Capital financial assets. capital assets. Financial assets and liabilities

29.11.2019

In ch. 19 outlined the logic for estimating capital financial assets using the /X^-model. This approach is very clear and simple (let us emphasize that it is algorithmically simple, but not in terms of estimating the initial parameters of the model), but it has a very significant drawback: the assessment is carried out without taking into account risk. Meanwhile, we know that the vast majority of transactions in the market always have a risky component, and therefore the assessment of the market characteristics of the goods traded on them must be carried out taking into account this component.
If there is only one product on the market, if the parameters of its sale are set by the monopolist, if the conditions for the functioning of the monopolist are predetermined, etc., then certainty is also high in relation to the traded asset. The situation changes radically when many counterparties (sellers and buyers) appear on the market, when an element of stochasticity is introduced into the conditions of production and sale, when competition forces market participants to resort to various tricks in relation to their behavior on the market, etc. The same takes place on the financial markets; Moreover, the factor of interconnection and interdependence between basic characteristics assets traded on them (which, as we know, are profitability and risk) manifests itself even in a more accentuated form (due to the significant homogeneity of goods, the speed of transactions with them, price volatility, etc.).

Thus, we have come to the obvious conclusion: the valuation of capital financial assets must be carried out considering the asset being valued in the context of the market, i.e. in its relationship and interdependence with other similar (to one degree or another) assets. In sec. 1.9 we mentioned the role of scientists in developing the theory and practice of valuation in the market of capital financial assets. In terms of stock valuation, the most famous research was W. Sharp, which served as the basis for the development of the so-called capital financial asset valuation model (CAPM), or a one-factor model.
The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between the profitability and risk of an individual financial asset and the market as a whole. Synonym: pricing model in the market of capital financial assets. As a market commodity, a traded security is subject to the laws of this market, including the logic and patterns of pricing. Among these patterns is the mutual influence of the main characteristics (i.e., price, value, risk, profitability) of traded goods on each other and the ability to control the values of these characteristics by forming combinations of goods. This pattern was noticed by the American researcher G. Markowitz, who created the portfolio theory.
The ideas and mathematical apparatus presented by Markowitz were largely theoretical in nature, however, in order to implement the theory he proposed, multiple calculations, although of the same type, were necessary in the course of sorting through various combinations of financial assets traded on the market. In this case, it was required not only to estimate the expected return of each stock, but also to calculate the pairwise covariances of the returns of different combinations. Computers in those years were low-performance, and therefore any optimization task turned out to be extremely expensive.
Therefore, a real breakthrough in the field of financial investment management was the simplified and more practical version of the mathematical apparatus proposed by W. Sharp in 1964, called the one-factor model. stock market, closely correlates with some factor inherent in this market and is one of its key characteristics. According to Sharpe, such a factor could be the level of prices in the market, the gross national product or some kind of price index. The main thing is that when this factor is isolated, it can really be argued that it largely determines the value of the expected return of any asset traded on this market.
Sharpe's technique has already made it possible to effectively manage large portfolios, including hundreds of capital financial assets. Research in this direction was also carried out by J. Traynor, J. Lintner, J. Mossin, F. Black and other "scientists. As a result of joint efforts, the CAPM model was developed, which explains, in particular, the behavior of the yield of any security circulating on the market.
The logic of the model is as follows. The main indicators in the market of capital financial assets used by investors are the average market return kt, the risk-free return kf, which is usually understood as the return on long-term government securities; the expected profitability of the security ke, the expediency of the operation with which is being analyzed; coefficient « (3, characterizing the marginal contribution of this stock to the risk of the market portfolio, which is understood as a portfolio consisting of investments in all securities quoted on the market, and the proportion of investments in a particular security is equal to its share in the total market capitalization. On average for the market p = 1 for a security that is more risky compared to the market, Р gt; 1; for a security that is less risky compared to the market, р lt; 1
It is obvious that the difference (kt - k^) is a market premium for the risk of investing funds not in risk-free, but in market assets1; the difference (?, - k is the expected premium for the risk of investing in this security. These indicators are proportionally related through the beta coefficient (the linearity of the representation will be proved below).
ke - k,) \u003d P (A, „ - k, (). (20.17)
Representation (20.17) is convenient for understanding the essence of the relationship between premiums and the risk of the firm's securities (recall that for the market P = 1). Since in practice we are talking about estimating the expected return on a particular security (or portfolio), the representation (20.17) is transformed as follows:
ke = k^ +p (20.18)
Both formulas express the Financial Asset Pricing Model (CAPM), which is used, in particular, to predict the yield of any security traded on the market. The model has a very simple interpretation: the higher the risk associated with a given firm compared to the market average (and the risk market is not defined), the greater the premium received from investing in its securities. As is known, on the basis of the predicted return and data on the expected returns generated by a certain security, its theoretical value can be calculated; therefore, the CAPM model is often referred to as the pricing model in the market of capital financial assets. Note that different representations of CAPM are known - in terms of profitability (the most common) and in terms of cost estimates (for more details, see; (Krushvits, 2000]).
As can be seen from model (20.18), the expected return (ke) of the shares of a certain firm AA is a function of three interrelated and interdependent parameters: the average market return, the risk-free return, and the p-coefficient inherent in this firm.
The Market Rate of Return is generally the return on the market portfolio. For example, km is taken as the average return on stocks included in the market portfolio used to calculate some well-known index (we will mention, in particular, Dow Jones 30 Industrials and Standard amp; Poor's 500-Stock Index) . The km values can be found in the files of the leading information and analytical agencies and stock exchanges.
Risk-free Rate of Return is the expected average annual growth rate of the economy in the long term, but adjusted for the current fluctuation due to changes in short-term liquidity and inflation. Unanimous opinion regarding values k,f no. Yes, American financial analysts agree that the yield on treasury obligations should be taken as kj, but there is no unanimity about which obligations to use - long-term or short-term.
The Beta-coefficient is the main factor that reflects the mutual correlations of the profitability of a given firm with the returns of securities circulating in a given market. It is a measure of the systematic risk of the shares of a given company, characterizing the variability of its return in relation to the average market return (ie, the return of the market portfolio). Can you say more? expresses the sensitivity of the return on the shares of this issuer in relation to the average market return. Meaning? fluctuates around 1 (for a market on average? = 1), so for a firm with high values of it, any change in the market on average can lead to even greater fluctuations in its profitability. In short, ? - an indicator of the riskiness of the company's securities.
The CAPM model is the main tool for assessing the feasibility of transactions with financial assets in the capital market. In contrast to the Gordon model, it no longer implies the need to assess possible dividends. The accuracy of estimating the corresponding CAPM parameters is of crucial importance. These indicators are inertial, and their values are evaluated, periodically adjusted and published by agencies for firms whose securities are quoted on the market, that is, the level of professionalism in evaluating kf? and kt is much higher than the average investor's individual assessment of the firm's prospects in relation to its expected earnings.
Like any theory of finance, the CAPM model is accompanied by a number of premises, which were formulated in an accentuated form by M. Jensen (Michael C. Jensen) and published by him in 1972. These are the prerequisites.
The main goal of each investor is to maximize the possible increase in their wealth at the end of the planning period by estimating the expected returns and standard deviations of alternative investment portfolios.
All investors can borrow and lend indefinitely at some risk-free interest rate, and there are no restrictions on short sales of any assets. All investors equally evaluate the value of the expected values of return, variance and covariance of all assets. This means that investors are on an equal footing in terms of predicting performance.
All assets are absolutely divisible and perfectly liquid (that is, they can always be sold on the market at the existing price).
There are no transaction costs.
Taxes are not taken into account.
All investors accept the price as an exogenously given value (i.e., they assume that their activity in buying and selling securities does not affect the price level in the market for these securities).
The number of all financial assets is predetermined and fixed.
It is easy to see that many of the formulated premises are purely theoretical. But even if we ignore the conventions of these restrictions, the possibility of practical application of the CAPM depends on the development of the financial market, the availability of proper statistics and consistency in its updating; in particular, the predictive power of the model is largely determined by the adequacy of the values of the p-coefficients. Each type of security has its own p-coefficient, which is the index of the return of this asset in relation to the return on average in the securities market. The value of the indicator (3) is calculated from statistical data for each company that lists its securities on the stock exchange and is periodically published in special directories. For each company, P changes over time and depends on factors related to the characteristics of the company's activities from a long-term perspective. Obviously, this primarily includes the level of financial leverage, which reflects the structure of sources of funds: other things being equal, the higher the share of borrowed capital, the more risky the company is and the higher its p.
The logic for calculating the p-factor is as follows.

