Calculation of enterprise value using the discounted cash flow method. Definition and application of the discounted cash flow method

The main advantages of the discounted cash flow method over the profit capitalization method are that the discounted cash flow method allows you to evaluate businesses with uneven and often negative financial results.

The discounted cash flow calculation can be displayed in the following formula:

PV = CF1/(1 + r))+(CF2/((1 + r) 2)+…+(CF i /((1 + r) i)+(FV/((1 + r) n) ( 1.3.1)

where PV is the current value;

CFi is the cash flow of the next year of the forecast period;

FV - the value of the enterprise's property in the post-forecast period;

r - discount rate;

n is the total number of years of the forecast period.

Main stages of enterprise valuation using the DCF method

Model selection cash flow.

Determining the duration of the forecast period.

Retrospective analysis and forecast (expenses, investments, gross sales revenue).

Calculation of cash flow for each year of the forecast period.

Determining the discount rate.

Calculation of the value in the post-forecast period.

Calculation of the present values ​​of future cash flows and the value in the post-forecast period.

Making final amendments.

Let's look at each stage separately and in more detail.

First stage. Selecting a cash flow model.

The discounted cash flow method in business valuation involves the use of net cash flows. First of all, you can allocate cash flow for equity and debt-free cash flow.

Debt-free cash flow does not reflect the planned movement and cost of borrowed funds used to finance the investment process. Discounting of expected debt-free cash flows should be done at a rate equal to the weighted average cost of capital of the enterprise. In this case, the value obtained by summing discounted debt-free cash flows and the expected residual value of the enterprise will be an estimate of the value of all capital invested in the enterprise. In other words, to estimate the value of its equity capital, it will be necessary to subtract the long-term debt of the enterprise planned at the valuation date.

Cash flow for equity capital allows you to directly, without additional adjustments, assess the market value of the enterprise's equity capital and reflects in its structure the planned method of financing investments. In other words, this indicator makes it possible to determine how much and on what terms borrowed funds will be raised to finance the investment process. For each future period, it takes into account the expected increase in the enterprise's long-term debt, decrease in the enterprise's liabilities, and payment of interest on loans in the order of their current servicing.

The share and cost of borrowed funds in business financing is already taken into account in the projected cash flow itself. Discounting cash flow for equity capital can occur at a discount rate equal to the investor's required return on investment only for his own funds- that is, at the discount rate for equity capital.

The procedure for calculating cash flow for equity and debt-free cash flow is presented in Table 2.

Table 2. Structure of net cash flows

In Table 2, the sign “-” indicates funds actually leaving the enterprise, and the sign “+” indicates funds actually arriving. The movement of short-term debt is not taken into account in the above methodology for determining cash flow - it is considered that its turnover fits within the turnover of the enterprise's funds within the period under review.

Under the growth of own working capital here we mean an increase in stocks of raw materials and materials, work in progress, as well as a stock of finished, but unsold or unpaid products - that is, everything in which own working capital and monetary resources aimed at replenishing them were tied up. It should be noted: negative or slightly positive values ​​of projected cash flows mean that it is impossible to judge the value of the company based on the method in question. In this case, it may be appropriate to use methods based on asset values.

To better understand the process of generating cash flows for equity and debt-free cash flows, Appendix 1 provides an illustrative example.

Second phase. Determining the duration of the forecast period. It is better to start forecasting future income by indicating the forecasting horizon and choosing the type of income that can be used in the calculations. The duration of the forecast period is determined taking into account the plans of the enterprise management for development (liquidation) in next years, changes in demand trends, dynamics of cost indicators (cost, profit, revenue), production and sales volumes. Duration of the forecast period in developed countries market economy usually 5-10 years, and in countries with economies in transition, in conditions of instability, it is permissible to reduce the forecast period to 3-5 years. Due to the difficulties in forecasting, the lack of reliable statistical information and the undeveloped planning system at enterprises, systems for assessing Russian enterprises usually take a forecast period of three to five years. If it can be assumed that there are no reasons for ceasing to exist, then it is assumed that the enterprise can exist indefinitely.

A more accurate forecast of income for several decades is impossible, even in a stable economy, so the period of further existence of the enterprise is divided into several parts:

forecast period, when the appraiser accurately predicts the dynamics of cash flows;

post-forecast period, the appraiser takes into account the average growth rate of the enterprise's cash flows for the remaining life.

Third stage. Retrospective analysis and forecast (expenses, investments, gross sales revenue).

For a more accurate calculation of cash flows, a detailed analysis of expenses, investments and gross revenue from products sold is required.

Retrospective analysis and forecast of gross revenue requires consideration and consideration of a number of factors, primarily production volumes and product prices, demand for products, retrospective growth rates, inflation rates, capital investment prospects, industry situation, enterprise market share and the general situation in economy. The gross revenue forecast must be logically compatible with the enterprise's historical business performance.

At the stage of forecasting and analysis of expenses, the appraiser must study the structure of the enterprise’s expenses, in particular the ratio of fixed and variable costs, assess inflation expectations, exclude one-time items of expenses that will not occur in the future, determine depreciation charges, calculate the cost of paying interest on borrowed funds, compare projected expenses with the corresponding indicators of competitors or the industry average. If cash flow is used for equity capital, then interest on servicing borrowed capital must be included in the expense item.

Investment forecasting and analysis includes three main components: own working capital, capital investments, financing requirements and is carried out, respectively, based on the forecast of individual components of own working capital, based on the estimated remaining service life of assets, based on the financing needs of existing debt levels and debt repayment schedules.

