In the article we will consider the capital productivity indicator of fixed production assets, as well as the calculation formula for an investment project.

Capital productivity. Definition

Capital productivity (English. Fixed assets turnover ratio) is a financial indicator that shows the intensity and effectiveness of the use of fixed assets. The capital productivity ratio is used to analyze the financial condition of an enterprise and shows the effectiveness of managing the company's funds when analyzing its dynamics.

Formula for calculating the capital productivity ratio of fixed assets

Capital productivity ratio shows how many products were sold (produced) per unit of production assets. The calculation formula is as follows:

To assess the efficiency of management of a company's production assets, the following indicators are used: , .

Normative value

The capital productivity ratio does not have a single standard value. Each enterprise determines its own acceptable levels of turnover of production assets. Analysis of capital productivity is carried out over several years, which allows us to assess the nature of the trend.

Dynamics of the capital productivity ratio	Financial condition of the enterprise
K fund ↘	Decrease in the financial stability of the enterprise and the efficiency of using production assets and capacities.
K fund ↗	Increased financial stability by increasing the efficiency and effectiveness of the use of production assets.
K fund ≥ K * fund	The excess of the indicator over the industry average values ​​of the coefficient indicates an increase in the competitiveness of the enterprise.
K fund< К * фонд	The enterprise's capital productivity is below the industry average ratio. This is an indicator of a decrease in the competitiveness of the enterprise.

Example of calculating capital productivity

Factor analysis of capital productivity

To determine the strength of influence of various economic factors on the level of capital productivity, factor analysis is used in practice. Let's consider a two-factor, four-factor and seven-factor model of capital productivity.

Two-factor model of capital productivity

The two-factor model shows how the value of the capital productivity ratio is influenced by the structure of production assets.

Where:

F a – active part of fixed production assets;
N – volume of manufactured and sold products of the enterprise;
F – fixed production assets.

Seven-factor model of capital productivity

The model makes it possible to assess the degree of interaction between the level of capital productivity of an enterprise and seven factors: the structure of fixed production assets, the structure of machinery and equipment in active assets, the shifts of machines and equipment, the average cost of a unit of equipment, the duration of a machine shift, and the efficiency of equipment operation. The formula looks like this:

Fmash – average cost of operating machines and machines;
T cm – number of machine shifts;
с – average cost of equipment;
Q d – number of machines and machines;
I – duration of the period under consideration;
T h – the number of hours worked by machines and machines.

Four-factor model of capital productivity

This model allows us to determine the nature of the interaction between the level of capital productivity of the enterprise and the level of specialization, the coefficient of average capacity of the enterprise, the structure of fixed production assets and the turnover of the active part of production assets.

Where:
N oc – the main products of the company;
W – average annual capacity of the enterprise.

Management of capital productivity of the enterprise

Management of capital productivity occurs on the basis of management of revenue and the size of the enterprise's fixed production assets. An enterprise’s capital productivity can be increased based on the following factors:

• Increase labor and equipment productivity.
• Increase equipment utilization.
• Automate production.
• Introduce new technologies and innovations into production and production.
• Develop a distribution network of buyers.
• Increase the quality and competitiveness of products.

The Internal Rate of Return (IRR) is the discount rate at which the net present value is zero. In other words, when discounting cash flow at the IRR rate, the present value of the return on capital is equal to the initial investment.

To find the IRR, the problem of discounted cash flow analysis is solved in reverse order: all positive and negative cash flows of the project are analyzed to determine the discount rate at which their present value is equal to the initial investment.
The internal rate of return method is also called return analysis. Although the term is imprecise and appears in various contexts, the IRR method is regarded as a typical example of impact analysis.
Practical calculation of IRR is usually based on an iterative process of selecting an appropriate discount rate for existing cash flows. Consider a simple project (Table 26):
Table 26
Initial data

For this project, the internal rate of return IRR should transform the following equation into an identity:
The required condition NPV = 0 is achieved at JRR =0.28.
One of the ways to determine IRR is graphical, in which several calculated points are connected by a smooth curve (Fig. 11). IRR can be determined faster and more accurately using a financial calculator or computer.
Returning to the example under consideration, we can say that it is advisable to invest in a given project if the opportunity cost of capital is less than the internal rate of return. If the opportunity cost of capital is less than 28%, NPV is greater than zero and vice versa. In other words, by comparing the IRR to the opportunity cost of capital, we are actually determining whether the project will have a positive NPV. This rule works flawlessly and is completely similar to the net present value rule if the NPV of the project is a constantly decreasing continuous function of the discount rate.

1000
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"2000
In practice, the internal rate of return is quite often used as the main investment criterion. However, there are situations in which this criterion is not correct.
For example, if a project requires expenses not only at the beginning, but also at the end, i.e. if the cash flow changes sign over periods. In this case, we will have as many IRR values ​​as the number of times the cash flow changes sign.
In practice, when calculating IRR, many firms assume that discount rates are the same for all cash flows, and this makes IRR less reliable than NPV.

The capitalization method based on the rate of return on capital, depending on the expected dynamics of changes in the flow of income and expenses, is divided into the discounted cash flow method and the capitalization method using calculation models.

The discounted cash flow method is the valuation of property with arbitrarily changing and unevenly received cash flows, taking into account the degree of risk associated with the use of the object. In this case, the value of the property is determined as the sum of the present values ​​of future income by separately discounting each of the periodic income streams and the projected future value of the property for which it can be sold at the end of the holding period. These calculations use a discount rate - the corresponding rate of return on capital, called the rate of return or rate of return.

