The correct procedure for calculating the present value of the reversion. The question is strange, perhaps the wording is incorrectly conveyed. Apparently, it is implied that the current value of the object does not depend on the forecast period. Capitalization ratio calculation

^ SOCIO-ECONOMIC ISSUES

UDC 347.214.2:656

S. V. Kolankov

Petersburg State University of Communications of Emperor Alexander I

JUSTIFICATION OF THE REVERSION PRICE WHEN ASSESSING THE MARKET VALUE OF REAL ESTATE

Methods for evaluating reversion in determining the market value of real estate objects are considered, and the scope of their application is clarified. It also shows the need to use all known approaches to assess the reversion: comparative, costly, profitable. The study proved that when applying the proportional reversion assessment method (as a share of the estimated market value of real estate), it is necessary to control the result obtained due to the possibility of an absurd situation. A mathematical interpretation of the scope of the proportional reversion estimation method is given.

income approach to real estate valuation, net operating income, income capitalization, reversion, Gordon model.

Introduction

The legislation of the Russian Federation has established that one of the approaches to assessing the market value of real estate is the income approach, which includes four methods. In two of them: the method of discounting cash flow (DCF) and mortgage-investment analysis (IIA) - it is required to predict the probable sale price of the object of assessment at the end of the calculation period - reversion (Rev). Accounting for this pricing indicator is essential if it is predicted that by the end of the billing period the object will not lose its value, i.e., it will retain its value at least partially, and also that the risk of its sale on the market at the end of the billing period will not be too great . The latter is important due to the fact that the use of sufficiently large discount rates when discounting to the current point in time - the date of assessment - leads to negligible values ​​of the reduced

other indicators that do not significantly affect the final result of real estate valuation. In the practice of valuation activities, three methods are used to determine the value of Rev, however, in modern publications, there are no a number of important methodological provisions.

1 Peer review method

This method of estimating the sale price of an object at the end of the billing period is based on a survey of real estate market specialists who base their opinions on knowledge of market trends, opinions of colleagues, and analytical materials published in specialized publications.

This method has low reliability due to the uncertainty of the market situation in a fairly long term (5-10 years or more). In addition, ask for

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short terms determined by the contract for evaluation, a significant number of experts in practice is not possible. Therefore, as a rule, it is not possible to create a sufficiently large array of expert assessments of the Rev value, which allows one to mutually exclude the errors of various experts, and the use of assessments obtained relative to other objects is often unreasonable due to the individuality of the market.

Since such a forecast has a lower degree of reliability compared to the assessment of the current value and the pricing factors affecting it, it is advisable to use an increased discount rate when discounting Rev , . In practice, it is usually not possible to justify the excess of this discount rate reliably, therefore, we recommend using the interval method of calculation for this purpose (the method of boundary estimates). Its essence lies in determining the most probable minimum and maximum values ​​of the discount rate for the price of the proposed sale of the object. However, if we apply the same method to assess the value of the discount rate used to bring the remaining elements of the cash flow, then the result will be 4 values ​​of the market value of the object (table). This can make it difficult to agree on the final result of the assessment if

the calculations performed will differ significantly.

2 Direct capitalization method

This method is based on the capitalization of post-forecast net operating income (NORpost).

Here, several options for calculating Rev are possible (Fig. 1). Firstly, in the case when the object of assessment at the end date of the settlement period is not burdened with a loan: either it was acquired without using borrowed funds (Kp = 0), or their repayment has already been completed (T< Т). Во-вторых, в случае когда на дату завершения расчетного периода остается непогашенный остаток кредита (Кр Ф 0) или, другими словами, погашение кредита завершается после окончания расчетного периода (Т >Trasch). In the first case, the estimated sale price of the object is equal to the capitalized value of the post-forecast NOR, provided that the capitalization ratio is equal to the discount rate for the post-forecast period (Epost):

Re v = CHODposg/^posg, (1)

where NORpost is the annual value of NOR in the first year of the post-forecast period, rub./year.

