]→[Market extraction method for determining capitalization ratio]
Market extraction method is a tool for analyzing real and nominal rates, investment risks
A.N. Fomenko, practicing appraiser, Ph.D.
Introduction
Recently, the market extraction method is often used in practice when assessing the value of various assets to determine discount rates. Hereinafter, by asset we will primarily understand a real estate object, although the results presented are of a more general nature. Despite the fact that the income approach when using such rates loses its independence from the comparative approach, as noted in, the use of this method allows one to determine the actual market rates of return.
Most often, the market extraction method is implemented in the following version (and others):
Where
R— capitalization ratio;
NOR - net operating income;
WITH— asset value;
AP - annual rent;
A— share of operating expenses;
k— sample size;
index “0” corresponds to the current state (as of the valuation date).
Thus, according to formula (1), the current rate of return is essentially determined. But the direct capitalization method (DC) involves capitalizing the forecasted value of the NPV for one future period (etc.):
(2)
Where
Y— rate of return (discounting);
f— compensation fund factor (rate of return of capital);
t h—annual growth rate of NPR;
index “1” corresponds to the forecast value for 1 period (year) ahead.
So, there is a discrepancy between dependencies (1) and (2). Indeed, if we substitute the value of the capitalization coefficient calculated from dependence (1) into dependence (2), we will obtain a value estimate that is shifted relative to the true value, i.e., a systematic error will arise. One option for eliminating systematic error is to perform market extraction based on dependence (2), as, for example, proposed in.
Determining the real rate of return
Dependence (1) can be considered as an example of using the forecast value of the NOR in the absence of its growth (no inflation of the NOR). Since NAV inflation always exists in the real market, dependence (1), using a constant NAV value, allows us to determine the real capitalization ratio based on the real rate of return. Here and in the future, when writing formulas to simplify the calculations, we will omit the averaging expression (the sum of the sample elements divided by the sample volume), reducing the sample to one element. Taking into account the above, the dependence for calculating the real rate of return will take the form:
(3)
where the subscript "p" refers to real values.
However, when using relationship (3) to determine the real rate of return, it is essentially assumed that the inflation of all market segments is the same. Indeed, for next year the expression for extraction will look like this:
Where
OR - operating expenses for the year;
t AP is the annual growth rate (inflation) of rent;
t OR - annual growth rate (inflation) of operating expenses;
t c is the annual growth rate (inflation) of the asset value;
index “11” corresponds to the value next year.
If the inflation of rent and operating expenses are equal, they actually turn into inflation of the NPV, and dependence (4) takes the form:
(5)
It follows that when inflation of all input cost parameters is equal, inflation indicators (growth rates of NPV and asset value) are reduced, and the above dependence (5) for the next year, assuming the same rates of return of capital, takes the form of dependence (3).
At the same time, equal inflation in all market segments is possible only in an idealized market. In real markets (both developed and developing countries), the rate of price growth in various market segments, both in the short and long term, changes asynchronously. This leads to the fact that the real rate of income, defined as the current rate of return according to dependence (3), changes over time, i.e., it is a function of the relative inflation of market segments and acquires the features of a nominal rate. Graphs of the dependence of the current rate of return in the next year on the current rate of return in the current year (dependence (5)) with different inflation in the value of the asset (assuming that rent inflation is equal to operating income inflation) are shown in Fig. 1.
Rice. 1. Dependence of the current rate of return next year on the current rate of return
this year at t h = 10%, asset life is 20 years, rate of return of capital is determined using the Inwood method
To eliminate the time dependence of the real rate of return (eliminate its dependence on inflation of market segments), inflation can be considered either as an average value for a fixed forecast period, obtained taking into account its forecast for market segments for this period, or in a quasi-static approximation (assuming that inflation (growth rates) of NPV and asset value are the same) as the current rate of return.
In the future, we will limit ourselves to considering the real rate of return only in a quasi-static approximation.
It should be noted that the real rate of return can also be obtained using the market extraction method based on the equation for the discounted cash flow (DCF) method in the form:
Where
WITH rev — the cost of reversion (in real terms);
n— duration of the forecast period.
The presented equation can be solved numerically with respect to Y p (for example, using the parameter selection function in Excel).
At the same time, the real rate of return obtained on the basis of the DCF equation will coincide with the real rate of return determined on the basis of the PC equation only if the PC method uses the return of capital according to the Inwood method, and in the DCF method it is determined taking into account the return of capital also according to Inwood method (for depreciable assets with remaining economic life m, the value 
) or for non-wearable assets (as a special case) at .
The Inwood method is the most cost-effective method of returning capital because it requires minimal contributions. Despite the fact that in practice it is not always possible to implement it, when determining the real rate of return, it seems advisable to consider this particular method of capital return based on the assumption of the most efficient use of funds.
