Direct capitalization method example. Direct capitalization method: formula and calculation examples

League for the Development of Science and Education (Russia)

Khanty-Mansiysk branch

"INSTITUTE OF MANAGEMENT"

(Arkhangelsk)

TEST

by discipline

"PROPERTY VALUATION"

“METHOD OF DIRECT INCOME CAPITALIZATION WHEN ASSESSING REAL ESTATE OBJECTS”

Student: Klenova I.V.

Faculty: Economics

Course: fifth

Group: 51 - MZS

Specialty (code): 080507

Head: Kalashnikova I.A.

Khanty-Mansiysk. 2010

Introduction

Real estate valuation is considered throughout the world as one of the mechanisms for effective property management. Gradually in Russia, with the formation of a class of real estate owners, the problem of its effective use arises and, accordingly, the need for the services of an appraiser arises.

The main problems that appraisers are usually called upon to solve are related to the assessment of value. It is of great importance for a potential buyer or seller when determining a reasonable transaction price, for a lender when deciding to grant a mortgage loan, and for an insurance company when compensating for damage. If the government alienates property, the owner may need to have it appraised to challenge the government's offer of "just compensation."

Method of direct capitalization of income when assessing real estate.

This method is used only for profitable real estate, i.e. such real estate, the sole purpose of which is to generate income.

Income from real estate ownership can come in the form of:
- current and future cash receipts (including periodic payments);
- current and future tax savings;
- income from the increase in the value of real estate received when it is sold in the future or pledged against a mortgage loan;
- tax savings from the sale, exchange or gift of this property in the future;
- other possible cash receipts and benefits.

The income capitalization method is based on 3 principles real estate valuations:

1. The principle of expectation.
This principle characterizes the buyer's point of view on future years and their present value. Based on this principle, market value is defined as the current value of future benefits arising from ownership or other property rights to a given object.
The principle is based on the theory of changes in the value of money over time.

2. The principle of supply and demand. This principle characterizes the market’s point of view on the value of an object. Based on this principle, one can determine how the flows themselves Money and their relationship to cost, as well as trends in their change.
The principle states that the price of property is determined by the relationship between supply and demand in a given market segment.

3. The principle of substitution. This principle characterizes the point of view of an informed buyer who will pay for an object an amount greater than the cost of a similar object of the same utility in the same market segment and who, when forecasting future income, is guided by the analysis of relevant buyers of similar objects.
Based on this principle, it is clear that rents, profit margins, costs, discount rates and capitalization rates are determined by similar indicators in the market.

There are two methods of converting the income received from owning real estate into an estimated value:
1. Direct capitalization method, based on the use of the capitalization rate (R).
2. The method of discounting cash flows, based on converting future income from property ownership into their current value. Projected future earnings, discounted to present value using rates of return, reflect market expectations.

The main stages of the procedure for assessing real estate using the income capitalization method.

1. Estimate potential gross income. This is done based on an analysis of current rates and tariffs on the market for comparable properties.
Potential gross income (GPI) is the income that can be received from real estate at 100% occupancy without taking into account all losses and expenses.
PVD depends on the area of ​​the property and the rental rate.

PVD = S x Ca,

S - area in square meters. m., for rent;
Sa - rental rate per 1 sq. m.
As a rule, the amount of rent depends on the location of the property, its physical condition, the availability of communications, the rental period (term), etc.

2. Assessment of losses from underutilization and non-payment. It is carried out on the basis of an analysis of the market, the nature of its dynamics (trends) in relation to rented real estate.
DVD = PVD- discounts for downtime and non-payments.

3. Calculation of the costs of operating the property being assessed. Based on an analysis of the actual costs of its maintenance or typical costs in a given market.
When analyzing income and expenses, it is customary to use both retrospective (for past years) and forecast (forecast for the future) data. In this case, you can use data both before and after taxes. The only condition that must be taken into account when capitalizing income is cash flows for different objects should be calculated on the same basis, those. It is impossible to compare flows calculated on the basis of historical data with flows calculated on the basis of forecast data, the same applies to tax accounting.

Cost calculation

Periodic expenses to ensure the normal functioning of the facility and the reproduction of income are called operating expenses.

Operating expenses are usually divided into:
- semi-fixed costs or expenses;
- conditionally variable or operating costs;
- replacement costs or reserves.

TO conditionally permanent These include expenses the size of which does not depend on the degree of operational load of the facility. As a rule, these are property taxes, insurance of fixed assets, etc.

Conditional variables- these are expenses, the size of which depends on the degree of operational workload of the facility and the level of services provided. The main conditionally variable costs are management costs: utility costs (gas, electricity, water, heating, telephone, etc.); expenses for cleaning, maintenance of the territory, etc.

TO replacement costs include expenses that either occur only once or twice over several years or vary greatly from year to year. This is usually the cost of periodically replacing wear-out components of improvements. Such improvements include, but are not limited to, kitchen equipment (refrigerators, stoves, etc.), furniture, carpeting, drapes, as well as non-durable building components (roofs, elevators), and redecoration costs.
Replacement costs are calculated as annual contributions to the replacement fund (similar to accounting depreciation). The calculation assumes that money is being set aside (reserved), although most property owners do not actually reserve it. It should be noted that if the owner plans to replace deteriorating improvements during the ownership period (calculation horizon), then these deductions must be taken into account when calculating the value of the property using the method in question.

If, during the expected period of ownership, replacement of wear-out components is not provided, then the costs of their replacement are not taken into account, but wear and tear must be taken into account, keeping in mind possible resale (reversion). If the period of such deductions is precisely known, then when calculating the discounted cash flow method, it is possible to take into account expenses only in the period in which they are planned.
Since the main source of income generated by real estate is rent, it is necessary to carefully publish lease agreements typical for this type of real estate: terms of agreements, amounts of rent, frequency of payments, etc.

When determining cash flow based on historical data, accounting data (balance sheet, profit and loss account, etc.) or data on prices prevailing in a given market segment are usually used. In the latter case, the calculation is carried out in the same way as in the case of forecast data. When using historical data, it is often possible to use ready-made indicators of gross income, net operating income, etc.
The only thing you should pay attention to is the comparison and use of data for one period in one calculation.

Determining the final cash flow indicator (NCF), which is then recalculated into the current value of the object in several ways. The choice of recalculation method depends on the quality of the initial information on the market.

NOR - actual gross income minus all items of expenses, with the exception of debt on loans, taxes and depreciation.

Return on capital is the compensation that must be paid to an investor for the value of money, taking into account time, risk and other factors associated with a particular investment. Return on capital is also called return.

Return of capital means repayment of the original investment amount. The return of capital is called capital recovery.

In theory, the capitalization ratio for current income should directly or indirectly take into account the following factors:
1. Compensation for risk-free, illiquid investments.
2. Compensation for risk.
3. Compensation for low liquidity.
4. Compensation for investment management.

There are several methods for determining the capitalization coefficient (rate):
1. Market squeeze method.
2. Cumulative construction method (summed up).
3. Related investment method (investment group method).
4. Investment group method.
5. Method for determining the capitalization ratio taking into account the reimbursement of capital costs.
6. Elwood method (method of capitalization of debt and equity capital).

1. The market squeeze method is the simplest, fastest and most accurate for determining the value of any real estate using data collected in competitive and free markets on comparable sales of similar characteristics (investment motivation, socio-legal status, solvency, ways of financing and etc.) and the usefulness of real estate. Within the framework of the income approach, the cost is calculated using the formula:

V-cost;
I-CHOD;
R - capitalization coefficient (rate).

