home Credit Marginal return on capital formula. Moscow State University of Printing Arts

Marginal return on capital formula. Moscow State University of Printing Arts

When a person invests money or purchases a capital asset, he acquires the right to a set of future income from the sale of the relevant product, less the ongoing costs associated with its production - income that he expects to receive over the life of the asset. It is convenient to call this series of annual incomes Q1, Q2, ..., Qn the expected income from the investment.

The expected income from an investment is opposed by the supply price of capital property, which is not understood as market price, at which property of a given type can currently be purchased on the market, and as a price just sufficient to induce the producer to produce a new additional unit of this property, that is, what is usually called its replacement cost. The relationship that relates the expected income from a capital asset to its supply price or replacement cost, that is, the relationship between the expected income generated by an additional unit of a given type of capital asset and the price of production of that unit, gives us the marginal efficiency of capital of that type. More precisely, I define the marginal efficiency of capital as the value equal to that discount rate which would equate the present value of the series of annual returns expected from the use of the capital asset during its useful life with its supply price. This gives us maximum efficiency individual species capital property. The greatest of these marginal efficiencies can then be regarded as the marginal efficiency of capital as a whole.

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The reader should note that the marginal efficiency of capital is defined here in terms of expected income and the current supply price of the capital asset. It depends on the rate of return expected to be received by investing in newly produced property, and not on a retrospective assessment of what the investment brought in relation to its original cost at the end of the property's life.

If over a period of time there is an increase in investment in any this type of capital, its marginal efficiency decreases as investment increases, partly because expected income will fall as the supply of a given type of capital increases, and partly because, as a rule, increasing pressure on the capacity to produce the corresponding capital goods will cause an increase their offer prices. The second of these factors is usually more important when establishing equilibrium for short periods of time, but as longer periods are considered, the importance of the first factor increases. Thus, for each type of capital, we can construct a graph showing how much investment in that type of property must increase during a given period in order for its marginal efficiency to fall to any given value. We can then combine these graphs for all various types capital, thus obtaining a graph connecting the amount of total investment with the corresponding marginal efficiency of capital as a whole. Let's call it the schedule of investment demand, or, in other words, the schedule of the marginal efficiency of capital.

It is clear that the actual value of current investment will tend to increase until there are no longer any types of capital property left whose marginal efficiency would exceed the current rate of interest. In other words, the amount of investment tends to the point on the investment demand schedule where the marginal efficiency of total capital is equal to the market rate of interest (66). The same can be expressed as follows. If Qr is the expected income from property at time r and dr represents the present value of one pound sterling expected to be received in r years at the current rate of interest, then (Qrdr is the demand price for investment. Their value will reach a level at which (Qrdr will equal the bid price of the investment as defined above. If, on the other hand, (Qrdr does not reach the bid price, then the current investment in the property in question will not be made.

It follows that the incentive to invest depends partly on the schedule of investment demand and partly on the rate of interest. Only at the end of book four will it be possible to give a complete picture of the factors that determine the rate of interest in all their real complexity. However, I ask the reader to note to himself here that neither knowledge of the expected income from property, nor knowledge of the marginal efficiency of this property gives us the opportunity to judge both the rate of interest and current value property. It is necessary to deduce the rate of interest from some other source, and only then can we estimate the value of the property by "capitalizing" its expected income.

How does the above definition of marginal efficiency of capital relate to commonly used terms? The marginal productivity, or income, efficiency, or utility, of capital - these are terms that we all often use. However, when studying the economic literature, it is not so easy to find a clear statement of what economists usually mean by these terms.

There are at least three unclear points that require clarification. Let's start with the fact that it is not clear whether we are talking about an increase in product per unit of time in in kind due to the use of an additional natural unit of capital or an increase in the value of the product due to an increase in the value of an additional unit of capital used. In the first case, difficulties arise in determining the natural unit of capital, which, as I believe, is both impossible and unnecessary. Of course, it can be said that ten workers will harvest more wheat from a given piece of land if they can use some additional machinery; but I do not know any other way to reduce this to an understandable arithmetic relationship other than in value terms. However, the many discussions on this issue seem to have been concerned mainly with the physical productivity of capital in one sense or another, although the authors have not been very clear about it.

Secondly, the question arises whether the marginal efficiency of capital is some absolute value or it acts as a ratio. The contexts in which it appears, and the habit of treating it as a quantity of the same dimension as the rate of interest, seem to incline us to consider it a ratio. However, it is usually not explained which relationship of exactly two quantities is meant.

Finally, there is a distinction, the neglect of which gives rise to the most confusion and misunderstanding - the difference between the increment in value obtained through the use of additional capital in a given situation, and the series of increments obtained during the entire service life of the additional capital property, i.e., the difference between Q1 and Q1, Q2,Qn... This raises a whole problem about the role of assumptions economic theory. Most discussions of the marginal efficiency of capital have not paid any attention to all members of the series other than Q1.

This, however, cannot be justified unless one remains within the framework of a static theory where all Q's are equal. The accepted theory of distribution, which assumes that capital receives its marginal product in each current period of time, is valid only for a stationary state. The total current income from capital has no direct relation to its marginal efficiency. At the same time, the current income from the marginal unit of capital (i.e., the income from capital involved in determining the supply price of products) is equal to the marginal cost of use, which also has no direct connection with the marginal efficiency of capital.

