The problem of applying the direct capitalization method. Direct capitalization method. Generalized Inwood model. Calculation of the different components of the risk premium

The direct capitalization method is used to calculate the cost of the production complex (enterprise, workshop, line section) and involves the sequential solution of three tasks:

Determination of the average annual (average monthly) income from the ownership of the complex (CHOD);

- determination of the coefficient (rate) of capitalization (TO)",

- determination of the cost of the complex (FROM) based on the average annual (average monthly) net income and capitalization ratio according to the formula:

Coefficient (rate) of capitalization - the interest rate used to convert income into market value objects.

If investments were made in the estimated complex during the billing period, the formula for calculating the cost will be as follows:

where CHOD - net operating income;

TO- coefficient (rate) of capitalization;

AT- investment in property improvement.

An approximate list of income and expenses taken into account when calculating net operating income is given in the table:

	Indicators	Designation
	Income
1.	Income from the operation of property in the billing period, including:	D 1.
1.1.	Revenue from sales of products (services)	D 1.1.
1.2.	Income from rent (leasing)	D 1.2.
1.3.	Use of accumulated income for investments and repayment of loans	D 1.3.
2.	Proceeds from the sale of property	D 2.
	Total income D=D1+D2	D
	Expenses
1.	Expenses associated with the operation of the property during the billing period, including:	R 1.
1.1.	Production costs	R 1.1.
1.2.	Rental (leasing) maintenance costs	R 1.2.
1.3.	Depreciation deductions	R 1.3.
1.4	Taxes attributable to financial results	R 1.4.
2.	Expenses for the purchase or improvement of property	R 2.
	Costs in general P=P1+P2	R

Net operating income from the production complex is calculated using the formula:

CHOD \u003d D-R,

Where D - income in general;

R - expenses in general.

Of all the existing methods for determining the coefficient (rate) of capitalization, two are used in determining the cost of machinery and equipment:

1) market squeeze method (comparative sales analysis)- the capitalization ratio is determined on the basis of the analysis of market data on net income and the cost of objects for the sales that took place.

The capitalization ratio is determined by the formula:

where TO - general coefficient (rate) of capitalization;

CHOD - the value of net operating income for each sold object;

C P- Selling price.

This method the most preferable, simple and accurate, but it requires reliable and complete information about the objects of comparison. At the same time, it is important that the methods for assessing income for the objects being compared coincide with the method applied to the object being valued.

2)Summation method (cumulative construction) - capitalization ratio is defined as the sum of the rate of return (interest rate) and the rate of recovery (return) of capital.

K \u003d p + Kf.

Rate of return (interest rate) R consists of 4 parts:

Net interest (risk-free rate). Determined based on the price of securities government loan or bank deposit rates the highest category reliability;

Additional risk (risk compensation rate). The greater the risk of investing capital in a particular industry, the greater the interest rate;

The load of investment management (investment management). The more risky and complex the investments, the more competent management they require;

Lack of liquidity (low liquidity) is a risk associated with the possibility of losses during the sale of the object of assessment due to insufficient development or instability of the market. To calculate it, it is necessary to analyze the dynamics of prices in the machinery and equipment market, as well as time factors that determine the dynamics of sales (ie, the average waiting time for a transaction after preparing an object for sale, leading to possible losses of capital).

Capital recovery rate Kf determined by the formula.

The income approach is the most information-provided approach to business valuation in Russia. In addition, the income approach, despite its complexity, is the most powerful and flexible valuation tool. Let's take a closer look at the income approach.

The methods used in the income approach are:

Ё Direct capitalization;

Yo Discounting cash flows.

The direct capitalization method is the calculation of a capitalization ratio that converts future net income into business value.

This takes into account both the net profit itself received from the operation of the facility, received from the business, and the reimbursement of the fixed capital spent on the acquisition of the business.

The capitalization ratio that takes into account these two components is called the general capitalization ratio or net income capitalization rate.

There are several calculation methods overall coefficient capitalization:

Ё direct capitalization method (or direct comparison method);

Ё method of related investments (cumulative method) - borrowed and equity, land, buildings.

The direct capitalization method is based on directly converting net operating income (NOI) into value by dividing it by the capitalization ratio. The concept of NOR is the calculated steady value of the expected annual net income received from the subject business after deducting operating expenses and replacement reserves.

The definition of NOR is based on the assumption that the most typical year of business will be taken as the forecast calculation period.

The calculation of the NPV begins with the determination of the potential gross income (PDV) - the expected total amount of payment from the main activity of the enterprise and payment from additional services that are related to the main activity.

