Determination of the unsatisfactory structure of the company's balance sheet according to the criteria of current liquidity, provision with own funds, restoration or loss of solvency
According to the decree of the Government of the Russian Federation of 05.25.94, No. 498, the degree of insolvency of enterprises should be assessed according to three criteria characterizing the unsatisfactory structure of the balance sheet:
1. current liquidity ratio;
2. the ratio of the provision of own funds;
3. coefficient of recovery or loss of solvency.
The basis for recognizing the structure of the company's balance sheet as unsatisfactory, and the company as insolvent, is the fulfillment of one of the following conditions:
The current liquidity ratio at the end of the reporting period has a value of less than 2;
The equity ratio at the end of the reporting period is less than 0.1. Based on these coefficients, the territorial insolvency and bankruptcy agencies of enterprises make the following decisions: On recognizing the structure of the balance sheet as unsatisfactory, therefore, the enterprise is insolvent. On the existence of a real opportunity for the debtor enterprise to restore its solvency. On the existence of a real possibility of loss of solvency of the enterprise, if in the near future it will not be able to fulfill its obligations to creditors. These decisions are made regardless of whether the company has external signs of insolvency established by law.
Current liquidity ratio characterizes the general provision of the enterprise with working capital for conducting economic activities and the ability of the enterprise to timely repay urgent liabilities = tech assets / tech liabilities.
Equity ratio characterizes the availability of the company's own funds necessary to ensure its financial stability = (current liabilities-current assets) / total value of tech assets.
Recognition of an enterprise as insolvent does not always mean recognition of it as insolvent, does not entail the onset of civil liability of the owner. This is only recorded in the territorial bankruptcy agency as financial instability.
The normative value of the criteria is established in such a way as to provide measures to prevent the insolvency of the enterprise, as well as to stimulate the given enterprise to an independent exit from the crisis. If at least one of the above two ratios does not meet the standard values, the solvency recovery ratio is calculated for the next period of 6 months. If the current liquidity ratio is greater than or equal to 2, the security ratio is greater than or equal to 0.1, then the solvency loss ratio is calculated for the upcoming period of 3 months.
Solvency recovery rate is defined as the sum of the actual value of the current liquidity of the reporting period and the change in this ratio between the end and the beginning of the period in terms of 6 months.
К1Ф - the actual value of the current liquidity ratio at the end of the reporting period.
К2Ф - the actual value of the current liquidity ratio at the beginning of the reporting period.
T - reporting period in months
2 - the standard of the current liquidity ratio
(for 6 months)> 1, then the company has a real opportunity to restore its solvency in a fairly short period.
If the coefficient of recovery of solvency< 1, то у предприятия нет реальной возможности восстановить свою платежеспособность на данный момент и за достаточно короткий срок.
The loss of solvency ratio is determined:
If the coefficient of loss of solvency (for 3 months)> 1, this indicates that there is a real opportunity for the enterprise to lose solvency.
If there are grounds for recognizing the structure of the balance sheet as unsatisfactory, but if a real opportunity to restore solvency is identified, the territorial bankruptcy agency decides to postpone the decision to recognize the structure of the balance sheet as unsatisfactory, and the enterprise as insolvent for up to 6 months.
If there are no such grounds, then one of two decisions is made:
If the coefficient of recovery of solvency is> 1, then no decision is made to recognize the structure of the balance sheet as unsatisfactory, and the company is insolvent.
If the coefficient of recovery of solvency< 1, тогда решение о признании структуры баланса неудовлетворительной, а предприятие – неплатежеспособным так же не может быть принятым. Однако в виду реальной угрозы утраты платежеспособности оно ставится на учет в территориальный орган по банкротству, но только в том случае, если доля государственных предприятий в общей собственности более 25%.
A number of enterprises may become insolvent due to the state's debt to this enterprise. In this case, an analysis is made of the dependence of the company's solvency at the moment and the state's debt to the enterprise.
Interest- income from the provision of capital in debt in various forms (loans, credits, etc.), or from investments in production or financial. character.
Interest rate Is a value that characterizes the intensity of interest accrual.