What is striking, as I have already said, is the surprising lack of clarity on this issue. At the same time, I believe that the definition I have given comes very close to what Marshall had in mind. Marshall himself used the expression “marginal net efficiency” of a factor of production, or, in other words, “marginal utility of capital.” The following is a summary of the statements closest to the subject that I could find in his Principles (67). In order to convey the essence of Marshall's thought, I have combined together some phrases that are separated in his text:

"In any factory, additional machines costing £100 can be used in such a way that without additional expenses to provide an additional £3 to the annual net receipts of the factory, less depreciation on these machines. If investors invest capital wherever they expect to make a high profit, and if, after this is done and the equilibrium is established, the said income still covers, and exactly, the expenses of using these machines, then we may conclude from this that the annual rate percent is 3%. However, examples of this kind reveal only a part of those internal forces, which determine the cost. They cannot be expanded into either the theory of interest or the theory wages without falling into a vicious circle... Let us assume that the rate of interest is 3% per annum on quite reliable securities and that the production of hats absorbs a capital of 1 million pounds sterling. This means that hat makers can use £1 million worth of capital so profitably that they would rather pay 3% a year for its use than do without it at all. There may be machines that industrialists would not refuse even at 20% per annum. If this rate was 10%, then more machines would be used; at 6% – even more; at a rate of 4% - even more and, finally, at a rate of 3%, even more machines would be used. With the volume that is thus achieved, the marginal utility of the equipment, that is, the utility of that equipment whose price just covers the costs of its use, is measured at 3%."

From what has been said, it is clear that Marshall was well aware that we fall into a vicious circle when we try to determine, following this line of reasoning, what the rate of interest actually is (68). In the passage quoted he seems to agree with the above view that the rate of interest determines the level to which new investment will rise under a given schedule of the marginal Efficiency of Capital. If the rate of interest is 3%, then this means that no one will pay £100 for a car without expecting to increase his annual net income by £3 after paying costs and depreciation. However, in ch. 14 we will see that in other statements Marshall was less cautious, although he retreated whenever he felt that his reasoning was becoming too shaky.

Prof. Irving Fisher gave in his Theory of Interest (1930) a definition of what he called the “rate of return over cost” that coincides with my definition of the marginal efficiency of capital, although he did not use this term. “The rate of return over costs,” he writes, “is a discount rate that, when used in calculating the present value of all costs and the present value of all income, makes these values equal” (69). Prof. Fisher explains that the amount of investment made in any field depends on the rate of return (less costs) taken in comparison with the rate of interest. To stimulate new investment, “the rate of return (net of costs) must exceed the rate of interest” (70). “This new quantity we introduced plays a major role in that part of the theory of interest where the possibilities of investment are studied” (71). Thus, prof. Fisher applies his concept of the rate of return (minus costs) in the same sense and for exactly the same purposes as I use the concept of marginal efficiency of capital.

The greatest confusion about the meaning and meaning of the concept of marginal efficiency of capital arose from a failure to understand the fact that this efficiency depends on the expected income from capital, and not only on its current return. This can best be illustrated by pointing out the effect on the marginal efficiency of capital of expected future changes in the costs of production, whether as a result of changes in the price of labor (i.e., in the unit wage) or as a result of innovations and changes in technology. Products produced by currently manufactured equipment must compete throughout its service life with products produced by new equipment produced in subsequent periods, and perhaps at lower labor costs or with improved technology. technical means, which makes it possible to be content with a lower price of manufactured products; Moreover, this new equipment will be used on an ever larger scale until the price of output falls to the appropriate level. In addition, business profit (in in monetary terms) from the use of equipment - old or new - will decrease if cheaper products are produced overall. To the extent that such changes are foreseen in advance as more or less probable, the marginal efficiency of the capital currently put into action diminishes accordingly.

This is the factor by which assumptions about changes in the value of money affect the volume of current output. The assumption that the value of money is falling stimulates investment (and therefore increases total employment) because it shifts up the marginal efficiency of capital schedule, i.e., the investment demand schedule. The assumption of an increase in the value of money has a depressive effect, because it shifts down the graph of the marginal efficiency of capital.

This truth is precisely the basis of the theory developed by prof. Irving Fisher, on a problem which he originally called "Appreciation and Interest", namely, that there is a difference between the nominal (money) and real rates of interest, the latter being equal to the former only when adjusted for changes in the value of money. As this theory is presented, it is not easy to grasp its meaning, for it is not clear whether the possibility of foreseeing changes in the value of money is allowed or not. One of two things: if they don’t. are provided for in advance, they will not have an impact on current affairs; if provided, then the prices of cash goods will immediately be established at such a level that the benefits of the holders of money and the owners of goods will be balanced and the holders of money will no longer be able to gain or lose from changes in the rate of interest, compensating for changes in the value of the money lent, expected during the term of the loan . Prof.’s trick does not cancel this dilemma either. Pigou, who suggested that some people anticipate future changes in the value of money, while others do not.

It is a mistake to assume that the rate of interest, and not the marginal efficiency of the available fund of capital, is precisely the factor to which future changes in the value of money directly respond. The prices of existing assets always automatically adjust to changes in expectations about the future value of money. The significance of such changes in expectations is that they affect (through the marginal efficiency of capital) the willingness to produce new assets.

The stimulating effect of the expected rise in prices is not due to the increase in the interest rate in connection with this (it would be strange to stimulate output in this way - after all, if the interest rate increases, the stimulating effect is weakened to the same extent), but due to the increase in the marginal efficiency of a given capital fund. If the rate of interest were to rise pari passu with the marginal efficiency of capital, the expectation of rising prices would have no stimulating effect. After all, the incentive to expand output is determined by how much the marginal efficiency of capital increases relative to the rate of interest. Undoubtedly, the theory of Prof. Fisher would be much better stated using the concept of the “real rate of interest”, considering it to be that rate of interest which, if established in response to changes in expectations about the future value of money, would eliminate the influence of these changes on current output (72).