The method allows you to take into account the current value of cash flows, which can change arbitrarily and have different levels of risk. General model of the discounted cash flow method

where PV is the current value;

n - number of periods;

I n - income of the n period;

Y - discount rate.

Briefly, this model can be represented as follows:

where PV is the resale price of the object at the end of the ownership period (reversion);

n - holding period;

i is the year of the forecast period;

FV - reversion cost.

The discount rate is otherwise called the rate of return on investment. It characterizes the efficiency of capital investments, takes into account the entire total income (income on investments and income from changes in the value of the asset), and brings the initial investments and the realized economic effect into line with time and risk factors.

Among Russian appraisers, the practice has developed to estimate the period of ownership of an object in the range of 3-5 years.

Advantages of the discounted cash flow method:

· takes into account market dynamics;

· applicable in unstable market conditions;

· takes into account the uneven structure of income and expenses;

· applicable for objects under construction or reconstruction.

However, the method is quite difficult to use, and the probability of error in forecasting is high; the inaccuracy increases in the process of converting forecasted income into current value.

Income that is expected to be received outside the planning horizon is taken into account as income from the resale of the object (reversion) in the last year of the planning period.

In the event of a decline in property value, the return of capital must be taken into account. If the property's income streams change regularly, an adjustment factor must be applied to the capitalization rate.

The model capitalization method is based on the analysis of changing income streams using a general capitalization rate.

The overall capitalization rate is calculated taking into account the market value of the rate of return, the selected recapitalization model, financing conditions, rates of change in income and the value of the object. The main components of the capitalization rate are the discount rate and the yield rate. The discount rate is the required rate of return on invested capital, which is the ratio of the current value of the income received for each period to the cost of capital. The cost of real estate is high and for its acquisition and implementation of investment projects it is necessary to attract borrowed capital. In accordance with this circumstance, the discount rate includes the following components:

a) interest rate - the required rate of return on borrowed capital;

b) rate of return - the required rate of return on equity capital.

The recovery rate reflects the return on invested capital over the life of the property. The reimbursement rate is often called the rate of return on investment. It applies only to the portion of the investment that will be spent during the investment period. Due to the fact that land is not consumed, the reimbursement rate for land ownership is not taken into account.

In most cases, the largest of all components of the capitalization rate is the discount rate. Therefore, the capitalization rate begins to be determined by identifying the rate of return on risk-free, liquid capital investments that do not require large costs for investment management (for example, a deposit in a bank account of a reliable bank). This is the minimum rate that compensates for the depreciation of money over time. Then they add adjustments for risk, liquidity, and investment management. These components make up the discount rate (income rate and interest rate).

Any investor, in addition to income on capital, takes into account the return on invested capital. Therefore, the reimbursement rate is added to the discount rate. Capital recovery is the process of replacing the depleted portion of an initial real estate investment through earnings and reversion.

Reimbursement is the amount of periodic income that is necessary to return the investment during the investment period. The annual rate of reimbursement depends on the rate of change in income from the property, how long it has been earned, and the income from future resale of the property if ownership is not perpetual.

If an even flow of income is expected under perpetual ownership and the value of the fixed capital of the income-producing property remains constant, then the investment recovery factor does not need to be taken into account, and the capitalization rate will be equal to the discount rate.

If during the period under review there is a change in the value of the object, then the capitalization rate is determined as the sum of two coefficients: the rate of return and the rate of recovery of the principal amount. If there is a possible decline in the value of the capital invested in the property, some or all of the capital must be recovered from the current income stream.

The rate of reimbursement, or rate of return on investment, applies only to the portion of the investment that will be spent during the investment period (for land plots it is not taken into account, since the land is not consumed). The recovery rate is necessary to determine the amount required annually to recoup the investment over the holding period. The influence of inflation is reflected in the risk rate (a component of the discount rate), and the compensation rate reflects the effect of depreciation of real estate on the sale price.

The main options for reimbursing the cost of capital: return of capital in equal shares (Ring method), Inwood method, Hoskold method.

The Ring method is based on the fact that capital investment is reimbursed annually in equal installments over the life of the property. The reimbursement rate is calculated as the inverse of the remaining service life. The use of this method is justified for multifunctional real estate with significant wear and tear, residential real estate, and offices.

The method is applicable, in particular, if a steady decrease in net operating income is expected due to increasing depreciation of the property, short-term rentals, and the tenant's precarious financial position.

The Inwood method assumes the return of capital from the recovery fund at the rate of return for the investment, that is, the rate of return of the principal amount is equal to the rate of return on the investment. The recovery fund factor allows you to generate a cash flow that corresponds to the full return of the initial investment.

The Hoskold method is used when income streams flow evenly, in which case the amount of compensation is received every year and placed in a current account at an interest equal to the risk-free rate. The method assumes that the investor does not have available options to reinvest at a rate equal to the rate on the original investment. In this case, in order to secure the return of his funds, the investor forms a compensation fund, reinvesting at the lowest possible rate, i.e. at the risk-free rate.

Unlike the Inwood method, which uses a rate of return on investment, the Hoskold method, which uses a risk-free rate as the basis for capital recovery, is much less commonly used.