Fifth stage. Calculation of cash flow for each year of the forecast period.

To generate cash flows, direct and indirect methods are used. The difference between them is the different sequence of procedures for determining the flow value Money. The direct method is based on calculating the inflow (revenue from the sale of products, works and services, advances received, etc.) and outflow (payment of supplier bills, return of short-term loans received, etc.) of funds, that is, the initial element is revenue. Cash analysis by the direct method makes it possible to assess the liquidity of an enterprise, since it reveals in detail the movement of funds in its accounts and allows one to draw prompt conclusions regarding the sufficiency of funds for payments on current obligations, for investment activities and additional costs.

This method has a serious drawback - it does not reveal the relationship between the obtained financial result and changes in funds in the accounts of the enterprise.

The direct method involves studying data from Form No. 4 over time and constructing forecast balances. The use of this method requires a large volume of internal information, on the basis of which a cash flow forecast is made. The appraiser, as a rule, does not forecast cash flows using a direct method, but it is possible that the enterprise has a well-developed budgeting system. It should be borne in mind that a detailed cash flow forecast under the budgeting system is made for a period shorter than the forecast period when assessing a business. An enlarged forecast is made for the remaining periods. In this case, it would be reasonable to independently construct a cash flow forecast using the indirect method and compare the results obtained with the results of forecast balances within the framework of the direct method of generating cash flow. It should be borne in mind that access to budgeting system data is limited. If the assessment is made for a minority owner, then the only available method for generating cash flows is indirect, which will be based on financial reporting data

Fifth stage. Determining the discount rate.

Determining the discount rate depends on the type of cash flow. For cash flow for equity, a discount rate equal to the owner's required rate of return on equity is applied; for cash flow for all invested capital, a discount rate is applied equal to the sum of the weighted rates of return on equity and borrowed funds, where the weights are the shares of borrowed and equity funds in the capital structure.

For equity cash flow, the most common methods for determining the discount rate are the cumulative method and the capital asset pricing model. For cash flow for total invested capital, the weighted average cost of capital model is typically used. When determining the discount rate using the cumulative method, the calculation base is taken as the rate of return on risk-free securities, to which is added additional income associated with the risk of investing in this type valuable papers. Then adjustments are made (increasing or decreasing) to the effect of quantitative and qualitative risk factors associated with the specifics of a given company.

In accordance with the capital asset pricing model (CAPM - Capital Assets Pricing Model), the discount rate is determined by the formula:

R = Rf + in (R - Rf)(1.3.2)

where R is the rate of return on equity capital required by the investor; Rf - risk-free rate of return;

Rm is the total return of the market as a whole (the average market portfolio of securities);

B - beta coefficient (a measure of systematic risk associated with macroeconomic and political processes occurring in the country).

According to the weighted average cost of capital model, the discount rate (WACC - Weighted Average Cost of Capital) is determined as follows:

WACC = k d (1-t c) w d + k p w p + k s w s , (1.3.3)

where k d is the cost of borrowed capital;

t c - profit tax rate;

w d is the share of borrowed capital in the capital structure of the enterprise;

k p - cost of attracting share capital (preferred shares);

w p is the share of preferred shares in the capital structure of the enterprise; k s - cost of attracting equity capital (ordinary shares);

w s is the share of ordinary shares in the capital structure of the enterprise.

We will consider the definition and justification of the discount rate in more detail in the next chapter.

Sixth stage. Calculation of the value in the post-forecast period. Determination of value in the post-forecast period is based on the premise that the business is able to generate income after the end of the forecast period. It is assumed that after the end of the forecast period, business income will stabilize and in the remaining period there will be stable long-term growth rates or endless uniform income.

Depending on the prospects for business development in the post-forecast period, one of the following methods for calculating residual value is used:

method of calculating liquidation value, which is used if, in the post-forecast period, bankruptcy of the company is expected with the subsequent sale of existing assets. When calculating the liquidation value, it is necessary to take into account the costs associated with liquidation and the urgency discount (for urgent liquidation). This approach is not applicable to evaluate an operating enterprise that is making a profit, much less one that is in the growth stage;

cost calculation method net assets. The calculation technique is similar to the calculation of liquidation value, but does not take into account the costs of liquidation and the discount for the urgent sale of the company's assets. This method can be used for a stable business, the main characteristic of which is significant material assets;

the prospective sale method, which consists of recalculating cash flow and cost indicators using special coefficients obtained from the analysis of historical sales data of comparable companies.

Since the practice of selling companies on Russian market is extremely scarce or absent, the application of this method to determine the final cost is very problematic; According to the Gordon model, annual income of the post-forecast period is capitalized into value indicators using a capitalization ratio calculated as the difference between the discount rate and long-term growth rates. In the absence of growth rates, the capitalization rate will be equal to the discount rate. Gordon's model is based on the forecast of stable income in the remaining period and assumes that depreciation and capital investments are equal.

Calculation of residual value in accordance with the Gordon model is carried out using the formula:

FV term = (D (1+ G))/ (Kd - G) (1.3.4.)

where D is cash flow last year forecast period;

G - early average annual growth rate of income (profit) or cash flow, calculated as the coefficient of linear growth of cash flow for lookback period activities;

Kd - discount rate calculated on the basis of data prevailing on the valuation date by any suitable methods, - cumulative construction (CCM), capital assets (CARM) or the weighted average cost of capital (WACC) method, depending on the type of cash flow.

