Cost risk measure var. Financial analysis and investment assessment of the enterprise
The basis of any credit operation, that is, the transfer of money in debt to the borrower from the lender, is the desire to receive income. The absolute amount of income received by the lender for the transfer of money in debt is called interest money or interest. The origin of this name is due to the fact that the amount of the loan payment is usually determined as the corresponding percentage (in the mathematical sense) of the loan amount.
A loan can be paid at the end of the loan term or at the beginning (advance interest income). In the first case, interest is accrued at the end of the term based on the amount of the amount provided, and the amount of the debt together with the interest is subject to return. This method of calculating interest is called discursive. In the second case, interest income is paid in advance (paid at the beginning of the term), while the debtor is given an amount reduced by its amount, and only the original loan is subject to repayment at the end of the term. Interest income paid in this way is called a discount (i.e., a discount on the amount of the loan), and the method of calculating interest is called antisipative.
In world practice, the decursive method of calculating interest has become more widespread, therefore the term "decursive" is usually omitted, speaking simply about interest or loan interest. When using antisipative percentages, the full name is used.
One of the most important properties of cash flows is their distribution over time. With the help of the interest rate, the future value of “today's” money (for example, if they are going to lend) can be determined, as well as the present (modern, current) value of “tomorrow's” money - for example, those that are promised to be paid one year after the delivery of goods or the provision of services. In the first case, we are talking about the operation of accrual (accrual), therefore, the future value of money is often called accrued. In the second case, discounting or bringing the future value to its modern value (current moment) is performed. This value of money is called discounted, reduced or current.
The interest rate K shows the degree of intensity of the change in the value of money over time and is determined by dividing the interest income by the initial amount.
The interest rate is used in determining the increase in current value, so K is a kind of "mark-up".
Increasing the initial amount using the interest rate is called the decursive method of calculating interest.
In addition to the interest rate, there is a discount rate (or discount rate) Heap. It is equal to the ratio of interest income to the final amount.
The discount rate is used in determining the reduction in future value, that is, Kuch - "discount" biskont (German) - discount.
However, sometimes at a discount rate they add value. The calculation of interest using a discount rate (discount rate) is called the antisipative method.
With the help of the considered rates simple and compound interest can be charged.
In Russia, at present, the decursive interest calculation method is mainly used. The antisipative method is usually used for technical purposes, for example, to determine the amount, discounting which at a given discount rate and term, will give the desired result.
The project and its environment
Each project develops in a specific environment. Moreover, no matter what subject area it belongs to, this environment directly affects the project. All impacts are divided into several categories.
Socio-cultural environment (customs and customs of the area, ethical considerations of project activities, etc.)
The international political environment (the political situation on the territory, economic influence, resource intensity of the area, etc.)
Environment (environmental parameters, availability of natural resources, etc.)
The environment of the project may change during its implementation, changing its impact on it. Such changes are both positive and negative. Change management deals with the appropriate section of the project management discipline.
The project environment is called the project environment. The project environment can be divided into several types: external and internal, near and far.
The external environment of the project is that part of the environment that exists independently of the project.
The internal environment of the project is that part of the environment that exists only during the implementation of the project. The external environment of the project, which is independent of the particular enterprise, is called the distant environment of the project.
The external environment of the project arising within the framework of this enterprise is called the immediate environment of the project.
Let us consider in detail the components of the project environment and their impact on the project.
Project distant surroundings
Political characteristics and factors:
Political stability.
Government support for the project.
Nationalist manifestations.
Crime level.
Trade balance with member countries.
Participation in military alliances.
Economic forces:
The structure of the national economy.
Types of liability and property rights, including land.
Tariffs and taxes.
Insurance guarantees.
Inflation rate and currency stability.
The development of the banking system.
Sources of investment and capital investment.
The degree of freedom of entrepreneurship and economic independence.
The development of market infrastructure.
Price level.
The state of the markets: sales, investments, capital goods, raw materials and products, labor, etc.
at the level of an economic entity, the investment climate is elevated to the rank of one of the key macroeconomic factors that determine its investment activity.
The investment climate is a complex, capacious and complex concept. It can be considered on a multilevel basis. Complexity is expressed in the fact that the investment climate is formed under the influence of a combination of factors of a political, economic, social nature, etc., creating as a result the basic conditions for carrying out investment activities in a country or region. Multilevel means the possibility of differentiating the investment climate according to a territorial or sectoral principle.
In world practice, various methods of forming investment attractiveness are used. Her multi-level assessment includes assessment and forecasting:
Macroeconomic indicators of the investment market;
Investment attractiveness of sectors and sub-sectors of the economy;
Investment attractiveness of the regions;
Investment attractiveness of individual companies.