If the above formula converts NRR to value, then the following formula converts value to cap rate:

Based on market data on indicators such as sales price and NAV value of comparable real estate volumes, we can calculate the capitalization rate by dividing NAV by the sales price:

P = CHOD / selling price

The capitalization rate determined in this way is called the general rate.

It should be said that in order to more accurately calculate the capitalization rate, it is necessary to use data (sales price, NPV) for several comparable objects for which the valuation and sales data are close, because otherwise, it becomes necessary to reconstruct their operating statements in order to more objectively calculate the capitalization rate. The value of investment property can also be calculated by multiplying gross income, net income or other income indicators by the appropriate coefficient (multiplier).

The above-mentioned multiplier is obtained by dividing the sales price of real estate selected by the appraiser by the NPV value:

M= Sales price / CHOD

Co = CHOD x M

M indicates that the property being appraised is worth so many times more than current or projected income.

Cumulative construction method (summation method)

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

The interest rate is divided into several components:
1. Risk-free rate.
2. Bet on additional risk.
3. Compensation for low liquidity.
4. Compensation for investment management.
5. Adjustment for a projected increase or decrease in the value of real estate.

Risk-free rate

The risk-free rate is used as the base rate to which the other interest rate components are added.

To determine the risk-free rate, you can use both average European indicators for risk-free operations and Russian ones. If average European indicators are used, a premium for the risk of investing in a given country, the so-called country risk, is added to the risk-free rate.
The risk-free rate determines the minimum compensation for invested capital, taking into account the time factor (investment period).

Additional risk rate

All investments, with the exception of investments in government securities, have a higher degree of risk, depending on the characteristics of the type of real estate being valued. The greater the risk, the higher the interest rate must be so that an investor can take on the risk of any investment project.

Compensation for low liquidity

Liquidity measures how quickly a property can be converted into cash. Real estate is low-liquid compared to, for example, stocks and other securities. An adjustment for illiquidity is, in essence, an adjustment for long-term operation when selling a property or for the time it takes to find a new tenant in the event of bankruptcy or refusal to lease an existing tenant.

Investment Management Compensation

The riskier and more complex the investment, the more competent management it requires. Investment management should not be confused with property management, the costs of which are included in operating expenses.

Capital recovery rate

The value, equal to one divided by the number of years required to return the capital invested, is based on the time period over which a typical investor expects the capital invested in the property being valued to return.
It should be said that the values ​​of the components of the overall capitalization rate for different types of real estate are not the same.

Linked investment method.

Since most real estate is purchased using debt and equity capital, the overall capitalization rate must satisfy market income requirements for both parts of the investment.

Investment = debt capital + equity capital.

Lenders must expect to receive a competitive Interest Rate commensurate with the perceived risk of the investment (otherwise they will not extend the loan) and to repay the loan principal on a Periodic Amortization basis.
Likewise, equity investors must expect to receive competitive cash returns on their investment commensurate with the expected risk, or they will invest their money elsewhere.

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

R= annual maintenance payments. debt/mortgage principal

If the loan is repaid more frequently, then R is calculated by multiplying payments by their frequency (monthly, quarterly).

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

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

Rc = cash receipts before taxes / amount of equity invested

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

The overall capitalization rate (R) must satisfy a certain level of mortgage constant for the lender and income stream for the equity investor.

The credit (debt) share in total investments in real estate is equal to:

Mkred.= loan amount real estate value / real estate value

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

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

R = R3 x Microdistrict + Rc(1-Mkr.).

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

Rc= pre-tax cash receipts / equity value

Capitalization of debt and equity capital (Elwood method)

There is an opinion that the linked investment method has some disadvantages, because it does not take into account the length of the planned investment period, nor the decrease or increase in the value of the property during this period. In 1959, a member of the Institute of Assessment (IA) L.V. Elwood linked these factors with those already included in the tied investment method and proposed a formula that could be used to test or calculate the overall capitalization rate. In addition, simplifying methods for using his table have been developed.

The Elwood formula developed to calculate the total capitalization rate is as follows:

R = Rс - Mkr x C / Dep - app(SFF),

where R is the total capitalization rate;
Rc - rate of return on equity;
Mkr - the ratio of the size of the mortgage loan to the cost (loan share in the total capital);
C - mortgage coefficient;
Dep - decrease in property value over the forecast period;
arr - increase in property value over the forecast period;
SFF is the redemption ratio at rate Y for the forecast holding period.

The mortgage ratio can be calculated using the formula:

C = Y + P(SFF) - Rs,

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

You can find the mortgage ratio in Elwood's tables without having to calculate it yourself.

So, the Elwood method for calculating the capitalization rate can be represented as the following algorithm:

1. Collection of necessary information about the property being valued:

a) Rс (rate of return on equity capital). The rate of return on equity represents the real return on an investment that a typical investor expects to earn over the period of holding the property. It includes losses or mainly profits from sales (since most investors plan to sell the acquired property for more than it was purchased for).
The rate of return on equity is calculated based on market data and depends on the specifics of the specific valuation object.

b) Mcredit - (the ratio of the size of the mortgage loan to the cost) - the tax share (share of the loan) in the total capital invested in real estate.
Naturally, when calculating Mcredit, special (preferential) financing conditions are not considered.

c) Determining the typical terms of a mortgage loan and the interest rate on it.
When a mortgage loan does not have a fixed interest rate, the typical investor's interest rate bids over the settlement horizon are forecast. If such a forecast is impossible, it should not be used. this method calculating the capitalization rate for the property being valued.

d) Typical holding period (calculation horizon).
Although some investors purchase property with no intention of ever selling it (passing it on to inheritance), it is worth determining how long a prudent investor would be willing to hold the property. When calculating the mortgage C-ratio using the Elwood tables, the typical ownership period for real estate can be: S, 10, 15, 20 years.

e) arr, Dep - increase (decrease in the value of the property over the forecast period of ownership.
Most investors who purchase property believe that its value will increase in the future (otherwise they would not invest their capital).

f) Determination of the appropriate mortgage ratio using Elwood tables. Information for selecting tables:
- projected amortization (repayment) period;
- predicted interest rate on a mortgage loan;
- predicted holding period.

g) Selecting the appropriate sinking fund factor (SFF) (in the same section of Table C). The sinking fund factor can also be found in the table of the six functions of money.

h) Calculation of the total capitalization rate:

R - Rс - Mkr x C / Dep - app(SFF)

Accounting for capital cost recovery in capitalization ratio

As discussed earlier, the capitalization ratio for real estate includes return on capital and return on capital. Income streams on investments, the receipt of which is predicted in equal amounts over an unlimited period, and also if the value of the invested capital is not predicted to change, can be capitalized at the interest (discount) rate.

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

If a change in the value of an asset (loss or growth) is predicted, then it becomes necessary to take into account capital recovery in the capitalization ratio.

Let's consider the procedure for capitalizing the income stream in the following cases:
1. The cost of capital does not change.
2. The cost of capital is projected to decline.
3. The cost of capital is projected to increase.

1. The cost of capital does not change.

When analyzing real estate investments, the capitalization ratio should not include a capital recovery premium if the asset is resold at a price equal to the original investment and equal earnings are expected to flow.

2. The cost of capital is projected to decline.

When the value of invested capital is expected to decline, some or all of the investment recovered must be derived from current income. Therefore, the capitalization ratio of current income must include both the return on investment and the recovery of the expected loss.

There are three ways to recoup invested capital: - Straight-line return of capital (Ring method). - Return of capital according to the replacement fund and the rate of return on investment (Inwood method). - Return of capital based on the compensation fund and the risk-free interest rate (Hoskold method).