In valuation practice, the DCF equation with a half-period shift is often used. The equation is
This approach leads to smaller calculation errors in conditions where annual income consists of several periodic payments. Therefore, in the case of several periodic payments during the year, it is advisable to use the DCF method with a half-period shift for market extraction, or to adequately use the PC method in this case, it is necessary to use the adjusted NFR value, which is equal to
The adjustment value can be found from the following relationship:
Thus, to determine the real rate of return using the market extraction method, both the PC method and the DCF method, based on the return of capital according to the Inwood method, can be used.
Determination of nominal rates of return
The relationship between real and nominal rates of return can be obtained from the relationship:
where the index “n” refers to nominal values.
If in both cases the return of capital is carried out at a real rate, which seems justified, since by the end of the asset’s life it is necessary to accumulate an amount for its reproduction in real terms, then we obtain:
The results of calculating the relationship between real and nominal rates of return are shown in Fig. 2.
Rice. 2. Dependence of nominal rates of return on real rates for different levels of inflation NPV for the period
asset life is 20 years, the rate of return of capital is calculated using the Inwood method (in real terms)
It should be noted that when deriving dependencies (7) and (8), the default assumption is that the growth rate of NPV (inflation) is a constant value throughout the entire life of the asset. Strictly speaking, this is not true, at least for the current economic state of Russia. Therefore, it is more correct to take the average integral value of forecast inflation over the life of the asset as the estimated inflation.
In addition, the obtained dependencies were derived without taking into account income from the growth in value (inflation) of the asset. The features of calculating the contribution of the growth rate of the value of an asset to the nominal rate of return are discussed in sufficient detail in.
It should be noted that in the real market, for assets with different remaining economic lives (for example, for similar properties of different ages), the inflation rate is almost the same (provided that the remaining economic life is long enough). At the same time, the required rate of return on capital for such assets should differ due to differences in life expectancy. Therefore, when making calculations using the market extraction method, it is advisable to take into account separately inflation (growth rates) and the rate of return of capital as an element of depreciation. In this case, we can write the following relation:
— annual change in value (absolute inflation) of the asset; t c is the annual growth rate of value (relative inflation) of the asset.
It should be noted that for non-depreciable assets ( f R = f n = 0) and in the case of equal inflation of the asset and the NPV ( t With = t h) dependencies (9) and (10) turn into the well-known Fisher formula:
In general, the market extraction method for determining nominal rates of return can also be used on the basis of the DCF method. However, here the problem becomes multivariate and the nominal rate determined by the PC method does not coincide with the rate determined by the DCF method.
In some cases, you can try to ensure the same nominal rates of return for the DCF and PC methods by selecting the appropriate relationship for calculating the capitalization ratio (rate of return on capital), as shown in. However, apparently, the proposed selection method is more of an artificial mathematical technique than an economically sound investor behavior.
The fact is that the PC and DCF methods reflect fundamentally different models of investor behavior and, therefore, can produce different results.
Indeed, the dependence can be transformed to the following form:
or 
Thus, we have obtained the classic formula for calculating the return on invested capital. For example, in the case of lending, the ratio of annual interest payments on the loan to the loan amount.
Since the rate of return on capital is calculated taking into account the remaining economic life of the asset, it follows that the PC method is built on a model that assumes that an investor, after investing capital in an asset, will own it until the end of its economic life.
The DCF method (dependence (6)) assumes a different model of investor behavior when investing capital in an asset, namely: receiving income for a limited period of time (forecast period, which is less than the economic life of the asset) and selling the asset at the cost that will be at the end income period.
The multivariance of market extraction results when using the DCF method is due to a number of reasons.
Firstly, the calculated dependencies for the DCF method using nominal rates of return can take different forms.
Most often in practice, the DCF equation is used for a constant rate of return in the form
At the same time, it is possible to use DCF equations with rates of return variable by period:
When using spot rates:
When using forward rates:
(13)
Secondly, the duration of the forecast period when using the DCF method can also be different.
Thirdly, the cost of reversion can be determined in different ways:
- based on the capitalization of the NPV of the first year of the post-forecast period using the rate of return of capital according to the methods of Inwood, Hoskold, Ring or the Gordon model;
- by directly forecasting the current value of an asset for the first year of the post-forecast period using the growth rate of its value.
All this variety of calculation options using the DCF method leads to the fact that the calculated nominal rates differ from those obtained using the PC method. The results of calculating some options, provided that the value of the asset on the valuation date is the same and corresponds to a real rate of return of 10%, are given in table. 1.
