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In practice bigger distribution was gained by a stream postnumerando, in particular, this stream is the cornerstone of techniques of the analysis of investment projects. Some explanations for it can be offered proceeding from the general principles of the account according to which it is accepted to sum up the results and to estimate financial result of this or that action on the ends of the next reporting period. As for receipt of money on account of payment, in practice the eye is most often distributed in time unevenly and therefore it is more convenient to refer all receipts to the end of the period conditionally. Thanks to this agreement the equal temporary periods that allows to develop the convenient formalized algorithms of an assessment are formed. The stream prenumerando matters in the analysis of various schemes of accumulation of money for the subsequent their investment.

The assessment of a cash flow can be carried out within the solution of two tasks: a) the straight line, i.e. carries out an assessment from a future position (the scheme of capacity is realized); b) the return, i.e. carries out an assessment from a present position (the scheme of discounting is realized).

The direct task assumes a total score of the increased cash flow, i.e. future cost is its cornerstone.

The return task assumes a total score of the discounted (given) cash flow. As separate elements of a cash flow are generated in various time intervals, and money has temporary value, their direct summation is impossible. The main result of calculation is determination of the total value of the given cash flow. The settlement formulas used thus are various depending on a type of a stream - postnumerando or prenumerando.

It should be noted that the key moment in the considered schemes is the silent prerequisite that the analysis is kept with a position of "the reasonable investor", and immediately investing them for the purpose of obtaining the additional income. By it is explained that fact that at an assessment of streams in both cases, i.e. both at capacity, and when discounting, capitalization according to the scheme of difficult percent is supposed.

ASSESSMENT OF THE CASH FLOW WITH UNEQUAL RECEIPTS

The situation when monetary receipts by years vary, is the most widespread. The general problem definition in this case such is.

Let C1, C2,… .Cn - a cash flow; r - discounting coefficient. The stream which all elements by means of the discounting multipliers are brought to one timepoint, namely - by the present moment, is called brought. It is required to find the cost of this cash flow from a position of the future and from a present position.

ASSESSMENT OF THE FLOW OF POSTNUMERANDO

The direct task assumes an assessment from a future position, i.e. for the end of the period and when the scheme of capacity is realized.

The return task means an assessment from a position of a present situation, i.e. for the end of the period of the Lake. In this case the scheme of discounting is realized, and calculations need to be conducted on the given stream. Elements of the given cash flow can already be summarized; their sum characterizes brought, or flowing, the cost of a cash flow which if necessary can be compared to the size of initial investment.

ASSESSMENT OF ANNUITIES

One of key concepts in financial and commercial calculations is the concept of annuity. The logic put in the scheme of annuity payments widely is used at an assessment of debt and share securities, in the analysis of investment projects, and also in the analysis of rent.

ASSESSMENT OF URGENT ANNUITIES

The annuity represents a special case of a cash flow, namely, it is a stream in which monetary receipts in every period are identical in size. If the number of equal time intervals is limited, the annuity is called urgent. In it cases:

C1 = C2 = … … = CN = A

Postnumerando regularly arriving rent payments for use of the leased land plot can be an example of urgent annuity in case the contract provides regular payment of rent after the next period. The scheme of periodic monetary deposits on the bank account at the beginning of every month for the purpose of accumulation of the sufficient sum for large purchase acts as urgent annuity prenumerando, for example.

For an assessment of future and specified cost of annuity it is possible to use the considered computing formulas, at the same time thanks to specifics of annuities concerning equality of monetary receipts these formulas can be significantly simplified.

METHOD OF THE DEPOSIT BOOK

It is possible to give other interpretation of calculation of the current cost of annuity by means of a method of "the deposit book", which logician such is. The sum put on the deposit brings in the income in a type of percent; at removal from the deposit of some sum the basic size with which percent are charged, decreases. Just this situation also takes place in a case with annuity. The current cost of annuity is the size of the deposit with the total amount of the due percent which is annually decreasing by the equal sums. This sum of annual payment includes the percent added for the next period, and also some part of the main amount of debt. Thus, repayment of an initial debt is carried out gradually during all period of validity of annuity. The structure of annual payment constantly changes - initial stages in it prevail the percent added for the next period; eventually the share of percentage payments constantly decreases and raises a share of repayable part of a principal debt. We will consider logic and calculating procedures of a method on the elementary example.

Example

In bank the loan for five years in the sum 20000 dale, under 13% per annum charged according to the scheme of difficult percent on an unpaid balance is obtained. It is necessary to return the equal sums at the end of every year. It is required to determine the size of annual payment.