Harmonizing the results of assessment approaches

Various methods can be used in the assessment process,

but the decision on the relative importance of cost indicators obtained on the basis of various methods must be determined

a reasonable judgment of the appraiser, which is made by weighing the values ​​determined using two or more methods.

At the final stage, when agreeing on the results of the value of the valuation object, obtained on the basis of three approaches to valuation, it is necessary to carry out:

* checking the received data on the value of the cost;

* analysis of assumptions and limiting conditions caused by

completeness and reliability of the information used;

* derivation of the final value of the cost.

Deciding which cost estimates to give more weight to and how each method is weighted against the others is key in the final stage of the valuation process.

There are two basic weighing methods:

Mathematical weighing method;

Subjective weighing method.

The mathematical weighting method uses percentage weighting using the formula:

where n is the total number of assessment methods used;

i -- assessment method;

V i -- assessment results;

W, -- the weight (significance) of the results.

With subjective weighting, the goal is the same as with the mathematical weighting method, the goal is to arrive at a single estimated value, but this approach does not use percentage weighting. The evaluation conclusion is based on an analysis of the advantages and disadvantages of each method, as well as on an analysis of quantity and quality

data in support of each method. The professional experience and judgment of the appraiser are at the forefront.

To determine the relative weight of the results obtained within each approach to real estate valuation, the following factors must be taken into account:

b Degree of compliance of each of the applied approaches:

Purpose of the assessment;

Objectives of the assessment;

Functional purpose of the object being assessed;

Evaluable rights.

b What is the degree of reliability and sufficiency of the initial data used in each of the approaches.

b What is the preference of each approach from the point of view

market characteristics and location of assessment objects.

b What is the reliability of the calculations and analysis procedures carried out in

approaches used.

b What is the share of expert assessments and judgments in each

of the above approaches.

Taking into account all these factors makes it possible to weigh and ultimately draw a final conclusion.

Capitalization method based on rate of return establishes (using the rate of return on capital as the discount rate) the relationship between the values ​​of net operating income calculated for each year of the entire forecast period, and the cost of reversion at the end of the last year of the forecast period with the cost of the object.

The method includes a number of techniques that differ in the choice of the type of capitalized income and the method of capitalization:

• direct discounting techniques;
• modeling techniques;
• mortgage investment analysis techniques.

Direct discounting techniques provide determination of the value of a property through discounting the flows of net operating income (I O) and reversion V On using local (for periods) and average values ​​of the general rate of return Y O:

The average value of the general rate of return is determined by processing market information about the profitability of investment projects related to the acquisition and profitable use of objects, or using information about the profitability of alternative projects that are closest to the type of objects being assessed in terms of risk level.

To determine the average value of the total rate of return Y O, the following techniques are used:

• cumulative construction technique;
• comparison technique with alternative projects;
• sales comparison technique;
• market data monitoring technique.

Discounting technique with summation of risks (cumulative construction technique) consists of summing up values ​​that reflect the degree of risk of a given project. The general structure of the construction is as follows:

Where Y RF is the risk-free rate, which includes the non-inflationary component and the value of the inflation index; Y R – risk premium, which includes a premium for the following types of risks: physical, legal, economic, financial and social, both external (country risk) and internal, with the exception of the premium for the risk of low liquidity and the premium for risks associated with financial management , which are isolated in order to emphasize the distinctive feature of real estate from other financial instruments; Y L – premiums for the risk of low liquidity; Y FM – premiums for risks associated with financial management

Example 14. Determine the value of the property using the discounting technique with summation of risks, if it is known that: the owner intends to use the property for his own purposes for 3 years, after which he will resell it for 4,500 thousand rubles; net operating income from the valuation object is determined in the amount of 910 thousand rubles, 950 thousand rubles, 990 thousand rubles. respectively for the first, second and third years of ownership of the object; risk-free rate - 0.03; country risk premium - 0.06; premium for physical risks - 0.025; premium for economic risks - 0.015; premium for social risks - 0.03; premium for low liquidity risk - 0.04; premium for risks associated with financial management - 0.03.

1. Let us determine the average value of the general rate of return:

Technique for comparison with alternative designs consists of searching the financial market for investment projects with a similar degree of risk for subsequent adjustment of their rate of return in relation to real estate investments.

In this case, for the value of the general rate of return Y O, a range of possible values ​​is determined with boundaries below Y 1 and above Y 2:

Sales comparison technique consists of analyzing data on completed purchase and sale transactions in order to reconstruct the investor’s assumptions regarding the future benefits of owning real estate. Based on the project's cash flow pattern, the project's internal rate of return is determined.

Market Data Monitoring Techniques consists of analyzing historical market data in order to determine current prospective values ​​of profit rates. In this case, one should use correlations between trends in changes in the profitability of investments in real estate and trends in changes in other financial market instruments.

Model techniques provide the determination of the market value of the entire property for relatively simple special cases of capitalization of net operating income that does not change over periods, and the value of the reversion cost associated with the desired value by predicting its change over time:

Where d n = 1/(1+ Y O) n is the discount factor, and n = 1/(1- d n) n is the current value of a unit annuity.

In this case, the same general rate of return is used for all periods, determined similarly to the value of the general capitalization ratio:

Where SFF O = 1/S On is the compensation fund coefficient, S On = 1/(1+Y O) n –1 is the future value of a single annuity, Δ O = (V On – V O)/ V O is the value of the relative increase in the value of the object.

