Disk-e is a method of bringing the future. receipt-iden-th sr-tv (future income and expenses) to the current (at the estimated moment) of their hundred-ty. Disk is the future. act-iuse in order to determine their art in present. temp. Difference m / y future. the sum of incomes and their current cost-yusostavl. the price by which the inconvenience associated with the refusal to use this amount at the present time is estimated.
Bringing current money flows to the future. point in time called drip-she. That is, capi-I is the definition of the future. cost of current Money. Pr-ss, in which m are given initial. the amount and% rate, in financial calculations it is called the percentage of accumulation (capital th). disc-ia, naz. disk-i process.
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In the first case we are talking about movement. money flow from present. to the future, in the second - vice versa. The time period for which the effect is evaluated. investment th, called calculation horizon. Most often, when calculating the economic effect of investment, cash flows for the financial year are considered. The frequency of consideration of cash flows naz calculated lane. The initial year of the calculation horizon is considered to be the year of commencement of financing work on the implementation of the project. The end year of the calculation horizon can be determined by the standard period for the use of equipment or the planned (standard) period for updating the product.
Capital def. increase pervonach.velichinyden-x wed-in due to the addition of accrued-th% when moving from the current moment in time to the future. Disk-e - depreciation of future money amounts when they are reduced to the current moment in time.
- capitalization ratio;
- discount coefficient,
Where D– interest rate (discount rate) for the period (year, quarter, month); t- the number of settlement periods (years, quarters, months).
The difference lies only in the definition of the factor D, the cat-th in the formula of compound% is the interest rate, and in the formula the coefficient. disc - discount rate. Vkach-ve% of the rate used. % rates on long-term loans, average deposit rates, the refinancing rate of the National Bank of the Republic of Belarus.
Bank %-% rate, or the price paid by the bank to the owner financial resources for temporary use. Owner of capital provides the bank with its resources for use, places them on deposit, for which the bank charges interest at the deposit rate.
Loan fee rate- this is the price of the loan, which is paid to the bank by the user of this loan or inv-or. This rate is greater than the bank % rate by the bank margin.
The valuation of an ownership interest in a company is equal to the present value of future earnings from that ownership interest. All valuation approaches determine the present value of future property income, some more directly than others. The procedure for calculating the market value of an enterprise within the income approach involves:
Knowledge of the theory of money in time;
Determination of the capitalization ratio;
Discount percentage.
The concept of the time value of money is based on the following basic principle: a dollar now is worth more than a dollar that will be received in the future, for example, in a year, since it can be invested and this will bring additional profit. This principle is the most important provision in the whole theory of finance and investment analysis. The future value of money is the amount that the money invested at the moment will turn into after a certain period of time, taking into account a certain interest rate. Determining the future value of money is associated with the process of compounding the initial value, which is a gradual increase in the invested amount by adding the amount of interest payments to its original size. In other words, it is the concept on which the assumption that money should earn interest is based - the value of money today is higher than the value of the same amount received in the future. The "golden" rule of business says: The amount received today is greater than the same amount received tomorrow.
Another important indicator for determining the value of commercial real estate is the determination of the capitalization ratio. The capitalization rate is a rate of return that reflects the relationship between income and the value of the appraised object, an indicator that reflects the ratio of the expected annual income (NAR) to the value of the enterprise's real estate. This takes into account both the net profit itself received from the operation of the object being evaluated, and the reimbursement of the fixed capital spent on the acquisition of the object. The capitalization ratio that takes into account these two components is called the general capitalization ratio or net income capitalization rate. In this case, the net income used for capitalization is determined for a certain period, as a rule, for a year. Thus, the total capitalization ratio, (or full time capitalization) expresses the relationship between the annual net income received as a result of the operation of the facility and its market value.
The capitalization rate divides the income into two parts:
Reimbursement of capital investments in real estate;
Receiving income from the ownership of the object.
The income capitalization method is applied if:
Income streams are stable positive values;
Income streams are growing at a steady, moderate pace.
This method should not be used if revenue streams are unstable, the property is under construction or a significant renovation of the property is required, there is no information on actual sales and rental transactions of real estate, operating costs, and other information that makes it difficult to calculate the net operating income and rate capitalization.
The basic calculation formula is as follows:
where C is the value of the property, rub.;
CHOD - net operating income, rub.;
Rcap - capitalization ratio.
There are several methods for determining the capitalization ratio:
Method for determining the capitalization ratio, taking into account the reimbursement of capital costs;
Linked investment method or investment group technique (equity and debt capital);
Method of market extration (market squeeze).
To begin with, let's consider the methodology for determining the capitalization ratio, taking into account the reimbursement of capital costs.
where Rcap - capitalization coefficient;
Rdoh cap - rate of return on capital;
Decrease in the value of real estate (wearable part of assets);
Rnorm return - the rate of return of capital;
The rate of return on capital (R doh cap) is most often built using the cumulative construction method, where the risk-free rate of return, risk premiums for investing in real estate, premiums for low liquidity of real estate, premiums for investment management are summed up.