The next step in determining the NOR is to determine the effective gross income (EGI). To obtain the EDI, the estimated losses are deducted from the potential gross income. Since in appraisal activities there are no standards for determining these losses, then the best way to obtain information is to consider a similar business for which there is data over a long period of time, from which it is possible to learn the level of losses in practice.

NPC is calculated as the difference between the value of the EVD and the value of operating expenses (OR). CHOD = DVD - OR.

Operating expenses are called recurring expenses to ensure normal functioning business and income generation. Operating expenses are divided into:

Yo conditionally - constant;

E conditionally - variables (operational);

E expenses (reserve) for replacement.

Conditionally fixed OR include costs, the size of which does not depend on the volume of production. They are determined by the fact that the cost of the company's equipment must be paid even in the event of a stoppage of the enterprise. Fixed expenses include: payment on bonded loans, rent payments, part of the deductions for the depreciation of buildings and structures, insurance premiums, part of which is mandatory, as well as wages to higher management staff and specialists of the company, etc.

Conditionally variable RR include expenses, the amount of which depends on the degree of workload of the facility and the level of services provided. The main conditionally variable costs are the costs of management, utility bills, security, transport, etc.

Replacement costs are calculated as an annual contribution (reserve) to the replacement fund (similar to accounting depreciation).

The most difficult step in business valuation using the capitalization method is the determination of the capitalization ratio (or rate). In the Western classic version, the direct capitalization method provides for capitalization using a coefficient (rate) extracted from market transactions for which prices are known in advance. Practice shows that in Russian conditions it is almost impossible to find such information. As a result, calculating the NRR and capitalization rate becomes a very difficult task.

The essence of the method for determining the capitalization ratio or summation (cumulative construction) is that the risk-free interest rate is taken as the base rate and adjustments for different kinds risks associated with the characteristics of the business being assessed (premium for the risk of investing in real estate, premium for low liquidity, adjustment for investment management, etc.).

The definition of the risk-free rate according to the Western methodology is the rate of return on long-term government bonds. When using this risk-free rate, it is necessary to add a premium for the risk of investing in Russia (country risk) to it.

Thus, the capitalization method has its advantages and disadvantages. The advantage is that this method directly reflects market conditions, as it is analyzed from the point of view of the ratio of income and value. The disadvantage of applying the capitalization method in Russia is:

Ё insufficiency or lack of information about market transactions;

Ё incompleteness or incompleteness of the business (did not reach the level of stable income, suffered as a result of force majeure).

As already mentioned, the value of real estate when using the direct capitalization method is calculated by the formula (7.1), the value N01 in which is determined as a result of the execution of the reconstructed income statement.

Methods for calculating the capitalization rate are selected depending on the specific conditions in which the appraisal object operates. Most significant:

• * information on income and transaction prices based on a representative sample of comparable properties;
• * sources and terms of financing transactions;
• * the possibility of a correct forecast regarding the value of the object at the end of the forecast period.

Consider the existing methods for determining the total capitalization rate.

The method of analysis of market analogues is the main and most correct method for determining the capitalization rate. A knowledgeable rational investor takes into account all the consequences of acquiring real estate. Therefore, the price paid by the investor reflects his requirements for economic characteristics object of investment, among which the immediate (direct) is the capitalization rate. You can guess a lot about what will happen to real estate during the forecast period. Using the capitalization rate relieves us of this process, but only if we have reliable information on current and past sales and rental rates, i.e., a developed and informative market is required (Table 7.2). In this case, important conditions must be met:

• * the most efficient use of comparable objects coincides with that of the object of assessment;
• * financing conditions are typical;
• * the quality of management corresponds to the required;
• * coefficients of losses and operating costs differ slightly;
• * the location and decoration of the object do not fundamentally differ.

Table 7.2 Determination of the value of R0 by the method of market analogues

Index
Sale price, USD
NOI, USD/year
Capitalization rate Weight coefficient Weighted R	0,068	0,023	0,054	0,023
Weighted average R 0 = 16.8% (sum of previous row values)

Weight coefficients reflect the degree of similarity of analogues to the object of assessment in terms of the main pricing factors and are the result of the choice of the appraiser.

DCR Debt Coverage Method -- one of three methods for calculating the total capitalization rate in the case of using borrowed funds. The debt coverage ratio is the ratio of the annual debt service payments DS, calculated from the terms of the self-absorbing loan, to the net operating annual income NOI:

where DS is the annual debt service.