This group includes:

• equipment excluding depreciation;
• full depreciation techniques;
• linear depreciation techniques.

Equipment without depreciation applies in two cases: either there is an infinite income stream (SFF O >0), or the income stream is finite, but the sale price of the object is equal to the initial purchase price (Δ O =0), i.e. initial investment.

The value of such real estate is determined by dividing the net operating income by the appropriate rate of return (12).

Example 15. Determine the value of a property using modeling techniques without taking into account depreciation, if it is known that: the owner intends to use the property for his own purposes for 3 years, after which he will resell it for the purchase price; net operating income from the valuation object is determined in the amount of 910 thousand rubles. for each year of ownership of the object; the rate of return on capital is determined at 0.203

Let's determine the value of the property:

thousand roubles.

Full cushioning techniques is used in cases where operating income provides not only the formation of income on capital, but also a full return of capital (Δ O = -1, R 0 =Y 0 + SFF O).

As a result, (26) takes the following form:

To calculate the compensation fund factor (SFF O), the rate of return characteristic of the project being evaluated (Inwood technique) or the risk-free rate (Hoskold technique) is used.

Example 16. Determine the value of the property using the Inwood model full depreciation technique and the Hoskold model full depreciation technique, if it is known that: the owner intends to use the property for his own purposes for 3 years, after which he will resell it for the purchase price; net operating income from the valuation object is determined in the amount of 910 thousand rubles. for each year of ownership of the object; the rate of return on capital is set at 0.10; The risk-free rate is set at 0.06.

1. Inwood technique:

1.1 Let’s determine the overall capitalization ratio:

1.2 Let’s determine the value of the property:

thousand roubles.

2. Hoskold technique:

2.1 Let’s determine the overall capitalization ratio:

2.2 Let’s determine the value of the property:

thousand roubles.

Linear depreciation techniques used to determine the present value in cases where both income and the value of real estate change in a known regular manner.

To account for changes in the value of an asset, the basic Ellwood formula is used:

Where A is the adjustment amount.

Moreover, if the value of the object decreases, then adjustment A has a “+” sign, and if the cost increases, then the adjustment will have a “-“ sign.

The numerical value of the adjustment is determined by multiplying the relative change in value (Δ O) by the compensation fund factor (SFF O), and the general formula for the capitalization ratio takes the form (26).

Example 17. Determine the value of a property using model linear depreciation techniques, if it is known that: the owner intends to use the property for his own purposes for 3 years, the value of the property will decrease by 12% during the ownership period; net operating income from the valuation object is determined in the amount of 910 thousand rubles. for each year of ownership of the object; the rate of return on capital is set at 0.10.

1. Determine the value of the relative increase in the value of the object:

2. Let’s determine the overall capitalization ratio:

3. Determine the value of the property:

thousand roubles.

Mortgage investment analysis techniques provide determination of the value of real estate taking into account changes in its value and income, as well as taking into account financing conditions. There are two techniques for mortgage investment analysis:

• technique of mortgage investment analysis with discounting;
• model analysis technique (Ellwood technique).

Technique of mortgage investment analysis with discounting is based on adding the principal amount of the mortgage (V M) with the discounted present value of future cash receipts and proceeds from the resale of the asset:

Where d En = 1/(1+ Y E) n is the discount factor, a En = 1/(1- d En) n is the current value of a unit annuity, calculated for m periods at the rate of return on equity capital, Y E is determined by the same techniques , the same as the general rate of return, I E = NOI - DS - the amount of income on equity capital, V En = V On - V Mn - the cost of reversion for equity capital, defined as the difference between the total cost of reversion (V On) and the balance of loan payments ( V Mn).

Example 18. Determine the value of the property using the technique of mortgage-investment analysis with discounting, if it is known that: the owner spent 3,400 thousand rubles on the purchase of the property 2 years ago; a loan in the amount of 1,000 thousand rubles was received for the purchase of real estate. at 13% per annum for 6 years (annual debt service payment 250 thousand rubles); the owner intends to use the property for his own purposes for 3 years, after which he will resell it for 4,000 thousand rubles; net operating income from the valuation object is determined in the amount of 910 thousand rubles. for each year of ownership of the object; the rate of return on capital is set at 0.10.

1. Determine the loan balances at the time of assessment (3rd year of the loan) and at the end of the holding period (5th year of the loan):

Thousand rub.

Thousand rub.

2. Determine the value of the property:

Thousand rub.

Model analysis technique (Ellwood technique)

This technique is used for special cases of constant income and rates of return. This technique is based on a formula for calculating the overall capitalization ratio:

Where r O is the basic capitalization ratio, which takes as a basis the investor’s requirements for the rate of return on equity capital before adjustments for changes in income and property value. If income and property values ​​do not change, the base capitalization rate will correspond to the overall capitalization rate; P=[(l+Y m) N -1]/[(l+Y m) n -1] - the share of a self-amortizing loan paid by the end of the nth period, with a total term of the loan agreement equal to N years (see. above), Y m is the effective interest rate on this loan.

List of used literature:

1. Ozerov E. S. Economics and real estate management. St. Petersburg: Publishing house "ISS", 2003 - 422 p. – ISBN 5-901-810-04-Х
2. Vinogradov D.V. Discount rate: essence, methods of determination. // Encyclopedia of valuation "Market value" - MARKETVALUE.RU, 2006

4.6 Market (comparative) approach to assessing the value of real estate

The market (comparative) approach is a set of methods for estimating the value of a real estate property, based on comparison of the object of assessment with similar real estate objects for which information is available on the prices of transactions with them.