Currently, there are two ways to determine and calculate interest:
Decursive way. Interest is calculated at the end of each accrual interval. Their value is determined based on the amount of the provided capital. Accordingly, the decursive interest rate (interest) is the ratio of the amount of income accrued over a certain interval to the amount available at the beginning of this interval, expressed as a percentage.
Antisipative (preliminary) method. The provisional interest is calculated at the beginning of each accrual interval. The amount of interest money is determined based on the accrued amount. The interest rate will be, expressed as a percentage, the ratio of the amount of income paid over a certain interval to the amount of the accrued amount received after this interval.
The interest rate shows the degree of intensity of the change in the value of money over time. The absolute magnitude of this change is called percentage, is measured in monetary units (for example, rubles) and is denoted by I. If we denote the future amount S, and the modern (or original) P, then I = S - P. The interest rate i is a relative value, measured in decimal fractions or%, and is determined by dividing interest by the original amount:
In addition to interest, there is discount rate d (another name is the discount rate), the value of which is determined by the formula:
where D is the amount of the discount.
Comparing formulas (1) and (2), it can be noted that the sum of interest I and the value of the discount D are determined in the same way - as the difference between the future and present values. However, the meaning of these terms is not the same. if in the first case we are talking about an increase in the current value, then in the second, a decrease in the future value, a “discount” from its value, is determined. The main area of application of the discount rate is discounting, a process that is inverse to the calculation of interest. Using the rates discussed above, both simple and compound interest can be calculated. When calculating simple interest, the increase in the initial amount occurs in arithmetic progression, and when calculating compound interest - in geometric progression. The accrual of simple decursive and antisipative interest is made according to various formulas:
Decursive percentages: (3)
antisipative percentages:, (4)
where n is the length of the loan, measured in years.
However, the duration of the loan n does not have to be a year or an integer number of years. Simple interest is most often used for short-term transactions. In this case, the problem arises of determining the length of the loan and the length of the year in days. If we denote the length of the year in days with the letter K (this indicator is called time base), and the number of days of using the loan is t, then the designation of the number of full years n used in formulas (3) and (4) can be expressed as t / K. Substituting this expression in (3) and (4), we get:
for decursive percentages: (6)
for antisipative interest:, (7)
The most common combinations of the time base and loan duration (the numbers in parentheses indicate the value of t and K, respectively):
Exact interest with exact number of days (365/365).
Ordinary (commercial) interest with exact loan duration (365/360).
Ordinary (commercial) interest with approximate loan duration (360/360).
The inverse problem in relation to the calculation of interest is the calculation of the present value of future cash receipts (payments) or discounting. In the course of discounting at the known future value S and the specified values of the interest (discount) rate and duration of the operation, the initial ( modern, reduced or the current) cost P. Depending on which rate - simple interest rate or simple accounting rate - is used for discounting, two types of it are distinguished: mathematical discounting and bank accounting.
The banking accounting method got its name from the financial transaction of the same name, during which a commercial bank redeems (records) a promissory note or a bill of exchange from the owner (records) at a price below par before the expiration of the maturity date indicated on this document. The difference between the par and the redemption price forms the bank's profit from this operation and is called the discount (D). To determine the size of the redemption price (and, therefore, the amount of the discount), discounting is applied using the bank accounting method. This uses a simple discount rate d. The redemption price (modern value) of a bill is determined by the formula:
where t is the period remaining to maturity of the promissory note, in days. The second factor of this expression (1 - (t / k) * d) is called the bank accounting discount factor for simple interest.
Mathematical discounting uses a simple interest rate i. Calculations are performed according to the formula:
The expression 1 / (1 + (t / k) * i) is called the discount factor of mathematical discounting by simple interest.
The main area of application of simple interest and discount rates is short-term financial transactions, the duration of which is less than 1 year.
Calculations with simple rates do not take into account the possibility of reinvesting the accrued interest, because the accumulation and discounting are made relatively the same initial amount of P or S. In contrast to them compound interest rates take into account the possibility of reinvesting interest, since in this case the increase is made according to the formula not arithmetic, but a geometric progression, the first member of which is the initial amount P, and the denominator is (1 + i). The accrued cost (the last term of the progression) is found by the formula:
(10), where (1 + i) n is the multiplier of the increment of decomposition compound interest.