The residual value Vo using the Gordon formula is determined at the end of the forecast period.

For example, it is known that the forecast period is five years, the cash flow of the fifth year is equal to 150 million rubles, the discount rate is 24%, and the long-term growth rate is 2% per year. Substituting these data into the above formula, we obtain the value of the cost in the post-forecast period, rounded to 695 million rubles.

Seventh stage. Calculation of the present values ​​of future cash flows and the value in the post-forecast period.

The value of the enterprise's cash flows, discounted at a certain discount rate to the valuation date, is the current (discounted) value.

It turns out that the calculation of the present value PV can be done by multiplying the cash flow CF, which corresponds to the period, by the present value of the unit DF, taking into account the selected discount rate r. The formula is calculated:

DFi = (1/(1+ r) i (1.3.5)

When using this formula, cash flows are discounted if they would have been received at the end of the year. But if we assume that the cash flow was not concentrated at the end of the year due to seasonal production and other factors, it is necessary to determine the present value coefficient for the cash flow of the forecast period for the middle of the year using the formula:

DF = 1/(1+ r) i-0.5 (1.3.6.)

By subsequent summation of the values ​​of the current values ​​of cash flows of the forecast period, it is possible to determine the value of the enterprise in the forecast period.

When using the current value coefficient, you can determine the current value of the enterprise in the residual period using the discounting method using the formula:

DF term = 1/(1 + r) n (1.3.7)

The preliminary value of a business can be divided into several components: this is the current value of the enterprise in the residual period and the sum of the current values ​​of cash flows of the forecast period. The mechanism of the entire algorithm is presented in Table 3.

Table 3. Calculation of the present value of cash flows and reversions

Index				Post-forecast period
Cash flow CF i
Cost at the end of the forecast period				FV term? CF term/(r - g)
Present value factor DF		DF 2 =1/(1+ r) 2	DF 3 =1/(1+ r) 3	DF term=1/(1+r)n
Present value of cash flows	PV 1 = CF 1 DF 1	PV 2 = CF 2 DF 2	PV 3 = CF 3 DF 3	PV term = CF term DF term
Enterprise value	V = PV 1 + PV 2 + PV 3 + PV term

Eighth stage. Making final amendments. After determining the preliminary value of the enterprise's value, the next step is to make final adjustments to obtain the final value of the enterprise's market value. There are three amendments in total:

adjustment for long-term debt (used to determine the cost of equity using cash flow for all invested capital);

adjustment for the value of non-performing assets (assets that do not participate in generating income);

adjustment of the value of own working capital.

It is important to note that the DCF method provides an estimate of the cost of equity at the level of controlling interest. When determining the cost minority stake public joint stock company, the non-controlling discount must be deducted. For a closed joint stock company, it is necessary to make allowances for insufficient liquidity and non-controlling nature.

The first amendment is applied when making calculations when using the cash flow model for all invested capital. To determine the value of equity capital, the amount of long-term debt is subtracted from the value found.

The second amendment is made if, when calculating the value, the assets of the enterprise that are involved in generating cash flow are taken into account. But not all assets of an enterprise can be used in production. In fact, they have a cost that is not included in the cash flow. For now Russian enterprises have such non-functioning assets (equipment, real estate, machinery), since due to the protracted decline in production the ability to dispose of production capacity extremely small. These assets have some value that can be realized when they are sold. These assets are subject to a separate assessment, the result of which must then be added to the value of the business.

The cash flow discounting model includes its own working capital value, which is tied to the forecast level of product sales. But the required amount may not coincide with the actual amount of working capital. This will be the third correction.

If a company has excess working capital, its amount is added to the cost of equity capital. In the opposite case, if there is a lack of working capital, the cost of equity capital is reduced by the appropriate amount.

The adjustment for excess (deficit) of own working capital is defined as the difference between the actual and required values ​​of own capital.

When assessing a company’s business, it is important to avoid the following mistakes:

when predicting the amount of depreciation, it is necessary to take into account the capital investment plan, and it must be remembered that depreciation begins from the moment the capital investment object is put into operation;

the company's net profit must be adjusted to the amount of expenses associated with maintaining the facilities social sphere, Also

when forecasting, the current tax system should be taken into account;

projected revenue growth cannot exceed production capabilities companies; also, the projected revenue growth should reflect the prospects for industry development and retrospective trends in the company’s development;

the amount of costs should be adjusted for atypical or non-standard costs, which actually unreasonably inflate the cost and do not reflect the real situation at the enterprise;

when bringing planned cash flows to current value, the current value coefficient should be calculated based on the discount rate for the middle of the year; in the case of bringing the value of the business in the post-forecast period to current value, the current value coefficient should be determined for the end of the year.

The use of the discounted cash flow method is effective when the amounts of business income differ from each other. This can most often be seen in young, effectively developing businesses. Unlike the direct capitalization method, the discounted cash flow method is used using net cash flows rather than various income indicators. If the sale or liquidation of a business is not forecast, then cash flow forecasting is carried out until the moment when business income is stable and maintains a steady growth rate. The residual value of a business is found using the Gordon model, which is similar to the direct capitalization method. The final step in valuing a business using the discounted cash flow method is the process of making final adjustments for the presence of excess non-performing assets, and adding the value of these assets to the present value of the projected cash flows and the residual value of the business.