It should be noted that the expectation of a fall in the rate of interest will have a downward effect on the marginal efficiency of capital schedule, since it means that output from equipment produced today will have to compete for some part of its life with output from equipment that is efficient and lower net revenue. This expectation will not have a large depressive effect, since ideas about future interest rates on loans of different terms will be partly reflected in the aggregate of rates in force today. But some depressive effect is still possible, since products produced at the end of the life of the currently produced equipment may have to compete with products obtained from newer equipment corresponding to a lower rate of return due to the decline in the rate of interest in the periods following the end of the service life currently produced equipment.

It is important to understand the dependence of the marginal efficiency of a given fund. capital from changes in expectations, for it is this dependence that mainly determines the susceptibility of the marginal efficiency of capital to the rather sharp fluctuations that explain the economic cycle. Below, in chap. 22, we will show that a series of successive rises and falls can be described and analyzed in connection with fluctuations in the marginal efficiency of capital relative to the rate of interest.

The amount of investment is affected by two types of risk that are usually confused, but which need to be distinguished. The first of them is the risk of the entrepreneur or borrower, which arises due to doubts about whether he will actually be able to receive the expected income that he is counting on. If a person bets his own money, then we're talking about only about this type of risk.

But where there is a system of borrowing and lending money, by which I mean the making of loans on real security or on the good name of the borrower, there is a second kind of risk which we may call lender's risk. It may be associated either with doubts about the debtor’s honesty, i.e., with the danger of deliberate bankruptcy or other attempts to evade obligations, or with the possibility that the amount of security will be insufficient, i.e., with the danger of involuntary bankruptcy due to unjustified calculations of the borrower. One could add here a third type of risk - one that is associated with a possible change in the value of a unit of the monetary standard, as a result of which a money loan is to a certain extent a less reliable form of wealth than real property. However, such a possibility should be fully or almost entirely reflected and, therefore, compensated for in the price of real durable property.

Let us now note that the first type of risk represents, in a certain sense, necessary social costs, although they can be reduced both through mutual equalization of risk and by increasing the accuracy of foresight. But the second type of risk is a net addition to the cost of the investment that would not exist if the lender and borrower were one and the same entity. In addition, there is a partial duplication of business risk, the assessment of which is added twice to the net interest rate when determining the minimum expected income sufficient for the decision to invest. After all, if the enterprise is risky, the borrower will want the difference between the expected income and the interest rate at which he considers it appropriate to borrow money to be more significant. At the same time, the same motive will induce the lender to insist on a greater increase in the rate he charges above the pure rate of interest, in order to make it profitable for him to lend money (unless the borrower is in such a strong position and wealth that he is able to offer the safest security). The hope of a very favorable outcome, which somehow balances the risk from the borrower's point of view, cannot serve as a consolation for the lender.

This doubling of a certain amount of risk has, as far as I know, not been given much importance up to now, but it may turn out to be important in certain circumstances. During a boom period, the common assessment of risk on the part of both debtor and creditor tends to become unusually and unwisely low.

The graph of the marginal efficiency of capital is of fundamental importance because it is mainly through this factor (much more than through the rate of interest) that the projected future influences the present. The erroneous definition of the marginal efficiency of capital as the current income from capital equipment (this would be true only in a static situation where there is no changing future that could affect the present) led in theory to a severing of the connection between the present and the future. Even the rate of interest is essentially a short-term phenomenon (73); and if we reduce the marginal efficiency of capital to the same situation, we deprive ourselves of any possibility of directly including the influence of the future in the analysis of the existing equilibrium.

The fact that behind the constructions of modern economic theory there is often an assumption of a static state introduces into it a significant element of unreality. But the introduction of the concept of cost of use and marginal efficiency of capital, as they were defined above, will help, I think, to bring the theory closer to reality, limiting itself to a minimum of necessary amendments.

It is precisely because of the existence of long-life equipment in the field of economics that the future is linked to the present. Therefore our general principles thinking is consistent with the conclusion that calculations for the future should have an impact on the present through demand prices for equipment with a long service life.

Content

Any financial and economic activity requires constant investment of capital. To maintain and expand production process and increasing its efficiency, introducing new technologies and developing new markets requires direct investments (capital investments). The source of investment can be budgetary allocations, various types of loans, borrowings, the organization's own funds, and share capital.

The choice of sources of financing depends on many factors, including the industry and scale of the enterprise’s activities, technological features of the production process, the specifics of the products, the nature government regulation and business taxation, connections with banking structures, reputation in the market, etc.

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

The most important characteristic of an enterprise's capital is its value. The cost of capital is the price that a company pays for its use, i.e. annual expenses for debt servicing to investors and creditors. It is quantitatively measured in the form interest rate characterizing the ratio of the total amount of these expenses to the amount of total capital .

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

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

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

Calculation of the cost of capital is necessary at the justification stage financial decisions, to select the most effective ways investments of funds 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 borrowed funds arise from current operations and are used for financing current activities enterprises, therefore, when calculating the average cost of invested capital, they are not taken into account. Depreciation charges are a source of covering the costs of acquiring fixed assets. Just like accounts payable, they are taken into account when drawing up the capital budget, reducing the enterprise’s need for additional sources of funds. Their price is assumed to be 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. Own capital can be external(share capital) and internal(retained earnings).