The initial prerequisite for applying the market approach to real estate valuation is the presence of a developed real estate market. This method is based on the following principles of real estate valuation:

• the principle of supply and demand (there is a relationship between the need for a property and the limited supply of it);
• principle of substitution (an informed, reasonable buyer will not pay more for a property than the purchase price (offer) in the same market for another property that has similar utility.).

The essence of the market approach to assessing the value of real estate is to form a conclusion about the market value of an object based on processing data on the prices of transactions (purchase and sale or rental) with objects similar (analogous) to the object of assessment based on a set of pricing factors (objects of comparison). This means that the concept of market value essentially coincides with the concept of equilibrium price, which turns out to be a function of only the quantitative characteristics of an exhaustively complete set of price-forming factors that determine supply and demand for objects of comparison.

Elements and units of comparison. The number of comparison elements is very large, the number of their combinations is infinitely large, as a result one has to limit oneself only to those objectively controllable factors that affect transaction prices in the most significant way.

When studying the transaction market, the characteristics of the consumer properties of the object itself and the environment of its functioning are considered as price-forming factors (objects of comparison). In a comparative analysis of transactions, only those factors are studied by which the objects of comparison differ from the objects of evaluation and from each other. In the process of research, an exhaustive set of such factors is identified and the change in each factor from this set is assessed in monetary units.

Since the total number of pricing factors for any real estate property is very large, in the research process, through sensitivity analysis, factors are excluded from consideration, the change of which has a negligible impact on the change in the transaction price. Nevertheless, the number of factors whose influence must be taken into account turns out to be significant. To simplify the analysis procedures, the remaining factors are grouped and in this case the mentioned groups can be considered as elements of comparison. Table 4 provides a list of such groups, as well as comparison elements from these groups recommended for use in the analysis.

Table 4 Comparison elements taken into account when adjusting prices

Group of factors	Comparison elements for sales transactions
1. Quality of rights	1.1. Encumbrance of the object with lease agreements 1.2. Easements and public encumbrances 1.3. Quality of rights to a land plot as part of an object
2. Financing terms	2.1. Preferential lending by the seller to the buyer 2.2. Cash equivalent payment
3. Special conditions	3.1. Presence of financial pressure on the transaction 3.2. Non-market relationship between the sales price and the rental rate 3.3. Promise of subsidies or development benefits
4. Market conditions	4.1. Price changes over time 4.2. The difference between the offer price and the transaction price
5. Location	5.1. Prestige of the area 5.2. Proximity to centers of business activity and life support 5.3. Accessibility of the object (transport and pedestrian) 5.4. Quality of the environment (recreation and ecology)
6. Physical characteristics	6.1. Characteristics of the land plot 6.2. Dimensions and materials of buildings 6.3. Deterioration and need for repairs of buildings 6.4. Condition of the surrounding buildings
7. Economic characteristics	7.1. Opportunities for resource saving 7.2. Compliance of the object with the NNEI principle
8. Service and additional elements	8.1. Provision of communications and utilities 8.2. Availability of parking and (or) garage 8.3. Security system status 8.4. Availability of equipment for business

Let's consider the given comparison elements in more detail.

1. The quality of rights for analogous objects and the object of evaluation is associated with the degree of encumbrance of the latter with private and public easements, leading to a decrease in the value of the encumbered object in comparison with the object of full ownership.

1.1. Encumbering an analogous or appraised object with a lease agreement with rental rates that are not consistent with the dynamics of changes in market conditions during the period of validity of the lease agreement may lead to a decrease in income from the operation of the acquired object in comparison with the market level.

If such a reduction concerns an analogue object, then the transaction price with it is adjusted upward. If the analogous object is not encumbered by such a lease agreement, and the assessed object is leased on unfavorable terms, then the transaction price for the analogous object is adjusted downward.

1.2. The rights of ownership and use of an analogous object or an object of evaluation may be limited by private or public easement, as well as other encumbrances.

Any of the above restrictions may result in a decrease in the value of the property. Consequently, if the encumbrance concerns a similar object, then the price of the latter is adjusted upward. On the contrary, if the possibilities of using the valued object are limited, then the price of the analogous object is reduced by the amount of the adjustment.

1.3. The difference in the qualities of the right to a land plot as part of an analogous object or an object of assessment appears in cases where:

• the owner of the building during the transaction transfers to the buyer not the right of ownership, but the right to lease or other property right to the land plot;
• there is or is no ban on the subsequent sale of the object without changing (or with changing) the rights to the land plot.

In this case, the adjustment can be assessed by capitalizing changes in land use payments. Other cases of complications or prohibitions can only be taken into account on the basis of a comparative analysis of transactions and expert assessments of the contribution of specific features of the encumbrance.

2. When analyzing the terms of financing, the subjective contractual terms of settlements for a transaction that took place for an analogue object and planned for the evaluation object are considered. The following options are possible:

2.1. The seller credits the buyer for part of the payment for the purchase under conditions different from the conditions on the capital market (the interest rate on the loan is lower than the market one) or provides him with an interest-free deferment of payments.

2.2. Payment for a transaction with a similar object is made in whole or in part not in money, but in a cash equivalent (the amount of cash involved in the transaction is reduced), including by: transferring a package of securities, including mortgages; transfer of material resources.