By itself, the compound interest rate i is no different from the simple one and is calculated using the same formula (1). The compound discount rate is determined by the formula (2). As in the case of simple interest, it is possible to use a complex discount rate for calculating interest (anti-sipative method):
, (11) where 1 / (1 - d) ^ n is the multiplier of compound antisipative interest.
An important feature of compound interest is the dependence of the final result on the number of accruals during the year.
In financial calculations, the nominal compound interest rate is usually denoted by the letter j. The formula for increasing compound interest when calculating them m times a year looks like:
When calculating anti-sipative compound interest, the nominal discount rate is denoted by the letter f, and the accrual formula takes the form:
The expression 1 / (1 - f / m) ^ mn is the accrual factor at the nominal discount rate.
Compound discounting can also be performed in two ways - mathematical discounting and bank accounting. The latter is less profitable for the lender than accounting at a simple discount rate, therefore it is used extremely rarely. In the case of a one-time interest calculation, its formula is:
where (1 –d) n - discount multiplier of banking accounting at a complex discount rate.
for m> 1 we get
, (16) where f is the nominal compound discount rate,
(1 - f / m) mn - discount multiplier of bank accounting at a complex nominal discount rate.
Mathematical discounting at a compound interest rate i is much more widespread. For m = 1 we get
, (17) where 1 / (1 + i) n is the discount factor of mathematical discounting at a compound interest rate.
With repeated accrual of interest during the year, the mathematical discounting formula takes the form:
, (18) where j is the nominal compound interest rate,
1 / (1 + j / m) mn - discount factor of mathematical discounting at a complex nominal interest rate.
There are two fundamentally different ways of calculating interest: decursive and antisipative.
At decursive way interest is calculated at the end of each interval based on the amount of capital provided at the beginning of the time interval. Decursive interest rate ( i) is called loan interest and is determined by the formula:
i = I / PV,
where I PV- the amount of money at the beginning of the time interval.
At antisipative method interest accrual, they are calculated at the beginning of each accrual interval, based on the accumulated amount of money at the end of the interval (including capital and interest). Anti-sipative interest rate ( d) is called discount rate and is determined by the formula:
d = I / FV,
where I- interest income for a certain time interval; FV- the accumulated amount of money at the end of the time interval.
In practice, the most widespread is the deccursive method of calculating interest. The antisipative method is used in accounting for bills of exchange and other monetary obligations. The amount of money at the end of the accrual interval is considered the amount of the loan received. Since interest is calculated at the beginning of the time interval, the borrower receives the loan amount minus interest. This operation is called discount rate or bank account. Discount- this is the difference between the size of the loan and the amount directly issued, that is, the income received by the bank at the discount rate.
Both in the case of the decomposition and the anti-hypothetical methods, schemes for calculating simple and compound interest can be used. When using the simple interest scheme, they are charged on the amount of the initial deposit. Compound interest assumes the capitalization of interest, that is, the accrual of "interest on interest".
From the point of view of the lender, when conducting financial transactions of a short-term nature (less than a year), a simple interest scheme is more profitable, and for long-term operations (more than a year), a compound interest scheme. For long-term operations with a fractional number of years, the so-called mixed scheme is beneficial, when compound interest is charged over a whole number of years, and simple interest during a fractional part of a year.