Estimation of the cost of a bond loan

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

the ability to mobilize significant volumes Money and financing large-scale investment projects and programs on economically beneficial terms for the enterprise without the threat of investor interference in the management of its current financial and economic activities;
the ability to maneuver when determining the characteristics of the issue: all parameters of the bond loan (volume of issue, interest rate, terms, conditions of circulation and repayment, etc.) are determined by the issuer independently, taking into account the nature of the investment project carried out using funds raised;
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 commercial banks) and more favorable conditions 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 costs of the issuing enterprise for the preparation and servicing of a bond issue, on the other hand;

The cost of capital received from the placement of a bond issue for the issuing enterprise is calculated in the same way as the total yield of the bond for its owner, but taking into account the additional expenses of the 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 costs of the issue;

q* - coupon rate adjusted taking into account the “tax shield effect”;

Loan cost estimate

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 capital raised will be determined by the total 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 repayment method and coincides with the interest rate on the loan, i.e. the profitability of this operation for the lender (taking into account the “tax shield effect”).

In the presence of additional costs, the cost of borrowed funds, generally speaking, changes with different loan repayment options. 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 debt repayment method.

Cost of placement of ordinary shares

Ordinary shares, unlike preferred shares, do not guarantee their owners the payment of dividends. In this regard, this type of financing is the most risky and, accordingly, the most expensive. The inherent uncertainty of common stocks makes pricing difficult share capital. There are several approaches to solving this problem, the most common of which are: the Gordon model (discounted dividend method, constant growth dividend model, etc.); financial asset pricing model (CAPM); valuation based on bond yields of this enterprise; using the price/earnings ratio (P/E ratio). The choice of assessment method depends on the available data and the degree of their reliability.

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 using the formula:

WITHs =D 1 / Pm (1 –L) +g

C s is the cost of share capital,

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

D 1 - dividend paid in the first year,

g – dividend growth rate,

L – rate characterizing emission costs (in relative terms).

If the amount of dividends is difficult to plan in advance, you can use financial asset pricing model (CAPM, Capital Assets Pricing Model ).

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

When deciding to invest capital, investors take into account two factors - the level of profitability and the level of risk associated with this financial asset. Moreover, their estimates of these parameters coincide;
all investors have the same investment horizon;
all investors have the same attitude towards risk (these are not investors - speculators);
there are risk-free assets on the market and the opportunity 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, stock returns are influenced by only one factor - the behavior of the stock market as a whole.

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

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

Cs = E

E - required return on shares,

f is the return on the risk-free asset,

E m is the average return on 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 Model

Companies that actively issue bonds and have accumulated a sufficiently long credit history can use a simpler method of valuing equity capital. By adding a risk premium to the total return on its YTM bonds, the company obtains the expected return on its common stock. The size of the premium is calculated based on 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 capital in this case is:

C s = YTM + (E m - E mb),

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

EPS model

This model for estimating the value of equity capital 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 the amount of earnings per share,

Р m is the market price of one share.

Valuation of retained earnings

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

With p = D 1 / P m + g

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

Average and marginal cost of capital

The total price of all sources is determined by the average profitability formula, that is, by the formula arithmetic average weighted. The average cost of raising capital thus obtained is denoted by WACC(Weighted Average Cost of Capital) and is calculated as follows:

WACC = ∑ C k w k , where

C k - cost of each source of funds,

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

In the general case, it is impossible to give exact relationships between the costs of various sources of capital, but the following chain of inequalities most often occurs:

Loan 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 overall price of capital raised.

It should be borne in mind that the WACC value characterizes the average price of funds not already available to the enterprise, but additionally attracted to finance future projects. The following rule is usually true: the cost of capital increases as the need 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 return on shares and bonds of a 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 arises marginal cost of capital , reflecting the fact that when a certain threshold volume is reached, the next attracted monetary unit will cost the enterprise more.

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

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

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

In the absence of comparable debt obligations, and also 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.

BOOK FOUR

INCENTIVE TO INVESTMENT

I define with the price of his offer. ultimate efficiency

. It follows that incentive to invest depends on

It's important to understand

The volume of investment is influenced two types of risk A. The first one is

lender's risk third type of risk

the future influences the present

CHAPTER 15

BOOK FIFTH

CASH WAGES AND PRICES

CHAPTER 20 Busy Function

There are two reasons why the replacement of the ordinary supply curve by an employment function is in complete agreement with the methods and purposes of this book. Firstly , occupancy function expresses the phenomena that interest us in the units we have chosen without involving any other units of measurement, the quantitative determination of which is doubtful. Secondly , this function is more suitable than the usual supply curve for analyzing the problems of industry and production as a whole, as opposed to the problems of a particular industry or individual firm, for which external conditions are assumed to be given and unchangeable.

Thus, inevitable price volatility cannot affect activities of entrepreneurs, but only funnels existing random wealth into the pockets of a lucky few. This fact has gone unnoticed in some contemporary debates about price stabilization policies. In a society subject to change, such a policy cannot be entirely successful.

We have shown that if effective demand is insufficient, then underemployment occurs in the sense that there are unemployed people who would be willing to work for less than the existing real wage. As effective demand increases, employment increases while maintaining existing real wages or even lowering them until a point is reached where there is no longer a surplus. work force, which could be used on the basis of the level of real wages established at that time. In other words, it will no longer be possible to obtain an additional number of people unless money wages begin to rise faster than prices.

However, the significance of this finding is limited by a number of practical caveats.

1. rising prices may mislead entrepreneurs and induce them to increase employment beyond the level at which their individual profits, measured in units of output, become maximum. In other words, at the new price level, they may underestimate the marginal cost of use.

2. an increase in prices will lead to a redistribution of income to the benefit of the entrepreneur and the disadvantage of the rentier, and this may affect the propensity to consume. However, this process can not only begin when full employment has already been achieved, but will be continuous throughout the time that costs increase.