DCR ratio used by lenders as a claim on the borrower investment project if the latter is rated as riskier than other lending options. In this case, the lending institution limits the amount of DCR the minimum allowed value. When using this method, it is assumed that the value of real estate over a period of time will not change or, at least, will not decrease.

According to this method, the capitalization ratio is equal to the product of the mortgage debt ratio t, mortgage constant R m and debt coverage ratio:

Where t=Vm /V ,

Vm - the cost of borrowed funds;

V -- the cost of the object (the entire amount of investment);

mortgage constant, or capitalization rate for borrowed funds.

The parameters used in this method are public banking information (easily accessible). This method is not the main one, but rather is used as a corrective, giving an indicative value of the capitalization rate in cases where market data is not sufficiently reliable.

The method (tied investment is also used if the acquisition of real estate involves borrowed capital. In this case, the value of R 0 should take into account the interests of both equity and borrowed capital. These interests are expressed as the respective capitalization rates R e and R m .

The total capitalization rate in this method is determined as a weighted average of the above financial components with coefficients equal to the shares of debt and equity, respectively:

R o \u003d mR m + (1-m) R e.

The value of the capitalization rate for equity is determined from data on comparable properties by dividing the value of income before tax by the value of equity. This method is otherwise known as the investment group method and is applied on the assumption that the investor retains the property for the life of the self-absorbing loan and the value of the property at the end of the ownership period is zero.

EXAMPLE 2

The appraiser received the following information on the analogue object: t= 0.6; return on equity I e = $15,000/year; cost of own funds V e = 60 $000 Capitalization rate for borrowed funds R m = 15%.

The solution is given in table. 7.3.

Table 7.3 Calculation of the total capitalization rate

The linked investment method for physical components is similar to the linked investment method for financial components. Here, the total capitalization rate is defined as the weighted average between the capitalization rate for land R l and rate for improvement R b

R 0 =LR 1 +(1-L)R b ,

where L is the share of land value in real estate value.

This method is applicable if information on comparable properties allows to accurately determine the capitalization rates for the physical components of the property, as well as the share of components (land, improvements) in the total cost.

The calculation of the total capitalization ratio, adjusted for changes in the value of the asset, takes into account as income on investments, and compensation for changes in the value of the object for the period under review. The return on investment reflects the rate of return, or discount rate, or, more precisely, the final rate of return (final return), by virtue of the fact that the entire period of ownership is taken into account.

There is a functional relationship between the total capitalization rate and the final return:

where D \u003d FV -V / V - share change in value;

D x sff, i, n - a member of the equation that corrects or compensates for the change in value, or the rate of return (in case of loss of value).

This expression is the Ellwood equation, assuming that real estate is invested without borrowing capital. It is assumed that the income is of an annuity nature, and the value of the asset may change in one direction or another. With a decrease in value over the period of ownership, the investor requires that compensation for the lost value occur at the expense of periodic income; an increase in value as a portion of income can be replaced by a present value equivalent in the form of an additional stream of income.

Replacing the change in value with an equivalent periodic income allows, instead of discounting, to use the capitalization rate as a discount rate adjusted for the change in the cost of initial capital to determine the present value. The compensation fund factor sff allows you to generate a cash flow equivalent to the amount of change in the initial cost. This factor represents the periodic contributions to the recovery fund (for loss of value) as a share of the original cost, or to the compensation fund for an increase in value.

If the cost of capital does not change, then in the above expression the value D is equal to zero and income can be capitalized at a capitalization rate equal to the discount rate, i.e. R 0 =Y 0 .

In the case when the income stream is infinite, and the capital is depreciating, the return of capital is provided at the expense of income, and the parameter sff tends to zero. Here the cost is also determined by dividing the annual income by the capitalization rate equal to the discount rate R 0 = Y 0 . When forecasting a loss of value, the return of the initial capital should be ensured by reinvesting part of the periodic income. The basic assumption when a loss of value is forecast is that a uniform periodic income stream contains a return on investment and a return on initial capital. Accordingly, the capitalization rate includes the rate of return on capital and the rate of return, which forms contributions to the capital compensation fund. The original expression looks like

R 0 \u003d Y 0 + sff, i, n,

since D = -1 and the compensation fund must take into account the return of the entire initial capital.

Definition of R0 depends on the conditions under which the compensation fund is formed.

These conditions are dictated by the available reinvestment options. In this case, the Inwood method and the Hoskold method are used.