Table systematized formulas for determining the accumulated amount of money, that is, the future value of the deposit, in the case of deccursive and antisipative methods of calculating interest. In this case, the following designations are used:
FV- future (increased) amount of money;
PV- the real (current) amount of money;
i- loan interest rate;
d- discount rate;
n- the number of years in the interest calculation interval;
m- the number of intra-annual interest accruals;
t- the duration of the interest accrual interval for short-term transactions, days;
T- the length of the year, days;
w- an integer number of years in the accrual interval;
f- fractional part of the year in the accrual interval.
table
Formulas for calculating the accumulated amount of money under various conditions of interest accrual
| Conditions for calculating interest | Interest calculation method | |
| Decursive | Antisipative | |
| simple interest, an integer number of years in the accrual interval | FV = PV´ (1 + in) | FV = PV / (1 - dn) |
| compound interest, an integer number of years in the accrual interval | FV = PV´ (1 + i) n | FV = PV / (1 - d) n |
| simple interest, the term of the operation is less than a year |  |
|
| mixed interest accrual scheme with a fractional number of years in the accrual interval | FV = PV´ (1 + i) w (1 + if) | FV = PV / [(1 - d) w (1 + if)] |
| compound interest, intra-annual accruals with an integer number of years in the interest accrual interval | FV = PV´ (1 + i / m) nm | FV = PV / (1 –d / m) nm |
Concept estimating the value of money over time plays a fundamental role in the practice of financial computing. It predetermines the need to take into account the time factor in the process of carrying out any long-term financial transactions by assessing and comparing the cost of money at the beginning of financing with the cost of money when it is returned in the form of future profit.
In the process of comparing the cost of funds when investing and returning them, it is customary to use two basic concepts - the future value of money and their present value.
Future value of money (S) - the amount of funds invested at the moment, into which they will turn after a certain period of time, taking into account a certain interest rate. Determining the future value of money is associated with the process of increasing this value.
The present value of money (P) is the sum of future cash receipts, adjusted for a certain interest rate (the so-called "discount rate") to the present period. Determining the present value of money involves the process of discounting that value.
There are two ways to determine and calculate interest:
1. Decursive way of calculating interest... Interest is calculated at the end of each accrual interval. Their value is determined based on the amount of capital provided. Decursive interest rate (loan interest) is the ratio of the amount of income accrued over a certain interval to the amount available at the beginning of this interval (P), expressed as a percentage. In world practice, the decomposition method of calculating interest has become the most widespread.
2. Antisipative method(preliminary) interest accrual. Interest is calculated at the beginning of each accrual interval. The amount of interest money is determined based on the accrued amount. The anti-sipation rate (discount rate) is the percentage ratio of the amount of income paid over a certain interval to the amount of the accrued amount received after that interval (S). In countries with developed market economies, the antisipative method of calculating interest was used, as a rule, during periods of high inflation.
66. Financial planning at the enterprise. To manage is to foresee, i.e. predict, plan. Therefore, the most important element of entrepreneurial economic activity and enterprise management is planning, including financial.
Financial planning is the planning of all incomes and directions of spending the enterprise's funds to ensure its development. Financial planning is carried out by drawing up financial plans of different content and purpose, depending on the tasks and planning objects. Financial planning is an essential element of the corporate planning process. Every manager, regardless of his functional interests, should be familiar with the mechanics and rationale of executing and controlling financial plans, at least as far as his activities are concerned. The main tasks of financial planning:
Providing the normal reproduction process with the necessary funding sources. At the same time, target sources of financing, their formation and use are of great importance;
Respect for the interests of shareholders and other investors. A business plan containing such a rationale for an investment project is for investors the main document that stimulates capital investment;
Guarantee of the fulfillment of the company's obligations to the budget and off-budget funds, banks and other creditors. The capital structure optimal for a given enterprise brings the maximum profit and maximizes payments to the budget with the given parameters;
Identification of reserves and mobilization of resources for the effective use of profits and other income, including non-operating income;
Ruble control over the financial condition, solvency and creditworthiness of the enterprise.
The purpose of financial planning is to link revenues to the required expenditures. If income exceeds expenses, the excess amount is sent to the reserve fund. If expenses exceed income, the amount of the lack of funds is replenished by issuing securities, obtaining loans, receiving charitable contributions, etc.
Planning methods are specific methods and techniques for calculating indicators. When planning financial indicators, the following methods can be used: normative, calculation and analytical, balance, method of optimizing planning decisions, economic and mathematical modeling.