The visible asymmetry between Inflation and Deflation may cause some confusion. While deflation of effective demand below the level required for full employment will reduce both employment and prices; inflation above this level will only affect prices. This asymmetry is simply a reflection of the fact that wage-earners always able to refuse work on a scale at which real wages fall below the marginal burden of labor for a given level of employment, they are not able to demand the provision of work on a scale at which real wages do not exceed the marginal burden of labor at a given level of employment.

CHAPTER 21 Price Theory

I consider it wrong to divide Economic Science into the Theory of Value and Distribution, on the one hand, and the Theory of Money, on the other. The true boundary must lie between the Theory of a Single Industry or a Firm, where factor rewards and resource distribution between different ways the use of a given amount of them, and the Theory of Production and Employment in general.

Possible complications that will actually affect the course of events:

1) effective demand will not change in exact proportion to the quantity of money;

2) since resources are not homogeneous, there will be diminishing rather than constant returns as the degree of their use gradually increases;

3) since resources are not equal in their degree of efficiency, the supply of some goods will be inelastic when there are still unused resources suitable for the production of other goods;

4) the wage unit will tend to increase before full employment of all resources is achieved;

5) the remuneration of the funds included in the marginal costs of production will not change in the same proportion.

The increase in effective demand will be spent partly on increasing the rate of resource use and partly on raising the price level. So instead of constant prices with unused resources and prices rising in proportion to the amount of money under conditions of full use of resources, we practically have prices gradually increasing as factor employment increases. That's why Price Theory , i.e. Analyzing the relationship between changes in the quantity of money and changes in the price level in order to determine the elasticity of prices in response to changes in the quantity of money must address the five complicating factors listed above.

1. A change in the quantity of money affects the amount of effective demand by influencing the interest rate. If the matter were limited to this, then the quantitative effect could be derived from three elements: a) the schedule of liquidity preference; b) a graph of marginal efficiency, and c) an investment multiplier.

2. The presence of diminishing or constant returns depends on whether whether employees are remunerated strictly in proportion to their productivity. Thus, an increase in output will be combined with a rise in prices, regardless of even any change in the unit of wages.

3. If it were available perfect balance in relative quantities of specialized unused resources, then the point of full use would be reached for all of them simultaneously. As production volume increases, a whole series of “bottlenecks” will arise, when the supply of certain goods ceases to be elastic, and their prices begin to rise to the level necessary to switch demand to other goods and services.

The general price level will not rise very much as output increases as long as there are still efficient unused resources of all kinds. But as soon as the volume of production increases so much that " narrow places", then we can expect a sharp rise in prices for some goods.

4. The upward trend in the wage unit may appear even before full employment is achieved. A proportion of any increase in effective demand will be absorbed by the upward trend in the wage unit.

Thus, in addition to the final critical point of full employment, with the achievement of which money wages must rise in response to an increase in effective demand expressed in monetary units in the same proportion as the prices of goods purchased with wages increase, we have a consistent series earlier semi-critical points, upon reaching which an increase in effective demand will also cause an increase in money wages, although not in exact proportion to the increase in the prices of goods purchased with wages.

5. The remuneration rates of different factors, expressed in terms of money, will exhibit varying degrees of inflexibility, and these factors may also have different elasticities of supply in response to changes in the monetary remuneration offered. If not for this, then the price level would be determined by two factors: the unit of wages and the size of employment. Most important element The marginal cost of production, which will vary in a different proportion than the unit of wages and fluctuate within much wider limits, is the marginal cost of use.

The long-run relationship between national income and the quantity of money will depend on liquidity preferences, and the stability or volatility of prices in the long run will depend on the intensity of the upward trend in the unit of wages relative to the rate of growth in the efficiency of the production system.

BOOK FOUR

INCENTIVE TO INVESTMENT

CHAPTER 11 Marginal efficiency of capital

I define marginal efficiency of capital as a value equal to the discount rate that would equalize the present value of a series of annual incomes expected from the use of capital assets during their service life, with the price of his offer. If for some time there is an increase in investment into any given type of capital, its ultimate efficiency decreases as investment increases , - because the expected income will fall with an increase in the supply of this type of capital, because,

llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllan increased load on the capacity for the production of the corresponding capital goods will causing an increase in their supply price. Capital efficiency depends on the expected return on capital, not just its current return.

Thus, for each type of capital, we can construct a graph showing how much investment in this type of property must increase during a given period in order for its marginal efficiency to fall to any given value. It follows that incentive to invest depends on schedule of investment demand and the interest rate.

It should be noted that the expectation of a fall in the rate of interest will have a downward effect on the marginal efficiency of capital schedule, since it means that output from equipment manufactured today will have to compete for some part of its life with output from equipment that is efficient and has lower net revenues. This expectation will not have a large depressive effect, since ideas about future interest rates on loans of different terms will be partly reflected in the aggregate of rates in force today. But some depressive effect is still possible, since products released towards the end of the service life of currently produced equipment may will have to compete with products produced by newer equipment corresponding to a lower rate of return due to the decline in the rate of interest in the periods following the end of the service life of the equipment currently produced.

It's important to understand the dependence of the marginal efficiency of a given capital fund on changes in expectations, for it is precisely this dependence that mainly determines the susceptibility of the marginal efficiency of capital to the rather sharp fluctuations that explain the economic cycle. A series of successive rises and falls can be described and analyzed in connection with the fluctuations of the marginal efficiency of capital relative to the rate of interest.

The volume of investment is influenced two types of risk A. The first one is risk of the entrepreneur or borrower , arising from doubts about whether he will actually be able to receive the expected income he is counting on. If a person puts his own money at stake, then we are talking only about this type of risk.