Inwood method assumes that the compensation fund is formed at an interest rate equal to the rate of return on investment. This method is used for permanent annuity income.

A good illustration of the method is provided by a self-depreciating loan, where the capitalization rate for the loan, i.e. the mortgage constant, is the sum of the interest, which in this case is the rate of return on the amount of the loan, and the fund factor determined by the rate of the loan interest.

A self-absorbing loan, issued for 10 years at 12% per annum, provides monthly payments of $ 1,000. What is the initial loan amount?

EXAMPLE 4

It is assumed that the asset, based on 10% per annum, brings $10,000 in annual income for 5 years, after which it depreciates completely.

The investor purchased this asset on the condition that 10% per annum take into account, in addition to income, the return of the initial capital. What was the price of the asset purchased based on Inwood's assumption?

R o \u003d Y o + sff \u003d 0.1 + sff (5 years, 10%) \u003d 0.1 + 0.164 \u003d 0.264;

Hoskold method assumes that the investor does not have available options to reinvest at a rate equal to the rate on the original investment. .

Suppose an investor has acquired an asset with a significantly higher return than other opportunities, while recognizing the risk to which his investment is exposed. To secure the return of their funds, the investor forms a compensation fund, reinvesting at the lowest possible rate.

This is Hoskold's assumption - the compensation fund is formed at the "risk-free" rate.

Let's change the conditions of the previous problem, taking into account Hoskold's assumptions, assuming that the investor has access to reinvestment at 7% per annum, and the return on the initial investment is 20%.

R0 = 0.1 + sff(5 years, 7%) = 0.1 + 0.174 = 0.274 ;

Formation of a compensation fund with a linear return of capital is done like this. Determination of the capitalization rate by the rate of return and the linear fund of compensation (Ring's method) assumes the return of capital in equal installments during the period of ownership of the asset.

The rate of return in this case is the annual share of the initial capital allocated to an interest-free compensation fund. This share at 100% capital recovery is equal to 1/n, where n is the depreciation time calculated in years.

The expression for the total capitalization rate according to the Ring method is as follows:

Net income attributable to an office building with a remaining term economic life 15 years, equals $25,000 for the 1st year, the rate of return for the object is estimated at 15%. What is the cost of the building? By the end of its economic life, it is completely depreciated. This example is consistent with Ring's assumption of a linear return on capital, which is commonly used when valuing depleting assets, such as those subject to depreciation (Table 7.4).

Table 7.4 Flow reaching the first 5 years (USD)

Table 7.4 shows that a linear return on capital is characteristic of diminishing returns. If the problem was solved by the Inwood method, then the cost would be too high.

In an equity change in value, the rate of return takes into account a partial refund, or compensation, of the original cost, subject to an assumption about the method of compensation.

Real estate, brings in 10 000 dollars of net income. It is assumed that by the time of sale in 5 years, its value increases by 30%, i.e. D = 0.3. The discount rate for such objects is 15%. Calculate the value of the property, assuming that the rate to compensate for the change in value is determined at a rate equal to the rate of return.

R 0 \u003d Y 0 - 0.3 sff \u003d 0.15 + 0.3 x sff (5 years, 15%) \u003d 0.15 - 0.3 x 0.148 \u003d 0.106 (10.6%);

The same conditions as in example 7, but it is assumed that the property brings in 10,000 dollars of net income in the 1st year and the decrease in value is linear (by 30%).

The direct capitalization method is used to calculate the current value of a business if there are reliable historical data to estimate the income of the enterprise. 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 approximately equal current income or the growth rate of future income will be moderate.

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

The preliminary cost of a business object according to the method of direct capitalization of income is determined on the basis of taking into account the annual income of the PR and the capitalization rate K cap according to the formula

It is obvious that the lower the value of the capitalization rate, the greater will be the value of the business object with a constant annual income and vice versa.

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

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

Example 19. Determine the value of the business for the production of products of the type BUT based on the information presented in table. 4.3.

