The monetary flow management process is carried out in stages. We mentioned this earlier in the article "Cash flows of the company: Control Features" (see "Economist Directory" No. 3 for 2010). One of the most important stages of analyzing the cash flow report - the calculation and interpretation of financial efficiency factors cash streams (See Table). This system of indicators allows you to expand the traditional set of financial coefficients, making emphasis on the analysis of the monetary flow of the organization.
Assessment of cash flow can also be assessed by calculating liquid cash flow (Liquidity Cash Flow, LCF) for rapid diagnostics financial state Organizations:
LCF \u003d (FL 1 + Cl 1 - Cash 1) - (FL 0 + CL 0 - CASH 0),
where FL 1, FL 0 - long-term loans and loans at the end and the beginning of the analyzed period;
Cl 1, Cl 0 - short-term loans and loans at the end and the beginning of the analyzed period;
Cash 1, Cash 0 - cash on the checkout on the settlement and currency accounts in banks at the end and the beginning of the analyzed period.
Liquid cash flow is an indicator of excessive or deficient balance of the organization's funds. His difference from other liquidity indicators is that liquidity coefficients reflect the ability of the organization to repay their obligations to external creditors, and the liquid cash flow characterizes the absolute amount of funds derived from their own activities. It is an internal performance of the organization's performance and is important for both creditors and investors.
Monetary planning
One of the steps of monetary flow control is the planning stage. Cash flow planning helps the financial manager to determine the sources of funds and evaluate their use, as well as identify the expected cash flows, and therefore the prospects for the growth of the organization and its future financial needs.
The main task of drawing up a cash flow plan is to test the reality of sources of funds and the validity of expenses, synchronization of their occurrence, determine the possible need for borrowed funds. The cash flow plan can be drawn up directly or indirectly.
In addition to the annual cash flow plan, you need to develop a short-term plan for short periods of time (month, decade) in the form of a payment calendar.
Payment schedule - This is a plan for organizing production and financial activities, in which all sources are calendarly interconnected cash receipts and expenses for a certain period of time. It fully covers the monetary turnover of the organization; makes it possible to link cash receipts and cash payments and cashless form; Allows you to ensure constant solvency and liquidity.
Payment calendar is composed financial Services Enterprises, while the planned indicators of the cash flow budget are divided by months and smaller periods. Terms are determined on the basis of the frequency of basic payments of the organization.
In the process of drawing up a payment calendar, the following tasks are solved:
· Organization of accounting for a temporary docking of cash receipts and upcoming expenses of the organization;
· Formation of an information base on the movement of cash tributaries and outflows;
· Daily accounting of changes in the information base;
· Analysis of non-payment and organization of measures to eliminate their causes;
· Calculation of need for short-term financing;
· Calculation of temporarily free cash organization;
· Analysis financial market From the position of the most reliable and advantageous placement of temporarily free cash.
The payment calendar is drawn up on the basis of a real information base on the monetary flow of the organization, which includes: contracts with counterparties; acts of reconciliation of calculations with counterparties; accounts for payment of products; invoices; bank documents on the receipt of funds to accounts; money orders; Shipment schedules of products; Payment schedules wages; state of calculations with debtors and creditors; law deadlines payments on financial liabilities before budget and extrabudgetary funds; Internal orders.
To effectively draw up a payment calendar, a financial manager must control information about cash balances in bank accounts, consumed by means of medium residues per day, the state of market securities of the Organization, planned receipts and payments for the coming period.
The methodology for drawing up a payment calendar is widely represented in the special literature on financial management.
Balancing and synchronization of cash flows
The result of the development of a cash flow plan can be both shortage and excess money. Therefore, at the final stage of cash flow control, they are optimized by balancing in terms of volume and in time, synchronization of their formation in time and optimizing the cash balance at the current account.
Both deficiency and excess cash flow have a negative impact on the activities of the enterprise. The negative effects of the scarce cash flow are manifested in a decrease in liquidity and the level of solvency of the enterprise, the growth of overdue payables of raw materials suppliers and materials, increasing the share of overdue debts on obtained financial loans, delays in the payment of wages, growth of the financial cycle duration, and ultimately - in reducing profitability Use own capital and assets of the enterprise.