In this case, the market value of the mentioned means of payment is assessed and it is the amount corresponding to this value (and not the amount specified in the real estate purchase and sale agreement) that is considered the price (or the corresponding part of the price) of the transaction.

3. The group of factors called conditions of sale includes other subjective conditions of the transaction agreement, external to the object and considered if they differ from the conditions provided for by the definition of the type of value being assessed.

3.1. Financial pressure from circumstances related to bankruptcy or the sale of obligations leads to a forced acceleration of the transaction, i.e. the exposure time of the object on the market is obviously reduced compared to the market marketing period. In this case, the sale is made urgently by reducing the price.

Taking into account the influence of financial pressure on a transaction of family ties, partnerships and other relationships is possible only at the level of expert assessments based on an analysis of the real situation. Most often, such assessments are difficult to make, and transactions with similar objects burdened with this type of pressure are excluded from consideration.

3.2. Taking into account the impact on transaction prices of non-market relationships between rent and transaction price is necessary in cases where the buyer and seller are connected by purchase and sale and rental relations at the same time.

A common situation is where the buyer gives permission to the seller to rent the premises being sold (in whole or in part) for a long time after the sale. To reduce tax payments, the parties agree on a simultaneous reduction (against market prices) of the purchase and sale price and contract rental rates. An adjustment to the transaction price of an analogue object can be made based on the condition that the seller credits the buyer.

These elements of comparison also include the case of the sale of an analogue object by the lessor to the lessee on the terms provided for by the option, the terms of which do not correspond to market conditions on the date of sale.

3.3. The presence or prospect of receiving government or other subsidies for infrastructure development or the possibility of preferential lending for the development of an object can additionally stimulate buyers, ensuring that the transaction price exceeds the market-based value. The amount of the adjustment can be estimated based on the assumption that the subsidies will reduce the buyer's future contribution to infrastructure development by this amount. Such an assessment is carried out by comparing specific data on the rates of allocation of funds for infrastructure in the area where the assessment object is located and the analogue object. When promising preferential lending, the adjustment is assessed based on the current value of the difference between annual payments for preferential and market lending.

4. Market conditions are associated with changes in the relationship between supply and demand, including due to changes in priorities for the functional use of objects of the type being assessed. These changes also affect the difference between the offer price and the transaction price.

4.1. Market conditions determine the change in real estate prices over the period of time from the moment of the transaction with a similar object to the date of valuation. Adjustments are subject to differences in market prices for real estate objects that have a purpose similar to the object of evaluation, but were previously transferred from the seller to the buyer at a time “distant” from the moment of evaluation by more than one month. An approximate estimate of the amount of adjustment for the time of a transaction with a similar object is carried out on the basis of an analysis of changes over time in the inflation index, prices for construction products, as well as prices for real estate transactions in various market segments.

4.2. If the offer price for a similar property is known, it is adjusted by making an adjustment (usually downward), determined on the basis of expert assessments of real estate market operators.

5. Location factors include:

5.1. The prestige of the area where the object is located, as a social factor, characterized by the concentration of famous users or objects in the microdistrict, including historical and architectural monuments, protected areas, and other attractions.

5.2. Its remoteness from the center of business activity and life support (situs), including from administrative, public, financial, trade, warehouse complexes, and sources of resource supply.

5.3. Transport and pedestrian accessibility of the property, including its proximity to main and auxiliary highways, car parking and public transport stops.

5.4. The quality of the immediate environment, including the type of development and architectural features of buildings, proximity to a recreational area - forest, park, lake, river, as well as distance from sources of environmental discomfort - landfills, chemical and other hazardous industries.

The influence of differences in all factors of this group on the prices of transactions with analogous objects and objects of evaluation is taken into account when adjusting the chain of transactions using comparative analysis techniques based on market data.

6. The land and improvements have physical characteristics.

6.1. The characteristics of the land plot include: size, shape, topographic and geological parameters, the level of preparedness (getting rid of vegetation and unevenness) of the land plot and the quality of the soil cover. At the same time, the most important topographic parameters of the site are surface unevenness, the presence of slopes, hills, ditches and rock formations.

Of the geological parameters, the strength characteristics (bearing capacity) of the earth's crust rocks under the site, the presence and regimes of groundwater, deserve the greatest attention.

Information about the possible occurrence of mineral resources (as a source of possible encumbrance in the future) is also useful.

6.2. Among the characteristics of improvements, the main attention is paid to the size of the building, including construction volume, number of storeys and floor number of the premises. The dimensions of the premises are taken into account, including the total area of ​​all premises, the area of ​​the main, auxiliary and technical premises, and the height of the ceilings. The type and quality of materials from which structural elements are made have a significant impact on transaction prices.

6.3. Important factors include: the condition of structural elements, the need for their reconstruction and repair, the appearance of the building (architectural style) and the condition of the facade, the orientation of the entrance (to the courtyard or to the street).

6.4. In addition to the characteristics of the building itself, the characteristics of the environment are also significant: the type and architecture of the surrounding buildings, the condition of the facades of buildings and the improvement of the territory, soil and air pollution.

Adjustments for differences in most factors in this group are made based on comparisons of transaction prices. Adjustment for differences in the size of premises and building volume is carried out on the basis of data on the market value of a unit of area or unit of volume of a building of a given type. Adjustments for differences in the area of ​​land plots within the analogous object and the object being assessed are determined on the basis of data on the market value of a unit area of ​​the land plot. When assessing and making adjustments to the prices of transactions with analogous objects that have dimensions different from the dimensions of the object being assessed, it will be useful to use techniques for adjusting unit prices.