The discounting method is based on an economic law that reflects the essence of the method and describes the diminishing value of money. According to this law, over time, money gradually depreciates (loses its value) compared to its current value. Other changes may occur to the value of money. So that in calculations (for example, when calculating potential economic efficiency investment) to take into account the process of such change, you need to take the current moment of assessment as the starting point, and then bring the size of future cash flows (inflow and outflow of funds) to the present moment, determining the amount of change in the value of money.

Discounted Cash Flow is just a calculation that allows you to do this using a discount factor. How to calculate discounted cash flow will be shown in the article.

DCF value

The English phrase Discounted Cash Flow, meaning discounting cash flows, is usually presented in formulas as the abbreviation DCF or, in the Russian version, DCF. An investor making a decision about the most profitable investment uses this result in a number of other methods, representing income approach, for more accurate forecasting of the future situation and selection of economic and financial strategies. Among them:

• NPV– net present value (NPV) method. Its calculation formula, similar to the DCF formula, differs in that NPV also includes initial investment costs.
• IRR– internal rate of return.
• NUS- equivalent to annual annuity.
• P.I.– profitability index.
• NFV– net future value.
• NRR– net rate of return.
• DPP– discounted payback period.

For example, the introduction of the DCF parameter into the formulas for calculating the payback period (DPP) makes the calculation results practically more reliable, since it is the change in the value of money over time that allows us to assess the overall prospects of the project in motion. By taking into account the movement factor in performance assessment investment projects Such methods are also called dynamic.

Discounting methods are included as components of the income approach, and as such help to calculate the overall price of a business and its potential. Even with instability of financial flows, the discounted cash flow method is justifiably applicable, since it demonstrates high accuracy. To increase accuracy, the calculation is carried out taking into account specific characteristics and methods of receiving funds.

However, the Discounted Cash Flow Method also has disadvantages. Among the main ones, two are most often mentioned:

• Changes in economic, political, social environment affects the discount rate, but it is always quite difficult to predict changes in this rate for any long period.
• It is also difficult to predict changes in the size of future cash flows, taking into account all external and internal circumstances.

However, the method is actively used if there is a possibility that the profitability of future financial flows will begin to differ from the current profitability, if the flows depend on seasonality, if the construction project is at the implementation stage, and in a number of other cases. In order to bring net cash flow (NCF) to the current moment, a discount factor is used.

Discounted Cash Flow Formula

The coefficient is necessary to reduce potential profitability to current value. To do this, the value of the coefficient is multiplied by the value of the flows. The coefficient itself is calculated using the following formula, where the letter “r” denotes the discount rate (it is also called the “rate of return”), and the letter “i” in the value of the degree denotes the time period.

where, in addition to the previous designations, “CF” means cash flows in time periods“i”, and “n” is the number of periods in which financial flows are received.

In valuation practice, cash flows – Cash Flow (CF) – are understood as:

• taxable income,
• net operating income
• net cash flow (excluding costs for reconstruction of the facility, operation and land tax).

The calculation algorithm involves going through several stages, including analysis of discounted cash flow.

1. Determining the period for forecasting. As a rule, a predictable period of time with stable economic growth rates is forecast. In countries with well-developed market economies it is 5-10 years. In domestic practice, a period of 3-5 years is traditionally considered.
2. Forecasting incoming and outgoing cash payments. This is done through retrospective analysis based on financial statements (if any), studying the state of the industry, market characteristics, etc.
3. Calculation of the discount rate.
4. Calculation of cash flow for each period of time.
5. Bringing the received flows to the initial period by multiplying them by the discount factor.
6. Determining the total value is the stage at which the total accumulated discounted cash flow is calculated.

The key parameter in the formula is the bet amount. It determines the rate of return that an investor who invests money in a project should expect. The amount of the bet depends on a number of factors:

• weighted average cost of capital,
• inflationary component,
• additional rate of return for risk,
• return on risk-free assets,
• interest on bank deposits,

There are several methods for assessing it in investment analysis. The most popular methods for calculating the discount rate are given below.

Methods for determining the discount rate differ in different approaches, each of which is characterized by specific advantages and disadvantages.

• CAPM model valuation of capital assets, introduced in the 70s by W. Sharp to determine the return on shares. Strength The model is considered to take into account the connection market risk and stock returns. In the original model, this factor was the only one taken into account. Transaction costs, opacity of the stock market, taxes and other factors were not taken into account. Later, to increase accuracy, Yu. Fama and K. French used additional parameters.
• Gordon model. Another name for it is the constant growth dividend model. The “minus” of the method is that it is applicable only if the company has ordinary shares with constant dividend payments, and the “plus” is the relative simplicity of the calculation.
• WACC model– weighted average cost of capital. One of the most popular methods for demonstrating the rate of return that must be paid for the investment portion of capital. The economic meaning of the method is to calculate the minimum acceptable value of profitability (profitability level). This result can be applied to the evaluation of investments in an existing project.
• Method for estimating risk premiums. The method uses additional risk criteria not provided for in other models. However, this assessment is subjective, which is one of the disadvantages of the method.
• Method expert assessment . Among the advantages are the ability to take into account non-standard risk factors and subtle customization analysis. Among the disadvantages is the subjective perception of the situation. The expert evaluates meso-macro and micro factors that, in his opinion, will affect profit rates. Each project will have its own specific set of significant risks.