Straight-line return of capital (Ring method)

The Ring method assumes that the principal amount is repaid annually in equal installments. With straight-line capital reimbursement, the annual total payments are reduced. This indicates that straight-line capitalization corresponds to diminishing income streams and is not applicable for income streams of equal magnitude, because leads to an underestimation of their estimates.

Return of capital according to the replacement fund rate of return on investment (Inwood method)

The rate of return on investment, as a component of the capitalization ratio, is equal to the replacement fund factor at the same interest rate as for the investment. Part of the total income stream constitutes NOL, while the remainder of the income stream provides capital replacement or return. In the event of a 100% loss of capital, the portion of the income going to replace the capital, being reinvested at the interest rate, will grow to the original principal amount: i.e. full capital recovery occurs.

3. The cost of capital is projected to rise

Typically, when investing in real estate, the typical investor expects future growth in the value of the initial capital invested. This calculation is based on the investor’s forecast of an increase in the price of land, buildings and structures based on the principles of information, increased demand for certain real estate, etc. In this regard, there is a need to take into account the increase in the cost of capital investments in the capitalization ratio.

Conclusion

Ownership of property has a comprehensive beneficial material and spiritual impact on citizens:

Gives a person a feeling of confidence, trust and respect for people and things, a desire to invest their labor and capital in the development of the economy;

Arouses in people instinctive impulses and spiritual incentives for hard work to preserve and improve property, sparing no effort and resources;

Creates a need for strong state power in the center and locally;

Awakens and educates in people a sense of justice, the need for order and legality in all spheres of life and activity, including the real estate market.

List of used literature

Afanasyev Yu.N., Nikolaev O.A., Minaev V.S. Economics of real estate. – Tula, 1996.

Balabanov I.T. Real estate transactions in Russia. – M.: Finance and Statistics, 1996.

Korostelev S.P. Fundamentals of the theory and practice of real estate valuation. – M., 1998.

4. Popov G.V. Valuation of profitable real estate. – M., 1995.

Introduction………………………………………………………………………………2

Method of direct capitalization of income when assessing real estate……..

The main stages of the procedure for assessing real estate using the income capitalization method………………………………………………………

Conclusion…………………………………………………………………

Bibliography………………………………………………………...

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Chapter 4. Income approach

Chapter 3. Comparative approach

Direct method comparative analysis sales is based on the premise that market entities carry out purchase and sale transactions by analogy, based on information about similar transactions. It follows that this method is based on the assumption that a prudent buyer for a property put up for sale will not pay a greater amount than that for which an object of similar quality and suitability can be purchased.

The method involves collecting data on the sales market and offers for real estate properties similar to the one being evaluated. 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 can be used to determine the market value of the property being appraised.

The main stages of the assessment procedure with this method:

1. Market research in order to collect information about completed transactions, quotes, assumptions for sales of real estate similar to the subject of assessment.

2. Selection of information in order to increase its reliability and obtain confirmation that the transactions occurred under free market conditions.

3. Selecting suitable units of measurement and conducting a comparative analysis for each selected unit.

4. Comparison of the object being evaluated and objects selected for comparison, sold or being sold on the market for individual elements; introducing amendments to the prices of comparable analogues; determining the price of the object being valued.

5. Establishing the value of the valued object through analysis comparative characteristics and leading them to one cost indicator or group of indicators. In conditions of insufficient or low reliability of information about the market, instead of a valuation of an object, the output data can be presented in the form of a group of indicators or a price range.

Briefly, the essence of the method can be expressed by the formula:

This calculation is carried out for each analogue object, then the results are agreed upon.

Adjustments to the sales prices of comparable properties are made in two ways: elements of comparison and units of comparison.

The following indicators are usually considered as elements of comparison:

1) property rights– comparison of objects can be made only when transferring identical rights to the object of evaluation and its analogue. If the rights are encumbered by tax or long-term lease, then this must be taken into account in the transaction by adding the current value of the tenant's rights or accounts payable.

2) financing terms– settlements between the parties to the transaction can be made in different ways: cash or non-cash funds, barter, return or transfer of debts to a third party. Often the transaction is financed by the seller, i.e. providing the buyer with a mortgage loan. In this case, it is necessary to calculate the present value of the credit incentives to determine how much the buyer saved (or the seller lost).

3) terms of sale– must reflect the presence of specific atypical relationships between the seller and the buyer (for example, family relationships, time constraints, etc.). The amount of adjustment can be calculated by comparing the transaction price with the average market price in a given segment of the real estate market.

4) Date of sale– adjustments to the date of sale should reflect the actual change in the purchasing power of funds in the real estate market. The consumer price index, which is published by the State Statistics Committee of the Russian Federation (RT), is taken as an indicator of changes in the value of money.

5) location– the city area, distance from the city center (district), accessibility of transport and social services (schools, shops), environmental conditions, landscape, etc. are taken into account.

6) physical characteristics – amendments are made taking into account the degree of cumulative wear and tear, the total (usable) area, purpose and use, architectural, planning and design solutions, the presence or absence of any improvements on the site and land plot.

To calculate the amount of corrections, the following methods can be used:

· Methods based on analysis of paired sales– two objects are selected, ideally an exact copy each other, with the exception of location, the presence of which explains the difference in the price of these objects.

· Expert methods pop calculation ravok - based on market information, for example, average market prices for housing in city districts. Amendments are made in percentage terms.

· Statistical methods for calculating corrections– is based on identifying the relationship between changes in prices of real estate objects and changes in any of its characteristics. This method is the most labor-intensive.

After selecting suitable analogue objects and adjusting the value of each of them to determine the value of the valued object, it is necessary to reconcile the results using the following methods:

1) minimum correction method– the value of the valued object is determined as the adjusted value of the analogous object with the smallest absolute value of adjustments, i.e. the smaller the number and magnitude of amendments made, the more weight This sale is in the process of approval.

2) weighted average cost method– the value of the valued object is determined as the weighted average of the adjusted value of all analogous objects. In this case, each result is assigned specific gravity, for example, from the gross amount of adjustments.

The final value of the value of the appraised object is obtained by assigning unit weights to the adjusted values ​​of comparable sales.

The price of the selected analogue, to which the smallest number and magnitude of corrections were applied, will be most comparable to the object being valued, i.e. the highest specific weight is assigned. For example: .

We will evaluate the property using the comparative sales analysis approach. To do this, we will select 3 analogue objects. Let's present the selected analogues in table form:

Table 7

Information on the sale of property: residential two-story buildings

The direct capitalization method is used to calculate the current value of a business if reliable historical data is available to estimate the enterprise's income. At the same time, as noted above, the future income of the business object is quite stable in each subsequent period of time and will be approximately equal to current income or the growth rate of future income will be moderate.

The income used is earnings before interest and financial costs, net profit, net cash flow, and the amount of dividends paid. The choice of type of income depends on the specifics of the business.

The preliminary cost of a business object using the method of direct capitalization of income is determined based on the annual income PR and the capitalization rate K cap using the formula

Obviously, what less value capitalization rates, the greater the value of the business object will be if the annual income is constant and vice versa.

Estimating the value of a business using the income capitalization method is sufficient simple method, reflects directly market conditions.

The method should not be used if there is no information on market transactions, if the business object does not have stable income.

Example 19. Determine the cost of a business producing products of the type A based on the information presented in table. 4.3.

