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marginal return on capital. Return on equity - value

Any financial and economic activity requires a constant investment of capital. To maintain and expand production process and improving its efficiency, introducing new technologies and developing new markets, direct investments (capital investments) are needed. The source of investment can be budget allocations, various loans, credits and loans, own funds of the organization, share capital.

The choice of funding sources depends on many factors, including the industry and scale of the enterprise, technological features of the production process, the specifics of products, the nature of state regulation and taxation of business, relations with banking structures, reputation in the market, etc.

Ratio specific gravity individual components in the total volume of attracted capital characterizes its structure . The structure of the capital used by an enterprise determines many aspects of not only financial, but also its operating and investment activities, and has an active impact on the final result of this activity. It affects the return on assets and equity, financial stability and liquidity ratios, forms the ratio of profitability and risk in the process of enterprise development.

The most important characteristic of the capital of the enterprise is its value. The cost of capital is the price that an enterprise pays for its use, i.e. annual expenses for servicing debts to investors and creditors. It is quantified as interest rate characterizing the ratio of the total amount of these expenses to the amount of the total capital .

The concept of the cost of capital is one of the basic ones in the theory financial management. It characterizes the level of return on invested capital that the company must provide in order not to reduce its market value. The lower the cost of borrowed funds, the higher the investment opportunities of the enterprise, the more profit it can receive from the implementation of its projects, respectively, the higher its competitiveness and stable position in the market.

In addition, the cost of capital (with possible adjustments for inflation and risk) is often used as a discount rate in the process of analyzing future cash flows and evaluating the effectiveness of business investments.

The cost of capital indicator is also an acceptance criterion management decisions regarding the use of leasing or a bank loan for the acquisition of fixed assets.

The indicator of the cost of capital in the context of its individual elements (the cost of borrowed funds) is used in the process of managing the capital structure based on the mechanism financial leverage.

The calculation of the cost of capital is required at the justification stage financial solutions, to select the most effective ways investments and optimal sources of their financing .

	Sources of company funds

Sources of short-term funds		Sources of long-term capital

Accounts payable	Short-term loans and borrowings	Equity	Borrowed capital

		Ordinary shares	Bank loans
		Preference shares	Bond loans
		Retained earnings and other equity funds

Short-term borrowings arise from current operations and are used to finance current activities enterprises, therefore, when calculating the average cost of invested capital, they are not taken into account. Depreciation allowances are a source of covering the costs of acquiring fixed assets. As well as accounts payable, they are taken into account in the preparation of the capital investment budget, reducing the need for the enterprise in additional sources of funds. Their price is taken equal to the average cost of long-term capital attracted from other sources. Depending on the sources, long-term invested capital is divided into own and borrowed. Equity capital can be external(share capital) and internal(retained earnings).

Estimation of the cost of a bonded loan

The main advantages of a bonded loan as a tool for attracting investments from the point of view of the issuing enterprise are:

the possibility of mobilizing significant volumes Money and financing of large-scale investment projects and programs on economically beneficial terms for the enterprise without the threat of investors interfering in the management of its current financial and economic activities;
the possibility of maneuvering in determining the characteristics of the issue: all parameters of a bonded loan (issue volume, interest rate, terms, terms of circulation and redemption, etc.) are determined by the issuer independently, taking into account the nature of the investment project carried out at the expense of attracted funds;
the possibility of accumulating funds from private investors, attracting financial resources legal entities for a sufficiently long period (longer than the term of loans provided by commercial banks) and on more favorable terms, taking into account the real economic situation and the state of the financial market;
ensuring an optimal combination of the level of profitability for investors, on the one hand, and the level of expenses of the issuing enterprise for the preparation and servicing of a bonded loan, on the other hand;

The cost of capital received from the placement of a bonded loan for the issuing enterprise is calculated in the same way as the total yield of the bond for its owner, but taking into account additional costs issuer associated with this issue.