There are a number of other simple and complex methods, but in the following example, the discount rate will be calculated for clarity and transparency of the basic formula as the sum of the “risk-free rate” and the “risk premium”. The first component of the equation - the risk-free rate - in the calculation example is equal to 15% - the key rate Central Bank RF. This is part of the return on a risk-free asset. The second component – ​​the risk premium – is established by experts in the amount of 8% based on a conditional assessment of production, innovation, social, technological and other risks. This is the rate of return on existing risks. In total, the discount rate will be considered equal to 23%.

Calculation example

Our calculation example will correspond to the domestic tradition of choosing a forecast period in the range of 3-5 years. Let's take an average of 4 years for a conditional project with a discount rate of 23%.

1. Let us write down for each year the projected amount of income in rubles (CI) and the amount of cash expenses (CO). Here we choose an annual interval for analysis and will calculate the discounted cash flows first for each individual year, and then the discounted cash flow in total for all 4 years. The projected expense will be stable, but the income will vary from year to year.
   • First year: +95 thousand and -30 thousand.
   • Second year: + 47 thousand and -30 thousand.
   • Third year: + 54 thousand and -30 thousand.
   • Fourth year: + 41 thousand and -30 thousand.
2. We calculate the difference between income and expenses for each year. It turns out that the amounts of such differences for periods 1-4 will be 65, 17, 24 and 11 thousand rubles, respectively.
3. We bring financial flows to the initial period. We use coefficients 1/(1+0.23) to calculate i, which discount each flow. Here, in place of the dividend will be the difference between income and expenses for each year, which we calculated at the previous stage. In place of the divisor is a coefficient, and the value of 0.23 is a discount rate of 23%, and “i” to the power corresponds to the number of the year for which we are making the calculation.
   • 65000/(1+0,23) = 52845
   • 17000/(1+0,23) 2 = 11237
   • 24000/(1+0,23) 3 = 12897
   • 11000/(1+0,23) 4 = 4806
     (*Results are written in rubles, rounded to whole numbers).
4. We add the received amounts together, which gives DCF = 81,785 rubles.

Since the indicator ultimately has a positive value, we can talk about further analysis of the project’s prospects. Investment analysis requires using the discounted cash flow method and comparing the final values ​​for several alternative projects so that they can be ranked by attractiveness.

One of the ways to value a company is the discounted cash flow (DCF) method. This method considers the value of a company as the sum of the cash flows it generates over the expected investment period. It allows the investor to calculate the value of the company's future earnings and assess the feasibility of investing in its shares.

The discounted cash flow method (DCF method) is used when a company's cash flows are unstable and vary significantly from year to year. It is suitable for evaluating young and growing companies and is effective in conditions of economic uncertainty.

Evaluation algorithm

The valuation of a company using the DCF method is carried out in the following sequence:

1. The expected period of investment in the shares of the analyzed company is determined - the so-called forecast period, for example, 5 years.

2. The company's prospects and the rate of its further growth (Growth Rate) in the forecast (within 5 years) and post-forecast (over 5 years) periods are analyzed. The assessment takes into account:

• the economic situation (inflation, interest rates, purchasing power) and its impact on the company’s industry;
• market potential and company industry dynamics;
• the company's development strategy and its investment policy;
• analyst forecasts (adjusted for the risk of error).

You can find out what experts expect from a company on financial websites in the Analyst Estimates section. An example of such a forecast for Intel Corporation (INTC) on Yahoo!Finance.

3. Investment risks are assessed and the rate of return or discount rate required by the investor is determined.

• To determine the cash flows of equity capital, the CAPM asset valuation model is used.
• For the cash flow of all invested capital, a discount rate equal to the weighted average cost of capital (WACC) is applied.

4. Based on the results of the company's reports, the value of free cash flow (FCF) is estimated. At the same time, it is important for the investor to use not the total free cash flow of the company (Free Cash Flow to the Firm, FCFF), but the one that remains directly to the owners (Free Cash Flows to Equity, FCFE).

• The formula for calculating free cash flow to equity (FCFE) can be found.

5. Based on the resulting free cash flow to equity (FCFE) and the expected growth rates, the following are calculated:

• The company's future cash flows for each year of the forecast period (over 5 years).
• The value of all cash flows of the post-forecast period (after 5 years), the so-called. terminal or final value of the business (Terminal Value).

To calculate the terminal value of a company, the Gordon constant growth model is used, which assumes that further business growth will proceed at a stable pace:

	FCFE value of the last year of the forecast period;
R	the rate of return required by the investor, expressed as a decimal fraction;
G	expected growth rate of the company in the post-forecast period;
n	last year of the forecast period: 5 – with a forecast for 5 years.

6. Once the free cash flow values ​​for each forecast year have been predicted and the terminal value has been determined, you can proceed directly to calculating the company value (Enterprise Value). To do this, the net present value (NPV) formula is used. It allows you to discount the amount of future payments, i.e. bring it to the current (at the present time) value (Present Value).

7. Then it remains to determine the value of the company per one ordinary share. To do this, the Enterprise Value should be divided by the number of company shares (Shares Outstanding). The resulting value is the Fair Value. By comparing it with the current market value, you can assess how attractive the security is for purchase.

There are several approaches to assessing the profitability of an operating enterprise. One of them is a method based on cash flow discounting. The relevance of this approach is due to the fact that cash flow management plays a huge role for all parties interested in effective activities company, allows you to manage the cost of an existing business and allows you to increase the financial flexibility of the company.

Cash flow, as opposed to indicator net profit, allows you to correlate the inflow and outflow of funds, taking into account depreciation and amortization, capital investments, accounts receivable, changes in the structure of the company’s own working capital.

