advantages and disadvantages of the net asset method

Advantages: 1) the method is based on reliable information about real assets that are owned by the enterprise, which eliminates the abstractness inherent in other valuation methods. 2) In the conditions of the formation of the real estate market, this method has the most complete information base, and also uses costly valuation methods traditional for the Russian economy.

Flaws: 1) The net asset method does not take into account the efficiency of the enterprise and its development prospects. 2) The method does not take into account the market situation of the relationship between supply and demand for similar enterprises.

Liquidation of an enterprise means the termination of its activities without the transfer of rights and obligations through succession to other persons. Liquidation value is the amount of money that the owner of a business can receive upon liquidation of the business and separate sale of its assets.

The assessment of liquidation value is carried out in the following cases:

1. The company's cash flows are not large compared to the value of its net assets; The enterprise value under the net asset method is significantly higher than the value calculated under the income approach. The owner makes a decision on voluntary liquidation.

2. Liquidation of an enterprise can occur forcibly as a result of declaring it bankrupt in accordance with federal law (“On Insolvency (Bankruptcy)” No. 127 of October 26, 2002)

3. A legal entity may be forcibly liquidated in accordance with Article 61 of the Civil Code in the following cases: a) by decision of its founders; b) by a court decision (the court found: the enterprise operates without a license; the enterprise carries out activities prohibited by law; there have been repeated violations of the law on the part of the enterprise)

Types of liquidation value:

1. Ordered liquidation value (the sale of assets is carried out within a period of time sufficient to obtain highest price for each of the assets sold);

2. Forced liquidation value\auction value (occurs when the assets of an enterprise are sold as quickly as possible - usually at one auction);

3. Liquidation value of the termination of the existence of the assets of the enterprise (in this case, the assets of the enterprise are not sold, but are written off and destroyed, and the enterprise is built at this location);

An important feature of assessing liquidation value is high degree interests of 3 parties. Typically, the assessment results are provided and any problems that arise are discussed only with the customer. When liquidating an enterprise, the assessment results are used by a third party - creditors, judicial authorities.

Procedure for assessing the liquidation value of an enterprise:

1. Development of a calendar schedule for liquidation of enterprise assets;

2. Calculation of the current value of the enterprise’s assets;

3. Determination of the amount of debt obligations of the enterprise;

4. Calculation of the liquidation value of the enterprise.

To develop a business, you need to be able to calculate cash flows with the highest possible accuracy. This can only be done if all financial flows expected in the future are correctly brought to the current moment. The most important condition for this is the correct calculation of the discount rate. The most common is to calculate the discount rate using the cumulative method.

The essence and features of the cumulative calculation method

The cumulative construction method is used to calculate the capitalization rate and discount rate. With its help, a number of assets (real estate, equipment, machinery) are assessed. You can also use it to calculate the capitalization ratio; in this case, the value of the required criterion is the difference between the magnitude and rate of increase (decrease) in business profitability.

Today there are a number of in various ways determine the value of the discount rate, however, they all have their own characteristics and are used under different conditions:

• CAPM model(capital asset valuation) and its variations (Carhart, Sharp, Fama and French models, MCAPM). It is well suited for large firms that issue their own shares and are traded on the stock market. The advantage of the method is high accuracy in determining the expected profitability. Disadvantages include ignoring taxes and taking into account only market risk. In addition, this method does not fit well with Russian realities with insufficient development of the securities market.
• Gordon model. It is relevant for companies paying dividends from shares. Based on the dividend yield, it is able to provide a clear understanding of the rate of return. However, it is not suitable for companies that do not pay dividends or do so irregularly.
• WACC model. It is used to evaluate companies that attract additional capital to implement investment projects. It is good for accounting for the return on debt and equity capital. However, the calculation process uses the same approaches as Gordon, CAPM, cumulative accumulation and profitability models, so the WACC method is affected by all their shortcomings.
• Assessment based on return on equity (ROA, ROCE, ROE, ROACE). Suitable for companies (LLC, CJSC) that are not listed on the stock market, based on their financial statements. In this case, it is not the rate of return that is determined, but only the current state of the company (the profitability of its capital).

Compared to all the above methods, the cumulative method of calculating the discount rate stands out in that it can be used to consider and weigh all the risks that could affect the profitability of the initiative being implemented.

It can be used even for new initiatives (startups) that do not yet have financial indicators. It is applicable to investment projects, real estate business, and capitalization of companies. Often used when valuing closely held companies that cannot be valued using the CAPM method because there are no similar peer companies.

True, with all its advantages, the method of cumulative construction of the discount rate is characterized by subjectivity, since the value of a particular risk must be assumed using both research data and the own conclusions of specialists.

Options for graphically recording the method

Calculating the discount rate using the cumulative method is to determine the size of the risk-free rate, as well as the size of premiums for various types of risks and adjust all this for the rate of inflation. The essence of the methodology is that, subject to a risk-free investment, investors expect an appropriate rate of return, and if there are possible dangers, they want greater profitability from the project. The more risks, the greater the percentage of profitability expected by the participants of the endeavor.

The general formula looks like this:

• r – discount rate;
• r f – risk-free interest rate;
• r p – premium for possible company risks;
• r p – risk premium associated with working in a particular country;
• I – rates of inflation processes (consumer prices).

Here we take as a basis two main risks - country and company, but there is also a list of risks that need to be taken into account. Some of them may only appear in certain industries or areas of business. Therefore, the formula is often written in this form:

R = Rf + R1 +… + Rn

wherein:

• Rf – the value of the risk-free rate;
• R1 +… + Rn – all possible premiums for potential risks.