In the second case, the value of Rev must be reduced by the value discounted to the date of the end of the forecast period

TABLE. Variants of the result of calculating the market value of real estate, depending on the discount rates used

Other cash flow elements Е 2min С1 С3

Notes: E, K, E_ , E , - minimum and maximum values ​​of discount rates,

g 1mm’ 1max’ 2mm’ 2max’ g ’

used for discounting, respectively, Rev and other elements of the cash flow; C1, C2, C3, C4 - values ​​of the market value of real estate obtained at different discount rates.

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Rice. 1. Methods for estimating Rev by direct capitalization of post-forecast NORs:

Тcr - duration of the loan agreement, years;

Thread - the period that has elapsed from the date of issuance of the loan to the date of the beginning of the billing period, years; Trasch - duration of the settlement period, years

annual loan repayments. Then formula (1) will take the form:

Re v = chODpost/epost - PMT KF5, (2)

where PMT is the annual loan repayment payment, rubles/year; Kf5 - multiplier of the fifth function of compound interest (PV/PMT), calculated at E and term T, equal to the duration in years from the end date of the settlement period to the date of completion of the loan repayment.

This period can be defined as:

If a reasonable assumption is made about a probable regular change in net operating income during the post-forecast period, the Gordon model can be applied, in which the denominator of formulas (1), (2) decreases by the value p, which characterizes the rate of change (increase or decrease) in NORpost . So, for example, according to the Gordon model, formula (1) will take the form:

Tk = Tkr (Thread + Tasch), (3)

where Current is the term for the final repayment of the loan after the end of the billing period, years.

Since the present value of the NPV is valued at an annual discount, the present value of the PMT must also be valued on an annual basis. This provision was introduced to ensure the comparability of the results of the capitalization of the NFS and RMT.

In each of these cases, the NPV may remain unchanged during the post-forecast period or, conversely, its change at a constant rate.

The above expressions (1), (2) are used if the net operating income is planned to remain unchanged.

where p is the predicted rate of change in NPC in the post-forecast period, %/year.

To apply the Gordon model, the following restrictions must be met: the constant rate of change in the NOR over the years of the post-forecast period, the condition that these rates do not exceed the discount rate (E > p) in the case of forecasting income growth in the post-forecast period, as well as the lack of equality between the discount rate and the rate of change CHOD:

3 Proportional method

Using this method, the sale price of an object at the end of the billing period is determined in

Proceedings of Petersburg Transport University

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shares of the estimated market value of real estate. For example, if it is assumed that during the billing period the value of the object will increase by 25% compared to today's value, then the sale price is presented as:

Re v \u003d (1 + q) -sdp \u003d 1.25 -sdp, (6)

where Cdp - the market value of the object, estimated by the income approach, rub.; D - the projected change in the price of the object during the billing period, a fraction of a unit.

In this case, the calculation formula of the DD11 method or the traditional IIA technique will contain one unknown - Cdp, which occurs twice in the calculation equations. For example, the formula of the traditional IIA technique for the case when at the end of the billing period the loan has not yet been repaid will have the following form:

Sdp \u003d KF5 (CHOD-PMT) +

Kf4-[Sdp (1 + D)-VA2] + VAD,

where Sdp - the market value of real estate on the date of assessment, rub.; Kf5 and Kf4 - coefficients of the fifth (PV/PMT) and fourth (PV/FV) functions of compound interest, respectively, determined for the forecast period at a given rate of return on equity, taking into account the annual capitalization, a fraction of a unit; CHOD - net operating income from the object, rub./year; RMT - annual payments to repay the loan, rub./year; BAL2 - balance (unpaid balance) on the loan as of the date of sale, rubles; BALt - the same as of the valuation date, rub.

After some algebraic transformations, we obtain the following expression for estimating the market value of an object:

Sdp \u003d [Kf5 (CHOD - PMT) - Kf4 x

x BAL2 + VNA ] / .