For the best understanding of logic of a method deposit the book it is expedient to argue from the creditor's position. For bank this contract represents investment at a rate of 20000 dale., i.e. outflow of money, as it is shown on the scheme. Further within five years the bank will annually receive the sum in the end of the year And, and each annual payment will include percent for the expired year and part of the main amount of debt. So, as within the first year the borrower used the loan at a rate of 20000 dale., payment which will be having made at the end of this year, consists of two parts: percent in a year in the sum 2600 dale. (13% from 20000) and repayable part of a debt in the sum (And - 2600 dale). Next year calculation will be repeated provided that the size of the credit which the borrower possesses, will make already smaller sum in comparison with the first year, namely: (20000-A + 2600). From here it is visible that eventually the sum of percent decreases, and the share of payment increases. This financial contract can be presented in the annuity form postnumerando in which its current cost, an interest rate and duration of action is known. Therefore for finding of size annual payment And it is possible to use a known formula.

ANNUITY ASSESSMENT WITH THE CHANGING PAYMENT SIZE

In practice situations when the size of payment changes towards increase or reduction over time are possible. In particular, at the conclusion of lease contracts in the conditions of inflation the periodic increase in payment compensating negative influence of the change in price can be provided. The annuity assessment in this case can be also carried out by simple calculations by means of financial tables. We will consider technology of calculations on the elementary example.

Example

The site for ten years is leased. The rent will be carried out annually according to the scheme postnumerando with the following provisions: in the first six years 10 million rubles, in the remained four years 11 million rubles. It is required to estimate the specified cost of this contract if the interest rate used by the analyst is equal 15%.

It is possible to solve this problem in various ways depending on what annuities will be allocated by the analyst.

First of all we will note that the specified cost of a cash flow has to be estimated from a position of the beginning of the first time interval. We will consider only two versions of the decision from several possible. All these options are based on property of additivity of the considered algorithms concerning the size of annuity payment.

1. The initial stream can be imagined as the sum of two annuities: the first has And = 10 and ten years proceed; the second has And = 1 and four years proceed. On a formula it is possible to estimate the specified cost of each annuity. However the second annuity in this case will be estimated from a position of the beginning of the seventh year therefore the received sum needs to be discounted by the beginning of the first year. In this case estimates of two annuities will be brought to one timepoint, and their sum will give an assessment to the specified cost of an initial cash flow.

PV = 10*FM4 (15%, 10) + FM2 (15%, 6) * 1*FM4 (15%, 4) =

= 10*5,019+2,855*1*0,432=51,42 million rubles.

2. The initial stream can be imagined as a difference of two annuities: the first has And = 11 and ten years proceed; the second has And = 1 and, having begun in the first year, comes to an end in the sixth. In this case calculation looks so:

PV = 11*FM4 (15%, 10) - 1*FM4 (15%, 6) =

=11*5,019-1*3,784 = 51,42 million rubles.

TERMLESS ANNUITY

The annuity is called termless if monetary receipts proceed rather long time (in the western practice the annuities calculated on 50 and more years belong to the termless).

Example

To determine the current cost of termless annuity with annual receipt of 420 thousand rubles if the percent on fixed deposits offered by the state bank is equal 140/0 annual.

PV = 420: 0,14 = 3 million rubles.

Thus, if the annuity is offered at the price which isn't exceeding 3 million rubles, it represents favorable investment.

Conclusion

Summing up the result it is possible to draw the following general conclusions:

1. Management of cash flows is one of the most important activities of the financial manager. It includes calculation of time of the address of money (a financial cycle), the analysis of a cash flow, its forecasting, definition of an optimum level of money, drawing up budgets of money.

2. The purpose of management of money consists in investing surplus of the monetary income for receiving profit, but at the same time to have their necessary size for implementation of obligations for payments and simultaneous insurance on a case of unforeseen situations.

3. The analysis of cash flow allows to explain with a known share of accuracy a divergence between the size of the cash flow taking place at the enterprise in the reporting period and the profit got for this period.

4. The models developed in the theory of stockpile management and allowing to optimize the size of money can be applied to money. In the western practice the greatest distribution was gained by Baumol's model and Miller's model - Orr.

5. Improvement of management of in cash of the enterprises consists in the correct analysis of monetary receipts and definition of their type. One of basic elements of such financial analysis is the assessment of a cash flow like postnumerando and prenumerando, a widespread special case of these streams is the annuity.