Let there be a set of profitability indicators for a group of companies for a number of periods (k9), where k, is the profitability indicator of the r "-th company (/" \u003d 1, 2, in the /-th period O \u003d 12, ..., u). Then general formula calculating the p-coefficient for an arbitrary /-th company has the form
M
where Cov(kj, - amp;„,) is the covariance between stock returns and the average
L i-I
overnight yield;

k, - - X - yield of securities of the 1st company on average for all periods.

From the above formulas, conclusions can be drawn. First, the indicator p can indeed be considered as a characteristic of the riskiness of a financial asset, since it reflects the relationship between the variations in the return of an asset and the market on average. Secondly, since the profitability of a risk-free asset does not depend on the market, i.e., does not fluctuate in dynamics, the numerator in (20.19) is equal to 0, and therefore p = 0 for this asset. Thirdly, for an average market financial asset (or market portfolio) the numerator and denominator in (20.19) are the same, i.e. for such an asset (portfolio) Р = I
The above calculation algorithm according to the formula (20.19) is laborious, and therefore you can use a simpler algorithm that gives an approximate value of the p-coefficient.

Let ku be the return on shares of the 1st company in the 7th year, and kt) be the average return on the market = 1, 2, ..., u) for all analyzed periods. If the CAPM model is applicable to the market, then, as follows from the model, the p-coefficient is an elasticity coefficient, and its value can be calculated as the ratio of the increment in the return on shares of the 1st company to the increment in the average market return.
(20.20)
We emphasize that the algorithm given by formula (20.20) is very approximate, since increments can be calculated in different ways. An acceptable variant may be as follows: (1) calculate the average (for example, over the years) values of the return on the shares of a given company and for the market as a whole; (2) build a linear regression equation that reflects the dependence of the average return on shares of a given company from the average return on the market; (3) the regression coefficient (i.e., the coefficient at the parameter kt) and will be the p-coefficient.
Example
In table. Table 20.2 shows the dynamics of the profitability of the company NN by years.
Table 20.2
Dynamics of profitability indicators
Year
Profitability of the company NN. % \ Average market yield. % \12
18
4
9
18
1.6
10
12
8
10
13
14
2
4
5
4 7