The investment climate is negatively affected not only by the direct restrictions on the activities of foreign firms contained in the legislation, but also by the vagueness and especially the instability of the legislation of the host country, since this instability deprives the investor of the ability to predict the development of events, which reduces the profitability of the investment.
Among the economic parameters, the main focus in assessing the investment climate is given to the general state of the economy, the situation in the currency, financial and credit systems, the customs regime, and the possibilities for using labor (the cost of labor and its ratio with the average level of skill of workers and labor productivity).
The price of money is a payment for the temporary use of “other people's” money; it is determined in the form of simple or compound interest. Interest - this is the income from the provision of capital in debt, that is, the money charged for the use of money. If interest has a value expression, they are usually called interest money. By lending money today, the owner exposes himself to the risk of not returning it, that is, not receiving income from possible investments, reduces his liquidity. Therefore, he seeks to recover losses - to receive income from providing money in debt. This income is called interest money.
Interest rate - a value characterizing the rate of interest accrual.
Interest Calculation Period - the period of time for which interest is accrued (the period for which money is provided).
Accrual interval - the minimum period after which interest is accrued.
There are two ways to accrue interest: decursive and antisipative.
Interesting way of calculating interest - increase in the initial amount for interest rate. Interest (more correctly - interest money) is paid in the end each accrual interval.
A destructive interest rate (i) called a loan interest,- this is the percentage ratio of the amount accrued over a certain interval of income I (interest money) to the amount available at the beginning of this interval - P.
Increase (increase) in the initial amount of debt - an increase in the amount of debt due to the addition of accrued interest.
S \u003d P + I, (4.1)
I \u003d S - P, (4.2)
where S - accumulated amount.
Build factor K ndefined as follows:
Interest rate i is a relative value, measured in fractions of a unit and is determined by dividing interest money by the initial amount.
. (4.4)
The formula for calculating the interest rate is identical to the calculation of the statistical indicator “growth rate”.
Determination of accrued amount S called compounding . Determination of the initial amount R – discounting.
The day of receipt and the day of final repayment of the loan are considered one day (boundary day). Interest on loans and deposits is usually accrued daily. In this case, either the exact number of days in a year (360/365) or banking (30 days) can be used.
At antisipative interest calculation method (preliminary)interest is paid at the beginning of the period for which interest is accrued. Example: interest charged by a bank in accounting for bills; on factoring credit and so on. The amount of the loan is the accumulated amount S. Based on it, interest is accrued. The borrower receives the loan amount minus interest.
The difference between the size of the loan S and issued amount R called a discount, denoted by D and represents the amount of interest money.
D \u003d S - P. (4.5)
The discount rate, expressed in fractions of one and determined by dividing the amount of discount by the amount Ris called discount rate d .
. (4.6)
You can see that the amount of interest I and the amount of discount D are defined in the same way. However, in the first case, we are talking about an increase in current value, a kind of "mark-up", that is, the future value of "today's money" is determined. In the second case, the present value of future money is determined, that is, a “discount” is determined from the future value (diskont in German means “discount”).
Most often, the antisipative method is used for purely technical purposes - when discounting, as well as when taking into account bills in the bank and when paying for factoring services. In all other cases, in world practice, the decursive method of calculating interest is more common.
The antisipative method is used in countries with developed market economies during periods of high inflation, since the antisipative method builds up more rapidly than with the decursive accrual method.
In the business practice of the Republic of Belarus, the decursive method of calculating simple interest is currently mainly used. Interest on accounts is calculated in accordance with the agreement between the bank and the client. Interest is accrued on credit and deposit account accounts for the period, including the day the loan was issued or money was credited to the deposit, and the day preceding the loan repayment or deposit (account closure). If the interest rate is changed, interest at the new rate is accrued from the day it is established.
Basic concepts and definitions of financial mathematics:
Interest- income from the provision of capital in debt in various forms (loans, credits, etc.), or from investments of a production or financial nature.
The initial amount of money (present, modern, current, reduced) is the amount of capital available at the initial moment of time (or the amount of capital invested in the operation in question).
Interest rate - a value characterizing the rate of interest accrual.
Building (Compounding) - increase in the initial monetary amount due to the addition of accrued interest.
Accrued (future) amount of money - The initial amount of money together with accrued interest.
Discounting- determination of the current financial equivalent of the future cash amount (bringing the future cash amount to the present moment of time).
Build factor - a value showing how many times the initial capital has grown.
Accrual period - the period of time during which interest is accrued. It can be expressed in days or in years, is both an integer and an integer.
Accrual interval - the minimum period of time after which interest is accrued. The accrual period may consist of one or more equal accrual intervals.
The time base for calculating the percent T -the number of days in a year that is taken to calculate interest. Depending on the method for determining the duration of a financial transaction, either an exact or an ordinary percentage is calculated.