Where there is a system of borrowing and lending money, by which I mean the making of loans on real security or on the good name of the borrower, there is a second kind of risk - lender's risk . It can be associated either with doubt about the debtor's honesty, i.e. with the danger of deliberate bankruptcy or other attempts to evade fulfillment of obligations, or with the possibility that the amount of security will be insufficient, i.e., with the danger of involuntary bankruptcy due to unjustified calculations of the borrower. One could also add here third type of risk - one that is associated with the possible a change in the value of a unit of the monetary standard, as a result of which a money loan is to a certain extent a less reliable form of wealth than real property. The first type of risk is in a certain sense necessary social costs, although they can be reduced both through mutual equalization of risk and by increasing the accuracy of foresight. But the second type of risk is a net addition to the cost of the investment that would not exist if the lender and borrower were one and the same entity.

The schedule of the marginal efficiency of capital is of fundamental importance, because it is mainly through this factor (much more than through the rate of interest) that the expected the future influences the present. The erroneous definition of the marginal efficiency of capital as the current income from capital equipment (this would be true only in a static situation where there is no changing future that could affect the present) led in theory to a severing of the connection between the present and the future. Even the rate of interest is essentially a short-term phenomenon; and if we reduce the marginal efficiency of capital to the same situation, we deprive ourselves of any possibility of directly including the influence of the future in the analysis of the existing equilibrium.

It is precisely because of the existence of long-life equipment in the field of economics that the future is linked to the present. Therefore, our general principles of thinking correspond to the conclusion that calculations for the future must have an impact on the present through the prices of demand for equipment with a long service life. The scale of investment depends on the relationship between the rate of interest and the schedule of the marginal efficiency of capital, which relates this value to the size of current investments, and the marginal efficiency of capital reflects the relationship between the supply price of capital property and its expected income.

Return on equity (ROE) is a general indicator of a company's profitability. ROE shows how much profit a company generates on the money invested by investors.

The key question this metric helps answer is how effectively are we using shareholder investments to generate profits?

Many analysts consider ROE to be the single most important financial indicator for investors and the best indicator of the effectiveness of the management team.

Companies with high ROE (especially those with little or no debt - see also debt-to-equity ratio) are able to grow without major capital expenditures, which in turn allows management to reinvest capital to improve business operations without raising money. additional funds from shareholders. A high ROE also means there is no need to borrow cash.

Along with many other profitability measures, ROE is most useful when comparing similar companies within the same industry.

How to take measurements

Information collection method

ROE is calculated based on data taken from financial systems and financial reporting.

Formula

ROE is calculated by dividing net income by shareholders' equity:

ROE = (Net profit for period t / Average share capital for period t) × 100%.

where the amount of share capital is calculated as the difference between total assets and total liabilities. In the end it remains sum of money which is owned by shareholders.

ROE is usually calculated on an annual basis, but reporting on this indicator is carried out on a quarterly accrual basis.

The source of information is the company's profit and loss statement.

Because the necessary information is easily accessible, labor and data collection costs are minimal.

Target values

As with any indicator of profitability and efficiency, the higher the indicator, the better. The highest return on investment is desired. Over the past decade, S&P 500 companies have had ROE in the 10% to 15% range. In the 1990s. return on capital exceeded 20%. It is recommended to stick to 15-20% as a target value.

Example. Let's look at a simple example (adapted from www.buffetsecrets.com/return-on-equity.htm). An investor who bought a business for $100,000 has the same amount of capital. This amount represents the total amount of capital provided by the investor.

ROE = (Net profit for period t / Average share capital for period t) × 100% = 10%.

However, if an investor borrows $50,000 from a bank and pays $3,500 in interest annually, the calculation will change. The total capital invested in the business will remain the same - $100,000, but the capital invested personally by the investor is now equal to $50,000.

The amount of profit will also change. Net profit is now only $6,500 (10,000 - 3,500).

The return on capital (equity plus borrowed funds) will remain at the same level - 10%. But the return on equity will change and become higher - 13%:

ROE = (6500 / 50,000) × 100% = 13%.

Notes

To comparatively assess changes in profitability over a given period, companies can calculate ROE using the amount of capital at the beginning and end of the period under review.

Note also that by investing JD, you are investing at the point where the investment opportunity line just touches the interest rate line and has the same slope. Now the investment opportunity line represents the return on marginal investment, so that JD is the point at which the return on marginal investment is exactly equal to the interest rate. In other words, you can maximize your wealth if you invest in real assets until the marginal return on investment falls to the interest rate. By doing this, you will borrow or borrow from the capital market until you achieve the desired ratio between consumption today and consumption tomorrow.

The rule of the rate of return is to invest until the moment when the marginal return on investment is equal to the rate of return of equivalent investments in the capital market. This moment corresponds to the point of intersection of the interest rate line with the investment opportunity line.

GNI can be considered as the maximum level of payback or return on investment, which is a criterion for the feasibility of making investments.

IN real life individuals are not limited to investing in securities in the capital market. They can also purchase equipment, machinery and other real assets. Therefore, in addition to the line depicting the profitability of purchasing securities, we can also draw a line of investment opportunities, which will show the profitability of purchasing real assets. The return on the “best” project may be significantly higher than the return on the capital market, so the investment opportunity line may be very steep. But if the individual does not have inexhaustible inspiration, the line gradually levels out. This is shown in Figure 2-4, where the first $10,000 investments provide a further cash flow of $20,000, the next $10,000. give a cash inflow equal to only $15,000. On the tongue economic terms this is called the diminishing marginal return on capital.

The internal rate of return is sometimes considered as a limiting level of return on investment, which can be a criterion for the advisability of additional investments in a project.