Calculate the value of the p-factor. Solution
During the study period, the return on NN shares varied from 4% to 18%, while the average market return changed from 8% to 14%. Therefore, from (20.20) it follows
Thus, NN shares are about 2.3 times more risky than the average market portfolio. In other words, the return on a company's stock varies more than the market. Hence the conclusion: by giving preference to the shares of the company NN, you can win more, but you can also lose more.
You can make a more accurate calculation by building a regression equation and finding the regression coefficient.
k=-12.4+2.6*..
With this calculation, we get that p \u003d 2.6, i.e., the company's shares are approximately
2.6 times more risky than the market.
On the whole, for the securities market p = 1; for individual companies it fluctuates around 1, with most p-values ranging from 0.5 to 2.0. The interpretation of the p-value for the shares of a particular company is as follows:
p = 1; shares of this company have an average degree of risk prevailing in the market as a whole;
P lt; one; the securities of this company are less risky than the market average (for example, p = 0.5 means that this security is half as risky as the market average);
p gt; one; securities of this company are more risky than the average in the market;
an increase in the ^-coefficient in dynamics means that investments in the securities of this company become more risky;
a decrease in the p-coefficient in dynamics means that investments in the securities of this company become less risky.
An example is the averaged data on the 0-coefficients of the series American companies in 1987-1991 :
The highest p values were for American Express, 1.5; "Bank America" - 1.4; "Chrysler" - 1.4;
the average values of P had the company "Digital Equipment Co" - 1.1; "Walt Disney" - 0.9; "DuPont" - 1.0;
The lowest p values were for General Mills - 0.5; "Gillette" - 0.6; "Southern California Edison" - 0.5,
It should be noted that there is no single approach to the calculation of p-coefficients (in particular, with regard to the number and type of initial observations). Thus, the well-known American banking house Merrill Lynch, which publishes market indicators, uses the Samp; P 500 index and monthly data on the profitability of companies for 5 years, i.e. 60 observations, as km when calculating the p-coefficients of companies; Value Line uses the NYSE Composite Index, which includes returns on common stocks from more than 1,800 companies, and uses 260 weekly observations.
In 1995 (3-coefficients appeared on the domestic securities market. Calculations were carried out by the information and analytical agency "Analysis, Consultation and Marketing" (AKamp; M), however, the list of companies, as a rule, did not exceed one and a half dozen, covering mainly , energy and oil and gas complex enterprises.The values of p-coefficients varied significantly.Thus, in January 1997, the oil industry had p = 0.9313, and the petrochemical industry - 0.1844. Beta-coefficients are periodically published in the press.
Example
Assess the feasibility of investing in shares of company AA with p = 1.6 or company BB with p = 0.9 if k:f = 6%; km = 12%. An investment is made if the yield is at least 15%.
Solution
The estimates needed for making a decision can be calculated using the CAPM model. According to formulas (20.18) we find:
for company AA: ke = 6% + 1.6 (12% - 6%) = 15.6%;
for company BB: ke =6%+ 0.9 -(12% - 6%) = 11.4%.
Thus, the investment is expedient only in the shares of the company AA.
As can be seen from (20.18), CAPM is linear with respect to the risk level p. This most important property of the model makes it possible to determine the p-coefficient of a portfolio as a weighted average of the p-coefficients of its financial assets.
P, \u003d YOM *. (20.21)
i=l
where p* is the value of the ^-coefficient A-ro of the asset in the portfolio;
Pn - the value of the p-coefficient of the portfolio;
o* - the share of k-ro asset in the portfolio;
n is the number of different financial assets in the portfolio.
Example
The portfolio includes the following assets: 12% shares of company A, having p = 1; 18% shares of company B, having p = 1.2; 25% shares of company C, having P = 1.8; 45% shares of company D, having p = 0.7. Calculate the value of the p-coefficient of the portfolio.
Solution
According to the formula (20.20)
Рр = 0.12-1+0.18-1.2+ 0.25-1.8+ 0.45-0.7 = 1.1.
Portfolio risk is slightly higher than the average market risk.
Securities market line. The logic of the relationship between the indicators included in the CAPM model can be demonstrated and explained using a graph called the Security Market Line (SML) and reflecting the linear relationship "profitability-risk" for specific securities. Let us find the relationship between the expected return (k) and the risk of the security (r), i.e. we construct the function ke = /(r). The construction is based on the following assumptions: (a) the return on a security is proportional to its inherent risk; (b) risk is characterized by P; (c) an “average” security, i.e., a security with average market values of risk and return (or a market portfolio), corresponds to p = 1 and a yield k, „\ (d) there are risk-free securities with a rate and p = 0 .

We assume that the required dependence is linear. Then we have two points with coordinates (0, kt) and (1, kt). From the course of geometry it is known that the equation of a straight line passing through the points (d'|, y\) and (xr, r/2). given by the formula
l - x,
U~U\
(20.22)
* 2~*1U7-U1
Substituting the initial data into the formula, we obtain the model (20.18). In addition, you can build the desired graph (Fig. 20.11). For clarity, we used the data from the previous example with the securities of companies AA and BB.

Now it remains to show that ZLYA is indeed a straight line. This means that all securities must lie on this line. Two situations need to be considered: (a) the point lies below 3mb (this means that the corresponding security is overpriced, i.e., it promises a lower return than the average market); (6) the point is above 5M1 (this means that the corresponding security is undervalued, i.e. it promises higher returns than the average market).
Let's look at the first situation first. In fact, it is divided into two sub-options with securities having p lt, respectively; 1 and p gt; 1. Suppose that there is a security M with P = 0.8 and a yield of k - 9%, and a security McP = 19 and A = 17%. If we are in an efficient market, then according to the CAPM, the yields of securities N and M should be (again, for clarity, we use the data of the example) 10.8% and 17.4%, respectively, i.e.
No. k, \u003d 6% + 0.8- (12% - 6%) \u003d 10.8%;
M: ke = 6% + 1.9 (12% - 6%) = 17.4%.
In other words, both securities are located below the 5A/1 line, which is shown in Fig. 20.11. Let us show that this is impossible. Indeed, by simple steps, the investor could earn a higher return than investing in paper N. 20% - in a risk-free asset with P = 0. The market portfolio will give him 12%, and the risk-free asset 6%, i.e. in this case, the expected return will be
ke \u003d 0.8-12% + 0.2-6% \u003d 10.8%.