Table 4.3

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

Name of indicator	Meaning
Background information for evaluation
1. The cost of an industrial building, thousand rubles.
2. Useful life of an industrial building
3. Rate of return for an industrial building
4. The cost of a land plot, thousand rubles.
5. Rate of return on land, %
6. Annual volume of production and sales, units.
6. Selling price, thousand rubles.
7. Proceeds from the sale of products, thousand rubles.	48,000 x 1.780 = 85,440
8. Costs of production and marketing of products, thousand rubles.
9. Service life of the production line, years
10. The rate of return of the analogue of the 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%)	3400 x 0.08 = 272
15. Net income attributable to the production building, thousand rubles. (page 1 x page 11)	25600x0.1133 = 2900
16. Net annual income attributable to the production line, thousand rubles. (p. 13 - p. 14 - p. 15)	18 797-272-2 900 = = 15 625
17. Cost of business, thousand rubles.	15 625:0,3004 = = 52 014

Solution

The income in this example is the net annual income from the production and sale of products before taxes, defined as the difference between the revenue from the sale of the planned volume of production and the costs of production and distribution. Given that constituent parts businesses are a production building and a production line, for each component its own capitalization rate was 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 8%) and the remaining service life of 30 years.

Capital recovery (return) ratio for an industrial building:

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

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

Reimbursement ratio for the production line:

Capitalization rate for the production line:

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

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

The cost of the production line for the production of products BUT is determined by the formula

The calculation results are given in Table. 4.3. Based on the calculations, it follows that the projected net annual income from the production line will be 15,625 thousand rubles, while maintaining the considered conditions, the estimated cost of the business will be 52,014 thousand rubles.

Example 20. The entrepreneur plans to install equipment for the production of products that are in demand, the cost of which is 7500 thousand rubles, the useful life is ten years, the maximum daily productivity is 4000 units. products. Based on the analysis of analogue enterprises located in the area, the degree of utilization 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 loading equipment at 65 and 70% may be 30 and 28%. Operating conditions: selling price of a unit of production - 2 thousand rubles; direct material costs for the production of products are 25% of the price; direct labor costs with deductions are 20% of the selling price. To motivate labor, it is expected to increase wages by 3 and 5% if the degree of equipment utilization is 65 and 70%. Annual costs for maintenance and repair - 12% of the cost of equipment. To organize production, you need to rent production room an area of ​​20 m 2. Rent per month - 1.2 thousand rubles / m 2. Other types of expenses are forecast to be 4% of operating income. The risk-free reinvestment rate is 7%. Determine the value of the business and evaluate the impact of the degree of equipment utilization on the value of the business.

Solution

To solve, 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. Efficiency,
3. Probability of loading for new production, Р 3
4. Selling price of a unit, thousand rubles.
5. Number of working days per month, D r, days
6. The number of parts produced per day according to the 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 manufactured products per year, units. (page 6 x page 5x12 months)
8. Operating income for the year by 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. Wages with accruals per year, thousand rubles. (page 8 x 20%)
13. Surcharge 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 deductions, thousand rubles
16. Rent, thousand rubles.
17. Other types of expenses, thousand rubles (4% x x page 8)
18. Direct costs for products, thousand rubles (p. 11 + p. 12)
19. Overhead costs for products, thousand rubles. (page 13 + page 14 + page 15 + page 16 +
20. General expenses for products, thousand rubles (page 18 + page 19)
21. Total costs, taking into account the probability of loading by 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. Forecasted profit before income tax for the option, thousand rubles. (page 8 - page 20)
24. Forecasted profit after deducting income tax, thousand rubles. (page 23 x 0.76)
25. Forecasted profit after deducting 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 deducting income tax, thousand rubles.		216 924+ 171 650 + + 171 189 = 559 763

The ending

Taking into account the possible degree of loading of the equipment, we determine the volume of production per day and per year for each option. Production output per day, taking into account the maximum load Do tah and efficiency factor K u s:

The results of calculations - in table. 4.4 page 6. Output for the 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 "by the formula

where B| - operating income under the first option

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

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

Calculate the total costs per year for each option "using the initial information. The main types of costs:

• direct material - according to the condition, they amount to 25% of the price or of operating income (p. 11);
• wages - 20% of the 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% (p. 13);
• maintenance and repair costs are 12% of the original cost:

Depreciation deductions are calculated on a straight-line basis, taking into account the initial cost and useful life (10 years):

N am \u003d 1: T= 1: 10 \u003d 0.10 AM \u003d 0.10x 7500 thousand rubles. = 750 thousand rubles. (page 15);

The rent is calculated taking into account the area production equipment 20 m 2, rent per month - 1.2 thousand rubles / m 2, rental payments for the year 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 total overheads for each option are shown on pages 18 and business results are presented on pp. 23-26.

To assess the value of the business, we calculate the value of the capitalization rate, given 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 the life of the equipment is 10 years will be:

Capitalization rate for business valuation:

Based on the data obtained, it follows that, taking into account the 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 is 559,763 thousand rubles, the return on sales at net profit - 38.28% (559,763: I 462,118 x 100%), weighted average business value - 1,325,189 thousand rubles.