Table 1
| No. | Type of bet | Rate value in %, with the duration of the forecast period, years | Payment terms | ||||
| 1 | |||||||
| 1 | RealY R | 10 | 10 | 10 | 10 | 10 | PC and DDP method, dependencies (3) and (6), f- Inwood method |
| 2 | NominalY n | 11,44 | — | — | — | — | PC method, dependence (7), f- Inwood method |
| 3 | Y n | 11,17 | — | — | — | — | PC method, dependence (8), f- Inwood method |
| 4 | Y n | 11,50 | — | — | — | — | PC method, dependence (7), f- Ring method |
| 5 | Y n | 23,44 | — | — | — | — | PC method, dependence (9), f- Inwood method |
| 6 | Y n | 23,17 | — | — | — | — | PC method, dependence (10), f- Inwood method |
| 7 | Y n | 23,50 | — | — | — | — | PC method, dependence (9), f- Ring method |
| 8 | Y n | 23,20 | — | — | — | — | |
| 9 | Y n | 12,78 | 14,01 | 15,11 | 16,08 | 16,92 | DDP method, dependence (11), WITH rev - PC method, f- Inwood method |
| 10 | Y n | 12,78 | 14,03 | 15,19 | 16,26 | 17,25 | DDP method, dependence (12), WITH rev - PC method, f- Inwood method |
| 11 | Y | 12,78 | 14,23 | 15,77 | 17,43 | 19,21 | DDP method, dependence (13), WITH rev - PC method, f- Inwood method |
| 12 | Y n | 36,44 | 29,15 | 26,76 | 25,54 | 24,80 | DDP method, dependence (11), WITH t With) |
Note. When calculating nominal rates of return Y n accepted: t h = 10%, t c = 12%.
The given examples show that the value of the nominal rate of return significantly depends on the calculation method. Therefore, in order to obtain adequate results when using the market extraction method to determine the nominal rate of return, the extraction process must be carried out using a relationship that will later be used when carrying out valuation calculations.
Calculation of investment risks
To determine the rate of return, practicing appraisers quite often use the cumulative construction method. Its essence is that the rate of return is presented as the sum of the so-called risk-free rate of return and premiums (surcharges) for investment risks (etc.). In this case, various methods for determining risks are used: from expert assignment of values to the construction of calculation and analytical models. However, in practice, all these methods have elements of subjectivity.
The market extraction method creates the ability to determine the risks of different investments based on market data.
Usually, the yield to maturity rates on government securities (bonds) are considered as risk-free rates. However, market data on bond yield rates are conditionally risk-free, since they contain inflation risks. Therefore, the bond yield rates used by appraisers are nominal.
To ensure comparability of the magnitude of inflation risks for the risk-free rate and the rate of return of the asset being valued, they usually strive to select a bond with a maturity close to the holding period of the asset.
If we determine the nominal rate of return using the market extraction method and select the (nominal) risk-free rate, we can determine the total risk of the investment. The calculated dependence has the form:
Where
r n - total investment risk (in nominal terms);
Y br - risk-free rate of return.
The results of calculating investment risks for the nominal rates of return calculated above (see Table 1) are given in Table. 2 (the numbering of the corresponding columns in Table 1 is retained). In the calculations it was assumed that Ybr = 5%.
table 2
| No. | Type of risk | The value of the total risk in %, with the duration of the forecast period, years | Payment terms | ||||
| 1 | 2 | 3 | 4 | 5 | |||
| 2 | Nominal r n | 6,44 | — | — | — | — | PC method, dependence (7), f- Inwood method |
| 3 | r n | 6,17 | — | — | — | — | PC method, dependence (8), f- Inwood method |
| 4 | r n | 6,50 | — | — | — | — | PC method, dependence (7), f- Ring method |
| 5 | r n | 18,44 | — | — | — | — | PC method, dependence (9), f- Inwood method |
| 6 | r n | 18,17 | — | — | — | — | PC method, dependence (10), f- Inwood method |
| 7 | r n | 18,50 | — | — | — | — | PC method, dependence (9), f- Ring method |
| 8 | r n | 18,20 | — | — | — | — | Fisher formula (calculation by tс) |
| 9 | r n | 7,78 | 9,01 | 10,11 | 11,08 | 11,92 | DDP method, dependence (11), WITH rev - PC method, f- Inwood method |
| 10 | r n | 7,78 | 9,03 | 10,19 | 11,26 | 12,25 | DDP method, dependence (12), WITH rev - PC method, f- Inwood method |
| 11 | r n | 7,78 | 9,23 | 10,77 | 12,43 | 14,21 | DDP method, dependence (13), WITH rev - PC method, f- Inwood method |
| 12 | r n | 31,44 | 24,15 | 21,76 | 20,54 | 19,80 | DDP method, dependence (11), WITH rev - forecast based on the growth rate of asset value ( t With) |
Strictly speaking, since the PC and DCF methods assume different holding periods for the asset, the risk-free rates used for these methods should be different. However, this is usually not taken into account in practical assessments.
In conclusion, I would like to note that there is a temptation to determine the real risk-free rate using the known real rate of return and the calculated total investment risks. In this case, you can accept the assumption that the nominal risks for the asset are equal to the real ones, or use the amendment proposed in to calculate the real risks.
However, such a calculation seems unlawful, since the predicted risks when investing in the asset being valued and the predicted risks for bonds, as perceived by participants in the market for the assets being valued and the securities market, differ significantly. Apparently, these differences are associated with the high dynamics of the securities market and the speculative component present in the real profitability of participants in this market. Obviously, if you try to subtract the calculated risks from the real rate of return of an asset, then in some cases you may end up with negative values of real risk-free rates. Therefore, real risk-free rates of return for government bonds can only be determined based on an analysis of the securities market, which is beyond the scope of this publication.