Risk-free rate of return - the rate of interest in highly liquid assets, i.e. it is a rate that reflects the actual market opportunities for firms and individuals to invest money without any risk of non-return.
Risk premium calculation:
Premium for low liquidity. When calculating this component, the impossibility of an immediate return of investments invested in a real estate object is taken into account, and it can be taken at the inflation rate for a typical exposure time of objects similar to the one being assessed on the market;
Premium for the risk of investing in real estate. 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 premiums in insurance companies of the highest reliability category;
Investment management bonus. The more risky and complex the investments, the more competent management they require. It is advisable to calculate the investment management allowance taking into account the underload factor and losses in the collection of rental payments.
The capitalization ratio includes the rate of return on investment and the rate of return on capital. If the amount of capital invested in real estate remains unchanged and will be returned when it is resold, 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 in the capitalization ratio the return of the principal amount of capital. The rate of return of capital shows the annual amount of reimbursement of funds invested in the property in the event that, for any reason, the loss of these funds (in whole or in part) during the period of ownership of the property is predicted.
There are three ways to calculate the rate of return of capital (Rnorm return):
Straight-line return on capital (Ring's method);
The return of capital on the reimbursement fund and the rate of return on the investment (Inwood method), it is sometimes called the annuity method;
Return of capital on the compensation fund and the risk-free rate of interest (Hoskold's method).
Ring method. This method is appropriate when it is expected that the principal will be repaid in equal installments.
where n is the remaining economic life, years.
Inwood method. Used if the capital return amount is reinvested at the rate of return on the investment.
where SFF - compensation fund factor SFF = Y/((1+Y)n-1);
Y is the rate of return on investment.
Hoskold method. Used when the rate of return on the initial investment is somewhat high, making reinvestment at the same rate unlikely.
where Yb is the risk-free rate.
The decrease in the value of real estate (?), which will occur after n years, takes into account the value of the subsequent resale of the property in the capitalization ratio.
0 if the value of the appraised object does not change,
The share by which it is planned to reduce the value of the appraised object, if the value of the appraised object decreases,
The share by which it is planned to increase the value of the appraised object if the value of the appraised object increases.
Calculation of the capitalization ratio using the market squeeze method. Based on market data on sales prices and NPV values of comparable properties, you can calculate the capitalization ratio:
where CHODi - net operating income of the i-th analogue object, rub.;
Сi is the selling price of the i-th analogue object, rub.
Another method for calculating the capitalization rate is the linked investment method.
If the property is acquired with equity and debt, the capitalization ratio must meet the return requirements for both parts of the investment. The value of the coefficient is determined by the method of linked investments, or the technique of the investment group. The capitalization ratio for borrowed capital is called the mortgage constant and is calculated using the formula:
where Rm - mortgage constant;
DO - annual debt service payments, rub.;
K - the amount of the mortgage loan, rub.
The capitalization ratio for equity is calculated using the formula:
The overall capitalization ratio is defined as a weighted average of:
where M is the mortgage debt ratio.
From all of the above, it is worth noting that without calculating the capitalization rate for a property, it is simply not possible to obtain data on the effectiveness of the capital invested in it. Having received all the necessary data, you can easily calculate the capitalization rate.
The next indicator needed to calculate the value of a property using the income approach is the discount factor.
The discount rate is a factor used to calculate the present value of an amount of money received and paid in the future.
where i -- interest rate;
n is the number of periods.
There are several methods for determining the discount factor:
Cumulative construction method;
Comparison method of alternative investments;
Selection method;
monitoring method.
The 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 particular property.
The risk premium is calculated by summing the risk values inherent in a given property.
Selection method - the discount rate, as a compound interest rate, is calculated on the basis of data on completed transactions with similar objects in the real estate market. This method is quite labor intensive. The calculation mechanism consists in the reconstruction of the assumptions about the amount of future income and the subsequent comparison of 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 ratio) cannot be extracted directly from the sales data because it cannot be calculated without identifying the buyer's expectations of 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 sale price, how the forecast of future cash flows was built. If the appraiser has completely received the information of interest to him, then he can calculate the internal rate of return (final return) of a similar object. It will be guided by the obtained value when determining the discount rate.
Although each property is unique, under certain assumptions it is possible to obtain extraction discount rates that are consistent with the overall accuracy of future forecasts. However, it should be taken into account that transactions of sale and purchase of such delivered objects, the existing use of which is the best and most effective, should be selected as similar ones.
The usual algorithm for calculating the discount rate using the allocation method is as follows:
Modeling for each analog object for a certain period of time according to the scenario of the best and most efficient use of income and expense flows;
Calculation of the rate of return on investments for the object;
Process the obtained results in any acceptable statistical or expert way in order to bring the characteristics of the analysis to the object being evaluated.
The monitoring method is based on regular monitoring of the market, tracking transactions of the main economic indicators real estate investment. Such information should be summarized for various market segments and published regularly. Such data serve as a guideline for the appraiser, allow for a qualitative comparison of the obtained calculated indicators with the average market ones, checking the validity of various kinds of assumptions.