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

Example 21. The current annual income to 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 the business object may increase by 48% with an optimistic development of economic events, by 32% with the most probable development, and by 10% with a pessimistic forecast. Determine the capitalization ratio, the current value of the business object and the resale value in six years, given that the probability of an optimistic forecast is 20%, a pessimistic forecast is 30%.

Solution

Calculate the recovery factor rate, taking into account the 18% rate of return on investments:

The current value of the appraisal object:

The resale value of the object, taking into account the 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	Forecast option
	OPTIMISTIC	most likely	pessimistic
1. Current income in real estate, thousand rubles.
2. Income growth rate, %
3. Forecast probability
4. Rate of compensation factor, %
5. Deferred income rate, %
6. Adjustment rate of capitalization, %
7. The current value of the object, thousand rubles.
8. The cost of the object of resale, thousand rubles.
9. Weighted average present value	27090x0.10 = = 2709	23,956 x 0.50 = = 11,978	20,661 x0.30 = = 6,198
Probable weighted average current value of a business object, thousand rubles.		2 709 + 11 978 + 6 198 = 20 885
10. Weighted average value of the object of business resale, thousand rubles.	40,093 x0.10 = = 4,009.3	31622x0.5 == 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 rate of growth of income from a property in the future leads to a decrease in the deferred income rate, which leads to an increase in the adjustment rate for capitalization of income, and therefore, to a decrease in the present value and resale value of the property. For example, a decrease in the income growth rate from 48% to 10% led to a decrease in the deferred income rate from 5.08% to 1.06%.

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

Example 22. OJSC plans to expand the sales volume of products, for this it is necessary to rent two trading floors in different parts of the city, the area of ​​\u200b\u200beach of them is 300 m 2 and 450 m 2, unused area in each trading floor- 6 and 8% of the area, the cost of rent per month for 1 m 2 - 500 rubles. and 430 rubles, the cost of commercial equipment, respectively, is 125 thousand rubles. and 190 thousand rubles. Investments will be made at the expense of own funds and borrowed funds. The first object will be financed by 30% from borrowed funds, the interest rate on the loan is 25%, the rate of return on the first object is 2.10. The second object will be financed by 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. The interest rate on equity at the time of appraisal is 15%.

At the time of valuation, the amount of own funds of the OJSC was 3 million rubles. Assess the sufficiency of own funds and the feasibility of investing in objects, the minimum level of return for the owner.

Solution

The initial data and calculation results are presented in Table. 4.6. The solution is carried out in the following sequence.

Table 4.6

Calculation of net operating income from investments in business facilities

Continuation

Estimated indicators for business objects
9. Potential gross income for the year, PVD, rub. (page 1 x 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 (p. 1 xp. 1.1: 100)		450 x 0.08 = 36
11. Losses from underutilization of premises 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. (p. 9 x p. 8: 100), including:
14. Depreciation, rub. (page 2 x x page 3: 100)	125,000x0.12 == 15,000	190,000x0.11 = = 20,900
15. Net operating income for the year NPC, 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. The value of the object on the date of assessment, rub.
17. The 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 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 (p. 17 + p. 18)	(878 750+ 1 632 500)/ 2 = 1 255 625	3 406 660): 2 = = 2 602 495

The ending

Let's calculate the potential gross income from the property that can be obtained from real estate at 100% use, excluding losses and expenses, taking into account the usable area, rent per month:

where S- area of ​​the object of assessment;

AR PL - rent per month.

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

Calculate losses from underutilization of the property - losses from underutilization of premises:

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

Calculation results on page 11.

Calculate the actual gross income, taking into account the estimated losses from underutilization of the property:

Calculation results in p. i.

We calculate the estimated costs of operating the property being valued - operating costs necessary to ensure the smooth operation of the facility and the reproduction of income, taking into account the conditions of the problem:

where PVD - potential gross income;

H op - the share of operating expenses in the potential gross income.

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

Calculate the projected net operating income (NOR) as the difference between the actual operating income and operating costs (excluding depreciation A):

The calculation results are on page 15.

NPV is the value of the object of evaluation of the RMS on the date of evaluation. At the time of appraisal, the value of the first object of appraisal was 1,005 thousand rubles, the cost of the second object was 2,144,440 thousand rubles.

We determine the average price of each object based on the cost of the object as of 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 OS equipment , which the object of evaluation has:

The calculation results are presented in pages 17-19.