Investing in security N is not profitable, since you can get a higher return for the same money, that is, a return on invested capital. This means that the security is overvalued, i.e. overpriced. In an efficient market, the demand for it will fall, which will lead to an increase in profitability until it is exactly on the SLM line.
The situation with security M is also impossible. The key to the reasoning in this case is the CAPM premise that all investors can receive and provide loans in an unlimited amount at a certain risk-free interest rate kf Then the actions of a typical investor are as follows: he takes a loan for 90% of the amount he plans to invest, and money (own and borrowed) invests in the market portfolio, while receiving 12% per annum. With such a strategy of behavior, the investor from the entire amount invested by him will receive 22.8% of the income (190-12%) and must give 5.4% (90-6%) for the use of funds raised, i.e. his net income will be 17. four%. Investing in security M is not profitable, in the conditions of this market, you can always find a strategy that provides greater profitability. Paper M is also overvalued, and therefore the demand for it will fall, the price will decrease and the yield will rise to the level corresponding to the market with this level of risk, i.e., described by the CAPM model.
Similar considerations are made in the second situation, when the security is undervalued and, in terms of the SML chart, lies above the line of the securities market. The higher than the market yield will cause demand for these securities, the price will rise, the yield will decrease, and again there will be stabilization on the SML line. The above reasoning concerned a specific security, but there are a lot of securities on the market, and therefore, can the SML line be a broken line? Theoretical reasoning shows that it cannot, because otherwise the valuation of many assets would be distorted, the equilibrium in the market would be disturbed, and in the course of purchase and sale operations, the situation would eventually level out, it would stabilize in relation to the relationship between the returns of individual assets and the market generally.
A generalization of the concept of a “securities market line” is the Capital Market Line (CML), which reflects the “return-risk” relationship for efficient portfolios, which, as a rule, combine risk-free and risky assets.
The capital market line can be used to comparative analysis portfolio investment. As follows from the CAPM model, each portfolio corresponds to a point in the quadrant in Fig. 20.11. There are three options for the location of this point: on the CML, below and above this line. In the first case, the portfolio is called efficient, in the second - inefficient, in the third - superefficient.
Other ways of using CML are known. In particular, by selecting financial assets in a portfolio, an investor can find what the return should be for a given level of risk.
As noted above, the CAPM model was developed based on a number of assumptions, some of which are not implemented in practice; for example, taxes and transaction costs exist, investors are in unequal conditions, including in relation to the availability of information. Therefore, the model is not ideal and has been repeatedly subjected to both criticism and empirical verification. Especially intensive research in this direction has been carried out since the late 1960s.
XX century, and their results are reflected in many articles by Western experts. There are different points of view about the model, so we will give the most typical ideas about state of the art this theory from a review by Y. Brigham and L. Gapensky. According to Brigham and Gapensky, the CAPM model describes the relationship between the expected values of variables, so any conclusions based on empirical testing of statistical data are unlikely to be valid and cannot disprove the theory.
According to many scientists, one of the main drawbacks of the model is that it is one-factor. Pointing to this drawback, well-known experts J. Weston and T. Copeland give such a figurative example. Imagine that your small plane is unable to land due to heavy fog, and when you ask the controllers for help, you are informed that the plane is 100 miles from the runway. Of course, the information is very useful, but hardly sufficient for a successful landing.
In the scientific literature, there are three main approaches that are alternative to the CAPM model: the theory of arbitrage pricing, the theory of pricing of options, and the theory of preference of situations in time.
The Arbitrage Pricing Theory (ART) is the most famous theory. The concept of ART was proposed by a well-known specialist in the field of finance S. Ross. The model is based on the natural assertion that the actual return of any stock consists of two parts: the normal (or expected) return and the risky (or uncertain) return. The last component is determined by many economic factors, for example, the market situation in the country, estimated by gross domestic product, the stability of the world economy, inflation, interest rate dynamics, etc. Thus, the model should include many factors and most general view described by the following relationship:
(A "/„) bJn + e, (20.23)
where kj - actual yield j-th a security;
kj - expected return j-th valuable paper;
/ - the actual value of the i-ro economic factor;
f is the expected value of the i-th economic factor;
/gt;, - sensitivity of the /-th security to the economic factor;
6j - the influence of specific factors not included in the model on the change in the yield of j-a security.....
This model has advantages and disadvantages. First of all, it does not provide for such rigid initial assumptions that are characteristic of the CAPM model. The number and composition of relevant factors are determined by the analyst and are not regulated in advance. The actual implementation of the model is associated with the involvement of a complex apparatus of mathematical statistics, therefore, until now, the APT theory has a theorized character. Nevertheless, the main advantage of this theory, which is that profitability is a function of many variables, is very attractive, because this theory is considered by many scientists as one of the promising ones.
Two other alternatives to the CAPM model - the Option Pricing Theory (ORT) and the State-Preference Theory (SPT) - have not been developed for one reason or another and are in the process of formation. The description of the content of these theories, the mathematical apparatus used and the developed models is beyond the scope of the book. In particular, with regard to the latter theory, it may be mentioned that its exposition is of a highly theorized nature; for example, implies the need to obtain accurate estimates of future market conditions. The origin of the theory of option pricing is associated with the names of F. Black, M. Scholes and R. Merton, and the theory of preferences - with the name of J. Hirschleifer. The reader can find the most complete presentation of these theories in the work of T. Copeland and J. Weston, and a brief summary in the work of L. Krushwitz (see: (3) about a specific security with an expected return ke.

An investor will only choose risky securities if he is offered an additional reward in the form of a premium on the yield offered on risk-free securities. This explains the fact that both km and ke are always greater than krf, otherwise no one would buy corporate securities.