Table 4.3

Calculation of a business for the production of products of the typeA

Indicator name	Meaning
Background information for assessment
1. Cost of the industrial building, thousand rubles.
2. Useful life of an industrial building
3. Rate of return for an industrial building
4. Cost of land, thousand rubles.
5. Rate of return on land, %
6. Annual production and sales volume, units.
6. Sales price, thousand rubles.
7. Revenue from sales of products, thousand rubles.	48,000 x 1.780 = 85,440
8. Costs of production and sales of products, thousand rubles.
9. Service life of the production line, years
10. Rate of return for an analogue production line

Estimated indicators

11. Capitalization rate for an industrial building
12. Capitalization rate for the production line
13. Net annual income from production before taxes, thousand rubles. (page 7 - page 8)	85 440 - 66 643 = = 18 797
14. Net income attributable to the land plot, thousand rubles. (page 3 x page 4: 100%)	3,400 x 0.08 = 272
15. Net income attributable to the production building, thousand rubles. (page 1 x page 11)	25,600x0.1133 = 2,900
16. Net annual income attributable to the production line, thousand rubles. (page 13 - page 14 - page 15)	18 797-272-2 900 = = 15 625
17. Business cost, thousand rubles.	15 625:0,3004 = = 52 014

Solution

The income in this example is the net annual income from production and sales of products before taxes, defined as the difference between the proceeds from the sale of the planned volume of products and the costs of production and sales. Considering that components business are a production building and a production line; each component has its own capitalization rate calculated. To calculate the capitalization rate of an industrial building, we take into account the rate of return on investments in similar objects (according to the condition of 8%) and the remaining service life of 30 years.

Capital recovery (return) coefficient for an industrial building:

Capitalization rate for an industrial building at a reimbursement rate of 3.33%:

To calculate the capitalization rate for a production line, we take into account the annual rate of return from the analogue (25%) and the remaining service life of eight years.

Recovery rate for production line:

Capitalization rate for production line:

The net income attributable to land BH 3 is determined as the product of the current value of the land plot and the capitalization coefficient for the land (calculation on page 14 of Table 4.3). The net income attributable to the industrial building BH, f1, is determined as the product of the current value of the building and the capitalization ratio for the industrial building (calculation on page 15 of Table 4.3).

Net income attributable to the production line is determined by the formula

Cost of production line to produce products A determined by the formula

The calculation results are given in table. 4.3. Based on the calculations carried out, it follows that the projected net annual income from the production line will be 15,625 thousand rubles; if the considered conditions remain the same, the estimated cost of the business will be 52,014 thousand rubles.

Example 20. To produce products that are in demand, an entrepreneur plans to install equipment, the cost of which is 7,500 thousand rubles, the useful life of ten years, the maximum daily productivity of 4,000 units. products. Based on an analysis of analogue enterprises located in the area, the utilization rate of such equipment is 0.65, 0.58 and 0.70, the capitalization rate for analogues is 35%. According to the forecast, the probability of equipment utilization at 65 and 70% can be 30 and 28%. Operating conditions: selling price per unit of production - 2 thousand rubles; direct material costs for production are 25% of the price; direct labor costs with deductions amount to 20% of the selling price. To motivate labor, it is expected that wages will increase by 3 and 5% if the equipment utilization rate is 65 and 70%. Annual maintenance and repair costs are 12% of the equipment cost. To organize production, you will need to rent a production space with an area of ​​20 m2. Rent per month - 1.2 thousand rubles/m2. Other types of expenses are forecast to amount to 4% of operating income. The risk-free reinvestment rate is 7%. Determine the cost of the business and assess the impact of equipment utilization on the cost of the business.

Solution

To solve this, we will compile an analytical table. 4.4.

Table 4.4

Determining the value of a business using the method of direct capitalization of net profit

Index	1st option	2nd option	3rd option
2. Coefficient beneficial use,
3. Load probability for new production, P 3
4. Unit sales price, thousand rubles.
5. Number of working days per month, D r, days
6. Number of parts produced per day according to option, units.	4,000 x x 0.58 = = 2,320	4,000 x x 0.65 = = 2,600	4,000 x x 0.70 = = 2,800
7. Number of products produced per year, units. (page 6 x page 5x12 months)
8. Operating income for the year according to the option, thousand rubles. (page 4 x page 7)
9. Operating income for the year taking into account the probability of the option, thousand rubles. (page 8 x page 2)

Continuation
Index	1st option	2nd option	3rd option
10. Weighted average operating income for the year, thousand rubles.		561 254 + 449 280 + + 451 584= 1462 118
AND. Material costs for production, thousand rubles. (25% x page 8)
12. Salary with accruals per year, thousand rubles. (page 8 x 20%)
13. Additional payment taking into account labor motivation, thousand rubles.		299,520 x x 0.03 = = 8,986	322,560 x x 0.05 = = 16,128
14. Annual costs for maintenance and repair of equipment, thousand rubles.
15. Depreciation charges, thousand rubles.
16. Rent, thousand rubles.
17. Other types of expenses, thousand rubles. (4% x x page 8)
18. Direct costs of products, thousand rubles (page 11 + page 12)
19. Overhead costs for products, thousand rubles. (page 13 + page 14 + page 15 + page 16 +
20. Total costs for products, thousand rubles. (page 18 + page 19)
21. Total costs taking into account the probability of loading according to the option, thousand rubles. (page 3 x page 20)
22. Weighted average expenses for the year, thousand rubles.		275 829 + 223 424 + + 226 335 = 725 588
23. Projected profit before income tax according to the option, thousand rubles. (page 8 - page 20)
24. Projected profit after deduction of income tax, thousand rubles. (page 23 x 0.76)
25. Projected profit after deduction of income tax, taking into account the probability of loading equipment according to the option, thousand rubles. (page 3 x page 24)
26. Weighted average profit after deduction of income tax, thousand rubles.		216 924+ 171 650 + + 171 189 = 559 763

Ending

Taking into account the possible degree of equipment utilization, we will determine the production volume per day and per year for each option. Product output per day, taking into account maximum load U tah and efficiency factor K is:

The calculation results are in table. 4.4 page 6. Product output per year for each option:

Let us determine the average annual income of the enterprise, taking into account the predicted probability of loading for each option" using the formula

where B| - operating income according to the first option

R - probability of equipment loading according to the first option" (calculation results are presented on pp. 8-10).

The weighted average operating income from production, taking into account the probability of occurrence of each option, will be 1,462,118 thousand rubles.

Let's calculate the total costs per year for each option" using the initial information. Main types of costs:

• direct material - according to the condition, they amount to 25% of the price or operating income (p. 11);
• wages - 20% of price or operating income (p. 12);
• labor motivation costs: if the degree of equipment utilization increases compared to the first option, then the enterprise will increase wages by 3 and 5% (page 13);
• maintenance and repair costs are 12% of the original cost:

We calculate depreciation charges using the linear method, taking into account the initial cost and useful life (10 years):

N am = 1: T= 1: 10 = 0.10 AM = 0.10x 7500 thousand rubles. = 750 thousand rubles. (page 15);

The rent is calculated taking into account the production equipment area of ​​20 m2, the monthly rent is 1.2 thousand rubles/m2, the annual rent payments will be:

Other types of expenses - 4% of operating income (p. 17).

Based on the data obtained, the total direct costs (direct material and direct labor costs) and the total overhead costs for each option are given on page 18 and page 19. Calculations of profit for each option before tax and after tax, as well as the value of the weighted average net profit in the results of the business are presented on pp. 23-26.

To assess the value of a business, we will calculate the value of the capitalization rate, taking into account that the risk-free reinvestment rate is 7%, the capitalization rate of analogue objects is 30%.