Note that although the firm continues to grow operating income and makes new investments after the fifth year, these marginal investments do not create any additional value since they earn at the cost of capital level. The straightforward conclusion is that it is not growth that creates value, but the combination of excess returns and growth. This leads to a new perspective on the quality of growth. A firm can increase its operating income at a rapid rate, but if it does so by making large investments at or below its cost of capital, then it will not be creating value, but actually destroying it.

To calculate present value, we discounted the expected future return at the rate of return Σ yielded by comparable alternative investments. This rate of return is often called the discount rate, marginal rate of return, or opportunity cost of capital. It is called opportunity cost because it represents the income that an investor gives up by investing in a project rather than in securities. In our example, the opportunity cost was 7%. The present value was obtained by dividing $400,000. by 1.07

Risk premiums always reflect the risk contribution of a portfolio. Let's say you are building a portfolio. Some stocks will increase portfolio risk, and you will only buy them if they also increase your expected return. Other stocks will reduce portfolio risk, and so you are willing to buy them even if they reduce the portfolio's expected returns. If the portfolio you choose is effective, each type of investment you make should work equally hard for you. Thus, if one stock has a greater marginal impact on portfolio risk than another, the former should provide a proportionately higher expected return. This means that if you plot a stock's expected return against its marginal risk contribution to your efficient portfolio, you will find that the stocks fall along a straight line, as in Figure 8-8. This is always true: If a portfolio is efficient, the relationship between each stock's expected return and its marginal contribution to portfolio risk should be straightforward. The opposite is also true: if there is no direct relationship, the portfolio is not effective.

As we will show in Part V, the same relationship holds for the real economy. In an economy where there is no government that takes a portion of citizens' income in the form of taxes, equilibrium requires that saving equal investment. Moreover, if this is true, then the return on savings should have a certain relationship with the marginal product of capital - although in the real world the relationship between these quantities is more complex than in the Robinsonade model. Relationship between investment and interest rate When the island economist had the opportunity to earn more by making a loan than he could get at the equilibrium level of saving and investment, he decided to make a loan. This loan was alternative way savings of 50 pineapples, so the economist's total savings remain the same. However, since he agreed to lend 50 pineapples to natural scientists, he abandoned the original plan of pineapple cultivation, i.e., capital investment. He did this because by giving a loan he could get more income. The higher market interest rate (60%) forced the economist to reduce the amount of planned investment.

Interest, being the price paid in any market for the use of capital, tends to such an equilibrium level at which the total demand for capital in this market at a given rate of interest is equal to the total fund (84) entering the market at the same rate of interest. If the market we are considering is small - say, a single city or a single industry in a developed country - the growing demand for capital in that market will be immediately met by a growing supply of capital through inflows from neighboring areas and other industries. But if we consider the whole world, or even just one large country, as a single capital market, then the aggregate supply of capital can no longer be interpreted as changing rapidly and significantly under the influence of changes in the rate of interest. After all, the general fund of capital is the result of labor and assumptions, and extra labor(85) and the additional assumption, which would be prompted by an increase in the rate of interest, cannot quickly reach any significant value in comparison with labor and abstinence, the result of which is the already existing total fund of capital. Therefore, a widespread increase in the general demand for capital will for some time be associated not so much with an increase in supply as with an increase in the rate of interest (86). This growth will induce capital to partially withdraw from those areas of use where its marginal utility is lowest. Slowly and gradually - this is exactly how an increase in the rate of interest will increase the entire capital fund" (87). "It is never out of place to recall that talking about the rate of interest in relation to old capital investments can only be done in a very limited sense (88). For example, we can apparently say that a capital of approximately 7 billion pounds. Art. invested in various sectors of the English economy at a net interest rate of about 3%. But this way of expression, although convenient and justified for many purposes, cannot be considered strict. What should be said is that if the rate of net interest on the investment of new capital in each of these industries (i.e., on marginal investment) is taken to be about 3%, then the total net income generated by the entire mass of capital invested in various industries , and capitalized on a 33-year payback basis (i.e. based on a 3% rate), would be approximately £7 billion. Art. The point is that the value of capital already invested in reclaiming soil, erecting a building, laying a railroad, or making a car is the discounted value of the future earnings (or quasi-rents) expected from it. And if its prospective profitability decreases, then its value will correspondingly decrease, which will now be the capitalized value of this lower income minus deductions for depreciation." (89)

The latter stages of a boom are characterized by an optimistic estimate of the future returns of capital goods, sufficiently distinct to balance the influence of the growing surplus of these goods and the increasing costs of their production, and also, probably, the rise in the rate of interest. The very nature of organized investment markets, dominated by buyers often uninterested in what they are buying, and speculators more concerned with anticipating the next change in market sentiment than with making informed estimates of future returns on capital goods, is such that when a market dominated excessive optimism and excessive purchasing, panic begins, it acquires sudden and even catastrophic force (130). Moreover, fear and uncertainty in the future, which accompany a sharp drop, naturally give rise to a rapid increase in liquidity preference, and consequently, an increase in the interest rate. The collapse of the marginal efficiency of capital, which tends to be accompanied by an increase in the rate of interest, can seriously exacerbate the decline in investment. And yet, the essence of the matter lies in a sharp drop in the marginal efficiency of capital, especially those types of capital whose investments in the previous phase were the largest. Liquidity preference, excluding cases associated with increased trade and speculation, increases only after the collapse of the marginal efficiency of capital.