Coefficient (can be interpreted as an indicator of the riskiness of a given security. From (2.22) it clearly follows that for the average market portfolio (i.e., if ke = km) β = 1. For a security that is more risky compared to the market, the premium should be higher, i.e. β > 1. For a security less risky than the market, β As can be seen from model (2.21), the expected return (ke) of the shares of a certain company AA is a function of three interrelated and interdependent parameters: ( 1) the average market return, (2) the risk-free return, and (3) the inherent β-coefficient of a given firm.These indicators are quite inertial, and their values are estimated, periodically adjusted and published by specialized agencies for firms whose securities are quoted on the market, i.e. The level of professionalism in assessing krf, β, and km is much higher than in an individual assessment by an ordinary investor of the company's prospects in relation to its expected income (dividends).

Risk assessment. Transactions with financial assets, including in the context of mobilizing funding sources, are risks by definition. In the most general form, risk can be defined as the probability of some undesirable event occurring (in principle, one can speak exactly the opposite - about the probability of some desired event occurring). Regardless of the type of risk, it is usually assessed in terms of probability; As for the expected outcomes in a risk situation, they are most often described in the form of some losses (or gains), and their value expression, of course, is not the only possible one. Exist different kinds risk depending on the object or action, the riskiness of which is assessed: political, industrial, property, financial, currency, etc. definitions, much less a rigorous evaluation algorithm. In other words, the term "risk" is often used as a generalized description of the state of anxiety and uncertainty in relation to a given object or situation.

The risk of a single desired (or undesirable) event is described by two main characteristics; (a) the likelihood of its implementation; and (b) the significance of the consequences of its implementation. In other words, we should be talking, in fact, about the evaluation and subjective optimization of the combination (k, r), where k is a characteristic of some outcome (for example, the amount of loss), r is the probability of an event with such an outcome. The actual magnitude of the risk is assessed through the indicators of variation: the more variable the expected values of the outcomes, the more risky the event that generates these outcomes. The main measure of risk is the standard deviation, which shows the average deviation of the values (x)) of the variable characteristic relative to the center of distribution, in this case, the arithmetic mean (.r). This indicator, sometimes called the standard deviation, is calculated by the formula:

When applied to listed shares as the main type of capital financial assets, formula (2.23) is not directly used by individual investors, and the level of risk is expressed through the β-coefficient.

More on the topic Valuation Models in the Markets of Capital Financial Assets:

6.3.1. MODELS FOR DETERMINING THE COST OF OWN CAPITAL
3.1. Social responsibility of private business as a factor\r\ninvestment activity in the social sphere
2.4 Institutional continuity in accounting (evolution of concepts and practices)
1.1 Capital as an object of value measurement in accounting
5.1 Methodology for assessing liabilities in terms of changes in the value of assets in accounting

- Copyright - Advocacy - Administrative law - Administrative process - Antimonopoly and competition law - Arbitration (economic) process - Audit - Banking system - Banking law - Business - Accounting - Property law - State law and management - Civil law and process - Monetary circulation, finance and credit - Money - Diplomatic and consular law - Contract law -

Under financial investment refers to the process of investing property in financial assets. Financial assets – financial resources, representing a set of cash and securities owned by the company.

Financial assets include:

– cash, including cash on hand, and funds in bank accounts;
– securities: shares, shares of other companies, stock options, etc.;
– receivables;
– financial investments;
- settlement documents on the way, etc.

The definition of financial assets does not include intangible and tangible assets, advances received, inventories, etc., since their possession does not give rise to the right to receive certain financial assets in the future, although it may bring profit.

Financial assets – the right to income derived from the use of real assets.

In other words, real assets are the source of income, while financial assets serve to characterize the distribution of income received. Investing funds in financial assets gives the right to receive profit from the use of real assets, the acquisition of which was carried out at the expense of investments.

Features of financial assets:

1) serve as an investment object;
2) are the ownership of income, reflecting the movement of loan capital;
3) are not real wealth and are presented in the form of payment and financial obligations regarding the movement of financial resources;
4) do not participate in the process of production, release of goods, provision of services at the enterprise.

Financial assets are traded in financial markets.

Financial markets perform the following functions.

1. In these markets, large firms find additional sources of funding.
2. With the help of financial markets, the public is informed about the state of affairs in large business structures.
3. Assets circulating in these markets serve as the object of investment, insurance, hedging and speculation.

Capital financial assets include stocks and bonds. Securities are traded on financial markets and have several valuations, the key of which are: 1) the current market price ( rt); 2) intrinsic or theoretical cost ( V). These estimates do not always match.

Three situations are possible in terms of the relationship between the market price and the intrinsic value of a capital financial asset:

There are three approaches to assess V:

1) technocratic - the current value of a financial asset is estimated based on the processing of price statistics;
2) followers of the fundamentalist approach believe that any security has an inherent value, which can be estimated as the discounted value of future earnings generated by this security:

(7.12)

3) followers of the theory of "walking at random" suggest focusing on the "invisible hand" of the market. In their opinion, if the market has a sufficiently high efficiency, then it is impossible to beat it, and any calculations are practically useless.

Debt securities are bonds.

According to the methods of payment of income, bonds are distinguished:

– with a fixed coupon rate;
- floating coupon rate;
- uniformly increasing coupon rate;
– payment by choice;
- mixed type.

By the nature of circulation, bonds are distinguished:

- ordinary;
- convertible.

Zero coupon bond valuation:

where V is the intrinsic value of the security.

Valuation of perpetual bonds:

Valuation of an irrevocable term coupon bond with a constant income:

where is the annual coupon yield; M- par value of the bond.

Valuation of a revocable term coupon bond with a constant income.

There are two options.