Cb * = [ Nq* + (N – P)/ n] / [(N + 2 P)/3]

P - the amount received from the placement of one bond, taking into account the cost of the issue;

q* - coupon rate adjusted for the "tax shield effect";

Credit cost assessment

From a financial point of view, there are no fundamental differences between issuing bonds and receiving bank loan. In both cases, the price of the attracted capital will be determined by the full profitability of the operation, which, in turn, depends entirely on the structure of the corresponding cash flow.

If the borrower does not incur additional costs associated with obtaining a loan, its cost does not depend on the method of repayment and coincides with the interest rate on the loan, i.e. the profitability of this transaction for the creditor (taking into account the "tax shield effect").

In the presence of additional costs, the cost of borrowed funds, generally speaking, changes with different options for repaying the loan. However, the possible difference is usually not too large (no more than 1% - 3%, depending on the interest rate on the loan and the amount of costs) and in practice is not taken into account when choosing a method of debt repayment.

The cost of placing ordinary shares

Ordinary shares, unlike preferred shares, do not guarantee the payment of dividends to their owners. Concerning this species financing is the most risky and, accordingly, the most expensive. Inherent Uncertainty in Common Stocks Complicates Pricing share capital. There are several approaches to solving this problem, of which the most common are: the Gordon model (discounted dividend method, constant growth dividend model, etc.); financial asset valuation model (CAPM); bond yield valuation this enterprise; using the price/earnings ratio (P/E ratio). The choice of estimation method depends on the available data and their degree of confidence.

The main model for valuing ordinary shares is Gordon model (or constant growth dividend model). It can be used for enterprises that regularly pay dividends to owners of ordinary shares, constant or increasing according to the laws of geometric progression.

According to this model, the cost of ordinary shares for an enterprise is calculated by the formula:

Withs=D 1 / Pm (1 -L) +g

C s - cost of equity,

Р m - market price of one share (placement price),

D 1 - dividend paid in the first year,

g is the dividend growth rate,

L is the rate that characterizes the cost of emission (in relative terms).

If the amount of dividends is difficult to plan in advance, you can use model for determining the value of financial assets (CAPM, Capital assets Pricing Model ).

The advantage of this model lies in the simplicity of calculations and the ease of interpretation of their results. However, its full use requires the presence of a mature financial market with a well-developed information infrastructure. It is also necessary to have reliable information about the results of the enterprise for previous years. CAPM is based on a number of assumptions and assumptions that characterize the stock market and its participants, and to a large extent idealize the real situation. Among them, the main ones are the following:

when making a decision to invest capital, investors take into account two factors - the level of profitability and the level of risk associated with this financial asset. At the same time, their estimates of these parameters coincide;
all investors have the same investment horizon;
all investors have the same attitude to risk (these are not investors - speculators);
there are risk-free assets in the market and the ability to borrow and lend capital at a risk-free interest rate;
the financial capabilities of investors do not influence their investment decisions;
asset prices are not affected by the behavior of individual investors;
there are no transaction costs in the market.

According to the CAPM model, only one factor influences the profitability of a stock - the behavior of the stock market as a whole.

An indicator of the riskiness of an individual stock is the Beta (B) coefficient, the main tool of the CAPM model. The cost of capital received from the issue of ordinary shares Cs, is defined as the required return on shares to be placed, which, in accordance with the CAPM model, is calculated using the following formula:

E = f+ B (E m - f),

Cs = E

E is the required stock return,

f is the return on a risk-free asset,

E m - average profitability in the stock market.

To use this formula, there is no need to calculate the coefficient B, which characterizes the riskiness of shares, and the market index. All these indicators are calculated and provided by special rating agencies.

Bond Value Usage Model

Companies that are actively issuing bonds and have accumulated a sufficiently long credit history can use a simpler method of evaluating equity capital. By adding a risk premium to the total return on its YTM bonds, the company obtains the expected return on common stock. The premium is calculated on the basis of the average market yield of shares E m and the average market yield of bonds E mb . The formula for calculating the cost of equity in this case is:

C s \u003d YTM + (E m - E mb),

YTM is the yield to maturity of a bond issue calculated over the full life of the bond.