Empirical evidence suggests that there is a stable relationship between discounted cash flow and the company's market price, but accounting profits do not correspond well with market value, because not in all cases accounting profit is considered a characterizing factor of the company’s price.

Company price calculation when using the provided method, it is carried out in the following manner: analyzed and predicted gross income, costs and investments, cash flows are calculated for each reporting year, the discount rate is determined, the received cash flows are discounted, the residual value is calculated (using the net asset method, with support for determining the liquidation price of assets or based on the Gordon model), the current values ​​of upcoming cash flows are summed up and residual value, the results obtained are adjusted and verified.

Calculation of enterprise value

The calculation can be performed based on two types of cash flows: for equity and invested (debt-free) capital.

In the case of calculating cash flow for equity, the value of the information received for the company manager is taken into account, because the enterprise's need for additional attraction of financial resources is taken into account.

In practice, debt-free cash flow is used by investors to finance a merger, acquisition or purchase of a company by raising new borrowed funds.

Cash flow for equity is calculated as: Net profit for period n + Depreciation (depreciation for period n) - Capital investments for period n + (-) change in long-term debt for period n (increase or decrease) - increase in own working capital.

Debt-free cash flow is estimated using a similar formula, but there will be no increase or decrease in long-term debt, and the amount of debt-free cash flow increases by the amount of interest payments adjusted for the tax rate.

It should be noted that monitoring of cash flows is carried out based on the foreseeable 5 years. Due to the fact that the possibility of deviation from the forecast is quite large, a spectrum of forecasts is compiled - pessimistic, most likely and optimistic. Any forecast is given a certain weight and the weighted average profitability is calculated. For both equity and debt capital, cash flow can be nominal (in prices of the current period) or real (prices are adjusted for inflation). Cash flow discounting is carried out at the end and at the middle of the year; it should be noted that it is preferable to use discounting at the middle of the year to obtain clearer results.

Determining the discount rate

When determining the discount rate, it should be taken into account that it is considered as the lower limit level of investment return at which the investor allows the possibility of investing his funds in this company, given that there are alternative investments that involve generating income with varying degrees of risk. In this case, risk is understood as the probability of a discrepancy between the expected results from investments and the actual results obtained, as well as the probability of loss of property due to the bankruptcy of an enterprise, political and other emergency events. Accordingly, the higher the risk, the higher the discount rate.

The "discount rate" as defined by the American Society of Appraisers is a factor used to calculate the present value of a sum of money received or paid in the future. Thus, the discount rate is used to determine the amount an investor would pay today (present value) for the right to receive expected future earnings.

For Several methods are used to calculate the discount rate, the most preferred of which are: CAPM capital asset pricing model and summation model. When calculating the discount rate for debt-free cash flow, use weighted average cost of capital model.

1. The CAPM model is based on the idea that an investor needs additional income that exceeds the possible income from fully hedged securities such as government bonds. Additional income is compensation to the investor for investing in risky assets. The model is used to determine the required rate of return based on three components: nominal risk-free rate, average profitability of non-loan transactions in the economy and a coefficient measuring systematic risks (b) (examples of systematic risks include the emergence of an excessive number of competing objects, the introduction and operation of any restrictions, etc.)).

When calculating the nominal risk-free rate, you can use both average European indicators for risk-free operations and Russian ones. To improve the accuracy of the calculation, the risk-free component of the discount rate can be determined based on quotes of domestic government securities and based on average European data. If average European indicators are used, a premium for the risk of investing in a given country, the so-called country risk, is added to the risk-free rate. Russian indicators are taken based on the weighted average rate of return of banks of the highest category of reliability, and are used when a potential investor has the opportunity to make an alternative investment exclusively in Russia.

The coefficient (b) is calculated based on the amplitude of changes in prices for shares of a given company compared to changes in prices on the stock market as a whole. Investing in a company whose stock price is highly volatile is riskier because the company's stock price could fall quickly. Accordingly, if the coefficient b>1, we can talk about increased riskiness of investments in this enterprise, if b<1, то инвестиционный риск меньше среднего сложившегося на данном рынке. Как правило, рассчитываются отраслевые коэффициенты b , которые служат мерой риска для инвестиций в данную отрасль. Второй метод расчета заключается в анализе ключевых факторов макроэкономического, отраслевого и финансового рисков, оказывающих влияние на компанию.

2. The summation model involves adjusting the rate of return of a risk-free security by the risk premium for a given company. The risk premium is added to the risk-free rate of return and is calculated on the basis of risks that take into account the size and financial structure of the company, diversification of production and clientele, quality of management and other risks.

3. The weighted average cost of capital (WACC) model involves calculating a discount rate based on the share of equity capital in the financing (liabilities) of the enterprise, an individual discount rate determined by the capital asset price method (according to the capital asset valuation model) or by the cumulative discount rate method, share of borrowed funds, discount rate on borrowed funds (lending rate on the company's obligations), income tax rates.

Determining the amount of business income in the post-forecast period

After discounting the received cash flows, it is necessary to determine the amount of income from the business in the post-forecast period. When calculating, it is necessary to take into account that the residual value represents the present value of the cash flow received after a discrete forecast period, and includes the value of all cash flows for all periods that remain beyond the scope of a given forecast year. As mentioned, calculating residual value can be approached in several ways. Let's look at each of them in more detail.

The net asset value valuation method assumes using the residual book value of assets at the end of the forecast period as the residual value. Obviously, this method is not suitable for a profitable enterprise.