Russian appraisers most often calculate the discount rate using the cumulative construction method (formula). This is due to the greatest simplicity of calculating the discount rate using the cumulative construction method in the current conditions of the real estate market.
Any, even the most complex, discounting operations are reduced to the discounting formula:
where PV is the future value, rub.;
FV - current value, rub.;
i - discount rate;
n - term (number of periods);
Once the discount rate is known, the value of the commercial real estate can be derived using the discounted cash flow method. The discounted cash flow method is the most versatile method for determining the present value of future cash flows. Cash flows can change arbitrarily, flow unevenly and differ high level risk. This is due to the specifics of such a thing as real estate. Real estate is acquired by an investor mainly because of certain benefits in the future. The investor views the property as a set of future benefits and assesses its attractiveness in terms of how the monetary value of these future benefits correlates with the price at which the property can be acquired.
The discounted cash flow method evaluates the value of real estate based on the present value of income, which consists of projected cash flows and residual value.
The discounted cash flow method has its own calculation algorithm:
Definition of the forecast period. The definition of 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 valuation practice, the average value of the forecast period is 5-10 years; for Russia, a typical value will be a period of 35 years. This is a realistic period for which a reasonable forecast can be made.
Forecasting the amount of cash flows from the real estate object for each forecast year.
Forecasting cash flows, including reversion, requires:
Careful analysis based financial reporting submitted by the customer on income and expenses from the property in the 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 evaluating real estate using the discounted cash flow method, several types of income from the object are calculated:
Potential gross income;
Actual gross income;
Net operating income;
Cash flow before taxes;
Cash flow after taxes.
Post-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 excluding operating costs, land tax and redevelopment;
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 the actual gross income as part of operating expenses.
Economic and tax depreciation is not a real cash payment, so accounting for depreciation in income forecasting is redundant.
Loan servicing payments (interest payments and debt repayment) must be deducted from net operating income if the investment value of the object (for a specific investor) is assessed. When evaluating the market value of a property, you do not need to read the loan maintenance payments.
Business expenses of the property owner must be deducted from the actual gross. income, if they are aimed at maintaining the necessary characteristics of the object.
Thus:
CHOD = DDD - RR - Real estate owner's business expenses related to real estate, (14)
Cash Flow Before Taxes = NPV - Capital Investment - Loan Service + Loan Growth, (15)
After-tax cash flow for real estate = Pre-tax cash flow - Property owner's income tax payments (16)
The cost of reversion can be predicted using:
Setting the sale price based on the analysis of the current state of the market, monitoring the cost of similar objects and assumptions regarding the future state of the object;
Making assumptions regarding changes in the value of real estate over the period of ownership;
Capitalization of income for the year following the year of the end of the forecast period, using a self-calculated capitalization rate.
The cost of the reversion should be discounted (by the factor of the last forecast year) and added to the sum of the current values of the cash flows.
Thus, the value of a property is equal to the sum of the present value of the projected cash flows and the present value of the residual value (reversion).
valuation reorganization discounting costly
To develop a business, it is necessary to be able to calculate cash flows with the highest accuracy. This can be done only if all the 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 the calculation of the discount rate using the cumulative construction method.
The essence and features of the cumulative calculation method
The cumulative construction method is used to calculate the capitalization indicator and the discount rate. With its help, a number of assets (real estate, equipment, machinery) are evaluated. It can also be used to calculate the capitalization ratio, in which case the value of the required criterion is the difference between the value and the rate of increase (decrease) in business profitability.
Today there are a number of various ways determine the value of the discount rate, however, they all have their own characteristics and are used under different conditions:
- Model CAPM(assessment of capital assets) and its varieties (Carhart, Sharpe, Fama and French models, MCAPM). It is well suited for large firms that issue their own shares that are traded on the stock market. The advantage of the method is high accuracy in determining the expected return. The disadvantages include ignoring taxes and taking into account only market risk. In addition, this method is poorly suited to Russian realities with insufficient development of the securities market.
- Gordon Model. It is relevant for firms that pay dividends from shares. Based on dividend income, it is able to give a clear understanding of the rate of return. At the same time, it is not suitable for companies that do not pay dividends or do it irregularly.
- Model WACC. It is used to evaluate firms that attract additional capital for the implementation of investment projects. It is good for accounting for the return on debt and equity. However, in the calculation process, the approaches inherent in the Gordon, CAPM, cumulative accumulation and profitability models are used, so the WACC method is affected by all their shortcomings.
- Evaluation in terms of return on equity (ROA, ROCE, ROE, ROACE). Suitable for companies (LLC, CJSC) that are not listed on the stock market, in terms of their financial statements. In this case, it is not the rate of return that is determined, but only the current state of the company (profitability of its capital).
Against the background of all the above methods, the cumulative method for calculating the discount rate is distinguished by the fact that it can be used to consider and weigh all the risks that can affect the profitability of the initiative being implemented.