Conclusion
The article discusses the features of using the market extraction method to determine real and nominal rates of return. Dependencies are derived that establish a connection between nominal and real rates of return, which, under certain conditions, coincide with the well-known Fisher formula.
Also presented are the calculation results confirming that adequate use of the market extraction method to determine nominal rates of return is possible only if the same dependencies are used for extraction and for valuation. The fundamental possibility of calculating and comparing investment risks based on market data is shown.
Literature
1. Ozerov E.S. Economic analysis and real estate valuation. St. Petersburg: MKS, 2007. pp. 188-243.
2. Esipov V.E., Makhovikova G.A., Terekhova V.V. Business valuation. St. Petersburg: Peter, 2006. pp. 99-100.
3. Fomenko A.N. Features of using VRM when determining the capitalization ratio using the market extraction method. — www.appraiser.ru
4. Mikhailets V.B., Artemenkov I.L., Artemenkov A.I. The income approach and the discounting principle when valuing income-producing illiquid assets. Revision of the concepts of the income approach and development of a transactional pricing model // Questions of assessment. 2008. No. 1.
5. Fomenko A.N. Possible error and uncertainty in the results of estimation calculations when using various discounting techniques. — www.anf-ocenka.narod.ru
6. Leifer L.A. Income approach to real estate valuation. Typification of models of forecasted cash flows // Questions of assessment. 2007. No. 3.
7. Fomenko A.N. Using a variable discount rate when estimating the value of real estate within the framework of the income approach. — www.anf-ocenka.narod.ru
8. Real estate valuation / Ed. A.G. Gryaznova, M.A. Fedotova. M.: Finance and Statistics, 2005. pp. 146-149.
9. Kozyr Yu.V. Implications of the effects of interest rates on risk premiums. — www.appraiser.ru
Source: Fomenko A.N. The market extraction method is a tool for analyzing real and nominal rates, investment risks // Assessment Issues. 2008. No. 3. P. 30-37.
The capitalization rate can be calculated:
market extraction method;
method of cumulative construction.
To determine the value of the capitalization coefficient of a real estate property, as a rule, the market extraction method is used. The use of another method (cumulative construction) must be justified.
Determining the capitalization ratio using the market extraction method is made by dividing the net operating income of a similar property by its market value.
The calculation of the capitalization rate using the market extraction method is usually carried out using the following formula:
Where TO− capitalization coefficient (rate), %; CHOD– annual net operating income generated by a similar property, rub./year; V– market value of a similar object, rub.
To implement the market extraction method, at least three to five objects are selected that belong to the same market segment as the object being assessed with the most effective use. For each of these properties, the sales price/offer price and the actual/proposed rental rate must be known.
The appraiser calculates net operating income for each of these objects based on the analysis of the market segment. In relation to each of the similar objects selected for calculating the capitalization ratio, typical losses from underutilization and losses in collecting rent for the market segment are applied, as well as the rate of operating expenses per useful unit leased.
The value of the coefficient must be within the range of values of the capitalization coefficient defined for the market/market segment to which the valuation object belongs (it must be contained in the conclusions of the analytical section for the market/market segment to which the valuation object belongs).
The requirements for justifying all indicators used are similar to the requirements set out in Chapter. 7, 8 of the textbook.
The results of determining the capitalization ratio using the market extraction method should be presented in the form of a table. 8.4.
Table 8.4
Determining the capitalization ratio using the cumulative construction method is made by summing up the various risk factors associated with investing in the property being valued (the rate of return) and the rate of return, which means the repayment of the amount of the initial investment over the period of ownership of the property.
Capitalization rate calculation ( TO, %) using the cumulative construction method, as a rule, according to the formula
K = BS + R + L + IM + NV,
Where BS– risk-free rate, %; R– compensation for the risk of investing in the property being valued, %; L– compensation for low liquidity of the property, %; THEM– compensation for investment management, %; NV– capital return rate, %.
Under the risk-free rate (FR) return on capital is understood as the rate of return on the least risky investment of capital (for example, the rate of return on deposits of banks of the highest category of reliability or the rate of return to maturity on government securities).
The risk-free rate can be determined by:
data from an analysis of rates on long-term foreign currency deposits offered by the largest banks in Irkutsk (information source: information weekly "Delo", section "Deposits");
data from an analysis of the annual effective yield to maturity of government currency bonds of the Russian Federation with a maturity period comparable to the remaining effective service life of the property being valued (for example: Russia-2030-11t (FED-30); maturity date: 03/31/2030), according to Internet project "Bond Market - RUSBonds" of the information agency "Finmarket".
Based on the condition of investment alternativeness, the risk-free rate can be defined as the average (weighted average) yield on bank deposits and the yield to maturity on government securities.
The deposit currency must correspond to the selected type of real/nominal cash flows.
The accepted value of the risk-free rate must be justified.