Attention is drawn to the fact that the parameter D is in the denominator of expression (8). It can be assumed that

a situation where the denominator is equal to zero. Consequently, the function will have a gap at a certain value of D, at which the denominator of expression (8) is close to zero, and the value of the market value of Mdp is plus/minus infinity. The indicated value D can be called the critical value of this parameter - D.

From the graph (Fig. 2) it can be seen that the critical value of D can be called such, at which the result of the assessment changes its sign from positive to negative. The value of the limit value D depends on the ratio of CHOD with BALV BAL2; RMT. This graph shifts to the right with an increase in the duration of the billing period and with an increase in the discount rate E.

It should also be noted that an absurd situation may arise, in which further planning of an increase in the sale price compared to the estimated value will lead to a sign change from “plus” to “minus” of the calculation result. According to the schedule (Fig. 2), it is possible to determine the scope of the IIA method in the case of using the third option for determining the sale price of an object at the end of the billing period:

Oo< Д < Д

At the same time, for the value of the market value of the MDP, the following relations are true:

lim SdP (D) = +o,

D^Dcrit-0 D 4 7

*Aim. n Sdp (d) = -°. (ten)

In any of the above cases, the amount of the reversion should be determined without taking into account the value added tax, minus the commission paid to the intermediary (real estate agent) when making a transaction with objects of this type, at the rate prevailing on the market as of the date of assessment, and income tax (income ) paid by the seller when making a transaction with a real estate object in accordance with the legislation in force on the date of valuation.

ISSN 1815-588X. Izvestia PGUPS

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Rice. 2. Graph of the change in the market value of the appraised object with the third method of determining Rev

Conclusion

Published works , , do not specify some issues of estimating the value of Rev, which can have a significant impact on the conclusion about the most probable sale price of real estate in the current typical market conditions. The methodological provisions proposed in this paper make it possible to more reasonably determine the value of Rev, thereby increasing the credibility of the independent appraiser's report.

Bibliographic list

1. Order of the Ministry of Economic Development of the Russian Federation dated July 20, 2007 No. 256 “On approval of the federal valuation standard “General concepts of valuation, approaches to valuation and requirements for valuation (FSO No. 1)””.

2. Economics of real estate: textbook. allowance. - 2nd ed., corrected. and additional / S. V. Kolankov. - Moscow: UMTs ZHDT, 2013. - 478 p.

3. Order of the Governor of St. Petersburg dated August 1, 1996 No. 113-r “On the procedure for assessing state-owned real estate and rights to it”.

5. Financial mathematics: theory and practice of financial and banking settlements / E. Kocho-vich; per. from Serbian - Moscow: Finance and statistics, 1994. - 268 p.

6. Analysis and evaluation of income-generating real estate / J. Friedman, N. Ordway; per. from English. - Moscow: Delo, 1997. - 480 p.

7. Methods of income capitalization: a course of lectures / SV Gribovskiy. - St. Petersburg: ROSSTRO-PRESS, 1997. - 172 p.

8. Evaluation of the effectiveness of investments in transport construction, taking into account uncertainty and risk / S. G. Oparin // Scientific and technical statements of St. Petersburg State Technical University - 2010. - No. 4 (102). -FROM. 60-65.

Proceedings of Petersburg Transport University

Calculation of discount rate and capitalization ratio

The discount rate is the rate used to convert future earnings into present value. Quantitatively, it is equal to the rate of return, the value of which depends on the risk associated with the object being evaluated.

The methods for calculating the discount rate are as follows:

1) Capital asset valuation model;

2) Method of market extraction;

3) The method of cumulative construction.

Capital asset valuation model. The capital asset valuation model is practically not used to calculate the discount rate in real estate valuation.

Market extraction method. The market extraction method involves estimating the discount rate based on an analysis of the actual return received by investors when investing in similar real estate. This method allows you to most objectively assess the risks and calculate the rate of return for real estate, however, its application requires obtaining reliable information on comparable properties.

In this thesis project, we use the cumulative construction method to determine the discount rate.