It can be used even for new initiatives (start-ups) that do not yet have financial indicators. It is applicable to investment projects, real estate business, capitalization of companies. Often used in company valuation closed type, which cannot be estimated using the CAPM method, since there are no similar firms-analogues.
True, for all its merits, the method of cumulative construction of the discount rate is subjective, since the value of a particular risk has to be assumed, using both research data and the own conclusions of specialists.
Options for graphical recording of the method
The calculation of the discount rate using the cumulative method is to determine the size of the risk-free rate, as well as the premiums for different kinds risks and all this is adjusted for the rate of inflation. The essence of the technique lies in the fact that, under the condition of a risk-free investment, investors expect an appropriate rate of return, and in the presence of possible dangers, they want a higher profitability from the project. The more risks, the greater the percentage of profitability expected by the participants in the undertaking.
The general formula looks like this:
- r is the discount rate;
- r f is the risk-free interest rate;
- r p is the premium for the company's possible risks;
- r p is the risk premium associated with working in a particular country;
- I - the rate of inflationary processes (consumer prices).
Here, two main risks are taken as a basis - country and company, but there is also a list of risks that need to be taken into account. Some of them may appear only in certain industries or areas of management. Therefore, the formula is often written in this form:
R = Rf + R1 +… + Rn
wherein:
- Rf is the value of the risk-free rate;
- R1 +… + Rn - all possible bonuses for potential risks.
Since this technique allows taking into account potential dangers for an investment project, both of a general nature (the level of economic development, the political situation) and specific ones (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 is the risk-free rate;
and indicators denoted by the letter C are individual risk premiums for:
- C1 is the size of the enterprise;
- C2 - sources and structure of financing of the firm;
- C3 - territorial and commodity diversification;
- C4 - diversification of potential customers;
- 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 estimated in the range from 0 to 5%, all values are added to the risk-free rate indicator.
How is the definition of the elements that make up the formula
To apply the cumulative discount rate method, you must determine all the indicators taken into account in the formula. You should always start by setting a 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 highest reliability rating, although, like other financial instruments, they do not provide a full guarantee against losses.
- The second option is focusing on the profitability of bank deposits. Usually the calculation is made at the interest rates of long-term deposits in the most reliable state and commercial banks.
Sometimes, although less frequently, other methods of setting the risk-free rate are used. You can use the level of profitability of securities of foreign countries, the Central Bank of Russia, interest on interbank loans.
The next stage required to account for the discount rate is the risk premium. Let us dwell in more detail on each group of risks.
Country. It characterizes the general dangers of doing business in a particular state and is important when attracting foreign investors. This may include state structure country, general political and economic situation, predictability of government actions, stability 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 the Moody's rating, all states have indices from AAA (risks at the level of 0.2%) to B (5%).
Company risks(set on a scale from 0 to 5%):
- Enterprise size. How bigger company, the less competitors it has in the market, therefore, the danger is small. 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, small firms have an advantage in some industries ( catering, retail, service sector).
- Capital structure. If borrowed funds predominate or the company has low liquidity, then the size of the risk premium should be increased.
- Diversification by territory or industry is the result of studying the range of products and the possibility of its sale (degree of development of the trading 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 customers.
- The predictability of the inflow of funds is inextricably linked with the previous indicators, as well as the profitability of the project.
- Quality of management and conscientiousness of partners. Problems can arise when the interests of the project participants differ significantly. The low quality of management includes the dangers of improper selection of personnel, organization of work, misuse of funds, etc.
Typically, these indicators are determined by the expert method, using the method of interviewing representatives of the management of the enterprise and specially invited specialists. There are strong and weak sides. On the one hand, the cumulative method makes it possible to maximally take into account the dangers for a particular firm 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 in assessing potential hazards, appraisal firms develop 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 discount rate calculation
Let's try to calculate the discount rate based on these parameters. The company producing household appliances is going to organize the production and sale of its products in several regions of Russia. Half of the capital is own, the rest is borrowed money. The expected duration of the initiative is 3 years.
First, let's focus on the basic indicator - the size of the risk-free rate. Given that the loan will be issued in a commercial bank, it is better to take the average interest 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 subject to the same dangers as the company in question.
After that, with the help of the leaders of the undertaking, we calculate the risk premiums:
- The size of the company is average, 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 are taken on credit, and liquidity is low, it would be logical to add 3% to the indicator.
- Commodity diversification - it is planned to release 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 the company's stable position in the market (2%). The total premium will be 3%.
- Diversification of the client base. The company will produce new products focused mainly on the individual consumer. 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 by initial stage. Surcharge 1.5%.
- Quality of management and partners. Here you can take the average value of the indicator, since it is difficult to determine it accurately (2.5%).
- Other specific hazards. Considering market saturation competitive products And a large number players, it is advisable to apply an average indicator close to the average (2.2%).