Earnings per share model

This model for estimating the cost of equity is based on earnings per share, and not on the amount of dividends paid. According to this model, the cost of capital is determined by the formula:

C s = EPS / P m ,

where EPS is earnings per share,

Р m - market price of one share.

Valuation of retained earnings

The net profit of the enterprise belongs to its owners - shareholders. By refusing to receive dividends and agreeing to reinvest their profits, shareholders expect to receive income at least as much as they used to receive. The rate of return on the company's common stock will be the price of its retained earnings. Since profit retention does not require any additional costs, this value is not adjusted for the value of the company's costs associated with the issue of shares. Accordingly, when determining the price of equity capital according to the Gordon model, the expression for calculating the value of retained earnings will take the following form:

C p \u003d D 1 / P m + g

When using other methods, issue costs are not taken into account and the calculation formulas do not undergo any changes.

Average and marginal price of capital

The aggregate price of all sources is determined by the formula for the average return, that is, according to the formula arithmetic mean weighted. The average cost of raising capital obtained in this way is denoted WACC(Weighted Average Cost of Capital) and is calculated as follows:

WACC = ∑ C k w k , where

C k - the cost of each source of funds,

w k - the share of this source in the total amount of invested capital.

Exact relationships between the costs of various sources of capital cannot generally be given, but the following chain of inequalities most often occurs:

Credit cost< Стоимость облигационного займа < Стоимость привилегированных акций < Стоимость нераспределенной прибыли < Стоимость обыкновенных акций

Thus, an increase in the share of debt financing within reasonable limits can lead to a decrease in the total price of capital raised.

It should be borne in mind that the value of WACC characterizes the average price of funds not already available to the enterprise, namely, additionally attracted to finance future projects. The following rule is usually true: the value of capital increases as the demand for it increases. This is due to the fact that increasing the volume of borrowed funds increases the financial risk associated with this enterprise, and banks will provide a new portion of loans at a higher interest rate. The same consideration underlies the increase in the required yield of shares and bonds of the new issue. In addition, the demand for these financial instruments is limited; in order to place new securities, the offered yield must be increased.

As a result, the concept marginal price of capital , reflecting the fact that when a certain threshold volume is reached, the next attracted monetary unit will cost the enterprise more.

The value of WACC is minimum acceptable norm profitability of investment projects in which the company is going to invest attracted capital and is often used as a discount rate when calculating investment performance indicators.

A feature of the assessment of borrowed capital is that the issuing enterprise has the right to include the amount of interest payments within certain limits in the composition of expenses that reduce the income tax base. The resulting “tax shield” effect reduces the price of capital for the issuer.

In accordance with Articles 265, 269 of the Tax Code of the Russian Federation, non-realization expenses that reduce the taxable base include interest on debt obligations of any kind, regardless of the nature of the loan or loan provided. At the same time, accrued interest is recognized as an expense, provided that their amount does not deviate by more than 20% from the average level of interest charged on debt obligations issued in the same reporting period on comparable terms.

In the absence of comparable debt obligations, as well as at the choice of the taxpayer, the maximum amount of interest recognized as an expense is taken equal to the refinancing rate of the Central Bank of the Russian Federation, increased by 1.1 times for a debt obligation issued in rubles, and equal to 15% for debt obligations in foreign currency.

The marginal cost increases as more and more funds are raised and shows how much investment can be made without changing the target capital structure.

The boundary of the effectiveness of additional attraction of capital from the standpoint of the level of its weighted average cost. It characterizes the increase in the cost of capital in comparison with the previous period. The calculation of the marginal cost of capital is carried out according to the formula:

where PSK is the marginal cost of capital;

Increase in the weighted average cost of capital;

The increase in the amount of capital.

Comparing the marginal cost of capital with the expected level of profitability for business operations that require additional capital raising, it is possible in each specific case to determine the measure of the effectiveness of such operations (primarily this applies to investment operations).