The following options are possible:
There are several ways to accrue interest and, accordingly, several types of interest rates. Depending on the accrual method used, financial results can vary quite a lot. Moreover, the difference will be the greater, the greater the invested capital, the applied interest rate and the duration of the accrual period.
The general idea of \u200b\u200bthe various methods of calculating interest is given by the following scheme:
Interest Calculation Methods |
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Decursive |
Antisipative |
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Simple s / s |
Sophisticated s / s |
Simple s / s |
Sophisticated s / s |
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Accrualn times a year |
Continuous Interest |
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The most common is recursiveinterest accrual method. With this method, interest I accrued at the end of each accrual interval. Their value is determined based on the amount of capital provided P. Decent interest rate (loan interest) i represents the percentage of the accrued over a given interval of income (percent) to the amount available at the beginning of this interval. The value of the interest rate characterizes the rate of interest.
The following mathematical expression corresponds to this building operation:
S = P + I = P + iP = P (1 + i)
The reverse of this operation is the operation discounting, i.e. determining the current value of P equivalent to the future sum of S:
P = S / (1 + i)
From the point of view of the concept of time value of money at a given interest rate of the amount Pand Sequivalent, we can also say that the amount P is an current financial equivalent future amount S.
At antisipative In the (preliminary) method, interest is accrued at the beginning of each accrual interval. The amount of interest money is determined based on the amount of future cash. Antisipative interest rate (discount rate) d there will be a percentage ratio of accrued income to future cash amount.
In this case, the formula for determining the value of the accumulated amount is as follows:
S = P + I = P / (1 - d)
Accordingly, for the discount operation, called in this case bank accounting:
P = S (1 - d)
In practice, antisipative interest rates are usually used when accounting for bills. The interest income received in this case is called a discount - a discount on the future amount.
With both methods of accrual, interest rates may be simpleif they apply to the same initial amount of money during the entire accrual period, and complicatedif after each interval they are applied to the sum of the initial capital and interest calculated for the previous intervals.
Formulas for determining the future cash amount for various options for calculating interest for the period n years:
S = P (1 + ni) - for case simple decursive interest
S = P (1 + i) n - for case compound decursive interest
S = P / (1 - nd) - for case simple antisipative interest
S = P / (1 - d) n - for case compound antisipative interest
If the accrual period is expressed in days, the simple interest formulas will take the form:
S \u003d P (1 + t / T i)
S \u003d P / (1 - t / T d),
where t is the duration of the accrual period.
Factors showing how many times the future cash amount is greater than the value of the initial capital are called accumulation factors. The inverse of the building factors are the discount factors, which allow you to determine the current financial equivalent of the future cash amount.
In some cases, when analyzing the effectiveness of various financial transactions, it may be useful to determine equivalent interest rates. Equivalent interest rates - these are interest rates of various types, the use of which under the same initial conditions gives the same financial results. Under the same initial conditions in this case we mean the same amount of initial capital and equal periods of accrual of income. Based on this, we can make equivalence equation and derive the ratio for the rates in question.
For example, for simple loan and discount rates, such ratios will look as follows:
d = i / (1 + ni); i = d / (1 - nd).
An equivalent lending rate reflects the profitability of the relevant accounting transaction and is useful in comparing the profitability and effectiveness of various financial instruments.
Accounting for inflation in financial calculations
Inflation is characterized by a decrease in the purchasing power of the national currency and a general increase in prices. For various participants in a financial transaction, the inflationary process does not act in the same way. So, if the lender or investor can lose part of the planned income due to the depreciation of funds, the borrower is able to repay the debt with money of reduced purchasing power.
In order to avoid mistakes and losses, the inflationary effect should be taken into account when planning financial transactions.
We denote by S a the amount whose purchasing power, taking into account inflation, is equal to the purchasing power of the sum S in the absence of inflation. Inflation rate a the relation between the inflationary change of a certain quantity for a certain period and its initial value, expressed as a percentage (the relative indicator is used in the calculations):
a \u003d (S a - S) / S 100%
From here: S a \u003d S (1 +a)
This means that with inflation rate a, prices rise over the period by (1 + a) times. The factor (1 + a) is called the inflation index I a.
If the period in question consists of several intervals, at each of which the inflation rate is a, the prices as a whole will rise (1 + a) n times. The total result is expressed as follows:
S a \u003d S (1 + a) n
From here follows the first important conclusion regarding the inflationary process:
Inflationary growth is similar to the increase in initial capital by the compound interest rule.Only in this case we do not receive income, but lose it.
Another useful consideration concerns calculating a rate of return that could offset inflationary losses and provide capital gains.
Let a be the annual inflation rate,
i - the desired return on the financial transaction (cleared of the effects of inflation)
i a is the rate of return compensating for inflation.