The rate of return on investment at a rate of 7% and an equipment service life of 10 years will be:

Capitalization rate for business valuation:

Based on the data obtained, it follows that, taking into account possible options for loading equipment, the weighted average operating income for the year will be 1,462,118 thousand rubles, the weighted average profit after deducting income tax from the production and sale of products will be 559,763 thousand rubles, return on sales by net profit - 38.28% (559,763: I 462,118 x 100%), weighted average cost of business - 1,325,189 thousand rubles.

Let's evaluate the impact of load levels on business value. When using equipment at 58% of maximum capacity, operating income is 1,336,320 thousand rubles, net income after payment of income tax is 16,485 thousand rubles, return on sales is 38.65%. When using equipment at 70%, operating income is 1,612,800 thousand rubles, profit after payment of income tax is 611,391 thousand rubles, return on sales is 37.91%. This means that with an increase in equipment utilization by 12%, operating income will increase by 276,480 thousand rubles. (1,612,800 - 1,336,320), or 20.69%, net profit after income tax increases by 94,906 thousand rubles. (61 1 391 - 516 485), or by 18.38%, and the cost of the business will also increase by 224 683 thousand rubles. (1,447,422 - 1,222,739), or by 18.38%. With an increase in equipment utilization rate by 1% under the specified conditions, the cost of business increased by 1.53% (18.38: 12).

Example 21. The current annual income of the business object is 3,500 thousand rubles, the rate of return is 18%. According to the forecast, it is expected that in the next six years the value of a business object may increase with an optimistic development of economic events by 48%, the most likely development - by 32%, and with a pessimistic forecast - by 10%. Determine the capitalization ratio, the current value of the business object and the resale value in six years, taking into account that the probability of an optimistic forecast is 20%, and a pessimistic forecast is 30%.

Solution

Let's calculate the rate of compensation factor taking into account the rate of return of 18% on investments:

Current value of the subject of assessment:

Resale cost of an object taking into account a 10% increase in value:

Using the values ​​of the current value of the object and the resale value of the object, we calculate the weighted average values ​​of these indicators. The calculation results are summarized in table. 4.5.

Table 4.5

Calculation of the current value of a business object and resale, taking into account the increase in its value

Index	Forecasting option
	OPTIMISTIC	most likely	pessimistic
1. Current income to the property, thousand rubles.
2. Income growth rate, %
3. Probability of forecast
4. Compensation factor rate, %
5. Deferred income rate, %
6. Adjustment capitalization rate, %
7. Current value of the object, thousand rubles.
8. Cost of the resale object, thousand rubles.
9. Weighted average present value	27,090x0.10 = = 2,709	23,956 x 0.50 = = 11,978	20,661 x0.30 = = 6,198
Probabilistic weighted average current value of a business object, thousand rubles.		2 709 + 11 978 + 6 198 = 20 885
10. Weighted average cost of a business resale object, thousand rubles.	40,093 x0.10 = = 4,009.3	31,622x0.5 = = 15811	22,727 x 0.30 = = 6818.1
Probable weighted average resale value, thousand rubles.		4009,3 + 15 811 +6 818,1 = = 26 638,4

Based on the data obtained, the following conclusions can be drawn. A decrease in the growth rate of income from a property in the future leads to a decrease in the rate of deferred income, which leads to an increase in the adjustment rate of income capitalization, and, consequently, to a decrease in the current value and resale value of the property being assessed. For example, a decrease in the rate of income growth from 48 to 10% led to a decrease in the rate of deferred income from 5.08 to 1.06%.

The current value of a business object, depending on the rate of income growth and the likelihood of the forecast being realized, can vary from 20,661 thousand rubles. up to 27,090 thousand rubles, the weighted average current value is 20,885 thousand rubles. The resale price of an object can range from 22,727 thousand rubles. up to 40,093 thousand rubles, the weighted average resale cost is 26,638 thousand rubles.

Example 22. The OJSC plans to expand the volume of product sales; for this it is necessary to rent two sales rooms in different areas cities, the area of ​​each of them is 300 m2 and 450 m2, unused space in each sales area is 6 and 8% of the area, the cost of rent per month for 1 m2 is 500 rubles. and 430 rub., cost commercial equipment respectively equal to 125 thousand rubles. and 190 thousand rubles. Investments will be made using own funds and borrowed funds. The first object will be financed 30% from borrowed funds, the interest rate on the loan is 25%, the rate of return from the first object is 2.10. The second object will be financed 45% from borrowed funds, the interest rate on the loan is 20%, the rate of return from the second object can be only 1.76. Interest rate on equity at the time of valuation - 15%.

At the time of assessment, the amount of the JSC's own funds was 3 million rubles. Assess the sufficiency of own funds and the feasibility of investing them in objects, the minimum level of return for the owner.

Solution

The initial data and calculation results are presented in table. 4.6. We carry out the solution in the following sequence.

Table 4.6

Calculation of net operating income from investments in business objects

Continuation

Estimated indicators for business objects
9. Potential gross income for the year, PVD, rub. (page 1 x page 4x12 months)	300 x 500 x 12 = = 1,800,000	450 x 430 x 12 = = 2,322,000
10. Unused area, m 2 (page 1 x line 1.1: 100)		450 x 0.08 = 36
11. Losses from underutilization of premises at U B, rub. (page 10 x x page 4x12 months)	15 x 500 x 12 = = 90,000	36 x 430 x 12 = = 185,760
12. Actual gross income of DVD, rub. (page 9 - page 11)
13. Operating expenses, rub. (page 9 x page 8: 100), including:
14. Depreciation, rub. (page 2 x page 3: 100)	125,000x0.12 = = 15,000	190,000x0.11 = = 20,900
15. Net operating income for the year ChOD, rub. (page 12 - - page 13 + page 14)	1 710 000- 720 000 + + 15 000= 1 005 000	2 136 240- 12 700 + + 20 900 = 2 144 440
16. Cost of the object as of the valuation date, rub.
17. Minimum price of the object (75% x page 16 + page 2)	1,005,000 x 0.75 + + 125,000 = 878,750	2,144,440 x0.75 + 190 000= 1 798 330
18. Maximum price of the object (150% x page 16 + page 2)	1,005,000 x 1.50 + 125 000= 1 632 500	2 144 440 x 1.50 + 190 000 = 3 406 660
19. Average price of an object (page 17 + page 18)	(878 750+ 1 632 500)/ 2 = 1 255 625	3 406 660): 2 = = 2 602 495

Ending

Let's calculate the potential gross income from the property that can be received from the property with 100% use without taking into account losses and expenses, taking into account the usable area and monthly rent:

Where S- area of ​​the assessment object;

AR PL - monthly rent.

Calculations are presented on page 9 of the table. 4.6.

Let's calculate losses from underutilization of a property - losses from underutilization of premises:

where 5 M is the unused area of ​​the assessment object.

Calculation results on page 11.

Let's calculate the actual gross income, taking into account the estimated losses from underutilization of the property:

Calculation results in p. i.

Let's calculate the estimated costs of operating the property being assessed - operating expenses necessary to ensure the smooth functioning of the facility and the reproduction of income, taking into account the conditions of the problem:

where PPV is potential gross income;

N or - the share of operating expenses in potential gross income.

Depreciation deductions are highlighted in operating expenses, calculations are on pages 13 and 14.

Let's calculate the projected net operating income (NOI) as the difference between actual operating income and operating costs (excluding depreciation A):

The calculation results are on page 15.