The assessment of the cost of capital should be completed by the development of a criterion indicator of the effectiveness of its additional attraction. This criterion is marginal efficiency of capital. This indicator characterizes the ratio of the increase in the level of profitability of additionally attracted capital and the increase in the weighted average cost of capital. The calculation of the marginal efficiency of capital is carried out according to the following formula: PEC = ΔРк/ΔССК, where PEC is the marginal efficiency of capital; Δ Рк - increase in the level of return on capital; ΔССК is the increase in the weighted average cost of capital.

The stated principles of evaluation make it possible to form a system of key indicators that determine the cost of capital and the boundaries of its effective use.

Among the indicators considered, the main role belongs to the indicator of the weighted average cost of capital. It develops at the enterprise under the influence of many factors, the main of which are:

The average interest rate prevailing in the financial market; the availability of various sources of financing (bank loans, commercial loans, own issue of shares and bonds, etc.);

Industry-specific features of operating activities that determine the duration of the operating cycle and the level of liquidity of the assets used;

The ratio of the volume of operating and investment activities;

Life cycle enterprises;

The level of risk of ongoing operating, investment and financial activities.

These factors are taken into account in the process of purposeful management of the cost of equity and borrowed capital of the enterprise.

Question 19

The Capital Asset Pricing Model (CAPM) is a quantitative method for comparing the risk associated with an asset and its return. The purpose of applying the method: the CAPM model allows you to predict the profitability of a financial asset (iozh); in turn, knowing this indicator and having data on the expected income from this asset, it is possible to calculate its theoretical (forecast, intrinsic) value. For this, the basic formula of the capitalization method is used: V = I / R, where R = iozh + of; iozh - expected, or required, profitability; of - the rate of return of capital. The CAPM model is a quantitative method for assessing the return on investment in an asset in comparison with the return on the market using the coefficient β, which indicates the coincidence of trends in the price of a given (analyzed) security with the average trend in prices of securities for a group of enterprises. The basic formula of the CAPM model is: iexp = ibezr + β×(iryn - ibezr), where ibezr is the risk-free rate of return; iryn is the expected market rate of return. The coefficient β in the CAPM model is a measure of the systematic (non-own, market) risk of a given asset. In general, for the securities market, the β-coefficient is equal to one. For individual companies, it usually ranges from 0.5 to 2.0.

SARM model. The most important characteristic of this model is that the expected return on an asset is linked to its degree of riskiness, which is measured by the β-coefficient. In order to understand how the prices of financial assets are formed, it is necessary to construct a model. The valuation model for ordinary shares will look like this:

Ks = Krf + (Km – Krf) β

Ks - the price of ordinary shares as a source of financing.

Krf is the risk-free return on securities.

Km is the market value or required return on a portfolio of securities.

(Km - Krf) is the market risk premium.

β is a coefficient that characterizes the degree of volatility of the company's shares relative to the average share price on the market.

Most often, it is recommended to use the interest on long-term government obligations as a risk-free rate of return.

The β-coefficient reflects the level of volatility of a particular security in relation to the average and is a measure of earnings per share compared to the average income in the securities market.

Question 20. Weighted average (WACC) and marginal (MCC) cost of capital

weighted average cost of capital, WACC) is applied in financial analysis and business valuation. The total price of capital is the average of the prices of each source, in the total amount of capital. The indicator characterizes the relative level of the total cost of providing each source of funding and represents weighted average cost of capital

where - the share of the source in the value of the company's capital and its profitability (price).

The weighted average price of capital (WACC) is determined for a specific period of time, based on the prevailing economic conditions. This is based on the following assumptions:

1. the market and book values of the firm are equal;

2. The current structure of funding sources used is acceptable or optimal and should be maintained in the future.

The marginal cost of capital (MCC) is the cost of raising an additional unit of capital. The relationship between the assessment of the current and future cost of capital corporations provide using the indicator (Marginal Cost of Capital, MCC). It characterizes the increase in the amount of each new unit of it, additionally involved in economic circulation. Marginal cost of capital expresses the costs that the company will have to incur to reproduce the required structure capital under current financial market conditions. For example, a corporation intends to implement a new investment project to develop oil and gas field. To do this, it is necessary to attract additional sources of financing, which can only be obtained in the financial market. In this case, the forecast capital cost, which will be considered limit, may differ materially from the current market valuation. Calculation marginal cost of capital(MCC) is carried out according to the formula;

MCC = ∆WACC/∆Cap

Capital is a value that generates a stream of income. From this position, capital can also be called securities, and human capital, and production assets of the enterprise.