The essence of the normative method for planning financial indicators is that on the basis of pre-established norms and technical and economic standards, the need of an economic entity for financial resources and their sources is calculated. Such standards are tax rates, rates of tariff contributions and fees, rates of depreciation deductions, standards for the need for working capital, etc.
The essence of the calculation and analytical method for planning financial indicators is that based on the analysis of the achieved value of the financial indicator taken as the base, and the indices of its change in the planning period, the planned value of this indicator is calculated. This planning method is widely used in cases where there are no technical and economic standards, and the relationship between the indicators can be established indirectly, based on the analysis of their dynamics and relationships. This method is based on expert judgment.
The essence of the balance sheet method of planning financial indicators lies in the fact that by constructing balance sheets, a link is achieved between the available financial resources and the actual need for them. The balance method is used primarily in planning the distribution of profits and other financial resources, planning the need for receipts of funds in financial funds - an accumulation fund, a consumption fund, etc.
The essence of the method for optimizing planning decisions is to develop several options for planned calculations in order to choose the most optimal one.
The essence of economic and mathematical modeling in planning financial indicators is that it allows you to find a quantitative expression of the relationship between financial indicators and the factors that determine them. This relationship is expressed through an economic and mathematical model. An economic and mathematical model is an exact mathematical description of an economic process, i.e. description of factors characterizing the structure and patterns of changes in a given economic phenomenon using mathematical symbols and techniques (equations, inequalities, tables, graphs, etc.). Financial planning can be classified into perspective (strategic), current (annual) and operational. The strategic planning process is a tool that helps in making management decisions. His task is to ensure innovation and change in the organization to a sufficient extent. There are four main types of management activities in the strategic planning process: resource allocation; adaptation to the external environment; internal coordination; organizational strategic foresight. The system of the current planning of the financial activity of the company is based on the developed financial strategy and financial policy for certain aspects of financial activity. Each type of investment is linked to the source of funding. For this, they usually use estimates of education and spending of funds of funds. These documents are necessary to monitor the progress of financing the most important events, to select the optimal sources of replenishment of funds and the structure of investing their own resources.
The current financial plans of an entrepreneurial firm are developed on the basis of data that characterize: the financial strategy of the firm; results of financial analysis for the previous period; planned volumes of production and sales of products, as well as other economic indicators of the company's operating activities; a system of norms and standards for the costs of individual resources developed at the firm; the current taxation system; the current system of depreciation rates; average rates of credit and deposit interest in the financial market, etc. Operational financial planning consists in drawing up and using a plan and a cash flow statement. The payment calendar is compiled on the basis of the real information base of the company's cash flows. In addition, the company must draw up a cash plan - a plan for the turnover of cash, reflecting the receipt and payment of cash through the cash desk.
The price of money is a payment for the temporary use of "someone else'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 monetary payment charged for the use of money. If interest has a value, it is 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, and reduces his liquidity. Therefore, he seeks to compensate for losses - to receive income from lending money. This income is called interest money.
Interest rate- a value characterizing the intensity of interest accrual.
Interest accrual period- the period of time for which interest is calculated (the period for which the money is provided).
Accrual interval- the minimum period after which interest is accrued.
There are two ways of calculating interest: decourse and anti-sipative.
Decursive way of calculating interest- an increase in the initial amount for interest rate... Interest (more correctly - interest money) is paid at the end each accrual interval.
Decursive interest rate (i), called lending interest, Is the percentage ratio of the amount of income accrued for a certain interval I(interest money) to the amount available at the beginning of this interval - P.
Accumulation (growth) of the initial amount of debt- increase in the amount of debt due to the addition of accrued interest.
S = P + I, (4.1)
I = S - P, (4.2)
where S- the accrued amount.
Build ratio To n is defined as follows:
Interest rate i is a relative value, measured in fractions of a unit and is determined by dividing interest money by the original amount.
. (4.4)
The formula for calculating the interest rate is identical to the calculation of the statistical indicator "growth rate".
Determination of the accrued amount S called compounding ... Determination of the initial amount R – discounting.
The date of receipt and the day of the final repayment of the loan are considered one day (boundary day). Interest on loans and deposits is accrued, as a rule, on a daily basis. In this case, either the exact number of days in a year (360/365) or banking (30 days) can be used.