The cumulative construction method determines the value of the discount rate by successively cumulating (adding) premiums for the risks identified on the object being evaluated. The method of cumulative construction is universal and is used to evaluate various objects of property. However, the composition of the awards is individual. For real estate, premiums are calculated for the risk of investing in the property being valued, the level of liquidity, and investment management.

R n \u003d R b / r + P 1 + P 2 + P 3 + P 4

where R b / r - risk-free (base) rate of return;

P 1 - country risk;

P 2 - premium for low liquidity;

P 3 - premium for the risk of investing in the assessed object;

P 4 - award for investment management.

The risk-free rate of return is the rate of return on risk-free investment instruments that meet the requirements of reliability, liquidity and availability.

The concept of a risk-free rate of return was introduced into investment analysis by W. Sharp as the most acceptable type of base rate of return with which the return on any type of investment can be compared. Thus, for valuation purposes, the concept of the base rate of return as the minimum guaranteed rate of return at the valuation date is more important.

In this graduation project, we accept the risk-free rate in accordance with the average bank rate on deposits for 1 year in the city of Vologda. The data are summarized in Table 5.1.

Table 5.1

Country risk - reflects the uncertainty of future income streams due to the possibility of changes in the political or economic structure of the country. Russia is the country with the highest risk. The measure of country risk is considered to be the credit rating of the country, it is the same for all companies. The country risk is 5%.

The premium for the risk of investing in the property being valued. The premium for the risk of investing in specific real estate takes into account possible changes in the value of the object in the future, due to the loss of consumer properties.

1. Expert method. In this method, the premium is usually in the range of 0-5%.

2. The method of weighted risk assessment. The weighted assessment method divides risks into systematic and non-systematic, as well as static and dynamic.

In our case, we use the weighted risk assessment method for the calculation.

Calculation of the amount of risks is presented in Table 5.2.

Table 5.2

Premium for low liquidity. The calculation of the premium for low liquidity is based on the determination of the investor's loss of profitability during the exposure period of the property being valued. The typical exposition period of an object is the period of time from putting the object up for sale until the receipt of funds for the sold object, or the typical period of time that is necessary for the object to be sold on an open and competitive market, subject to all market conditions.

P liquid \u003d R b / r * q / 12

where P liquid - adjustment for low liquidity;

R b/r - risk-free (basic) rate of return;

q is the typical exposure time for the evaluated object.

In our case, the liquidity adjustment will be:

P liquid \u003d 10.44 3/12 \u003d 2.61

Investment Management Award. The value of this premium in the vast majority of reports is calculated by experts based on risk ranking on a five-point scale:

Low value - 1%;

Value below average - 2%;

Average value - 3%;

Value above average - 4%;

· High value - 5%.

The amount of the premium is determined by the complexity of managing the object, the availability of personnel reserves of professional managers and the real possibility of the investment manager influencing the profitability of the object.

Since the object being valued is a commercial property that is in demand, the sale of which does not require a long time and additional marketing costs, therefore, the premium for investment management can be taken at a rate of 2%.

The capitalization ratio is the interest rate that is used to convert annual income into value. The capitalization ratio includes the investor's rate of return on invested capital and the rate of return on capital.

K n \u003d R n + N VK

where K n - capitalization coefficient for real estate;

R n - the investor's rate of return on invested capital;

N V.K. - rate of return of capital.

The rate of return on capital is the rate of interest that provides a return on the initial investment. This component of the capitalization ratio allows, in the process of investment analysis, to divide the income annually brought by real estate into two components:

1) compensation of capital invested in real estate;

2) receiving additional income from the ownership of the object.