However, in the market for factors of production, capital is understood as production funds. It is a resource used to produce more goods and services.

Production capital is divided into basic and negotiable. Working capital is spent on the purchase of funds for each production cycle: raw materials, basic and auxiliary materials, labor.

Fixed assets are real durable assets. It serves for several years and is subject to replacement (reimbursement) as physical and moral wear and tear. In this regard, the owner of the fixed capital carries out depreciation deductions.

The return on capital will only be produced if the owner of the capital transfers it for productive use to the entrepreneur (or becomes an entrepreneur himself). Thus, it is income derived from the market for goods and services.

Loan interest(interest - i ) is the price paid to the owner of capital for the use of his funds for a certain time.

Suppose the market rate of interest i=10%. An entrepreneur can borrow funds and pay them back through certain period plus 10%. But the firm can also use its own funds, if available. In this case, the company refuses the opportunity to lend these funds to another borrower at 10%. Thus, it makes no difference whether the firm will use its own or borrowed funds. The possible investment costs in both cases are 10%.

The interest rate depends on the demand and supply of borrowed funds. Demand dk depends on the profitability of entrepreneurial investments, the size of consumer demand for credit, demand from the state and organizations. The lower the interest rate, the higher the demand for capital.

But capital is acquired in order to increase production with its help. From here - marginal return on capital:

MRPk =MR·MPk .

With the growth of investment funds, it tends to decrease, which is associated with the law of diminishing returns of production factors.

For this reason, the curve MRP k coincides with the demand curve dk(as well as in the labor market).

The larger the scale of capital investment in a country, the lower (ceteris paribus) the return from them or the profitability of production. This was first noted by D. Ricardo, then by K. Marx and A. Marshall. Therefore, in capital-rich industrialized countries, the level of return on capital may be lower than in less developed ones.

In addition to the downward trend in the interest rate in terms of perfect competition with the migration of capital between different sectors, it tends to equalize. There is an equalization of the opportunity cost of various investment projects.

Subjects capital supply (S k) are the savings households. The higher the interest rate, the more Sk. At the same time, the owners of capital refuse from the alternative use of their own capital (open their own business, buy land plot and etc.).

The larger the amount of capital offered for a loan, the greater its marginal opportunity cost or marginal opportunity cost (marginal opportunity cost - MOC ) – hence the curves s k and MOC k match.

The result of the interaction of demand and supply of capital is the equilibrium and the establishment of an equilibrium price of capital - i e.

Rice. 6.6. Equilibrium in the capital market

At the equilibrium point there is a coincidence marginal return capital ( MRP k) and marginal opportunity cost ( MOC k). The demand for loan capital coincides with its supply.

Distinguish between nominal and real interest rates. Rated shows how much the amount that the borrower returns to the lender exceeds the amount of the loan received. Real - Adjusted for inflation.

Among other things, the interest rate depends on the degree of risk (what kind of borrower?), the maturity of the loan (short-term, medium-term or long-term), the size of the loan, etc.

The company uses the proceeds to investment (Inv) .

A profit maximizing firm expands investment until MR will not be equal MC , i.e., the marginal return on investment does not equalize the sum of all marginal costs.

Marginal rate of internal payback(r- rate - norm) is the net marginal income as a result of investment, expressed as a percentage of each additional invested monetary unit (or the return on additional investment as a percentage):

r=(MR-MC)/MC.

Difference between marginal internal return on investment r and interest rate i called marginal net return on investment . Until r not less i, the firm can earn additional profit if i more r there is no point in investing. Thus, the profit-maximizing level of investment is the level at which r=i .