Compensation for the risk of investing in the property being valued (P). The risks of investing in a real estate property are determined by possible types of risk and factors related to the workload of the property, losses when investing in the property being assessed, which influence the level of risk.
Compensation for the risk of investing in the property being valued can be determined by expert analysis based on the scale given in Table. 8.5.
The accepted amount of compensation for the risk of investing in the property being valued must be justified.
Table 8.5
Scale for determining the risk value of investing in an asset (P)
depending on the nature of the risk
| Nature, degree of risk | Risk premium (R), % | Description of the risk in relation to the object of assessment |
| Short | 0 − 1,5 | Constant full load of the facility (location in the city center), guaranteed absence of natural and emergency situations, fast speed of elimination of the consequences of accidents and natural disasters, excellent condition |
| Average | 1,5 – 3,5 | The workload of the facility is “above average” (located within the city), the absence of force majeure, the average speed of eliminating the consequences of accidents and natural disasters, good, satisfactory condition |
| High | 3,5 – 5,0 | Low degree of workload of the facility (remoteness from populated areas), high probability of emergency situations resulting in low speed of elimination of their consequences for the facility, unsatisfactory or emergency condition |
Compensation for low liquidity of the property (L) is typical for objects for which a long period of exposure, searching for a buyer and converting the object into “real” money is typical. Compensation for low liquidity ( L, %) is calculated using the formula
,
Where BS– risk-free rate, %; n– typical exposure period, months; 12 − the total number of months in a year.
Typical exposure period for commercial real estate located in the area under consideration, most similar to the property being assessed ( n), is determined on the basis of an analysis of the market/market segment to which the valuation object belongs (it must be contained in the conclusions of the analytical section for the market/market segment to which the valuation object belongs).
The results of determining compensation for low liquidity of a real estate property should be presented in the form of a table. 8.6.
The coefficient used in direct capitalization corresponds to the overall capitalization rate, which can be determined by a number of methods.
Market squeeze method, or comparable sales analysis, consists of extracting capitalization rates from comparable sales when sufficient data is available for similar income-producing properties.
Comparable objects must coincide with the one being assessed in terms of their functional purpose and level of investment risk, and also correspond to it in terms of income, physical similarity, location, the ratio between gross income and operating costs, and the market expectation of the future behavior of property values.
The following data is collected for comparable objects:
- price of the object;
- generated income;
- operating cost ratio, as the ratio of gross income to operating costs;
- terms of financing the transaction, share of borrowed funds;
- market situation at the time of the transaction.
Example.
Determine the capitalization rate using the following data. Four compared objects were selected:
If the characteristics of all compared objects and the one being evaluated approximately coincide, and the data is obtained from reliable sources, then the capitalization rate is calculated as the arithmetic average and equals SC = 0.17545.
If there are discrepancies, then the capitalization rate is calculated as a weighted average of individual capitalization rates, and the specific weight of each of them is directly proportional to the degree of similarity of the comparable object and the reliability of information on it.
Cumulative construction method
capitalization rate divides it into its component parts: return on investment and capital recovery rate.
Return on investment is broken down into four parts:
- risk-free interest rate (can correspond to bank interest on capital or interest rate on government short-term bonds);
- risk adjustment depending on the riskiness of the capital investment;
- adjustment for low liquidity of this property;
- an investment management adjustment related to the costs of management efforts, in particular filing a tax return, etc.
Example.
The disadvantages of the summation method include the subjective approach of the appraiser to analyzing the situation and accepting the sizes of the components of the capitalization rate.
Example.
Using the direct capitalization method, determine the cost of a country house with a total area of 300 m2, with a land plot of 0.15 hectares, located in a prestigious holiday village at a distance of 35 km from Moscow.
1. Potential gross income from renting out an object based on an analysis of the rental market for comparable objects in the territory of this village was determined at the current rental rate of $90 per 1 m2 per year:
PVD = 300 · 90 = $27,000 per year.
2. In terms of the level of comfort and equipment, the country house is suitable for year-round living and, according to the rental conditions, it requires the presence of one tenant for a period of at least a year. The object load is thus either 100% or 0%. Conducted marketing research has shown that the shortfall in rent for the period from the moment of putting it on the market until the moment of renting out can be 10% per year.
Actual gross income:
DVD = 27,000 - 27,000 * 0.1 = $24,300 per year.
3. The total expenses of the property owner are related to taxes, routine repairs and other expenses and amount to $1,350 per year.
Net operating income:
CHOD = 24,300 - 1,350 = $22,950 per year.
4. The overall capitalization rate, calculated based on data on the sale of similar properties, was 19.3%.
Using the cumulative construction method, the rate was determined at 18%. Considering that the first method more accurately reflects the characteristics of a particular market, a decision was made on the final capitalization rate - 19%.
The cost of the assessed object will be:
22,950: 0.19 = 120,789 or $121,000
Other methods for determining the overall capitalization rate (debt coverage ratio method, mortgage investment analysis method) take into account the features of more complex real estate financing schemes.