In valuation practice, three methods are used to calculate the rate of return on capital:

1) the Ring method (assumes a linear return on capital invested in real estate. In this case, the return of capital does not imply its subsequent reinvestment to generate income. Usually, the Ring method is used when evaluating objects that are in the last phase of economic life. Such real estate is characterized by the direction of recoverable amounts to object maintenance);

2) the Inwood method (assumes a uniform annuity return of capital invested in real estate. The use of the Inwood method is advisable for objects that have not exhausted their economic life, provided that the rate of return calculated for real estate corresponds to the market investment climate);

3) the Hoskold method (as well as the Inwood method, it involves the reinvestment of initial investments reimbursed from the annual income from real estate, however, in this case, a risk-free rate of return is used. The use of this method is advisable if the object has not exhausted its economic life, but the rate of return that takes into account the investment risks of real estate does not meet market expectations).

According to experts, the straight-line return of capital (Ring's method) best meets the conditions for investing in Russia.

Calculate the annual rate of return on capital using the formula:

R cap \u003d 1 / VF - HV

where R cap - the rate of return of capital;

FZh - physical life according to the capital of the building;

HF - chronological age of the building.

R cap \u003d 1/100 - 0 \u003d 0.9%

Capital group of the assessed object II, the physical life of the building is 125 years. Since the building is under construction, the rounded return on capital will be 1%.

Thus, the discount rate calculated by the cumulative construction method and the capitalization ratio will be:

Table 5.3

Reversion Cost Calculation

The reversion cost is the value of the object at the end of the last forecast year. The need to calculate the cost of the reversion is due to the discrepancy between the length of the forecast period used in the discounted cash flow method and the residual economic life of the property being valued.

Methods for calculating the cost of the reversion are determined by the economic position of the object at the end of the last forecast year. If the economic condition of real estate is assessed as favorable, then it is advisable to calculate the cost of reversion by capitalization of income or by adjusting the value of real estate, calculated as of the date of assessment, by the amount of possible depreciation for the analyzed period. If at the end of the forecast period the economic situation is assessed as unfavorable, then the reversion is calculated at the liquidation or disposal cost.

Cash flow discounting

Since the cash flows and reversions were calculated for the corresponding years of the forecast period, they should be brought to the valuation date or discounted to determine the market value of the property being valued. Current income (annual cash flows) and reversion costs have different discounting methods. The cost of the reversion must be discounted (by the factor of the last forecast year) and added to the sum of the current values ​​of cash flows (sheet No. 12)

Calculation of market value as the sum of discounted cash flows

The basic formula for calculating the value of real estate under the discounted cash flow method is as follows:

C n \u003d UDP n / (1 + R) n + C K * (1 / (1 + R) n)

where C n - the value of the property on the date of assessment;

DP n - cash flow;

R is the discount rate of the cash flow of period t;

C R - reversion cost at the end of the forecast period.

The calculation of the market value of the property using the income approach is presented in Appendix 4.

comparative approach

The direct comparative sales approach is based on the premise that market entities carry out purchase and sale transactions by analogy, i.e. based on information about similar transactions. In other words, the approach is based on the assumption that a prudent buyer for a property put up for sale will pay no more than that for which you can purchase an object of similar quality and suitability.

This approach includes the collection of data on the sales market and offers for properties similar to the one being assessed. Prices for similar objects are then adjusted taking into account the parameters by which the objects differ from each other.

Once prices are adjusted, they are used to determine the market value of the property being valued.

Due to the lack of information about similar objects, a comparative approach cannot be applied in assessing the value of this property.

Coordination of the results and conclusion on the final cost of the shopping center in Vologda

The final element of the evaluation process is the comparison of results obtained from different approaches. When assessing the market value of the property, income and cost approaches were applied.

Approaches to the assessment have been assigned the following specific weights:

Cost approach -- 0.4;

Income approach -- 0.6;

Comparative approach -- 0.0 (Not used).

The rationale for not using the comparative and income approaches is given above. The market value of the object, determined by the income approach using the discounted cash flow method, was: 23285412 rubles. The market value of the object, determined by the cost approach method, was: 21644755 rubles.

The total cost of the property is 22532503 rubles.