Rice. 6.7. Firm equilibrium: r=i

The curve labeled "marginal internal rate of return" also shows the firm's demand curve for funds to invest, i.e. coincides with dk.

For economic entities investing in real assets, the price of capital takes the form of costs for its acquisition. Therefore, in the following, the term "cost of raising capital" will often be used to refer to the interest rate.

To better understand the mechanism of creating additional wealth as a result of investment, consider the investment production function F(K). It shows the dependence of the amount of additional future income on the amount of invested capital K. This function is increasing, since as the volume of capital investments grows, the amount of future income increases. However, under the law of diminishing marginal returns, with each additional unit of invested capital, income growth should slow down. Therefore, the graph of the function F(K) will have a bulge to the left - in the direction of the y-axis. Assuming that this function is differentiable, we can say that its first derivative (velocity) will be positive, and the second derivative (acceleration) will be negative. On fig. 5 schedule production function investment is presented together with a schedule of changes in the amount of invested capital, taking into account the interest accrued on the saved amounts (segment OR). The abscissa axis of this graph plots the amount of invested capital, and the ordinate axis shows the return on investment (the amount of future income), as well as the amount of the accumulated amount of initial investment, taking into account the accrual of interest at the rate r.

Figure 5. Graph of the production function of investment

Analysis of the graph allows us to formulate the main evaluation criteria economic efficiency investment. The most obvious is the criterion of economic profit - the excess of income from investments over the amount of invested capital, taking into account the interest accrued on it at the rate r. Graphically, the value of economic profit is represented by a segment parallel to the y-axis, connecting the F(X) function curve with the OR line. From fig. 5 it follows that investments bring economic profit until the OR line crosses the graph of the function F(X). However, effective investments are not just those that bring economic profit, but ensure its maximum value. In the vicinity of the point of intersection of the graphs of two functions mentioned above, the sum of profit takes on infinitesimal values and eventually vanishes. Therefore, one should not invest in expanding assets until the absolute amount of economic profit becomes equal to zero. The optimal amount of capital investment is reached much earlier - at the point K * on the x-axis, when the slope of the production function equals the angle α or, in other words, when the tangent to the graph of the function F (K) becomes parallel to the OR line. It is at this volume of capital investments that the value of economic profit will take its maximum value.

The angle α is determined by the interest rate r, which reflects the cost of raising capital. Since the OR line is a straight line segment, the value of the angle α remains unchanged throughout the graph - the level of the market interest rate r is a constant value. Therefore, each additional unit of capital raised has a price equal to r. That is, the level of the market interest rate reflects both the average and marginal costs of raising capital (MCA = 1 + r). In contrast to the price of capital, ultimate return investment (MRK) is a variable, since the graph of the function F (X) is a convex curve, the angle of inclination of which to the x-axis is constantly changing. The MRK value is determined by the tangent of the slope of the tangent function F(K) to the abscissa axis or the first derivative of the function F(K). Taking into account the newly introduced notation, we can formulate the criterion for the economic efficiency of investments as follows: the optimal amount of capital investment is reached at the point at which the marginal return on investment becomes equal to the marginal cost of raising capital.

More clearly the relationship between relative values marginal cost of capital (MCC) and marginal return on investment (RTO) are presented in fig. 6. The abscissa axis of the graph in this figure shows the absolute amount of invested capital, the vertical axis shows the relative values of MCC and RTO. The point K* on the abscissa, representing the optimal amount of capital investments, corresponds to the point of intersection of the MCC and RTO charts.

Figure 6. Graphs of Marginal Return on Investment (MRO) and Marginal Cost of Capital (MCC)

54. Criteria for the economic efficiency of investments: net present value and internal rate of return

In economic practice, to measure the return on investment, the concept of "profitability" is used, measured as the ratio of total investment income to the amount of invested capital. The most common measure of return is the internal rate of return (IRR), which is the effective interest rate that, when used to discount future investment returns, equates the present value of future returns to the initial capital invested. To measure the amount of capital raising costs, in practice, the weighted average cost of capital (WACC) is used, which reflects the average interest rate paid by an economic entity to all suppliers of capital. Both of these indicators (IRR and WACC) are, by their nature, average, and not limiting, values, so they cannot be fully identified with the parameters of RTO and MSS. However, wide practical use received a criterion of economic efficiency of investments, which consists in comparing the values of IRR and WACC with each other. Capital investment is considered effective if its internal rate of return exceeds the total cost of raising capital.