So, having all the necessary criteria, we determine the value of 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%
Consequently, the size of the discount rate in our case is 25.2% or rounded 25%. Based on this, it is necessary to consider the prospects of the project and the possibility of making a profit. However, we should not forget about another parameter - inflation. If we add to the result obtained also the inflation rate (5.38% in 2016), then the rate will increase to 30.58%.
Capitalization ratio must match the chosen level of income. The capitalization rate for an enterprise is usually derived from the discount rate by subtracting the expected average annual growth rate of income or cash flow (depending on which amount is capitalized). Respectively for the same enterprise, the capitalization rate is usually lower than the discount rate.
WITH mathematical positions, the capitalization rate is a divisor used to convert the amount of income (profit or cash flow) for one period of time into a measure of value.
So, to determine the capitalization rate, you must first calculate the appropriate discount rate. There are various methods for determining the discount rate, the most common of which are:
1. Model for valuation of capital assets;
2. Method of cumulative construction;
3. Weighted average cost of capital model.
With a known discount rate, the capitalization rate in general terms is:
R To= R d– g, where R d- discount rate, g - long-term growth rate of income (profit or or cash flow).
2) The method of discounting future income - 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 enterprise being valued and the capitalization/return rate of the corresponding investments.
When determining the market value of an enterprise using the discounted cash flow method, as a rule, the following sequence of actions is observed:
1) the duration of the forecast period is determined, and the type of cash flow that will be used as a basis for the assessment is selected; 2 gross income, expenses and investments of the enterprise are analyzed and forecast; 3 the discount rate is calculated; 4 cash flows are calculated for the forecast and post-forecast periods; 5 calculates the present value of future cash flows in the forecast and post-forecast periods; 6final amendments are made and the cost is determined.
Methods for calculating capitalization ratios and rates of return in business valuation. OPTION 1
Most often, when calculating investment projects, the discount rate is determined as weighted average cost of capital (WACC), which takes into account the cost of own (share) capital and the cost of borrowed funds.
WACC= Re(E/V) + Rd(D/V)(1 - tc),
where Re is the rate of return on own (share) capital, calculated, as a rule, using the CAPM model;
E - market value of equity ( share capital). It is calculated as the product of the total number of ordinary shares of the company and the price of one share;
D - market value of borrowed capital. In practice, it is often determined from financial statements as the amount of company loans. If 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 - the rate of return on the borrowed capital of the company (the cost of raising borrowed capital). Interest on bank loans and corporate bonds of the company are considered as such costs. At the same time, the cost of borrowed capital is adjusted taking into account the income tax rate. The meaning of the adjustment is that interest on servicing loans and borrowings is charged to the cost of production, thereby reducing the tax base for income tax;
t c - income tax rate.
To determine the cost of equity capital is used capital assets pricing model (CAPM).
The discount rate (rate of return) of equity (Re) is calculated by the formula:
Re = Rf + β(Rm - Rf),
where Rf is the risk-free rate of return;
β is a coefficient that determines the change in the price of a company's shares compared to the change in prices for shares for all companies in this market segment;
(Rm - Rf) - market risk premium;
Rm - average market rates of return on the stock market.
Rate of return on investment in risk-free assets (Rf). As risk-free assets (that is, assets in which investments are characterized by zero risk), government securities are usually considered.
coefficient β. This ratio reflects the sensitivity of the returns on securities of a particular company to changes in market (systematic) risk. If β = 1, then the fluctuations in the prices of the shares of this company completely coincide with the fluctuations of the market as a whole. If β = 1.2, then we can expect that in the event of a general rise in the market, the value of the shares of this company will rise 20% faster than the market as a whole. Conversely, in the event of a general decline, the value of its shares will decline 20% faster than the market as a whole.
Market risk premium (Rm - Rf). This is the amount by which average market rates of return in the stock market have exceeded the rate of return on risk-free securities for a long time. It is calculated on the basis of statistical data on market premiums over an extended period.
The approach described above for calculating the discount rate may not be used by all enterprises. First, this approach is not applicable to companies that are not public joint-stock companies therefore, their shares are not traded on the stock markets. Secondly, this method will not be able to be applied by firms that do not have sufficient statistics to calculate their β-coefficient, as well as those that are unable to find an analogue company whose β-coefficient they could use in their own calculations. To determine the discount rate, such companies should use other methods of calculation or improve the methodology to suit their needs. It should also be noted that the methodology for assessing the weighted average cost of capital does not take into account the share and cost (most often zero) of accounts payable in the structure of liabilities.
The cumulative method for estimating the discount rate is determined based on the following formula:
d = E min + I + r,
where d - discount rate (nominal);
E min - minimum real discount rate (risk-free rate);
I - inflation rate;
r - coefficient taking into account the level of investment risk (risk premium).
As a rule, 30-year US government bonds are taken as the minimum real discount rate.