Sensitivity analysis

It should be noted that the project is sensitive to changes in variable factors, in this case, an analysis was made of the object's sensitivity to changes in potential gross income, actual gross income, discount rate, net operating income, and operating expenses. A slight change in the discount rate, net operating income, operating expenses does not affect the final value of the value of the property. The most significant changes were revealed when the potential gross income and the actual gross income changed. The calculation is shown on Sheet 13.

As a result of the calculation, the following data were obtained: the cost of the object, calculated using the income and cost approach, taking into account rounding, is 22,500,000 rubles.

Analysis of the best and most efficient use of land

An analysis of the best and most efficient use of a land plot is presented in section IV. Management expertise.

Based on the developed business plan for the development of a real estate object, using the example of the Galaktika shopping center in Cherepovets, it can be said that the best and most efficient use of the property being assessed is its operation, provided that areas are leased out for manufactured goods. The market value of the property will be 22500000 rubles.

The calculation of utility bills for a period of 5 years is shown in Table 24.

Table 24

Justification of the discount rate

A discount rate is a factor used to calculate the present value of an amount of money received or paid in the future.

Cash flows and the discount rate must match each other and be calculated in the same way.

The discount rate is calculated using the cumulative construction method.

As in the calculation of the capitalization ratio, the risk-free rate was taken to be the average rate of return of Sberbank of Russia on ruble deposits for a period of more than 12 months, which is 9.45% as of the valuation date. The risk of investing in this property is taken into account at a rate of 50% of the risk-free rate.

The discount rate, taking into account the growth rate of utility bills of 15% for the remaining period (last year), is:

9.45% + (9.45 x 0.5) + 15% = 29%

9.45% - risk-free rate

(9.45 * 0.5) - the risk of investing in this property is taken into account in the amount of 50% of the risk-free rate.

15% - the risk of rising utility bills.

Calculation of the market value using discounted cash flows

Calculation of the market value using the DCF method according to the formula:

PV = + M,

where PV – current value;

FROM i - period cash flow t;

i t - discount rate of the cash flow of the period t;

M– cost of reversion, or residual value.

The residual value, or reversal value, must be discounted (to the last forecast year) and added to the sum of the current values ​​of the cash flows.

Thus, the cost of a one-room apartment is equal to:

Present value of projected cash flows +

The present value of the residual value (reversion).

Calculation of the cost of reversion.

Reversion - the residual value of the object when the flow of income ceases.

The cost of reversion can be predicted using:

setting the sale price based on an analysis of the current state of the market, monitoring the cost of similar objects and proposals 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 residual value of the reversion will be:

73795:0.15=491967 rub. (Chod of last year/cap ratio)

The current cost of the reversion will be:

M

M is the cost of reversion;

i - discount rate;

n is the estimated period.

491967 * 1 / (1 + 0.29) 5 \u003d 137,717 rubles.

The value of the object of assessment =Present Value of Projected Cash Flows + Present Value of Residual Value (Reversions).

165,567+137,717=303,284 rubles, rounded 303 300 rub.

Reconciliation of the results obtained by the income approach:

Table 26. Weighting factors

The cost of the object is determined by the formula:

S = S 1 XQ 1 + S 2 XQ 2 ,

where S is the reasonable market value of the appraisal object, rub.;

S 1 , S 2 , - the value of the object, determined using the methods of direct capitalization of income and discounted cash flows, respectively;

Q 1 , Q 2 - the arithmetic mean of the reliability of methods of direct capitalization of income and discounted cash flows, respectively.

The matching results are summarized in Table 30.

Table 27 . Reconciliation of results in determining the market value

Thus, based on the analysis and calculations performed, the final value of the market value of the apartment, determined by the income approach as of January 15, 2009, taking into account rounding, will be:

349,400 (three hundred forty-nine thousand four hundred) rubles.

4.3 Reconciliation of assessment results.

The traditional approaches in valuation activities have yielded the following results:

Table 28

The purpose of summarizing the results of all approaches used is to determine the advantages and disadvantages of each of them and, thereby, to develop a single cost estimate.