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

We calculate the capitalization ratio, or the price of capital, for each object of assessment 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 borrowed capital:

By the condition of the problem, we have:

for the first option:

for the second option:

The calculation results are shown on page 20.

Calculate the real value of the PC of each object by dividing the net operating income NOR by the capitalization rate K cap:

The calculation results are presented on page 21.

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

where D*. - the share of borrowed capital;

dx- price of borrowed capital;

D with, - the share of equity; dcc- price of own capital.

Calculations are presented on page 22.

For the first option:

Thus, the minimum return on own funds invested in the first business object, given financial structure investment should be 12.14%, i.е. for each ruble of equity capital should account for less than 12.14 kopecks. net profit. Otherwise, the investment will be unprofitable.

For the second option:

Thus, the minimum return on own funds invested in the second object of assessment, with a given financial structure of investments, should be 12.73%, i.e. for each ruble of equity capital should account for at least 12.73 kopecks. net profit. Otherwise, the investment will be unprofitable.

Let us determine the amount of equity that should be invested in investment objects, taking into account the share of equity (D ss) and the average acquisition price of the DH object with:

For the first option:

For the second option:

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

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 own funds of the OJSC 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 by the amount of equity:

For the first option:

For the second option:

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

The main capitalization methods are the direct capitalization method and the income capitalization method based on the rate of return on capital.

The choice of capitalization method in each case is influenced by the following factors:

– type of property;
– effective age and economic life of the object;
– reliability and extensiveness of information;
- characteristics of income from the object of assessment (amount, duration of receipt, rate of change).

Most commonly used following methods capitalization:

– direct capitalization, when the value of the object is determined by dividing the net annual income by the capitalization rate;
– gross rent method, based on property valuation, taking into account potential or actual income and gross rental multiplier;
– discounted cash flow method – valuation of the object, when cash flows are received unevenly, arbitrarily change, while taking into account the degree of risk associated with the use of property;
– remainder method - valuation of property, taking into account the influence of individual factors in the formation of income (in combination with the residual method, methods of both direct capitalization and capitalization of income at the rate of return can be used);
– method of mortgage investment analysis - property valuation based on accounting for the cost of own and borrowed capital.

The choice of a specific method of capitalization is determined by the nature and quality of the expected income.

In the current conditions of economic and political instability in Russia, due to the difficulty of making reliable forecasts, the direct capitalization method is widely used, which does not require such a thorough analysis of cash flows as with capitalization by the rate of return.

Direct capitalization - valuation of property while maintaining stable conditions for its use, a constant amount of income, no initial investment and at the same time taking into account the return of capital and income on capital.

The capitalization rate is usually calculated on the basis of an analysis of market information about analogues of the object of assessment by dividing the net annual income by the selling price of the analogue.

Considered in the previous chapter, the basic formula of the income approach

with direct capitalization, it is usually applied in the following form:

where PV – the current value of the property,

NOI – expected net operating income for the first year after the valuation date,

L is the total capitalization rate.

Normalized net operating income for 1 year, obtained by averaging income over several years, can be used as NOI.

The capitalization rate Dd reflects the risks to which the funds invested in the asset are exposed. Methods for calculating the capitalization rate are selected depending on the specific conditions in which the object of assessment operates: information on income and transaction prices based on a sample of comparable objects, sources and conditions for financing transactions, the possibility of a correct forecast regarding the value of the object at the end of the forecast period.

Direct capitalization possible using gross rental multiplier

Gross rent multiplier (RM)- the average ratio of the market price to the potential or actual gross income of a certain type of property.

The main conditions for applying the direct capitalization method:

- the period of receipt of income tends to infinity;
- the amount of income is constant;
- the conditions for using the object are stable;
- initial investment is not taken into account;
– the return of capital and return on capital are taken into account simultaneously.

At direct capitalization models are used based on determining the value of real estate by dividing the typical net operating income by the total capitalization rate obtained on the basis of an analysis of the relationship between income and sales prices of analogues of the appraised property. Here are some examples of direct capitalization models.

Advantages of the direct capitalization method:

– simplicity of calculations;
– a small number of assumptions;
– reflection of the state of the market;
– obtaining good results for a stable functioning property with low risks (building with one tenant and long-term lease).

Along with the sufficient ease of application of the method, one should take into account the complexity of the market analysis and the need to make adjustments for differences between the compared objects. The method should not be applied if there is no information on market transactions, the object is under construction or reconstruction, or if the object has suffered serious damage.