Amendments related to the need for repairs are calculated based on the cost of repair work with the addition of the entrepreneur’s profit, calculated according to the rate of return on capital invested in new construction.

7. Economic characteristics include characteristics that affect the profitability of an object.

7.1. Essential to the economics and value of a property are the opportunities to save resources.

The profitability characteristics of an object depend on the ratio of the usable area to the total area of ​​the premises: the greater this ratio, the greater the ratio of income to the costs of operating the object and the smaller the share of the amount to be reserved for the reproduction of the object (return of capital) in the net income from leasing the object . Adjustment for the difference in this characteristic for an analogue object and the object being assessed can be made by capitalizing overexpenditures on taxes, insurance, operating, utility bills and other operating expenses for “excess” square meters of auxiliary and technical premises.

The inability to control (in the absence of cost meters) and minimize losses of heat and other resources (due to the design features of improvements) leads to an increase in the operating expense ratio, as well as a decrease in net operating income and value. The loss of value due to the absence of meters can be estimated as the cost of installing them.

Loss of value due to design or design deficiencies, leading to differences in resource costs for the object being assessed and the analogue object, are assessed by the difference in operating expense ratios.

7.2. Pre-sale and post-sale use of a comparable property may not fully comply with the best and most efficient use (BUE) principle. For example, when fulfilling the mandatory requirement that the set of functions implemented at the facility comply with this principle, the facility’s potential for generating rolling or other income is often not fully realized, and additional incentive measures for tenants are not used to reduce losses from unpaid loads and non-payments. This circumstance should be taken into account by adjusting the price of a transaction with a similar object with a market-based adjustment to the amount of effective gross income.

8. The presence or absence of necessary or desirable service elements, including additional non-real estate components, may have a significant impact on the transaction price.

8.1. The absence or deficiencies of telephone lines, central or local heating systems, gas, water and energy supply systems, sewerage systems lead to a decrease in the value of the property. If these shortcomings exist in a similar object, the transaction price should be adjusted upward. If these shortcomings are inherent in the valuation object, then the transaction price with a similar object is adjusted downward. If there are trunk communications of the appropriate profile near the object, the amount of adjustment is determined by the cost of connecting to these communications, taking into account the profit of the entrepreneur. In the absence of main communications, adjustments are determined by the costs of creating autonomous systems for providing the facility with resources and waste removal (also taking into account the entrepreneur’s profit).

8.2. For the implementation of most income-generating functions, a very important condition is the availability of parking for vehicles. In this case, the reference option is considered to be when the minimum number of parking spaces is not less than the maximum possible. Any deviation from the “standard” requirement leads to the need for a corresponding adjustment of the transaction price (usually by capitalizing the buyer’s future costs for the permanent or temporary lease of part of the adjacent territories).

8.3. The presence or absence of technical security systems at the site (in sufficient quantity and proper quality), as well as contractual relations with a reliable security service, have (with rare exceptions in atypical cases) an impact on the transaction amount. In this case, the transaction price can be adjusted by adding (excluding) costs (with the entrepreneur’s profit) for installation (repair, replacement) of equipment and searching for a partner from among companies specializing in security.

8.4. Often, the sale price of a similar property includes items of property that are not elements of the real estate property: trade or office equipment, personal property of the owner or manager (first option). Sometimes these types of elements end up as part of the real estate that is the subject of assessment (second option). In such cases, the adjusted transaction price (calculated price of the valuation object) is found by reducing the price (in the first option) or increasing (in the second option) the price of the transaction with a similar object for calculation.

The implementation of factors in this group leads to an increase in rental rates. If these elements are inherent only to the analogue object and are not realizable for the valuation object, then the rental rate of the analogue object is subject to downward adjustment. The amount of adjustments is determined by a comparative analysis of market transactions under lease agreements, as well as estimates of additional costs for the purchase of services by tenants independently, “outsourced”.

Sequence of making adjustments carried out as follows:

• adjustments from the first to the fourth element of comparison are always carried out in the specified order; after each adjustment, the sales price of the comparable object is recalculated (before moving on to subsequent adjustments);
• subsequent (after the fourth element of comparison) adjustments can be made in any order; after each adjustment, the sales price of the comparable object is not recalculated.

Units of comparison for the analogue object and the object of evaluation(specific characteristics) are used to counter the noticeable shortage of reliable data on market transactions.

The following units of comparison are distinguished:

1. for a land plot without improvements, specific characteristics (unit prices) are used:

1.1. price per unit area of ​​land:

• square meter - for building plots in a populated area;
• “weaving” (hundred sq. m) – for plots for gardening or individual housing construction outside the populated area;
• hectare (ten thousand sq. m) - for agricultural and forest land;

1.2. price per unit of length (linear meter) of the border of the site along the “red line” (transport or pedestrian highway) - for commercial, warehouse, industrial facilities, the success of which business depends on the accessibility of the facilities for visiting by their buyers and users, for the delivery and dispatch of goods ;

1.3. price for a plot of area standard for this type of functional use;

2. for a land plot with improvements, as a specific characteristic, the specific price of a unit of measurement of the quantity of the pricing factor for the property component that makes the greatest contribution to the cost of the entire object is taken. If the cost of a building is obviously greater than the cost of a land plot, then the unit price for the building is used as the main unit of comparison for the entire object:

2.1. price per unit of useful (rental, total) building area (sq. m);

2.2. price per unit volume of the building;

2.3. price for an apartment or room;

2.4. the price for one element of an object that generates income (a seat in a restaurant or theater, a place or a room in a hotel);

There are no return rates from investment projects required by investors in Russia. There are examples of projects with return rates of 200% and higher. However, even this does not guarantee the project will receive investment.  