Let's return to what happens during a crisis. While the boom lasts, many new investments provide good current income. The collapse of hopes comes from sudden doubts about the expected profitability, perhaps because current profits show signs of contraction as the stock of newly produced capital goods continues to increase. If, at the same time, current production costs are regarded as too high compared to what they should be later, there is another reason for the deterioration in the marginal efficiency of capital. Once doubt arises, it spreads very quickly. Thus, in the initial stage of the crisis there will probably be many capitals whose marginal efficiency has become negligible or even turned into a negative value. But the period of time that must pass before the shortage of capital due to its use, deterioration and obsolescence becomes quite obvious and causes an increase in its marginal efficiency may be a fairly stable function of the average life of capital in a given period. If the characteristic features of the period change, then at the same time the typical time interval will change. If, for example, we move from a period of population growth to a period of population decline, then the defining phase of the cycle will lengthen. But, as can be seen from the above, there are good reasons why the duration of the crisis should be in a certain dependence on the service life of durable capital property and on the normal growth rate in a given historical period.

Incentives for saving and investment. High marginal tax rates also significantly reduce the rewards for saving and investing. Let's say you set aside $1,000 in savings. at 10% per annum, which gives you 100 dollars. interest income per year. If your marginal tax rate is, say, 40%, your after-tax interest earnings would be reduced to $60, and your after-tax interest rate would be only 6%. In such circumstances, even having the desire to save (that is, refuse current consumption) given a 10% return on your savings, you might choose to use all of your income for consumption if the return on savings is only 6%.

Let us remember that saving is a prerequisite for investing. Therefore, proponents of supply-side economics propose reducing marginal tax rates on savings. They also call for a lower tax on investment income to encourage people to invest increasing amounts of their savings in the economy. One of the determinants of investment spending is its net after-tax yield.

Let's consider the limiting case when B(t,t) and B(t,t-l) are not equal to zero and the expected time between transactions is approximately equal to the correlation intervals under study, in our case - 5 minutes. The idea is that you don't want to trade too often, otherwise you'll end up paying too much transaction costs. The average return within a single correlation time frame that you can get using this strategy, assuming the order is executed in that 5 minute time frame, is 0.03% (to account for prediction errors, we use a more conservative estimate than scale 0.04% for 1 minute used previously). Over the course of a day, this gives an average gain of 0.59%, which in a year would be 435% with reinvestment or 150% without reinvestment. Such a small correlation leads to a significant return if transaction costs are not taken into account and do not exist slippage effect (slippage occurs as a result of the fact that market orders are not always executed at the price specified in the order due to the limited liquidity of the markets and the time required to execute the order) It is clear that even small transaction costs, as in our case, 0.03 % or 3 per 10,000 investment is enough to destroy the expected profit when trading according to the strategy used. The problem is that you can't trade infrequently to reduce transaction costs, because if you do, you lose the correlation-based forecasting feature that only works within a 5-minute horizon. From this we can draw the following conclusion that the difference correlation is not enough for the strategy described above to be profitable due to the imperfection market conditions. In other words, market liquidity and efficiency drive the level of correlation, which is comparable to the absence of near-term arbitrage opportunities.

At the optimum, the return on the marginal investment is exactly as great as the market interest rate. Therefore it is true

This section examines the possibility of using models that link risk and return in relation to real estate investments. Along the way, we'll discuss whether the marginal investor's highly diversified assumption holds true for real estate investing and, if so, how best to measure model parameters—such as the risk-free rate, beta, and risk premium—to estimate the value of equity. capital We will also look at real estate investment risks that are not adequately addressed in traditional risk and return models, and discuss how to incorporate them into your assessment.

One of the first researchers to estimate the magnitude of the net losses of a monopoly was the American scientist Harberger, who in 1954 calculated the net losses for the US economy (the net loss triangle is often called the Harberger triangle in his honor). He estimates that the net loss in US manufacturing was about 0.1% of US GNP. However, there is a point of view that the amount of net losses in this study is underestimated due to incorrect calculations. In his calculations, Harberger assumed the elasticity of demand equal to 1. But this assumes that the marginal cost of production of goods by a monopolist is equal to zero. The Lerner index was estimated based on data on the deviation of the rate of return on investments in a given industry from the average return on industry. But if part of the industry is monopolized, then the average rate of return will include monopoly profit, and, therefore, its level will be higher than in conditions of free competition. If by normal profit we mean the profit received

Several are specifically devoted to interest. famous works Fischer Valuation and Interest (I896)9, Norm of Interest (907)]a, Theory of Interest (1930)". In them, he associated interest primarily with a purely psychological, impatience-related preference for present goods for future ones, which finds its expression in agio - time -nitse in the utility of goods relating to different points in time.In addition, the amount of interest, in his opinion, is influenced by the marginal rate of return on investments, which characterizes investment opportunities.

In cases where the deductibility of interest is not provided, financing from borrowed funds requires the enterprise to obtain a higher pre-tax return on investment than in other cases. If the assumption of diminishing marginal returns to capital is met, this means that in such cases, given the unavailability or limitation of financing, the equilibrium level of investment is set at a level lower than in the absence of taxation. If the tax depreciation rate is lower than the economic depreciation rate, the disincentive effect can be significant. There have been no published studies on economic depreciation rates in the modern Russian Federation. However, the Unified norms of depreciation charges inherited from Soviet times for the complete restoration of fixed assets in the Russian Federation, approved by Resolution of the Council of Ministers of the USSR dated October 23, 1990 No. 1072 and in force until Chapter 25 of the Tax Code came into force, were outdated and did not meet the needs market economy By

It can be assumed that with an increase in the capital stock, the latter ratio should at least not decrease. The second term on the right side of the last expression is equal to half the marginal return on capital, and it is positive if the implementation of the capital investment occurs immediately at the time of capital acquisition. The standard assumption is a decrease