The main disadvantage of this calculation technique is that it does not take into account the specific cost of capital of the company. In fact, this indicator has been replaced by inflation and a minimum yield comparable to government long-term bonds, which has nothing to do with the profitability of the company, the weighted average interest rate (for loans and / or bonds) and the structure of its liabilities.
both methods involve the use of a risk premium. The risk premium can be determined different ways: Guidelines for evaluating the effectiveness of investment projects recommend taking into account three types of risk when using the cumulative method: country risk; risk of unreliability of project participants; risk of non-receipt of project revenues.
Country risk can be learned from various ratings compiled by rating agencies and consulting firms (for example, the German firm BERI, which specializes in this). The amount of the risk premium characterizing the unreliability of project participants, according to methodological recommendations should not be higher than 5%. The adjustment for the risk of non-receipt of the income provided for by the project is recommended to be set depending on the purpose of the project. Many components of this methodology are assessed quite subjectively; there is no linkage of the risk premium to the specific risks of the project and taking into account the current activities of the company.
OPTION 2
Cumulative construction method provides for the construction of an interest rate as a result of the summation of several values. The basis is the so-called risk-free rate. The risk-free rate is adjusted for inflation (Fisher's formula), for the risk associated with the characteristics of the property being assessed and the industry, the country (the risk of objects leased to unreliable tenants; the risk of insufficient liquidity of the assets being evaluated; the risk of political instability, etc. ) All corrections are taken into account as a percentage. The sum of the risk-free rate and the adjustments made is the interest rate at which the capitalization ratio is calculated. The basis for making amendments may be well-known data, the opinion of an expert appraiser based on his knowledge and experience.
In general, the interest rate using the cumulative method can be represented as:
where Rr - interest rate (discount rate); i - risk-free interest rate; r - percentage of inflation; - systematic risks (of the economy as a whole); - non-systematic risks (inherent only in the enterprise).
Method according to the theory of capital assets САРМ (β-coefficient).
The Capital Asset Pricing Model (CAPM) was developed by W. Sharp. Its essence is that adjustments are added to the risk-free rate for the excess of the risk inherent in the company over the average market (average industry), multiplied by the volatility of the company's profitability:
where Rr is the rate of return determined by the capital asset valuation method; ir is the risk-free rate of return. Defined as the return on an asset known with absolute certainty over the time of analysis. It is calculated in two ways: 1) as the yield of government or especially reliable securities; 2) the total return on interbank interest rates and the return on stable, large banks. In both cases, the inflation component is taken into account. In government or especially reliable securities, it is laid down immediately, an inflationary premium is added to the total yield (Fisher's formula): R - average market yield in this industry; p - coefficient characterizing the variability of profitability shows a measure of relative systematic risk compared to the average value of risk in a given industry or the ratio of the amount of change in the company's profitability to the amount of change in the average market profitability in the industry, where δcom - the amount of change in the company's profitability; δ neg - the amount of change in the average market profitability in the industry.
The CAPM model provides for the total value of the products of the excess of risk by the variability of the returns of various risk factors. But in practical conditions, when assessing the value of a business, the product is calculated only relative to the average market profitability in the industry, the remaining necessary amendments are added based on expert opinion according to the formula
17. Types of final adjustments and the process for making them. Premiums and discounts in the valuation of controlling and non-controlling stakes. Methods for making adjustments for lack of liquidity.
Goals inflation adjustment documentation are: bringing retrospective information for past periods to a comparable form; taking inflationary price changes into account when making cash flow forecasts and discount rates.
The simplest way to adjust for inflation is to revaluation of all balance sheet items based on changes in the exchange rate of the ruble relative to the exchange rate of another currency, such as the dollar or the euro. The advantage of this method is simplicity and the ability to work without a large volume additional information. Disadvantages: Adjustment for the exchange rate gives inaccurate results, since the exchange rate ratios of the ruble and other currencies do not match their real purchasing power.
The second method of inflation adjustment– revaluation of assets and liabilities of the balance according to fluctuations in the levels of commodity prices. Here you can focus both on the mass of goods as a whole, and on each specific product or product group. This is a more accurate way of inflation adjustment.
The third way of inflation adjustment based on accounting for changes in the general price level: various items of financial statements are calculated in monetary units of the same purchasing power (in rubles of the base or current period as of the reporting date); for recalculations, the index of dynamics of the gross national product or the index of consumer or wholesale prices is used. The method increases the realism of the analysis, but does not take into account the varying degree of change in the value of individual assets.
After inflation adjustment, the financial statements are normalized.
Normalization of financial statements- this is an adjustment of reporting based on the determination of income and expenses that are characteristic of a normally operating business.
Control Award considered as a percentage of the redemption price exceeding the market price of shares.
Discount for the non-controlling nature of the package is the derivative of the control premium. This trend is based on empirical data. The allowance for non-controlling nature (minority interest) as a percentage is calculated using the following formula:
The average control premium fluctuates between 30-40%, and the discount from the cost for a smaller share fluctuates around 23%.
discount for insufficient liquidity is defined as the amount or percentage by which the value of the package being evaluated is reduced to reflect insufficient liquidity.