A 24-year-old young man has the opportunity to complete a one-year course worth 12 thousand rubles. and take a higher position. How much higher should the salary in a new position be for a young man to consider training appropriate, if his current annual salary is 21.6 thousand rubles? and he considers the return on investment rate of 16% per annum acceptable for himself. In the new position, the young man plans to work until retirement, i.e. 40 years. How will the answer change if a 54-year-old man is considering such a training opportunity?  

Calculating r using this complex formula is extremely difficult, and therefore estimative methods are usually adopted. In practice, we consider different rates of return and find them by comparing the current value with the amount of the original investment. To obtain the best estimate of (r), we consider some value of r that gives a small positive net present value, and a second value of r that gives a small negative net present value. Using graphical methods, we can then determine the internal rate of return between these two values ​​that gives a zero net present value.  

Model outcomes are found for each of the other 8 factors. The first 4 factors (market analysis) give us information about the annual sales volume, factors 7 and 8 provide data on current and fixed costs for the year. Together, these 6 factors allow us to calculate profit for the year. By combining the total values ​​of these 6 factors and the total values ​​of the required investment, period. useful life of the equipment and the residual value of the project, we obtain sufficient information to calculate the return on investment made for these results. Thus, the computer simulates the final values ​​for each of the 9 factors, and then, based on the simulated values, we calculate the return on investment. The process is repeated several times, each time we get a combination of values ​​for 9 factors and a return on investment for this combination. When a sufficient number of tests have been carried out, the rate of return can be represented graphically in the form of a frequency distribution, as shown in Fig. 14.8.  

This cost is the most difficult to calculate. Theoretically, it can be defined as the minimum rate of return on that part of the project that is financed by issuing shares, necessary to ensure that the market price of the shares remains unchanged. If a company invests money in projects that will produce returns that are less than required, the market price of the shares will suffer in the long run.  

It is reasonable to link industry funding to the volume of information received (expressed, for example, in bits). The current ratio of funds allocated for geophysical research and the information content of the results can serve as an approximate rate of return on investment. Having determined the numerical value of this norm, it is possible to compare the results obtained with real costs. Profit is subject to maximization - the difference between calculated (expressed by the volume of research funding based on the magnitude of the predicted results) and real research costs.  

Since the development of the territory usually takes some time and the sales proceeds are not received at a time, the real value of the land mass is determined by discounting the flow of net sales proceeds, taking into account the frequency of receipts and the expected rate of return of the project.  

The present value of the land mass, taking into account the uniform receipt of net income over 4 years and a return rate of 10%  

Capitalization by rate of return  

The rate of return capitalization method involves modeling future income streams several years in advance, calculating the value of the property at the end of its ownership period, and discounting the cash flows of income and resale proceeds of the property to its current value.  

Capitalization method based on rate of return  

In the rate of return capitalization method, the recalculation of future cash flows into present value is performed at a specific value of the rate of return corresponding to the risk of investment in a given type of real estate. Within the framework of this method, calculation models are distinguished  

Since the rate of return method of capitalization involves taking into account both the return on capital and the return of capital, the cost of reversion must be taken into account when forecasting income streams.  

To correctly understand the essence of the calculations being made, one should dwell on the difference between the concepts capitalization rate and discount rate. Firstly, the first concept refers to rates of income, and the second to rates of return. Secondly, the capitalization ratio reflects the relationship between net operating income and property value and does not separate income from capital and return of capital, and the discount rate is only a compound interest rate to calculate the present value of future income.  

Example 5.9. It is required to evaluate a real estate property, the income from which in the 1st year amounted to 300,000 rubles. It will be in operation for 5 years, the return rate is 10%.  

In valuation theory, other methods have been developed for determining the value of real estate within the framework of the income approach using the capitalization method based on the rate of return. First of all, they relate to cases of attracting mortgage loans when purchasing real estate. Since such cases practically never occur in Russian practice, these methods are not discussed in detail in this work.  

A, who works as a junior accountant with an annual salary of $48,000, has the alternative of completing a one-year training course costing $20,000 and accepting a position as a senior accountant. How much higher should the salary of a senior accountant be for training to be appropriate if A considers 15% per annum an acceptable rate of return on investment?  

The internal rate of return (IRR) on any investment can be defined as  

As the level of diversification increases, the rate of return increases and then decreases along a convex curve. Over an 18-year period, the record for highest operating efficiency was held by companies producing products related to distribution and technology (RMT). This group includes Sony and Matsushita. Next come companies with a dominant product (D). Nissan and Toyota belong to the S group, and Teijin and Bridgestone Thayer belong to the  

Hierarchy of goals. In accordance with their interests, persons who have one or another relationship with the enterprise form their goals. These goals are multidimensional, multi-level, subordinate and can be duplicated in the sense that the same goal can meet the interests of different categories of persons. These goals include increasing personal well-being, reliability