Financial components method - own and borrowed funds
Since most income-producing properties are purchased with borrowed funds, the overall capitalization rate must satisfy the requirements of both the bank and the investor.
The bank's requirements include obtaining a profit at a certain level, taking into account the risk of issuing a loan, and receiving equal periodic payments, including interest payments and repayment of the principal debt.
The investor's requirements include obtaining a return on invested capital during the holding period in an amount sufficient to justify an investment with a given level of risk and reimbursement of the initial investment.
The capitalization rate for borrowed funds is the mortgage constant.
The mortgage constant is the sum of the interest rate and the corresponding sinking fund ratio.
The capitalization rate for SKSS's own funds is calculated based on the investor's income after debt service payments and depreciation charges, but before taxes, according to the formula:
The total capitalization rate is calculated as the weighted average of the mortgage constant and the capitalization rate for the investor's own funds.
| SKo = SKzs * K + SKss(1 - K), | (3.5) |
where K is the share of borrowed funds in the purchase price of the object.
SKZS - determined on the basis of average market conditions for financing transactions for similar objects. SCSS is calculated based on information on comparable objects.
Example.
The valuation uses a comparable property that has a 70 percent debt-to-value ratio. The capitalization rate for borrowed funds is 16.2%. The property is typical for this market, the general capitalization rates of which are 18%.
Determine the capitalization rate for SKSS own funds.
Solution.
SKss = (SKo - K * SKzs) / 1 - K; SKss = (0.18 -0.7 0.162) / (1 - 0.3) = 0.222 or SKss = 22.2%.
Example.
To purchase an object, a loan in the amount of
$300,000 with a permanent mortgage - 17.5%. Loan terms meet typical market financing conditions. Analysis of similar objects indicates a CCCC of 19%. The object brings CHOD = $65,000.
Determine the cost of the object.
Solution.
Dzs = 300,000 * 0.175 = $52,500 - the share of borrowed funds in the private equity capital in absolute terms.
DSS = 65,000 - 52,500 = $12,500 - share of own funds in the private equity fund.
Sss = 12,500\0.19 = $65,789
Co = 65,789 + 300,000 = $365,789
Physical Components Method - Land and Improvements
The related investment formula (weighted components) can also be applied to the component parts of real estate: land (site) and improvements (buildings). Just as weighted capitalization rates are calculated for debt and equity capital in the financial components method, weighted capitalization rates for SKU land and SKU buildings (improvements) can be calculated provided that capitalization rates can be obtained with sufficient accuracy based on market data for each of the components, as well as the share of their contributions to the total value of the property:
| SKo = SKz * Z + SKu * (1 - 3), | (3.6) |
where Z is the share of the land plot of the value of the object.
Example.
The appraiser is analyzing a comparable property that has an NAV of $200,000. General capitalization rates in this market are 17%. The land included in the property was sold for $400,000 and leased to the former owner for
$55,000/year.
Find the capitalization rate for improvements (CCR).
Solution.
SKz = 55,000 / 400,000 = 0.137500;
Co = 200,000 / 0.17 = 1.176471;
Z = 400,000 / 1,176,471 = 0.34 or 34%;
Y = 1 - 0.34 = 0.66; SKu = (SKo - Z(SKz)) / U;
SKy = (0.17 - 0.34 * 0.1375) / 0.66 = 0.1867 or SKy = 18.7%.
where is the capitalization rate;
– the number of selected analogue objects;
– serial number of the analogue object;
– net present value of a similar object;
– market value of a similar object;
– specific gravity of the analogue (priority).
An example of determining the capitalization rate using the market method
To determine the capitalization rate, four analogues were selected and the capitalization rate was calculated for each of them.
Table 47
Information about analogue objects
|
Sales price of analogue (), thousand rubles. |
Net operating income (), thousand rubles. |
Capitalization rate |
||
|
Average capitalization rate (R) | ||||
Answer: R = 18,3%.
Summation method (cumulative)
Using the summation method, the capitalization ratio is a determination of the profitability that investors generate depending on the riskiness of the investment:
where is the risk-free rate of return, which reflects “the actual market opportunities for investing funds of firms and individuals without any risk of non-repayment” 4, which is accepted for fixed-term federal loan bonds and other investment options provided that there is no risk of non-repayment.
For example, as of March 4, 2009, the yield on OFZ-25057 securities with a maturity date in January 2010 was amounted to 11.07%, OFZ-25061 with a maturity date in May 2010. amounted to 12.89%, OFZ-46003 with a maturity date in July 2010. amounted to 12.84% (http://rosfincom.ru/market/money/). The risk-free rate can be taken using the arithmetic mean, i.e. equal to 12.27%. The period was taken within one year, because It is customary to capitalize income for the year.
– the risk of investing in real estate (takes into account accidental losses in the consumer value of the property and possible loss of ownership, an allowance can be taken based on the amount of insurance deductions in insurance companies of the highest reliability).