The capitalization rate is applied when converting future income from real estate into its current value.

The sales comparison method, the debt coverage ratio method, the investment group method, the actual gross income ratio method, and the balance method are used to calculate the capitalization rate.

Sales comparison method − the main method for determining the total capitalization rate. When determining the capitalization rate for the appraised object, the capitalization rate is first calculated for each of the sold analogues using the formula

where SP i is the selling price of the i-analogue.

Then, taking into account the methods of mathematical statistics, the weight coefficient x i , which reflects the degree of similarity of each of the sales to the object of assessment, the total capitalization rate is selected

.

As Ri a capitalization rate can be applied for alternative investments with a similar degree of risk, then x is the weighting factor of the 1st investment.

The analyzed analogues of the object of assessment should have the following characteristics similar: the remaining economic life, the level of operating costs, reversion values ​​and loss factors, risks, the ratio of land and buildings values, the date of sale, the method of best and most effective use, terms of financing, level of management quality. In addition, the location and decoration of objects should not fundamentally differ.

Debt Coverage Method applies if debt capital is used to finance investments in real estate.

Debt coverage ratio DCR calculated as follows:

,

where DS – annual debt service.

The total capitalization rate is determined by the formula

where Rm – total capitalization rate; m is the share of borrowed funds:

where Vm is the cost of borrowed funds, or the amount of the loan;

V – the cost of the object;

Rm is the capitalization rate for borrowed funds:

Data for the debt coverage ratio calculation is readily available, but this method provides an indicative value for the capitalization rate in cases where market data is not sufficiently reliable. Therefore, the coverage ratio method is used only as a corrective one.

Investment group method used when borrowed capital is involved in the purchase of real estate. At the same time, the capitalization rate can be calculated both in relation to financial and in relation to physical components.

Investment group method for financial components. The capitalization rate is a weighted average that takes into account the interests of both equity and borrowed capital:

where R m is the capitalization rate for equity, which is determined from data on comparable objects by dividing the value of income before tax by the value of own invested capital; R e , is the capitalization rate for borrowed funds.

Investment group method for physical constituents. The capitalization rate is determined by the formula

where L is the share of land value in the total property value; Rl- capitalization rate for land;

R h is the capitalization rate for improvements.

The capitalization rate for land is calculated as the ratio of income attributable to land to the value of land. The capitalization rate for improvements is determined by the ratio of income attributable to improvements to the cost of improvements.

Actual Gross Income Ratio Method applies if data on operating expenses and actual gross income are available:

,

where OER is the operating expense ratio; EGIM is the actual gross income ratio.

With direct capitalization, gross income ratios and the residual technique can be used to calculate the value of an object.

Application of gross income ratios. If operating expenses are not available, gross income figures are used and multiplied by the following appropriate factors:

– GRM – gross rent coefficient, if the period is equal to a month;

– G.I.M. – gross income ratio if the period is a year.

These coefficients are determined by the ratio of income and sale prices of objects and are the reciprocals of capitalization rates.

The value of the property in this case is determined as follows:

where PGI is the potential gross income;

PGIM – potential gross income coefficient calculated based on data on analogues of the appraised object:

,

EGI - actual gross income; EGIM is the actual gross income ratio:

,

SP is the selling price of the object of appraisal analogue.

Remainder method is used in cases where the cost of one component of the appraised object is known. There are residual methods for land and buildings, equity and debt capital.

The sequence of application of the residual method:

- calculation of the part of the annual income that falls on the component with a known value;
- calculation of the part of the annual income that falls on the component with an unknown value;
– calculation of the cost of an unknown component;
- determination of the value of property by adding the values ​​of its components.

Consider the residual method for buildings when the value of the land is known. Calculations will be performed in accordance with the above sequence using the following formulas:

,

where 1 L is the annual income attributable to land; V L - the cost of land; R L is the capitalization rate for land.

where J h , is the annual income attributable to the building; J 0 - the total annual income brought by the property.

where Vn, is the cost of the building; Rn is the capitalization rate for buildings.

,

where V is the value of the property.

Apply similarly:

– residual method for land – when the cost of the building can be determined quite accurately;
– balance method for equity – if it is possible to determine the term of the mortgage loan and the amount of the annual debt service payment;
- the residual method for borrowed capital - when the cost of equity capital is known.

In general, direct capitalization calculations require the availability of comparable sales data. Capitalization of income by the rate of return is less dependent on market data, but this method should reflect the actual expectations and preferences of potential buyers of such properties.