At antisipative method of calculating interest (preliminary) interest is paid at the beginning of the period for which interest is calculated. Example: interest charged by the bank when accounting for promissory notes; on a factoring loan, etc. The amount of the loan received is the accrued amount S... Based on it, interest is calculated. The borrower receives the loan amount minus interest.
Difference between loan size S and the amount issued R called a discount, denoted by D and represents the amount of interest money.
D = S - P. (4.5)
The discount rate, expressed in fractions of one and determined by dividing the amount of the discount by the amount R is called discount rate d .
. (4.6)
You can see that the amount of interest I and the amount of the discount D are defined in the same way. However, in the first case, we are talking about an increase in the current value, a kind of "markup", 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" from the future value is determined (diskont means "discount" in German).
Most often, the antisipative method is used for purely technical purposes - when discounting, as well as when accounting for bills in a bank and when paying for factoring services. In all other cases, in world practice, the more widespread is the decursive method of calculating interest.
The antisipative method is used in countries with developed market economies during periods of high inflation, since the increase in the antisipative method occurs at a faster pace than in the decourse method of accrual.
In the economic practice of the Republic of Bashkortostan, at present, the basic method of calculating simple interest is mainly used. Interest on accounts is calculated in accordance with the agreement between the bank and the client. On accounts of credit and deposit operations, interest is calculated for the period including the day the loan is issued or money is credited to the deposit, and the day preceding the repayment of the loan or the issuance of the deposit (closing the account). When the interest rate is changed, interest is charged at the new rate from the date of its establishment.
At the heart of any lending operation, that is, transferring money to a borrower from a lender, is the desire to receive income. The absolute value of the income received by the creditor for the transfer of money into debt is called interest money or percent. The origin of this name is due to the fact that the amount of payment for a loan is usually determined as the corresponding percentage (in a mathematical sense) of the loan amount.
The loan fee can be charged both at the end of the loan term and at its beginning (advance interest income). In the first case, interest is charged at the end of the term based on the amount of the amount provided, and the amount of debt is subject to return, along with interest. This method of calculating interest is called decursive. In the second case, interest income is received in advance (paid at the beginning of the term), while the debtor is given an amount reduced by its value, and only the original loan is subject to return at the end of the term. Interest income paid in this way is called discount(i.e., a discount on the loan amount), and the method of calculating interest is antisipative.
In world practice, the decursive method of calculating interest has become more widespread, therefore, the term "decursive" is usually omitted, speaking simply of interest or loan interest. When using antisipative percentages, the full name is used.
Types of interest rates
Let us first consider the decomposition method, when interest is calculated at the end of the loan term. From the quantitative point of view, a credit operation is characterized by the following basic relationship:
where R- the initial amount (loan amount); I- interest income - the amount of the loan payment; S - the amount to be returned (the full cost of the loan).
Loan payment amount I usually defined as a percentage of the amount of the loan itself - i T. This ratio is called the interest rate, more precisely, the interest rate for the period T:
(1.1.2)
The time period at the end of which interest income is received is also called interest period(the term "conversion period" is often used). The interest rate applies to the entire period of the loan agreement.
Since the terms of loans vary in a wide range (from several days to tens of years), in order to compare the terms of various loans, the interest rate is set in relation to a certain base period. The most common is the annual base period - in this case, they speak of the annual interest rate. If the conversion period is the same as the base, then the annual interest rate is the same as actual(1.1.2). If the term of the transaction has a different duration, then the annual interest rate, which serves as the basis for determining the interest rate for the period (actual interest rate), is called nominal. The interest rate for the period is calculated by the formula
where i- nominal annual interest rate; T- the term of the agreement, after which the loan must be returned together with interest.
If the conversion period fits an integer number of times a year, then the rate for the period is calculated by the formula
where T = 1 /m; m - the number of periods of interest accrual per year, or the frequency of interest accrual.