For example, an analysis of information on insurance companies for legal entities showed the following:
Table 48
Information about insurance companies
|
Insurance Company |
Interest rate for real estate insurance |
A source of information |
|||
|
from loss of property rights |
property insurance |
||||
|
JSC "ХХХХХХ" |
Insurance rules of JSC "ХХХХХ" |
||||
|
CJSC "ХХХХХХ" |
Insurance rules of CJSC "ХХХХХ" |
||||
|
Average value for maximum bets | |||||
Thus, by insuring real estate, you can get rid of investment risks. Total =1.8%.
– real estate liquidity risk (takes into account the impossibility of a quick return of funds invested in the property). One of the options for determining liquidity risk is the assumption that liquidity fundamentally depends on the period of exposure of the property on the market and the occurrence of probable losses in value when selling the property while it is in the register of the real estate market. The formula for finding risk is as follows:
where is the risk-free rate;
– typical period of exposure of an object on the market in years.
The use of the risk-free rate in the calculations is explained by the fact that risk-free assets predominantly have greater liquidity among investment objects.
The subject of assessment is characterized by an exposure period of 4 months. The risk-free rate is 12.86%. Determine the liquidity risk of the property.
– investment management risk – reflects the ability of real estate to generate greater income under professional management and vice versa. Risk can be taken into account at the average interest rate that management companies of closed real estate mutual funds take as a fee for asset management.
For example, an analysis of information on management companies of closed real estate mutual funds showed the following.
Income capitalization method– an approach to assessing the value of a business or investment project based on reducing income to a single cost. The method is used for express assessment of the value of business, investment projects and real estate, as well as for making comparisons to determine more investment-attractive objects. In this article we will focus on analyzing the method of capitalizing income for valuing a business or an existing investment project.
Advantages and disadvantages of the income capitalization method
Let's look at the advantages and disadvantages of the business valuation method based on the capitalization of its income in the table below ↓.
| Advantages | Flaws |
| Allows you to compare the investment attractiveness of a business or investment project based on income Ease of calculation Suitable for mature, large companies that have sufficient financial data to accurately forecast future revenues and growth rates |
It is applicable for a stable operating enterprise (business), when it is possible to correctly predict future cash receipts and income. Not suitable for evaluating venture projects and startups that have no cash flows at all and have not yet created a stable sales network and uniform income streams The objects of assessment are undergoing modernization and reconstruction Not suitable for valuing a business with losses Not suitable for valuing a business with active reinvestment and variable growth rates |
Due to the fact that in practice it is difficult to obtain constant financial data, therefore, the discounted cash flow method is often used in valuation.
It should be noted that the income capitalization method for business valuation is a variation of the cash flow discounting method with the condition that the income growth rate is constant.
Formula for calculating the value of a company using the capitalization method
The formula for calculating income capitalization is as follows:
V ( Englishvalue) – business (project) cost;
I( Englishincome) - income;
R – capitalization rate.
The table below describes in more detail how to calculate model indicators ↓.
| Model indicator | Description | Measurement | Features of application |
| Business cost | Shows the market value of the company's assets | ||
| Income | Calculated based on the indicators of the financial results statement (form No. 2). Income can be of the following types: · Revenue from sales of products/services · Company net profit (line 2400) · Profit before taxes (line 2300) · Amount of dividend payments Cash flow These indicators are taken as of the current assessment date; if they have changed significantly in recent years, then they are averaged over several years (3-5 years) |
||
| Capitalization rate | It is necessary to determine the method for calculating the coefficient. It depends on what period of data the calculation will be for (based on retrospective or forecast income data) |
As can be seen from the table, to carry out the assessment it is necessary to determine what income will be chosen for capitalization: net profit, profit before taxes or profit from dividend payments. The next step is to select a method for calculating the capitalization rate and obtain its estimate.
What type of income should I choose for assessment?
The choice of one type of income or another depends on what other business is being compared with and what financial statements are available. If enterprises only have
sales revenue, then this indicator is taken as the capitalized base. It can be noted that various types of data can be used in the assessment ↓.
| Data type | Direction of application |
| Retrospective data (historical) | To evaluate existing companies with financial statements going back several years. Historical values of income (net profit) of the enterprise for past periods (3-7 years) are used. The data is averaged and adjusted for current inflation. |
| Forecast data | It is used to assess the future value of an investment project and its investment attractiveness. Historical data is used to predict future profit values. The forecast depth is usually 1-3 years. |
| Combining historical and forecast data | Used to assess the investment attractiveness of an enterprise. Both retrospective and forecast data are used. |
What income indicator should be used in the model to calculate the base?
Let's consider what income indicators are chosen to evaluate a business.
Revenue It is usually used to evaluate enterprises in the service sector.
Net profit used to evaluate large companies.
Profit before taxes applied to small enterprises to exclude the influence of federal and regional benefits and subsidies in income generation.
Income in the form of dividend payments are used to value a company with ordinary shares on the stock market.
Cash flows are used to calculate the capitalized base for companies that are dominated by fixed assets. In this case, only the flow from equity capital or investment capital (own + borrowed) can be used.