1. The probability of early repayment is small. Then the formula for the valuation of an irrevocable term coupon bond with a constant income is used.
2. The probability of early repayment is high:

where is the redemption price of the bond; P - the maturity period of the bond.

Valuation of preferred shares:

Valuation of shares with a uniformly increasing dividend:

(7.17)

where g- constant growth rate of dividends.

Valuation of stocks with a variable growth rate of dividends:

(7.18)

where With– a period of unsystematic change in dividends.

Profitability of a financial asset In its most general form, it can be represented as follows:

The yield of a bond without the right to early redemption.

(7.20)

where FROM– annual coupon income; M - face value of the bond; R is the current market price of the bond; k- the number of years remaining until the maturity of the bond.

The yield of a bond with the right to early redemption:

(7.21)

where Y is the price of the bond redemption; t - the number of years remaining until the maturity of the bond.

Share return:

where is the first expected dividend; – the current market price of the share; g is a constant growth rate of dividends.

Example 7.4

A bond was issued with a nominal value of 50 thousand rubles, a coupon rate of 8% per annum and a circulation period of three years. On the market, it is sold for 48 thousand rubles. Determine its present value and yield to maturity if the discount rate is 6%.

Solution.

1) Calculate the current (intrinsic) value of the bond

2) Find the bond's yield to maturity

Thus, the intrinsic value of a bond is higher than its market value. This means that this security is attractive for investment. The yield to maturity on an annualized basis for this bond is 9.5%.

Example 7.5

A share with a face value with a current market price of 3450 rubles is circulating on the market. The last dividend paid is 380 rubles. and it is expected that in the future the growth rate of dividends will be 5% per year. Calculate the current value of the stock and its return at a discount rate of 12%.

Solution.

1) Determine the intrinsic value of the stock

2) Find the return on the stock

Thus, the stock is attractive for investment, and its annualized yield is 16.5%.

The model that describes the relationship between the rates of return and risk of an individual financial asset and the market as a whole is called pricing model in the market of capital financial assets, or CAMP financial asset valuation model.

Expressed by the formula

(7.23)

where is the expected return on the financial asset; – risk-free return; – average market profitability;

Beta coefficient characterizing the riskiness of the security being valued; () – market premium for the risk of investing in market assets; () is the expected risk premium for investing in this security.

Example 7.6

The expected (actual) yield of the security is 12.5%, the P-coefficient for it is 1.3; risk-free rate of return - 6%; the average market yield is 10%. Determine its required yield and the feasibility of investing in this security.

Solution.

Calculate the required yield on this security using the model SARM:

Thus, this security is investment-attractive, since the actual yield on it (12.5%) is higher than the required yield (11.2%).

Financial investments involve risk. Risk - the probability of a deviation from the planned result under conditions of uncertainty economic activity object under study.

Risk theories - classical (J. Mil, N. Senior) and neoclassical (A. Marshall, A. Pigou).

In determining the risk, it is necessary to take into account:

- the possibility of an event occurring;
– uncertainty of the occurrence of the event;
- an action, as a result of which an event may or may not occur.

In 1952, G. Markowitz in his book "Portfolio Formation" set the task of using the concept of risk when constructing investment portfolios for investors.

He came to the following conclusions.

1. The set of efficient investment portfolios is a subset of the set of feasible portfolios.
2. On an efficient path, feasible investment portfolios are both efficient in the sense that they give the investor the maximum expected return for a given risk, or minimal risk in the formation of the expected return.
3. The optimal investment portfolio is reached at the point of contact between the investor's indifference curve and the efficient trajectory (Fig. 7.1).

Rice. 7.1.Formation of the optimal investment portfolio from n-th number of financial assets on the efficient trajectory:

ABCD– effective trajectory; ABCDEFG is an admissible set of portfolios; N, S, K - optimal investment portfolio for conservative, moderate and aggressive investors, respectively

Important to remember

An effective investment portfolio is a portfolio that provides the investor with the maximum return for a given level of risk or the minimum level of risk for a given return. The optimal investment portfolio always belongs to an efficient trajectory and takes into account the interests of the investor (his risk appetite).

The main practical rule of the financial market: to increase the reliability of the effect of a contribution to risky fiat securities, it is advisable to invest not in one of their types, but to make a portfolio containing the largest possible variety of fiat securities, the effect of which is random.

The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between the risk and return indicators of an individual financial asset and the market as a whole. The idea of the model is this. The concept of a premium for the risk of investing not in risk-free, but in marketable assets is introduced:

where - premiums for the risk of investments in market assets; d r – average market return; d br is the risk-free return.

Expected risk premium for investing in this security:

and (2.4.13)

where is the risk premium for investing in a particular financial asset; d а – expected return on the financial asset, d r – average market return; d br is the risk-free return; b is the beta coefficient.

Profitability of a financial asset according to the CAPM model:

d a \u003d d br + b (d r - d br) = (2.4.14)

According to this model, the expected return on a firm's stock is a function of three interrelated parameters: the average market return, the risk-free return, and the firm's inherent beta.

This model is interpreted as follows. The higher the risk associated with a given firm, compared to the market average, the greater the premium received from investing in its securities.

It should be emphasized that when evaluating the risk of a particular asset, one can act in two ways: either consider this asset in isolation from other assets, or consider it an integral part of the portfolio. Risk assessments in these two options may differ significantly. An asset that has a high level of risk, when considered in isolation, may turn out to be practically risk-free from the perspective of a portfolio and for a certain combination of assets included in this portfolio. Therefore, most often the investor does not work with a single asset, but with some of their set, called a portfolio of securities, or an investment portfolio.

Task 1.1

There are 120 thousand rubles on your bank account. The bank pays 12% per annum. You are offered to enter the entire capital into a joint venture organization, promising a doubling of capital in 5 years. Should I accept this offer?