The law of increasing at a simple interest rate. Discounting; future and present value of money
Interest income under the law of simple interest is calculated on the basis that the nominal interest rate does not depend on the period of interest accrual:
Amount S also called the accumulated (accrued) value of the original amount R. Using formulas 1.1.1, 1.1.6, we get:
where s(T) = l + iT- multiplier (coefficient) of the accumulation, or accumulating multiplier for the period T.
Knowing the invested amount R and the interest rate i, it is easy to calculate by the formula (1.1.7) the value S for an arbitrary term of the loan agreement. The increase factor does not depend on the value of the initial amount and shows how many times the initial capital has grown. It is he who characterizes the profitability of a credit operation, allowing you to determine what a single amount will turn into by the end of the term (or after any period of time T). In financial mathematics, it is customary to calculate the results of financial transactions for single amounts, then multiplying the result by the initial value and obtaining the value of the accrued amount.
When working out various types of financial transactions, it is often necessary to solve the inverse problem: it is known what amount in the future is needed to obtain a certain result, the desired value is its current value. In other words, the problem is posed as follows: how much should be invested today in order to get a given value after a certain time interval? In this situation, the present value of a monetary amount is a projection of its specified future value. Such a projection of the sum from the future to the present is called discounting. The name of the term comes from the word "discount" - a discount from the price of a debt obligation with an advance payment of interest for using a loan. Discounting and accumulation are mutually opposite processes. The formula for discounting at a simple interest rate is as follows:
(1.1.8)
where v = 1/(1 + iT) - discount multiplier for the period T.
In the English-language literature, the combination of letters is traditionally used to denote the accrued amount FV (from Future Value of Money - future value of money); to indicate the present value - PV(fromPresent Value of Money is the real value of money).
The terms "accumulation" and "discounting" are also used in a broader sense, as a means of determining any value at some arbitrary point in time, regardless of the specific type of financial transaction involving the accrual of interest. Such a calculation is called bringing the cost indicator to a given point in time. The accrued, or future, value of a monetary amount means the projection of the currently set amount for a certain time interval forward into the future. Discounting is the projection of an amount given at a certain point in time in the future, at a certain time interval back, into the present.
Bringing a sum to a certain point in time consists in multiplying it by a reduction factor, which is equal to either the increment factor when reduced to a future point in time, or a discount factor when reduced to a previous (present) moment in time. It is convenient to combine the beginning of the time scale with the moment in time when the amount is set. Then the accumulation corresponds to the positive part of the time axis, and discounting - the negative. In this case, the reduction factor r (t) can be written as
(1.1.9)
where s (t) = s (T) is the build-up factor; v ( ׀ t ׀ ) = v Т - discount factor; T = ׀ t ׀ - the value of the calculation period (the value of the time interval on the numerical axis, taken modulo).
Dependence of this factor on time, i.e. from the value of the interest accrual period T = ׀ t ׀ defined by formula (1.1.9) is shown in Fig. 1.1.1 for a rate of 30% per annum.
Variable interest rate
Often during the term of the loan agreement, the interest rate changes. In this case, the interest is calculated separately for each period during which the interest rate is constant, and then at the end of the loan period, the interest calculated for the individual periods is summed up.
In general view at time intervals N, on each of which its own interest rate will be applied, the accrued amount of interest for the entire period will be
where k – the ordinal number of the time interval; i k, Tk – respectively, the nominal interest rate and the duration of the time interval (in years).
Sometimes in the literature there is an assertion that (1.1.10) is the amount of interest accrued in each time period. However, according to the simple interest scheme, the accrual and payment of interest is assumed only after the expiration of the loan agreement; their accrual and addition to the principal amount within the term of the loan is not provided. In this regard, a distinction should be made between the calculation and the calculation of interest. Interest calculation - this is a mathematical operation to determine the amount of interest-bearing money for any time period, as well as for the entire term of the loan agreement. Accrual the same percent - this is a specific accounting transaction, as a result of which the loan fee must either be transferred to the lender or added to the principal amount. Therefore, it is incorrect to talk about the accrual of interest when the interest rate changes within the loan term (since no accounting operations are carried out in this case); we can only talk about the calculation of interest for a particular period.
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