Since this technique allows us to take into account potential dangers for investment project both of a general nature (level of economic development, political situation) and specific (the state of a particular industry, global or regional market trends), sometimes the formula looks more detailed:

Re = Rf + C1 + C2 + C3 + C4 + C5 + C6 + C7

• Rf – risk-free rate;

and indicators denoted by the letter C are premiums for individual risks for:

• C1 – enterprise size;
• C2 – sources and structure of financing of the company;
• C3 – territorial and product diversification;
• C4 – diversification of potential clients;
• C5 – predictability and expected profit;
• C6 – possible low quality of management and unreliability of partners;
• C7 – other possible obstacles.

In this case, each risk is assessed in the range from 0 to 5%, all values ​​​​are added to the risk-free rate level indicator.

How to determine the elements that make up the formula

To apply the cumulative discount rate method, it is necessary to determine all the indicators taken into account in the formula. You should always start by setting the risk-free interest rate.

The rate can be determined in the following ways:

• You can take as a basis the level of profitability of government securities issued by the Ministry of Finance of the Russian Federation, such as OFZ or GKO. They have the maximum reliability rating, although, like other financial instruments, they do not provide a complete guarantee against losses.
• The second option is focusing on profitability bank deposits. Usually the calculation is made using interest rates on long-term deposits in the most reliable state and commercial banks.

Sometimes, although less frequently, other methods of establishing the risk-free rate are used. You can use the level of profitability of securities of foreign countries, the Central Bank of Russia, and interest on interbank loans.

The next stage necessary to take into account the discount rate is premiums for possible risks. Let us dwell in more detail on each risk group.

Country. It characterizes the general dangers of doing business in a particular state and is important when attracting foreign investors. This includes the state structure of the country, general political and economic situation, predictability of government actions, stability of the local currency, etc. This information is analyzed and regularly updated by reputable international consulting companies and rating agencies such as Fitch, Moody’s, S&P. According to Moody’s rating, all states have indices from AAA (risks at 0.2%) to B (5%).

Company risks(set on a scale from 0 to 5%):

• Size of the enterprise. The larger the company, the fewer competitors it has in the market, therefore the danger is low. If the enterprise is a monopolist in the production of a certain type of product, then it is equal to zero. At the same time, in some industries, small firms have an advantage (catering, retail, service industries).
• Capital structure. If borrowed funds predominate or the company has low liquidity, then the risk premium should be increased.
• Diversification by territory or industry is the result of studying the range of products and the possibility of selling them (the degree of development of the distribution network).
• Diversification of the client base. Studying the demand for the product, the presence of a sufficient number of buyers, the level of dependence on large purchases of individual clients.
• The predictability of the inflow of funds is inextricably linked with previous indicators, as are the profitability indicators of the project.
• Quality of management and integrity of partners. Problems may arise in cases where the interests of project participants differ significantly. TO low quality management can be attributed to the dangers of improper selection of personnel, organization of work, misuse of funds, etc.

Typically, these indicators are determined by the expert method, using a method of interviewing representatives of the management level of the enterprise and specially invited specialists. There are strong and weak sides. On the one hand, the cumulative method makes it possible to take into account as much as possible the dangers for a particular company in the current conditions. On the other hand, the subjective conclusions of experts may turn out to be erroneous, which will negatively affect the implementation of the initiative.

IN Lately To increase the level of objectivity when assessing potential hazards, assessment firms are developing methodological recommendations. In particular, a methodology for estimating the size of a company is proposed, based on the average cost of capital of enterprises with open data that produce a similar range of products.

Example of calculating the discount rate

Let's try to calculate the discount rate based on these parameters. Manufacturing company household appliances intends to organize the production and sale of its products in several regions of Russia. Half of the capital is own, the rest is borrowed. The expected implementation period of the initiative is 3 years.

First, let's look at the basic indicator - the size of the risk-free rate. Considering that the loan will be issued at a commercial bank, it is better to take the average interest rate on long-term deposits in reliable financial institutions as a basis. Let's say it's 9% per annum.

We do not take into account the country factor, since the project is being implemented within the country and all possible competitors are exposed to the same dangers as the company in question.

After this, with the help of the venture’s managers, we calculate the risk premiums:

• The size of the company is medium, the scale is interregional, so we will set a premium of 2%, based on the standard range for this criterion of 0-3%.
• Financial structure. Since half of the investments were taken on credit and liquidity is low, it would be logical to add 3% to the indicator.
• Product diversification – it is planned to produce 4 types of products, so the risk is reduced (1%). Territorial diversification - it is planned to cover 3-4 regions, which is not enough for a stable position of the company in the market (2%). The total premium will be 3%.
• Diversification of the client base. The company will produce new products aimed mainly at individual consumers. The presence of large wholesale buyers is not expected. Medium level hazards (2%).
• Predictability of income generation and profitability. The product has good consumer characteristics and can compete in terms of price with similar products from other companies. However, it takes time to deploy a marketing strategy, which can reduce the firm's profitability at the initial stage. 1.5% surcharge.
• Quality of management and partners. Here you can take the average value of the indicator, since it is difficult to accurately determine it (2.5%).
• Other specific hazards. Considering the saturation of the market with competitive products and large quantity players, it is advisable to use an average figure close to the average (2.2%).

So, having all the necessary criteria, we determine the discount rate for our company:

Re = Rf (9%) +Rp (0%) + C1 (2%) + C2 (3%) + C3 (3%) + C4 (2%) + C5 (1.5%) + C6 (2.5%) + C7 (2, 2%) = 25.2%

Therefore, the discount rate in our case is 25.2% or rounded 25%. Based on this, you need to consider the prospects of the project and the opportunity to make a profit. However, we should not forget about one more parameter – inflation. If we add to the obtained result the inflation rate (5.38% in 2016), the rate will increase to 30.58%.