NER represents the value of the object of assessment SOO on the date of assessment. At the time of valuation, the cost of the first valuation object was 1005 thousand rubles, the cost of the second object was 2144.440 thousand rubles.

We will determine the average price of each object based on the cost of the object on the valuation date and the cost of equipment and the assumption that the cost of objects can vary from 75% of net operating income (at a minimum) to 150% of net operating income (at a maximum) and the cost of operating equipment , which the object of assessment has:

The calculation results are presented on pages 17-19.

As a result of the calculations made, we found that average cost of the first and second business objects is 1255.625 thousand rubles. and 2602.495 thousand rubles.

Let's calculate the capitalization ratio, or the price of capital, for each valuation object for borrowed capital, using its share D (in sources of financing, the discount rate dlc, as well as the required return for the investor K pl. Capitalization ratio for debt capital:

According to the conditions of the problem we have:

according to the first option:

according to the second option:

The calculation results are shown on page 20.

Let's calculate the real PC value of each object by dividing the net operating income of the CHOD by the capitalization rate K cap:

The calculation results are presented on page 21.

Let us determine what the rate of return on equity invested in these investments should be, taking into account the structure of the capitalization ratio:

where D*. - share of borrowed capital;

d x - price of borrowed capital;

D s, - share of equity capital; dcc- price of equity capital.

Calculations are presented on page 22.

For the first option:

Thus, the minimum return on equity invested in the first business object, given the financial structure of the investment, should be 12.14%, i.e. for every ruble of equity capital there should be no less than 12.14 kopecks. net profit. Otherwise, the investment will be unprofitable.

For the second option:

Thus, the minimum return on equity invested in the second valuation object, given the financial structure of the investment, should be 12.73%, i.e. for every ruble of equity capital there must be at least 12.73 kopecks. net profit. Otherwise, the investment will be unprofitable.

Let us determine the amount of equity capital that should be invested in investment objects, taking into account the share of equity capital (D ss) and the average purchase price of a central heating facility with:

According to the first option:

For the second option:

Taking into account two options: RUB 878,938. + 1,431,372 rub. = 2,310,310 rub.

Thus, it is necessary to invest 2,310,310 rubles in these business objects. own funds. At the time of evaluation of the objects, the amount of the JSC’s own funds is 3 million rubles, i.e. the company has enough own funds to make investments.

Let's calculate the amount of the minimum net profit that an OJSC can receive as a result of the acquisition of these objects by multiplying the capitalization rate for equity capital by the amount of equity capital:

According to the first option:

For the second option:

The total net profit from investing own funds in business objects, if the conditions considered are maintained, will be 288,917 rubles.

A group of methods, united by the general term: “Direct capitalization method”, in the traditional version is widely used in Real Estate Valuation Reports. However, it is extremely rare that the Reports indicate assumptions and limitations on the applicability of the models used. And this is understandable. If you indicate the conditions (assumptions) under which this method can be applied, it will become clear that very often, in terms of the main positions, the real situation with commercial and residential real estate does not correspond to these assumptions. The problems of the legitimate use of these methods are discussed in the theoretical literature on real estate valuation (Gribovsky, Ozerov, Mikhailets, etc.). It should be especially noted that these issues are considered from the most general positions. However, as the analysis of Real Estate Valuation Reports shows, theoretical research in this area remains unnoticed by the majority of practicing Appraisers. Therefore, it seems to me useful to return to the problem from the perspective of a practicing appraiser. This article makes an attempt to standardize typical situations that are often encountered when assessing real estate in an unstable economy, characteristic of of this period in Russia, formulate packages of assumptions associated with these situations, and expand the range practical situations when the formulas of the direct capitalization method can be correctly used. The main attention is paid to models that take into account rising prices for real estate and rising rental rates. It’s impossible not to notice the fact that over the last 5 years, even “aging” properties have been growing in price at a rate significantly higher than inflation. To complete the picture of the problem under consideration, some provisions from these works are partially repeated here.

In accordance with the direct capitalization method (see, for example,) the capitalization ratio (R) in relation to the problem of real estate valuation, there is a certain coefficient that allows you to convert net operating income (D), expected in the next year, at the current value (PV) property using the formula:
PV = D/R (1)
In this case, the capitalization ratio consists of two elements:

• Rate of return on investment
• Investment return rate (capital recovery rate).

The rate of return on investment is determined by the market return of risk-free and liquid instruments and the risk premium associated with the uncertainty of future income and the insufficient liquidity of the property being valued. The capital recovery rate is determined by the amount of annual capital loss over the expected period of use of the property, the nature of the change in the amount of net income and the method of reinvesting the income received. There are three return on capital models described in the literature:

• Straight-line (Ringa model)
• According to the compensation fund (Hoskold model)
• Annuity (Inwood model)

In addition, the Gordon model has become widespread in practice, also linking annual income with market value, which is mainly used to estimate the cost of reversion. Ring's model assumes that the income stream will decline annually. Such an assumption in the context of constantly rising rental rates looks very doubtful. Therefore, this model is practically not used. Hoskold's method was also not found wide application when assessing real estate, since it refers to a situation where the money received from rent is accumulated for years on a deposit or in other risk-free and, accordingly, low-income instruments, which is not typical for the strategy of an effective owner. An analysis of the Reports reviewed by us and published in Internet resources shows that the Inwood model is most widely used, which, apparently, reflects the realities of the modern market to a greater extent.

Initially, the mentioned models and corresponding formulas were obtained from general considerations not directly related to the discounting method cash flows. But, as often happened in the history of the development of applied areas, the correct guesses were subsequently strictly confirmed from the standpoint of general theory. IN in this case the same thing happened. It turned out that it was possible to obtain the formulas for the direct capitalization method strictly mathematically, based on classical method discounting cash flows generated by the asset being valued. This made it possible not only to more correctly establish the scope of their application, but also to expand them to a wide class of real situations. The specific technique for such transformations can be found in many publications (see, for example,). The models below cover a variety of situations, including situations where the properties have not lost all of their value and only a portion of the original investment needs to be recovered. These formulas also take into account the expected growth in rental rates for the forecast period and the expected increase in real estate prices. Therefore, they are suitable for a wider range of practical situations encountered by the Property Appraiser in his practical work. Since all formulas are obtained based on the traditional cash flow discounting model for very general typical situations, they are in full agreement with the assessment results based on the discounted cash flow method.
Naturally, the proposed list of typical situations should not be considered exhaustive. Real life always richer and more diverse than any models.

Typical situation 1. (Traditional Inwood model)

The traditional Inwood model refers to a situation where the forecast period is the entire remaining life of an object, which ends with a complete loss of value of the valued object. Let us formulate the main assumptions under which this model fair:

• Expected service life of the facility n years.
• During the entire period of operation (forecast period), the object brings fixed income, equal D.
• At the end of its service life (forecast period), the object completely loses its value, i.e., future value FVn = 0.

In accordance with the discounting method, the current value under the formulated assumptions is determined by the following expression
(2)
It is easy to show (see, for example,) that the expression for the current value can be represented as:
,

Using the compound interest function K6(r,n), characterizing the contribution to depreciation of the unit, the formula for the current value will take the form:

Considering that

Where K3(r,n)- compensation fund factor equal to
(3)

we obtain the traditional formula for the capitalization ratio:
(4)
which is given in all books as the basic formula of the capitalization method with capital replacement according to the Inwood model.

Indemnity Fund Factor K3(r,n) characterizes the amounts of payments that, when reinvested with a yield r, will ensure accumulation over the period n years of an amount equal to one. This element in formula (4) reflects the need to reimburse capital spent on acquisition and lost over the expected lifespan.