Solution:

Let us introduce the notation:

R. is the initial amount.

r is the declared annual rate.

n is the number of years.

With compound interest, the accumulated amount in the bank for 5 years will be:

F= 120*(1+0.12) 5 = 211.48 thousand rubles

The above calculation indicates the economic benefit of the proposal (240>211.48)

Calculate the present value:

P \u003d 240 / (1 + 0.12) 5 \u003d 240 / 1.76234 \u003d 136.18 thousand rubles.

This calculation also indicates the profitability of the proposal (136.18>120).

Assuming that the risk of participation in the enterprise is assessed by introducing a risk premium of 5%, the present value will be equal to:

P \u003d 240 / (1 + 0.17) 5 \u003d 240 / 2.192448 \u003d 109.47 thousand rubles.

Under such conditions, participation in the enterprise becomes unprofitable (109.47<120).

Task 1.2

What is the preferred amount at a rate of 12% - $1,000 today or $2,000 in 8 years?

Solution:

F = P *(1+r ) n ; F n= 1000*(1+0.12) 8 = $2475.96

2475,96-2000=475,96

Accordingly, now it is more profitable to put money at 12% than to receive 2000 in 8 years.

Task 1.3

What are the conditions for granting a loan and why are more beneficial for a bank client: 24% per annum, monthly accrual or 26% per annum, semi-annual accrual?

Solution:

Let's determine the effective annual rate by the formula:

r \u003d (1 + r / m) m -1, where

r - interest rate;

m is the number of accruals per year;

We get:

For monthly interest:

r \u003d (1 + 0.24 / 12) 12 -1 \u003d 0.2682 or 26.82%.

For semi-annual interest calculation:

r \u003d (1 + 0.24 / 2) 2 -1 \u003d 0.2544 or 25.44%.

Since the effective interest rate with a semi-annual accrual is less than with a monthly one, it is more profitable for a client to take a loan at a rate of 26% per annum, the accrual is semi-annual.

Task 1.4

Payment under a long-term contract involves the choice of one of two options: 25 million rubles. after 4 years or 50 million rubles. after 8 years. At what interest rate is the choice indifferent?

Solution:

Let's make the equation of indifference:

, where

S - payment amounts;

i - interest rate;

n - term.

We get:

or 18.92%.

Thus, the choice is indifferent at an interest rate of 18.92%.

Task 1.5

The bank provided a loan of 100 thousand rubles. for 28 months at 16% per annum on the terms of a one-time repayment of the debt and accrued interest. Interest is calculated quarterly. Calculate the amount to be returned under various interest schemes.

Solution:

We use the formula for simple interest:

FV =PV *(1+t /T *r ), where

R V is the loan amount;

t is the duration of the period;

T is the number of months in a year;

r is the interest rate.

We get:

FV \u003d 100 * (1 + 28 / 12 * 0.16) \u003d 100 * 1.37333 \u003d 137.33 thousand rubles.

We use the formula for compound interest:

F n = P × (1 + r /m ) w × (1 + f × r /m ), where

declared annual rate;

the number of accruals per year;

integer number of subperiods;

fractional part of the subperiod.

We get:

F \u003d 100 * (1 + 0.16 / 4) 8 * (1 + 0.33 * 0.16 / 4) \u003d 100 * 1.368569 * 1.0132 \u003d 138.66 thousand rubles.

The amount returned when using a simple interest rate, the accrued amount will be 137.33 thousand rubles, when accruing a complex one - 138.66 thousand rubles.

Task 1.6

Citizen N wants to purchase a pension contract, under which he could receive 15 thousand rubles annually. during the rest of your life. The insurance company, using mortality tables, estimated that the client could live 20 years, and set 6% per annum. How much should you pay for a contract?

Solution:

We use the annuity:

A=R*
, where

R is the amount of the annual payment;

r - interest rate;

n - term.

We get:
thousand roubles.

Thus, the cost of the pension contract will be 172.05 thousand rubles.

Task 1.7

The company was offered to invest 100 million rubles. for a period of 5 years, subject to the return of this amount in installments (20 million rubles annually); after 5 years, an additional remuneration in the amount of 30 million rubles is paid. Should I accept this offer if it is possible to deposit money in a bank at the rate of 8% per annum? What if it's billed quarterly?

Solution:

When money is placed in a bank, by the end of the five-year period there will be:

When interest is calculated once a year:

F \u003d P * (1 + r) n \u003d 100 (1 + 0.08) 5 \u003d 146.9 million rubles.

When interest is calculated quarterly:

F \u003d P * (1 + r / m) nm \u003d 100 (1 + 0.08 / 4) 20 \u003d 148.6 million rubles.

In another option, the cash flow can be represented as an urgent postnumerando annuity with A=20, n=5, R=8% and a one-time receipt of the amount of 30 million rubles.

Based on the formula for the future value of a term postnumerando annuity, we get:

F=A*FM3(r,n)+30=20*FM3(8%,5)+30=20*
+30=20*5.8666+30=

147.33 million rubles

The investment offer is profitable when compared with the accrual of annual interest (147.33>146.9). It is most profitable to place money in a bank when interest is accrued quarterly (147.33<148,6).

Task 1.8

The insurance company accepts payments for six months in equal installments of 10 million rubles. within 4 years. The bank serving the company also calculates interest for half a year at the rate of 20% per annum with interest accrued for half a year. How much will the insurance company receive at the end of the contract?

Solution:

, where

m - the number of accruals;

j - the number of equal receipts of funds in a year

m = 2 j = 2 n = 4

million rubles

Thus, after the expiration of the contract, the insurance company will receive 114.36 million rubles.