After choosing income, it is necessary to adjust it - to current prices; for this, changes in the value of consumer prices from Rosstat statistics can be used, and it is also necessary to exclude income and expenses from assets that were one-time in nature and will not be repeated in the future.
- Income/expenses received from the sale/purchase of a fixed asset.
- Non-operating income/expenses: insurance payments, losses from production freezes, fines and penalties for lawsuits, etc.
- Income from assets not related to the main activities of the company.
Methods for calculating the capitalization rate
Capitalization rate is the current rate of return on a business's capital. The capitalization rate represents the value of capital (property) at the time of valuation.
Calculation using the market extraction method
This method is used to calculate the value of a business based on existing transactions on the market for the sale/purchase of the same types of business. In this case, it is necessary to know the income indicators of the businesses or projects being sold. The method is used for a replicated business, for example, a franchise.
The capitalization ratio is calculated using the following formula:
R – capitalization rate;
V – company value;
I ai – the amount of income created by the i-th analogue company;
V ai is the cost of selling the i-th company on the market;
n – number of similar companies.
Calculating the ratio as the average market price of sold companies is a rather labor-intensive process and there may often be a lack of financial data on the income or volume of transactions of similar enterprises. The second method of calculation based on the discount rate is more common in practice.
Calculation method for determining the capitalization rate
When using this method, it is necessary to calculate the discount rate. The capitalization ratio will be equal to the difference between the rate of profit and the average growth rate of income (net profit). For more information about methods for calculating the discount rate, read the article: → "". The calculation formulas are as follows:
|
Formula No. 1 |
Formula No. 2* |
 R – capitalization rate; based on projected profitability); |
 R – capitalization rate; r – discount rate (rate of return); g – the projected average growth rate of the company’s income ( based on historical income data). |
*you can notice that the second formula corresponds to.
The most commonly used methods for estimating the discount rate are:
- (CAPM, Sharpe model) and its modifications.
- Cumulative construction method.
What is the difference between capitalization rate and discount rate?
The table below shows the differences between the concepts of discount rate and capitalization rate ↓.
An example of calculating the value of a company in Excel for KAMAZ PJSC
For practice, let’s look at estimating the value of KAMAZ PJSC in Excel. To do this, it is necessary to obtain financial statements of the operation of the enterprise over the past few years. To do this, you can go to the official website of the company. Let's take 2015 Q1 and Q2. Due to the fact that net profit has high volatility, we take the change in the company’s revenue and determine the average rate of its growth.
Rate of change in revenue (g) = LN(C6/B6)
Average revenue = AVERAGE(B6:C6)
The next step is to calculate the discount rate. Since KAMAZ PJSC does not have sufficiently volatile shares on the stock market, the cumulative valuation method can be used to calculate the discount rate. To do this, it is necessary to assess risks in the following areas ⇓.
|
Type of risk |
Evaluation interval, % | Risk parameters | Value of assessment for the enterprise, % |
Explanation of the assessment |
| Risk free rate * | Yield on OFZ bonds of the Central Bank of the Russian Federation | 8,5 | – | |
| Key figure, quality and depth of management | Distribution of management decisions | The management structure is distributed among 11 members of the board of directors | ||
| Enterprise size and market competition | Assessment of the size of the enterprise (micro, medium, large) and the characteristic impact of competitive risk on the market | KAMAZ PJSC is a large and strategic enterprise, the level of competition risk is low | ||
| Financial analysis of the company | Assessment of the financial condition of the enterprise and the structure of borrowed and equity funds | The financial condition of the enterprise is not stable: a high share of state support (subsidies), a high share of borrowed capital, revenue is uneven | ||
| Product and territorial diversification | Assessment of product range and distribution network | The company has contracts with international partners and operates both in the regional and international markets. Wide range of products | ||
| Diversification of clientele (market volume) | Assessment of market demand for manufactured products, number of potential customers and market volume | The corporate and consumer segments of consumption are developed | ||
| Profit sustainability | Assessment of factors generating revenue and net profit of an enterprise. Predicting the direction of change | There has been a positive growth trend in net profit over the past 4 years. Profit flow is uneven. High percentage change in profit | ||
|
∑ Total discount rate: |
||||
*risk-free interest rate is taken as the yield on government OFZ bonds (see → change in yield) or the yield on highly reliable deposits in Sberbank PJSC with an A3 credit rating.
Capitalization rate = discount rate – average growth rate
Capitalization rate = 18-15 = 3%
Company value = D6/C8
The company's value was 486,508,123 thousand rubles.
The figure below shows the main indicators for assessing the value of a company ⇓.
conclusions
The income capitalization method is used to value companies with stable cash flows over a period of 5 or more years. In a situation of high competition, company profits are highly volatile, which makes it difficult to adequately apply this method. Also, the approach has many adjustments to income and expert decisions in assessing risks, which makes it subjective in decision making. The method is most accurate when assessing the market capitalization ratio and company value in comparison with similar ones.
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