These formulas are currently quite widely used in real estate valuation. However, given the assumptions that underlie it, greater caution should be exercised in its use.

Indeed, already long time rental rates are steadily growing, and there is no reason to assume that this growth will completely stop in the expected future. It also seems very questionable to assume that after the standard life has expired, the value of real estate will become zero. At least, if the land plot is owned by the owner of the property, even after the complete destruction of the property, the owner remains the owner of some capital in the amount of the cost of the land plot and part of the building elements. Therefore, it is not always possible to justify the assumptions formulated above.

However, such situations may occur when valuing special real estate. For example, income from the operation of gas pipeline systems serving the population is not growing (in real prices, without inflation), and the value of these structures falls as they age and becomes zero at the end of their life. A similar situation also occurs when assessing real estate related to the power supply of the population and other objects of social importance.

Typical situation 1a

This situation retains all the features of the 1st typical situation with only one additional assumption: The expected lifespan of the facility is very long (virtually unlimited).

Therefore, the amount to be returned extends over an infinite number of years, and the capitalization rate, as can be seen from the formulas (3), (4) r:
R = r (5)

Regarding the applicability of this formula, one should also keep in mind the comments related to the first situation

Typical situation 2

The calculation is carried out for a limited forecast horizon, during which the property, as well as the market, exhibit some stability (stationarity), which allows us to make the following assumptions:

In this case, calculating the present value of cash flow comes down to solving a simple linear equation with respect to PV:

After obvious transformations, we obtain a condensed formula for calculating the current value.

From here:
Or, reducing to standard form, we get:
(6)

The resulting formula, along with its derivation, is given in various publications (see, for example,). However, it is rarely used by practicing Appraisers. As noted above, in most cases the formula is preferred (4) . According to the author, the assumption of what part of the value the property will lose over 5 years, is more natural than guessing how many years it will take for the property to completely lose its value. And it seems completely doubtful to calculate the remaining service life based on the standard period, as is usually done when assessing based on the traditional Inwood formula (4) . This gives grounds to assert that this version of the capitalization ratio in some cases may be more justified than the traditional one (4) .

However, there remain limitations in the use of this formula related to the assumption of constant income and the absence of growth in the value of real estate. Such assumptions do not seem very realistic for current state the real estate market, with the exception of cases that occur, as noted above, when assessing special real estate.

Typical situation 2a

This situation retains all the features of the 2nd typical situation with only one clarification:

During the forecast period, no noticeable loss in the value of the property is expected, or its decrease will be compensated by a corresponding increase in prices. In this case, we can assume that the value of the property remains unchanged until the end of the forecast period (FVn = PV), and therefore, when the object is resold after n years, the initial investment will be returned in full. Under this assumption, there is no need to return the funds spent, and the capitalization ratio, as can be seen from the formula (6) , becomes equal to the rate of return:
R = r

Typical situation 3.

This situation reflects the effects associated with the increase in the market value of the property due to the general growth of real estate on the market and the simultaneous loss of value due to the depreciation of the property. Let us formulate the main assumptions made when deriving the calculation formula.

Under these assumptions, the equation for calculating the current value of a property will take the form:
(7)

After transformations similar to those described above, the capitalization ratio can be written as
(8)

The following circumstance should be noted here. The direct use of such a model is very limited. The fact is that the constancy of rental income with a simultaneous increase in real estate prices is not typical for the market. Therefore, the use of this model should be used with caution. It is easy to see that the resulting expression in particular cases transforms into the well-known formulas for the direct capitalization coefficient. Let's consider special cases:

1. There is no real estate growth, partial wear and tear is predicted:

The formula matches (6)

2. There is no real estate growth, complete depreciation is predicted

The formula matches (4)

Real estate growth is predicted, it is assumed that over the forecast period the loss of value due to wear and tear is insignificant:

4. There is no real estate growth, wear and tear during the forecast period is insignificant (the decrease in value can be neglected). In this case:

Typical situation 4

This typical situation refers to the case when rental rates increase at a rate equal to g, and the value of the property by the end of the forecast period will be zero. An appraiser is faced with this situation when the object being appraised is a building located on a plot of land leased for a short period (for example, 5 years). In this case, the rental rate increases with the market, but after a fixed period the building is subject to demolition, and therefore the cost of reversion of such a property can be considered equal to zero. Let us formulate the main assumptions corresponding to the situation under consideration, which were accepted when deriving the calculation formula.

(9)

After simple transformations, we obtain a simple formula for the current value, according to which the direct capitalization coefficient can be presented as:
(10)

It is easy to show that when additional assumptions are introduced, this formula transforms into known formulas. In particular, when g=0(no payment growth), formula (10) goes into formula (4) for a typical situation 1 .

Typical situation 5

Rental rates are assumed to increase at a constant rate g. The value of the property itself is growing at the same rate. However, no noticeable wear is expected over the forecast period.

The situation is quite natural. During periods of rapid growth in property prices over a short period, the effect of loss of value due to aging can be neglected.

Let us formulate the main assumptions corresponding to the situation under consideration, which are accepted when deriving the calculation formulas.

• Forecast period - n years. Throughout the forecast period, rents are growing, and accordingly the property generates net operating income, increasing annually at a rate equal to g.
• Annual payments generated by net operating income are received at the end of each year.
• The portion of periodic income representing the return of capital is reinvested at the rate of return on investment.
• At the end of the forecast period, the object does not lose its original value (loss of value due to wear and tear during the forecast period can be neglected).
• During the entire forecast period, the real estate market is expected to increase prices at an annual rate equal to g. Therefore, by the end of the forecast period, prices in the real estate market will increase by (1+g)^n once. Accordingly, the same growth is expected for the assessed object.

Under these assumptions, the equation for calculating the current value of a property can be written as:
(11)
After obvious transformations, we obtain the well-known Gordon formula:

Accordingly, the capitalization ratio takes the form:
(12)

Essentially, the use of the Gordon formula as the basic formula for the direct capitalization method is possible if it can be expected that over a very long period of time the increase in rent will be significantly more significant than its decrease due to depreciation of the building. This assumption in some cases seems quite justified. Indeed, in last years There has been a steady increase in rental rates and, accordingly, prices for real estate, significantly outstripping the loss of value due to physical wear and tear. As a result, for example, an office purchased three years ago today has a higher value than when purchased, despite its natural aging. In this situation, there is no need to talk about capital reimbursement. Thus, if we rely on the assumption that in a sufficiently long term, prices on the real estate market and the corresponding rental rates will grow at a constant rate equal to g, then the market value is determined by Gordon's formula. It should be especially emphasized that when deriving the formula, an infinite flow is not assumed. Thus, Gordon's model is valid not only for an infinite flow. It can also be used under softer assumptions regarding forecast market dynamics. For the legitimate use of the Gordon model, it is sufficient that property prices and rental rates supposedly grow “synchronously” (a term from ) at a constant annual rate.

This assumption in most cases looks more reasonable than assumptions about constant growth in the foreseeable future.

Typical situation 6

It is assumed that changes in the value of a property occur under the influence of two opposing factors. On the one hand, there is wear and tear, as a result of which real estate loses part of its value over the forecast period. On the other hand, the cost of real estate is growing along with the general growth of the market for similar properties. This situation is the most general, and from our point of view, most correctly reflects the real state of affairs in the real estate market. Let us indicate the main assumptions that were used in deriving the formula:

Under these assumptions, the equation for calculating the current value of a property can be written as:

After simple transformations, we obtain a formula for the capitalization ratio in the form:
(13)

This expression best reflects the general situation with real estate. Here it is taken into account that the object wears out (physically and morally) during operation and loses its initial value. At the same time, general processes in the market lead to an increase in its value and a simultaneous increase in income from its operation. From the point of view of this model, over time, the value of a property may increase, despite the fact that it is subject to wear and tear. This fits well with reality today, as we watch aging properties increase in value and at a very rapid rate.