As a result of the analysis of the applicability of each approach to assess the object under consideration, the following conclusions can be drawn.

The comparative approach reflects the price that may arise in the market, taking into account all market trends and buyer preferences. It is most applicable to the developed sectors of the real estate market, which is the housing market.

The cost approach is useful mainly for valuing objects that are unique in their type and purpose, for which there is no market, or for objects with little wear and tear. In assessing the costs of reproduction, the share of expert judgments is high. The main disadvantage of the cost approach, despite the high reliability of its results, is that the cost calculated by this approach does not take into account the cost of allocating a land plot and does not reflect the frequently changing situation in the real estate market.

The yield approach in this case reflects the marginal value that a potential investor would not pay more than based on the typical use of the property and the accepted rates of return.

After analyzing the goal of the assessment, the nature of the use of the object of assessment, the degree of completeness and reliability of the initial information, the magnitude of the error obtained for each of the approaches, we can conclude that the result obtained within the framework of the comparative approach corresponds to the highest degree of reliability. It is assigned a specific gravity of 0.7. The cost approach in this case does not fully reflect the market situation and the degree of reliability of the result obtained, it is estimated by the indicator of the specific weight of 0.2. The income approach, because it uses predictive values, is assigned a specific weight of 0.1. A summary of the results is given in Table 29.

Table 29

Based on the data given in the work and the above conditions, rounding the value obtained as of the valuation date, the object has a market value:

1,856,000 (one million eight hundred and fifty six thousand) rubles.

List of sources used

Tarasevich E.I. Real estate appraisal. - St. Petersburg. SPbGTU. 1997.

Simionova N.E. Property valuation methods: Business, real estate, land, machinery, equipment and vehicles.-Rostov n/a: Phoenix, 2006.

Friedman D., Ordway N. Analysis and valuation of income-generating real estate.-M.: Delo, 1997.

Gribovsky S. Valuation of profitable real estate. - St. Petersburg. 2000.

Gribovsky S.V., Ivanova E.N., Lvov D.S., Medvedeva O.E. Valuation of real estate. - Moscow: Interreklama, 2003.

The main sources of information used in the course work were lecture materials, data from open electronic and printed publications, where information about public offers is freely available, analytical materials, expert assessments of specialists from leading Yaroslavl real estate agencies. Among them are the periodicals "Iz ruk v ruki", "Apartments and prices", the online edition of the newspaper "Iz ruk v ruki", as well as websites http cost one-room apartmentsCoursework >> Economics

The work is assessed by the market cost one-room apartments, located at the address ... evaluation of the object 9.1 Technology definitions cost property Valuation involves... using the income approach to definition cost object, according to...

Reversion Cost Calculation

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

The cost of reversion can be predicted using:

• 1) setting the sale price based on an analysis of the current state of the market, monitoring the cost of similar objects and assumptions regarding the future state of the object;
• 2) making assumptions regarding changes in the value of real estate over the period of ownership;
• 3) capitalization of income for the year following the year of the end of the forecast period, using independently calculated capitalization rate.

Determining the discount rate

A discount rate is an interest rate used to calculate the present value of an amount of money received or paid in the future.

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

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

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

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

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

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

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

• 1) the method of cumulative construction;
• 2) method of comparison of alternative investments;
• 3) extraction method;
• 4) monitoring method.

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

Discount Rate = Risk Free Rate + Risk Premiums.

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

The cumulative construction method is discussed in detail in Section 4.1. of this benefit when calculating the rate of return on capital as part of the capitalization ratio using the capital cost recovery method.

Alternative Investment Comparison Method most often used in calculating the investment value of a property. The discount rate can be taken as:

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

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

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 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.

A discount rate (as opposed to a capitalization ratio) cannot be derived directly from the sales data, as 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 values ​​for the extraction discount rate that will correspond to the overall accuracy of the forecast of future periods. However, it should be taken into account that purchase and sale transactions of such comparable objects, the existing use of which is the best and most efficient, should be selected as similar ones.