The liquidation value valuation method involves calculating the liquidation value of assets at the end of the forecast period. American experts note a number of factors under the influence of which liquidation value is formed. These include the low psychological attractiveness of assets, the appearance of assets plays a large role, and the result of the sale is also influenced by industry and territorial factors, because the products of developing industries will be in great demand and, accordingly, will have a higher price than the products of backward industries and regions.

The calculation of liquidation value is carried out through the following steps:

1. A calendar schedule for liquidation of the enterprise’s assets is being developed (developed with the aim of maximizing the proceeds from the sale of the enterprise’s assets, taking into account the liquidity of the assets);

2. The current value of assets is calculated taking into account the costs of their liquidation (costs include costs of taxation, insurance, protection of assets before their sale (we discount at an increased rate), severance pay and payments to employees of the enterprise, management expenses, including consulting services, such as lawyer, appraiser, etc.;

3. The amounts of the organization’s liabilities are determined.

We reduce the current adjusted value of assets by the amount of the organization’s liabilities and as a result we obtain the liquidation value. This approach also cannot be called completely adequate when assessing an existing profitable enterprise.

Experts are inclined to calculate the residual value using Gordon models, which assumes that: in the remaining period, the amount of depreciation is equal to the amount of capital investment, the growth rate in the remaining period is stable.

The calculation is made by dividing the cash flow in the residual (post-forecast) period by the difference between the discount rate and the long-term growth rate, or by dividing the cash flow of the last forecast period multiplied by the growth rate increased by one and the difference between the discount rate and the long-term growth rate.

After summing up the values ​​of the current value of future cash flows and the residual value, we obtain a value representing the value of the enterprise, which does not include the value of excess assets that do not participate in the formation of cash flow. These assets are subject to a separate assessment, the result of which is then added to the value of the enterprise. “Social” assets are subject to careful analysis of the motives for their sale, the direction of using the income received and the consequences of this step for the company’s employees. The company being assessed may have a deficit of its own working capital and obligations related to environmental protection measures; in this case, it is also necessary to adjust the result obtained.

It is worth noting that the discounted cash flow method for valuing a business gives an estimate of the value of equity capital at the level of a controlling stake; in the case of determining the value of a minority stake in an open joint-stock company, a discount for non-controlling nature is deducted; for a closed joint-stock company, it is necessary to make a discount for non-controlling nature and for insufficient liquidity.

In order to fully evaluate an operating enterprise, it is allowed not only to use the income approach based on discounting cash flows, but also to use the market (comparative) and cost approaches. This allows you to avoid a certain amount of subjectivity and make the business assessment more accurate.

The head of the enterprise and the chief accountant will be able to independently calculate cash flow using the method presented above, but to determine the discount rate and calculate the residual value of cash flow, as well as to evaluate the business using cost and market approaches, it is necessary to involve an experienced and qualified appraiser expert who can objectively assess the value of the business and provide the necessary recommendations for effective management of the company's value.

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

where V is the current value of the property;

CF j - cash flow of the jth year period;

r - discount rate;

Vterm is the cost of subsequent sale (reversion) at the end of the forecast period;

P- duration of the forecast period, years.

Calculation algorithm for the DCF method.

• 1. Determination of the forecast period.
• 2. Forecasting the magnitude of cash flows from the property for each forecast year.
• 3. Calculation of the cost of reversion.
• 4. Calculation of the discount rate
• 5. Determining the value of a property

Determination of the forecast period.

The duration of the forecast period is determined by the duration of the stage of unstable cash flows of the property being valued.

In international assessment practice, the average forecast period is 5-10 years; in Russian practice, the typical forecast period is a period of 3-5 years.

Forecasting cash flows from a property for each forecast year.

The calculation of various levels of income from a real estate property can be represented by the formulas:

PVD = Area _ Rent rate (4.28)

DVD = PVD - Losses from vacancy and rent collection + Other income (4.29)

NOR = DVD - Real estate owner operating expenses associated with real estate (4.30)

In practice, Russian appraisers calculate the net cash flows of a property without taking into account the specifics of financing, i.e. in the DCF method, the values ​​of net operating income are discounted.

When assessing the market value of a property, the cash flow is the net operating income from the property.

However, if it is necessary to estimate the investment value of a property or the value in existing use, then the actual expenses of the owner or investor must be taken into account, therefore, the following levels of cash flows are used:

Cash flow before taxes = NPV - Capital investments - Loan servicing + Loan growth. (4.31)

Cash flow for real estate after taxes =

Pre-Tax Cash Flow - Income tax payments made by the property owner. (4.32)

Land taxes and property taxes must be deducted from actual gross income as part of operating expenses.

Economic and tax depreciation is not an actual cash payment, so depreciation is not part of the owner's operating expenses.

Capital investments made to maintain the property being assessed must be deducted from net operating income as operating expenses.

Loan servicing payments (interest payments and debt repayments) must be deducted from net operating income if the investment value of the property (for a specific investor) is estimated.

Calculation of the cost of reversion.

Reversion is the value of the future sale of the property at the end of the forecast period.

If we consider the investor’s cash flows for a real estate property, then first the investor invests in the property, then receives income from the property and at the end of ownership sells the property, i.e. receives a reversion of the original investment.

When calculating reversion, the appraiser needs to determine the value of the property at the end of the forecast period.