Task 1.9

Determine the real profitability (loss) of a financial transaction if, at an inflation rate of 3.5% in the first half of the year and 4.5% in the second, the nominal rate on a deposit for a period of 1 year is 7.6% per annum, and interest is accrued semi-annually. By how much should the interest rate be raised to compensate for inflationary losses.

Solution:

I and \u003d (1 + 0.035) 6 * (1 + 0.045) 6 \u003d 1.6

Thus, the real loss ratio was 0.36%.

2. VALUATION OF CAPITAL FINANCIAL ASSETS

Task 2.1

Bonds with a zero coupon face value of 1000 rubles. and maturing in 4 years are sold for 750 rubles. Analyze the feasibility of purchasing these bonds if there is an alternative investment opportunity with a rate of return of 9%.

Solution:

We determine the real price of bonds using the formula:

V t \u003d CF / (1 + r) n \u003d 1000 × 0.708 \u003d 708 p.

Since the real value is lower than the selling price, it is unprofitable to buy these bonds, it is more expedient to use an alternative option, since a higher income will be received.

Task 2.2

The face value of a bond with a maturity of 10 years is 100 thousand rubles, the coupon rate is 12%. The bond is considered risky, the risk premium is 2%. Calculate the present value of a bond if the market yield is 9%?

Solution:

The current value of the bond is determined by the formula:

Where

r=9%+2%, n=10

Vt= 100*0.12*5.889+100*0.35218=105.89 thousand rubles

Thus, the current value of the bond amounted to 105.89 thousand rubles.

Task 2.3

Two zero-coupon bonds are being sold on the market. Bond A with a face value of 10 thousand rubles. and maturing in 4 years is sold for 8 thousand rubles, bond B with a face value of 10 thousand rubles. and maturity in 8 years - for 6 thousand rubles. What is the best bond to invest in?

Solution:

Determine the yield on each bond using the formula:

, where CF is the face value of the bond; РV – selling price; n - term.

We get:

For four years: r =
or 5.74%;

For eight years: r =
or 6.59%.

Thus, the most profitable is a bond with a term of 8 years.

Task 2.4

Company A shares have β = 1.6. The risk-free interest rate and rate of return in the market are on average 11% and 15%, respectively. The latest dividend paid is $3 per share and is expected to increase steadily at a rate of 5% per year. What is the expected return on the company's stock? What is the market price of a share, assuming the market is highly efficient and in equilibrium?

Solution:

k e= k rf + β  (k m– k rf ) = 11 + 1.6 × (15 - 11) = 17.4%, where

k e

the expected yield of the security, the expediency of the operation with which is being assessed;

k m

average market return;

k rf

risk-free yield, which is understood as the yield of government securities;

a beta coefficient that characterizes the riskiness of the security being valued.

Share return

Doll.

Thus, the expected return on the company's shares was 17.4%, and the market price of the share was $25.40.

3. WORKING CAPITAL MANAGEMENT

Task 3.1

Company A places an order for raw materials at a price of 4 rubles. per unit batches of 200 units. each. The need for raw materials is constant and equal to 10 units. per day for 250 business days. The cost of fulfilling one order is 25 rubles, and the cost of storage is 12.5% of the cost of raw materials.

Solution:

The optimal order size is determined by the formula:

, where

EOQ- optimal stock purchase size in physical units

the size of the ordered batch of stocks, units;

annual need for reserves, units;

costs of placing and fulfilling one order;

the cost of holding a unit of inventory.

We get:
= 500 units.

The costs for the existing order policy are:

FROM t \u003d H * 362.5 rubles.

When moving from the current raw material ordering policy to a policy based on EOQ , the cost will be

FROM t \u003d H * 250 rubles.

The effect will be 362.5-250=112.5 rubles. in year.

Task 3.2

Using the Baumol model, on the basis of the given data, determine the policy for managing the DC on the company's current account.

The company's cash costs (V) amount to 3 million rubles. The interest rate on government securities (r) - 8%, the costs associated with each of their implementation (c) - 50 rubles.

Solution:

Baumol model

61237 rub. = 61.2 thousand rubles.

The average size of DS on the current account is equal to

Q / 2 = 30.6 thousand rubles

The total number of transactions for the conversion of securities into DC for the year

k = 3000000 / 61237 = 49.

The total cost of implementing such a management policy

CT \u003d 0.05 * 49 + 0.08 * 30.6 \u003d 2.45 + 2.45 \u003d 4.9 thousand rubles.

The company's policy for managing DCs and their equivalents is as follows: as soon as the funds in the current account are depleted, the company must sell part of its securities in the amount of approximately 61.2 thousand rubles. This operation will be performed 49 times per year. The maximum amount of DC on the account will be 61.2 thousand rubles, the average - 30.6 thousand rubles.

Task 3.3

The enterprise has concluded an agreement with the supplier providing for payment for the supply of raw materials according to the 3/15 net 60 scheme. What should be the supplier settlement policy if the current bank rate on short-term loans is 18% per annum?

Solution:

d/k net n

opportunity cost

d / (1-d) * 360 / (n - k) \u003d 3 / (100 - 3) * 360 / (60 - 15) \u003d 3/97 * 360/45 \u003d 24.7%

24,7% > 18%

It is advisable to use the right to a discount and pay for raw materials on the 15th day.

Task 3.4

In the store in June, the revenue of the grocery department amounted to 52 million rubles, and the gastronomic department - 41 million rubles, the inventory turnover in days was 35 and 32 days, respectively.

Define:

inventory turnover in turnover and in days for the store as a whole;

how will the turnover in the turnover of the store change if the turnover for the month increased by 10%, and the average inventory decreased by 5%.

Goods turnover

Department

Revenue

turnover,

days

Medium

reserves

(gr. 2 × gr. 3)

per month