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

• * modeling for each object of an analogue for a certain period of time according to the scenario of the best and most efficient use of income and expenditure flows;
• * calculation of the rate of return on investment 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.

Monitoring method is based on regular monitoring of the market, tracking the main economic indicators of investment in real estate according to transactions. Such information should be summarized for various market segments and published regularly. Such data serve as a guideline for the appraiser and allow a qualitative comparison of the obtained calculated indicators with the average market ones, checking the validity of various kinds of assumptions.

If it is necessary to take into account the impact of risk on the amount of income, adjustments should be made to the discount rate when evaluating single real estate objects. If income is generated from two main sources (for example, from basic rent and interest surcharges), one of which (basic rent) can be considered guaranteed and reliable, then one rate of income is applied to it, and the other source is discounted at an increased rate (for example, the amount interest surcharges depends on the tenant's turnover and is an uncertain value). This technique allows you to take into account a different degree of risk when receiving income from one property. By analogy, it is possible to take into account various degrees of risk of receiving income from a property object over the years.

Many 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.

Calculation of the value of a property using the DCF method

Calculation of the value of the property using the DCF method is carried out according to the formula:

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).

Current (present, discounted, present) value is the value of the entity's cash flows and reversions, discounted at a specified discount rate to the valuation date.

The fair value calculations are the multiplication of the cash flow (CF) by the corresponding period (n) unit fair value factor (DF), taking into account the selected discount rate (DR r). In investment analysis, this factor is often referred to as the discount factor.

Calculations are carried out according to the formula:

PVn= ΣCFi 1/(1 + r)i,

Clarify

where i is the number of the year of the forecast period.

This formula discounts cash flows as if they were received at the end of the year. However, this approach may underestimate the current estimate of expected returns. Therefore, if the cash flow is not concentrated at the end of the year due to the seasonality of production and other factors, the appraiser can discount the cash flows as if they were expected to be received in the middle of the forecast year, then the formula becomes

PVn= ΣCFi 1/(1 + r)i-0.5,

The discounting of the reversion cost is always carried out at the discount rate taken at the end of the forecast period, due to the fact that the residual value (regardless of the method of its calculation) is always the value at a specific date - the beginning of the post-forecast period, i.e. the end of the last year of the forecast period.

Examples of discount rates and the current value coefficients corresponding to them, which differ by years, are presented in Table. 7.7.

Table 7.7 shows that the further the period of receipt of one monetary unit from the current moment in time, the lower the current value of this monetary unit. So, at a discount rate of 20%, one ruble expected to be received in one year "costs" 83.333 kopecks today, and expected in four years - 48.225 kopecks.

Similarly, there is a relationship between the present value of money and the discount rate: the higher the discount rate, the lower the present value of monetary units received in the future.

When applying the discounted cash flow method in the assessment, it is necessary to sum up the current values ​​of the periodic cash flows that the object of assessment brings in the forecast period, and the current value of the business in the post-forecast period.

Table 7.7 - Discount rates and present value factors

The preliminary value of the business has two components:

1) the current value of cash flows during the forecast period;

2) the current value of the value in the post-forecast period.

The procedure for determining the current value of cash flows and reversions is presented in Table 7.8.

Table 7.8 - Calculation of the present value of cash flows and reversions

Example. Determining the value of the enterprise.

The forecast period is three years, the cash flow for the first forecast year is 110 million rubles, for the second - 144 million rubles, for the third - 147 million rubles. Cash flow for one year after the end of the forecast period (fourth year) is 150 million rubles, the discount rate is 24%. It is assumed that by the end of the forecast period, the income growth rate will stabilize and amount to 2% per year.

The present value ratios for the third forecast year and for the value of the enterprise at the end of the forecast period are the same, since the income of the fourth year was used in the Gordon model to determine the value of the business at the beginning of the fourth year, which coincides with the end of the third year and, therefore, the income from the possible sale of the business in the amount of 682 million rubles. should be discounted by (FM2(r, 3)).