• 1) comparative approach, in this case the appraiser determines the future sale price based on an analysis of the current state of the market, from monitoring the cost of similar objects and assumptions regarding the future state of the object and the future state of the real estate market;
• 2) the income approach, in this case the appraiser, based on the assumption that the property will achieve constant stable cash flows by the end of the forecast period, uses the method of capitalization of income for the year following the year of the end of the forecast period, using an independently calculated capitalization rate;
• 3) cost approach, in this case the appraiser calculates the cost of subsequent sale as the sum of the predicted value of the market value of the land plot and the cost of reproduction (or replacement) of the valued object at the end of the forecast period;
• 4) assumptions regarding changes in the value of the property during the forecast period.

Determining the discount rate.

The discount rate is the expected rate of return on invested capital in comparable risk investments or, in other words, it is the expected rate of return on available alternative investments with a comparable level of risk at the valuation date.

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

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

• · risk-free return on the market;
• · compensation for the risk of investing in real estate;
• · compensation for low liquidity;
• · compensation for investment management.

In the assessment process, it is necessary to take into account that there are nominal rates (including inflation) and real rates (net of inflation). When recalculating the nominal rate into the real one and vice versa, it is advisable to use the formula of the American economist I. Fisher:

r n = r r + I inf + r r * I inf, (4.33)

r r = (r n - I inf)/(1 + I inf), (4.34)

where r n - nominal rate;

r r - real rate;

I inf - inflation index (annual inflation rate).

It is important to note that when using nominal income streams, the discount rate must be calculated in nominal terms, and when using real income streams, the discount rate must be calculated in real terms.

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

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

• 1) cumulative construction method;
• 2) a method for comparing alternative investments;
• 3) isolation method;
• 4) monitoring method.

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

Discount rate (r) calculated by the formula:

r = r f + p 1 + p 2 + p 3 , (4.35)

where r f is the risk-free rate of return;

p 1 - premium for the risk of investing in real estate

p 2 - premium for low liquidity of real estate

p 3 - premium for investment management.

The cumulative construction method is discussed in detail in paragraph 5.1. of this chapter when calculating the capitalization rate taking into account the reimbursement of capital costs.

Method for comparing alternative investments used most often when calculating the investment value of a property. The discount rate can be taken as follows:

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

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

· Selection method - the discount rate, as a compound interest rate, is calculated based on data on completed transactions with similar objects on the real estate market.

Monitoring method is based on regular market monitoring, tracking, based on transaction data, the main economic indicators of real estate investments, including discount rates.

Let's consider an example of calculating the market value of a property using the discounted cash flow method.

The initial data for the property are presented in Table 4.4 in nominal terms. The forecast period is determined to be 3 years.

Table 4.4. Data on the property being assessed

	Indicators	Forecast period
	Total area of ​​the object, (S) sq.m.
	Rental rate, including VAT, (Car) rub./sq.m. per year
	Loss coefficient from underutilization and non-payment of rental payments (K losses), rel. units.
	Operating expenses
	Insurance costs, thousand rubles. in year
	Property tax (at the level of 2.2% of the residual book value of the building), thousand rubles. in year
	Land rent, thousand rubles. in year
	Repair and maintenance of the current condition of the property, thousand rubles. in year

No capital investment is required for the property being assessed, other than annual replacement costs.

The capitalization rate calculated in this case by the market extraction method is 18.2% (see Table 4.3).

The discount rate is determined in Table 4.5.

Table 4.5. Determining the discount rate

Indicators	Determining the value of the indicator
	Risk-free rate (r f), %	The OFZ yield to maturity was taken as the risk-free rate, which at the date of the assessment amounted to 7.1% per annum.
	Real estate investment risk premium (p 1),%
	Premium for low liquidity risk (р 2), %	The exposure period (Texp) on the segment of the assessed object is 4 months. p 2 = r f Texp; p 2 = 7.1% 0.33 = 2.4%
	Investment management risk premium (р 3), %	Determined by experts at an average level, accepted equal to 2.5%
	Discount rate (r)	Determined by cumulative construction method r = 7.1 + 2.5 + 2.4 + 2.5 = 14.4%

Solution. Calculation of the market value of a property using the discounted cash flow method within the framework of the income approach is presented in tables 4.6-4.7.

Table 4.6.

Cash flow calculation

	Indicators	Forecast period
	Potential gross income (PVI), thousand rubles. in year PVD = S C ar
	Actual gross income, thousand rubles. in year DVD = PVD (1 - K losses)
	Management costs (at the level of 2% of production costs), thousand rubles. in year
	Operating expenses, thousand rubles. per year (add up the corresponding indicators 4.1-4.5 from table 5.9)
	Cash flow (for real estate they use CHOD), thousand rubles. in year NOI = DVD - OR

Table 4.7.

Calculation of the value of a property

	Indicators	Forecast period
	Cash flow, thousand rubles in year СF=NOI = DVD - OR
	Current value of cash flows (PVC), rub.		5326,8/1,144 2 = 4 070,2	5907,4/1,144 3 = 3 945,6
	Cost of selling the object at the end of the forecast period (cost of reversion) (Vterm), thousand rubles. V term = CHOD 2010 /R
	Current cost of reversion, rub.				34313,8/1,144 3 =
	Market value of the property, calculated by the discounted cash flow method, thousand rubles. (formula 4.27)	(4 271,5 + 4 070,2 + 3 945,6) + 22 918,7 =

The market value of the property, calculated within the framework of the discounted cash flow method, is rounded to 35,206,000 rubles.