Returning to the graphs of intertemporal reallocation of resources (Fig. 1-4), remember that any increase in the wealth of an economic entity should be manifested in a shift of the budget line BD to the right. This statement extends to the case of wealth growth through investment. The graph in fig. Figure 7 shows how capital investment in expanding long-term assets shifts the budget line to the right.

Figure 7. Joint representation of the production function of investment and the schedule of intertemporal reallocation of resources

The graph of the production function (curve AE) in this figure is inverted with respect to the graph in fig. 5. This is due to the fact that in fig. 7, the use of saved resources (capital) for investment is reflected by movement along the abscissa axis not from left to right (from point O to point K *), as it was shown in fig. 5, and vice versa - from right to left (from point Y 1 to point L). This reflects the process of reducing the volume of goods available for current consumption, as a result of using part of these goods for investment. As a result, the economic entity will be able to consume in period 0 only the remaining part of the previously available current resources after investments (the segment OL on the x-axis).

If an economic entity were to simply save the corresponding amount of resources (Y 1 L) by lending to someone at an interest rate r, then point A would move up along the budget line to position G. Such a shift along the budget line does not change the amount of wealth. However, as a result of investments, there was an increase in the volume of future income by an amount equal to F(X) (the corresponding segment is marked on the y-axis of the graph with a curly bracket). At the end of the investment (point L on the x-axis), the graph of the production function turned out to be at point E, which lies above the original budget line BD. Consequently, the economic agent now has access to a new, larger consumption plan lying on the new, higher budget line B´D´ (the new line must be parallel to the original line BD, since the interest rate r remains unchanged). The intersection of this line with the abscissa axis occurs at point В´, shifted to the right from the origin of coordinates in comparison with point B. The value of this shift (segment ВВ´) reflects the increase in the wealth of an economic entity as a result of investments. Geometrically, you can determine the value of this segment, which will be equal to the discounted value of additional income from investments minus the amount of initial capital investments:

(4)

This indicator called the net present value of the investment (NPV). If we denote future investment returns as FCF, and the amount of invested capital as Inv 0 , then the formula for calculating NPV will take the following form:

(5)

The amount of wealth of an economic entity, taking into account the investments made (W´ = О´В´), will be equal to the sum of the initial wealth (W = OB) and its growth due to investments (the length of the segment ВВ´):

W´ = W + BB´ (6)

W´ = W + NPV (7)

Returning to the graph in Fig. 7, it should be noted that the situation presented on it reflects insufficiently effective use the economic subject of the resources available to him. The maximum amount of wealth growth would be obtained if the company stopped making investments after their marginal return (MRK) was equal to the cost of capital (MCC = r). In this case, the new budget line B´D´ would not cross the graph of the production function F(K), but only touch it at the point that provides the greatest economic profit for GE. An example of a situation with the choice of the optimal amount of capital investments is shown in Fig. eight.

Figure 8. Formation of the optimal capital investment budget

In this case, a noticeably larger amount of net present value (segment ВВ´ along the x-axis) was obtained with a much smaller amount of capital investments (segment Y 1 L on the same axis). This result due to the fact that only those investments were made, the marginal return of which (RTOs) turned out to be higher than the costs of raising capital (MCA). At the point of contact (E) of the budget line with the graph of the production function of investment, the return on investment was equal to the cost of capital, so the process of investing capital was stopped. In the practice of substantiating investment decisions, instead of the RTO and MCA parameters, the indicators of internal rate of return (IRR) and weighted average cost of raising capital (WACC) are used, respectively. Using practical terminology, two main criteria for the economic efficiency of investments can be derived.

marginal return on capital. Return on equity - value

Sources of company funds