According to Sh. Pratt ( Pratt Sh.P. Business valuation. Discounts and premiums/per. from English. M.: Kvinto-Management, 2005. S. 17.), the purpose of applying discounts and premiums is to adjust the underlying cost to reflect differences between characteristic features of the evaluated package (share) and the group of companies on the basis of which the calculations were made estimated cost. All data on premiums and discounts are calculated empirically.
The control premium is the value of the advantage associated with owning a controlling stake.
Discount for non-controlling nature - the amount by which the value of shares in the package being evaluated is reduced, taking into account its non-controlling nature.
The discount for insufficient liquidity arises due to the lack of liquidity of the shares, i.e. the possibility of their rapid conversion into cash at minimal cost and at a price close to the market.
However, with a deeper study of the problem, carried out in the specified manual by S. Pratt, a number of discounts and bonuses are considered:
– the premium for the strategic nature of the acquisition (the premium for taking over the entire company (100% of the stake)) is 20% of the cost of the controlling stake;
– discount associated with the change of key figure (considered as substitutions a risk premium associated with a key person in the company's management, which can be reflected in the income approach as part of the calculation of the discount rate and when calculating multiples in the comparative approach);
– discount due to actual or potential security obligations environment. Also considered as a replacement for the final adjustment in the income and comparative approaches;
– discount due to litigation against the company being valued;
– a discount associated with the loss of a customer base or suppliers. It is also considered as a substitute for the corresponding risk in the discount rate in the income approach or the adjustment to the multiples in the comparative;
- package discount - a value or percentage expression of the amount deducted from the market price of shares in order to reflect a decrease in the value of a block of shares (per share) in the case when big size package does not allow its implementation within a period of time characteristic of the normal volume of the package. This circumstance is due to the fact that there will be an excess supply of such shares on the market, which will lead to a fall in the rate;
– “portfolio” discount (discount for heterogeneity of assets) – occurs in the case of the sale of diversified companies in their entirety or in large parts, combining several lines of activity, which reduces the attractiveness of the purchase (due to additional problems in managing non-core assets and their further sale). The discount is determined from the sum of the cost of individual constituent parts companies.
The topic of determining interconnected discount and capitalization rates is very relevant, and not only among appraisers. Recently, the Royal Society of Certified Real Estate Experts (RICS) organized round table, dedicated to this topic and brought together leading real estate and valuation experts - Cushman & Wakefield , Colliers International , JLL , Valrus , Russian Society of Appraisers and others. Specialists discussed the problems of setting rates and short-term market prospects.
Before talking about the relationship between the discount rate and the capitalization rate, it is necessary to understand the concepts themselves. The discount rate reflects the return required by the investor for the appropriate level of risk and must be consistent with the cash flow, including it can be calculated for the real and nominal flow, the flow of income on equity or invested capital. The rate of return can be modeled on the basis of certain basic levels, taking into account amendments to them, reflecting differences in risks.
When considering the discount rate for real estate, it is important to understand that real estate is an asset, and cash flow per total invested capital is used to value it. By analogy with business valuation, the rate can be calculated using the WACC model, however, since the market valuation is mainly based on pre-tax flows, the real estate rate does not include an adjustment for tax leverage.
The capitalization rate reflects the relationship between annual income and the value of the object. It is important to understand that the traditional phrase “capitalization rate” is the ratio of the current net income actually achieved on the date of assessment to the value of the object. The capitalization rate is thus an indicator that provides the winding up of the DCF model for infinite or very long cash flow. This rate is related to the discount rate, but also takes into account the change in the investment itself.
Despite the fact that most appraisers are familiar with traditional models that reflect the interdependence of discount and capitalization rates, the economic meaning of the indicators embedded in these models is not fully understood by everyone. So the change in the value of an asset in the future can be decomposed into four main factors, which together can logically fit into a multiplicative model. The first is a change in the level of loading of the object, as well as the implementation of any additional investments. The second is monetary inflation. The third is general movement market. And the fourth is the loss of the value of the asset due to its wear and tear. In the calculation model used by the appraiser, each factor must be taken into account in an appropriate way.
1) Change in load and investment - by reflecting the movement of funds in the cash flow with consideration in the discounted cash flow model of the corresponding periods.
2) Monetary inflation - through the use of a discount rate appropriate to the flow. In the case when lease payments are indexed to inflation, or can be changed in another way, for example, by regular renegotiation in accordance with market dynamics, it is desirable to eliminate this factor from the model, reducing the number of uncertainties, using a real flow (at a constant price level at the date estimates) and the corresponding real discount rate, i.e. cleared of monetary inflation.
3) Depreciation - through the application of an appropriate rate of return (or alternatively - through the application of an appropriate level of repair costs in the cash flow, however, practice has proven that there is a certain economically viable lifespan and level of repair costs, that is, spend more to extend the lifespan buildings forever, economically impractical; Alternative option, that is, when there is still a need to extend the life of the building, it can be considered for monuments).