Naturally, this expression reduces to the previously obtained formulas when appropriate assumptions are included. For example, if we assume that wear will not noticeably appear during the forecast period (I=0), then the general expression for the capitalization ratio will take the form of the well-known Gordon formula:
Summary data

In conclusion, we present a table with formulas corresponding to various situations and corresponding assumptions

Table:

Description of the situation (Basic assumptions)	capitalization ratio
TS-1 Depreciation of real estate, complete loss of value by the end of operation. The income is constant.
TS-2 n equals I. There is no increase in prices on the real estate market FVn = (1 - I)PV The income is constant.
TS-1a Unlimited service life (endless income stream), Constant income
TS-2a No wear and tear, no real estate growth (FVn = PV).Income is constant	(regardless n)
TS-3 Depreciation of real estate. Partial loss of value. Depreciation, expressed as a percentage, for the period n equals I. Property values ​​are growing at an annual rate g. (FVn = (1+g)^n) The income is constant.
TS-3a g. (FVn = (1+g)^n). The income is constant.
TS-4 Complete loss of value by the end of use g.
TS-5 There is no wear. Property values ​​are growing at an annual rate g (FVn = (1+g)^n). Revenues are growing at an annual rate g.	(regardless n)
TS-6 Depreciation of real estate. Partial loss of value. Depreciation, expressed as a percentage, for the period n equals I. Real estate is growing at a pace g. (FVn = (1 - I)(1+g)^n). Revenues are growing at an annual rate g.

The conditions given in the left column in in brief show under what assumptions the corresponding formulas are obtained. However practical use The above formulas require a meaningful understanding of real situations. Every time you choose one or another model, you should clearly understand what expectations are associated with this property. At the very least, you should clearly answer the following questions:

In what direction will the rent for the property change in the foreseeable period?

What should be expected from the value of the property after the forecast period?

If this period is equal to the expected life of the asset (as is most often assumed in the direct capitalization method), then can the final value be assumed to be zero, or will some value remain (for example, the value of land)?

Clear answers to these questions will allow you to correctly formulate a package of assumptions (assumptions) and use adequate models.

Additional Notes

The resulting formulas naturally do not carry more information than the original equations that follow directly from the discounting method. Therefore, in practice, you can refuse to use the given compact formulas and include in the report only the numerical result of the solution on a computer. It is more important to clearly formulate and justify from a meaningful analysis of the problem the assumptions (assumptions) that form the basis of the methods and models used.

Direct capitalization formulas turn out to be useful for solving “inverse” problems of the discounting method. It's about about the problem associated with assessing the market value of rent and about the problem of determining the final return on income-producing real estate. The fact is that the direct use of the discounting method for these purposes is fraught with many pitfalls, and calculation through the direct capitalization method allows one to avoid many difficulties.

It is especially noteworthy that the discount rate r does not reduce to the current return. In conditions of rising real estate prices, it includes the growth rate (annual growth) as a term. More details in.

It should be noted that all of the above applies not only to real estate valuation. Since the direct capitalization method is also used in business valuation and in the valuation of machinery and equipment, most of the conclusions can also be attributed to the valuation of these objects.

In conclusion, I want to thank all my colleagues who sent me comments on the article and, first of all, V. B. Mikhailets, whose comments and his earlier published work made it possible not only to eliminate inaccuracies and typos in my previous article, but also to take a new look at problems of the discounting method in real estate valuation.

Literature

1. Jack Friedman, Nicholas Ordway. Analysis and valuation of income-generating real estate, Translation from English, Business, Ltd. M., 1995 – 480 p.
2. N.V. Radionov, S.P. Radionov, Fundamentals of financial analysis: Mathematical methods, systems approach. "Alpha", St. Petersburg, 1999, 592 p.
3. Mikhailets V. B. Once again about the discount rate in valuation activities and methods of the income approach. Questions of assessment N 1, 2005 p. 2-13
4. S.V. Pupentsova, st. Lecturer at the Department of Economics and Real Estate Management, St. Petersburg State Polytechnic University. Modern look on the use of modeling techniques in real estate valuation
5. Ozerov E. S. Economics and real estate management. St. Petersburg: Publishing house "ISS", 2003 – 422 p. – ISBN 5-901-810-04-Х
6. S.V. Gribovsky. Modeling of market processes in the assessment of land - free and with improvements. Nezh "Problems of real estate - economics, management, investment, assessment", vol. 1, 2005
7. Vinogradov D. V.

Valuation of property using the direct capitalization method provides for maintaining the level of profitability of the object and the conditions of its use.

Essence and characteristics

Real estate valuation is carried out in two ways - using direct capitalization or through discounted cash flows (DCF). Both ways are implemented under the condition that the price of the property directly depends on its potential ability to generate income. The calculations necessarily include the level of risk that accompanies the transformation of profit, which may develop in the future, into a specific indicator of the price of the object.

The key difference between these methods is different algorithms for accounting for generated profits. In direct capitalization, income received for a specific time period is taken into account. In the case of DCF, the indicators of the last few years are used as a basis, and potential profits from the resale of real estate after the reporting period has expired can be included here.

The choice of methodology is influenced by the following factors:

• reflection of current competitive trends in the algorithm;
• the amount of information on which the analysis is based, its type, completeness and reliability;
• the ability to use specific characteristics of the object that can affect the final cost - location, size, etc.

Under these conditions, it is worth highlighting cases when the direct capitalization method is considered the most appropriate:

• financial flows for a long time remain stable, although they are above zero;
• profit from the use of the facility gradually increases, albeit in small increments.

Calculation of the direct capitalization method

The use of this method reflects the total price of the object, which includes specific components, in particular, the cost of the building and land.

The general formula for the price of object “C” in a simple form illustrates the relationship between net operating income (referred to as NOR) and the capitalization ratio (Ccap):

NOR is taken as annual or average annual.

The considered calculation method is not used in two situations:

• the object is an unstable source of profit;
• construction of the property has not yet been completed or the property is subject to restoration.

Stages of using the direct capitalization method:

1. Calculation of the expected profit that an object can bring. The analysis may be based on annual performance or on average performance for the same period. The priority is to use the facility as efficiently as possible.
2. Determining the value of the capitalization ratio based on the rate of return and the rate of return of money. The price of reversion is not calculated here; the process is initiated only in relation to real estate objects.
3. Formation of the total price of property taking into account net operating income and capitalization ratio.

What makes it difficult to obtain a reliable picture is the fact that most real estate markets are quite opaque; they do not provide complete information about the actual rental or sale of objects. Another problem is the lack of clear statistics regarding loading intensity and associated operating costs. As a result, the process of obtaining key computational parameters becomes noticeably more difficult.

Advantages and disadvantages

The main advantage of the direct capitalization method and the reason for its active use is the convenience and ease of calculations. This is the simplest solution for analyzing real estate properties that generate profit as a result of long-term lease. Using this method, you can see the current market conditions, which is especially important, because significant number transactions in a specialized environment are considered specifically from the standpoint of price and future profit.

The considered algorithm is not always advisable to use if there is enough level information about completed transactions. It is useless in situations where the property does not produce a stable profit or has not yet been put into operation, which is a significant disadvantage.