Then, for the accumulated amount S, which in the conditions of inflation will turn into the sum S a, we can write the following expression:
S a \u003d P (1 + i) (1 + a)
The same result can be obtained in another way:
S a \u003d P (1 + i a)
Equating the right sides of the written equalities, we obtain the expression for calculating i a:
i a = i + a + ia
This is the well-known formula of I. Fisher, in which the quantity (a + i a) is "Inflation premium" - essential supplement that compensates for the effects of inflation.
Now we can formulate the second important conclusion:
To calculate the interest rate that compensates for inflation, to the required rate of return must be added not only the level inflation but also a productia.
In real practice, it often turns out to be useful to modify this formula, which allows you to find the real profitability of the operation in conditions of inflationary price increases:
i = (i a - a) / (1 + a)
Most of the operations associated with capital investment in the future do not imply a lump-sum receipt of the accrued amount, but a whole cash flow of income over a certain period. The main parameters of interest to the investor or creditor in this case are the current (reduced) value of the cash flow, its future (accrued) value, and also the profitability of the financial transaction.
We will use the following notation:
P is the amount of invested capital,
CF k - the value of the k-th element of cash flow,
i is the discount rate (usually a compound loan interest rate),
A is the present value (value) of cash flow,
S is the future value of cash flow
n is the number of cash flow elements.
Present value cash flow is the sum of all its elements brought (discounted) to the present moment of time:
A \u003d CF 1 / (1 + i) + CF 2 / (1 + i)? + ... + CF n / (1 + i) n
Similarly future value cash flow, this is the sum of its accrued elements at the time of the last payment:
S \u003d CF 1 (1 + i) n-1 + CF 2 (1 + i) n-? + ... + CF n
Financial return such a destructive interest rate is called, at a discount at which the present value of the cash flow of income coincides with the amount of invested capital: P \u003d A. To find such a rate in the general case, it is necessary to solve an equation of the nth degree.
Values \u200b\u200bof accrual and discount coefficients in case of using complex decursive rates can be found in the special tables given in the appendix.
To determine the profitability of a short-term financial transaction (less than one year), a simple loan interest rate is usually used, for a long-term transaction - a complex one.
All methods for forecasting currency risk can be divided into two groups:
* statistical methods based on quantitative analysis
* expert methods based on qualitative analysis
The basis of the quantitative assessment of currency risks is the Value at Risk (VaR) method, which determines the functional relationship between the probability of risk occurrence and external indicators. The VAR method is used by international institutions such as the Bank for International Settlements, the Banking Federation of the European Community and others to calculate capital adequacy. This technique is used by many European banks to measure market risks (which includes currency risk) of the bank.
VaR is the amount of losses, which with a probability of confidence level level (for example 99%), will not be exceeded. Accordingly, in 1% of events, the loss may amount to a value exceeding VaR. The VaR method is essentially a development of the classical method of measuring risk, based on the calculation of the standard deviation with the subsequent application of the normal distribution law. The advantages of assessing currency risks using the VaR method has the following advantages, because it allows you to:
* calculate risks for all possible markets
* calculate the risk of losses in accordance with the probability of their occurrence
Generally speaking, VaR can be defined as a statistical estimate of the maximum losses of the investor portfolio for a given distribution of market factors over a certain period of time in almost all cases (except for a small percentage of situations).
When calculating VaR, it is necessary to determine the basic elements that affect its value: probability distribution of market factors, confidence interval, i.e. the probability that losses should not exceed VaR, retention period (holding period). VaR calculation formula:
Var \u003dk *σ*
Y
Where k is the coefficient of a certain confidence interval, Y is the value of the asset, and σ is the currency rate volatility.
Volatility is equal to the square root of the variance: measures of the spread of the currency from its average. The next step in calculating the VaR indicator is the choice of the confidence interval, a quantitative characteristic of the forecast accuracy. Each confidence interval has its own coefficient. (factor k). The most commonly used are 95% confidence intervals (coefficient 1.65) and 97.5% (coefficient 1.96) and 99% (coefficient 2.33) intervals. The indicated intervals determine the probability of exceeding the calculated VaR.
There are three methods for calculating VaR: the variation-covariance method (analytical), historical modeling, and statistical modeling (called the Monte Carlo method). Most commonly used to calculate VaR variation-covariance method(parsed above). Its widespread use is due to the fact that it is easy to use, and the results of the accuracy of the calculation are at a high level. It is possible to use this method only if the studied statistics correspond to the normal distribution law, which in reality should mean the absence of any significant deviations of price values \u200b\u200bfrom the average level. The analytical method for calculating VaR can be implemented on any computer, however, when using it, one must reckon with the stationary normal distribution, which makes it unsuitable for Russian conditions.