4) Since the actual forecast of price changes in the market is not so much important for the assessment as the expectations of market participants reflected in the price of an asset, practically the only most adequate option to take these expectations into account in the rate is to obtain a rate based on the extraction of market data from comparable transactions, that is it is for the correct consideration of this factor that it is most important to be based on the determination of the capitalization rate and discounting in the market. Market movement can be considered both with and without monetary inflation. Which option to use depends on the data on which the forecast is based. At the same time, it should also be understood that expectations for changes in market prices should be considered for a period equal to the life of the asset, the period during which it can generate income, and for land - in general, indefinitely.
From the last point, we smoothly move on to the second important indicator, which is used in calculation models to move from the discount rate to capitalization. The ideal case is infinity, that is, when we consider a flow that takes into account the operation of the building, its demolition, construction of a new one, re-operation, etc. But since, due to the leveling of cash flows that are significantly distant in time, by the discount factor, as well as the fact that buildings occupy a larger share in the value of most real estate objects, and a critical change in the value of an asset occurs with the end of the building’s operation, in most cases it makes sense to consider the model as at least until this period, ignoring the value of the land plot remaining after the end of operation or without neglecting it.
All factors in the capitalization model should be considered for this period, should correspond to each other in time periods. Accordingly, for this period it is necessary to consider both the market movement and monetary inflation, if they are separated in the model. The significance of indicators over time, taking into account discounting, will not be the same, which must be taken into account when folding them into a single coefficient that will be used in the terminal model. In the long term, it may seem that the movement of the real estate market is comparable to inflation, that is, if you isolate monetary inflation, then nothing will remain, however, RICS studies show that in the long term, the real estate market is ahead of inflation by 1.5-2%, which in principle explained by the limited nature of land as a resource, the growth of the earth's population and agglomeration during the 20th century. Depreciation, if we consider the period before the end of the life of the asset, will be in the amount of the annual depreciation rate from the remaining useful life.
Information disclosed above. concerns the general approach to assessing market value. More difficult in practical implementation is modeling when it is required to calculate the investment value of an asset for a particular investor, provided that he owns this asset for a limited period of time, as well as the specific structure of the transaction, taking into account financing, taxation and other factors. For example, an investment fund may buy a building not to keep it until it collapses, but with the expectation of earning income for 3 years, then exit the project by selling the object. Here it is already impossible to neglect the individual factors of the model, simplifying them.
Colleagues from JLL consider the following factors to be important, which investors pay attention to in transactions, which, among other things, is reflected in the capitalization rate used in the transaction.
1) Financing structure. This factor has a big impact on cash-on-cash returns for the investor. In turn, investors are willing to pay a premium for assets that have an attractive financing structure.
2) Taxation. Property tax and are taken into account when calculating net operating income and directly affect the capitalization rate. In turn, it affects only indirectly. Despite the fact that, in practice, the most common indicator of the income side of an asset is EBITDA, for investors, the indicator of net income after tax is ultimately important.
It is important to understand that the following aspects affect the amount of income tax:
The transaction is carried out through the sale of the asset itself or SPV (project company). This directly affects VAT liabilities. However, lately tax service refunds VAT on the purchase transaction to the buyer within six months, which makes the purchase of real estate as assets very attractive.
Accumulated losses after the construction of the object - when buying an object through SPV, they can give additional income in the early years of the forecast period, resulting in a higher return for the buyer compared to purchasing the same asset a few years after commissioning.
Deal structuring – on/off-shore – has a significant impact on profit.
3) The currency of the asset's income. In the event that the revenue of the property being valued is nominated in rubles, but all comparable transactions on the market took place with assets, the income part of which was nominated in US dollars, then it would be an incorrect step to take the capitalization rate of these transactions as the base due to several interrelated reasons.
First, inflation. For comparison, 6.5% of the Russian Federation against 1.5% of the USA according to 2013 data.
Secondly, the cost of attracting financing: for example, a 7% fix for a USD dollar loan versus 12% for a ruble loan.
Thirdly, different indexation of ruble and foreign currency lease agreements.
4)Risk of revaluation of cadastral value.
According to Law No. 307-FZ dated November 2, 2013 on amendments to the Tax Code, the tax base for calculating property tax should be calculated based on the cadastral value of the property. In Moscow, the application of this law is already being implemented for commercial facilities with an area of over 5,000 square meters. m, from 2015 the threshold will be reduced to 3,000 sq. m, and since 2016 highly likely objects throughout the country will be transferred to this tax in full. Taking into account flaws in the methodology state evaluation For large commercial facilities, experts see the risk of a significant reassessment of the cadastral value for obsolete buildings and buildings with a large parking area, warehouses and other general utility premises. Accordingly, ceteris paribus, this risk may affect the capitalization rate.
In conclusion, we note that the risks are growing, and with them the cost of capital and, accordingly, the discount and capitalization rates are growing, which leads to a decrease in the value of real estate. However, the question of how much the cost will decrease is still open. This is another topic for discussion.
Thank you for your help in preparing the RICS (The Royal Institution of Chartered Surveyors) material.