The negative effects of excessive cash flow are manifested in loss real value Temporarily unused cash from inflation, loss of potential income from an unused part of monetary assets in the field of short-term investment, which ultimately also adversely affects the level of profitability of assets and equity capital.
According to I. N. Yakovlev, the scope of the scarce cash flow should be balanced due to:
1) attracting additional eigenvery or long-term borrowed capital;
2) improving working with current assets;
3) getting rid of non-core non-current assets;
4) reducing the investment program of the enterprise;
5) cost reduction.
The volume of excessive cash flow must be balanced due to:
1) an increase in the investment activity of the enterprise;
2) expansion or diversifying activities;
3) early repayment of long-term loans.
In the process of optimizing cash flows in time, two basic methods are used - alignment and synchronization. Alignment of cash flows is aimed at smoothing their volumes in the context of the individual intervals of the time period under consideration. This optimization method allows to eliminate seasonal and cyclic differences in the formation of cash flows (both positive and negative), optimizing in parallel average cash balances and increasing liquidity. The results of this method of optimization of cash flows in time are estimated by the standard deviation or variation coefficient, which in the optimization process should decrease.
Synchronization of cash flows is based on convariation Positive and negative species. In the synchronization process, an increase in the level of correlation between the two types of cash flows should be ensured. The results of this method of optimization of cash flows in time are estimated by the correlation coefficient, which in the process of optimization should strive for the value "+1".
The proof of the correlation is increased by accelerating or slowing the payment turnover.
Payment Turnover is accelerated by the following events.:
1) increase the size of discounts to debtors;
2) reduce the term of the commodity loan provided to buyers;
3) tightening credit policies on the demand of debt;
4) tightening the procedure for assessing the creditworthiness of debtors in order to reduce the percentage of insolvent buyers of the organization;
5) use of modern financial instruments, such as factoring, accounting bills, FORFUTING;
6) use of such types of short-term loans as overdraft and credit line.
The slowdown in the payment turnover can be carried out at the expense:
1) an increase in the term of the commodity loan provided by suppliers;
2) acquisitions of long-term assets by leasing, as well as transmission to the accusigation of strategically less significant sections of the organization;
3) translating short-term loans to long-term;
4) Reducing calculations with cash suppliers.
Calculation of the optimal cash balance
Cashs as a type of current assets are characterized by some signs:
· Routine - cash is used to repay the current financial obligationsTherefore, there is always a break in time between incoming and outgoing cash flows. As a result, the enterprise is forced to constantly accumulate free funds at the bank account;
· Precautions - the company's activities are not rigidly regulated, so cash cash is necessary to cover unforeseen payments. To this end, it is advisable to create an insurance stock cash cash;
· Speculativity - money is necessary for speculative considerations, since there is a permanent probability that the opportunity will suddenly appear for profitable investment.
However, funds themselves are an unprecedented asset; therefore, the main goal of the policy of management of them is maintaining them at the minimum necessary level sufficient to implement the effective financial and economic activities of the organization, including:
· Timely payment of invalid accounts, allowing you to use the discounts provided by them from the price of goods;
· Maintaining constant creditworthiness;
· Payment of unforeseen expenses arising in the process of commercial activities.
As noted above, in the presence of a large account on the current account cash The organization has expenses of missed opportunities (refusal to participate in any investment project). With minimal funds of funds arise the costs of replenishing this stock, the so-called cost costs (Commercial expenses due to purchase and sale of securities, or interest and other expenses associated with attracting a loan to replenish the balance of cash). Therefore, solving the problem of optimizing the balance of money at the current account, it is advisable to take into account two mutually exclusive circumstances: maintaining current solvency and additional profit from the investment of free funds.
There are several basic methods for calculating the optimal balance of cash: Mathematical models of Baumol-Tobin, Miller-Orra, Stone, etc.
Baumol-Tobin model
The most popular liquidity management model (cash balance at the current account) is the Baumol-Tobin model, built on the conclusions to which W. Bumol and J. Tobin came independently of each other in the mid-50s. In the model it is assumed that commercial organization Supports an acceptable level of liquidity and optimizes its inventories.
According to the model, the enterprise begins to work, having the maximum acceptable (appropriate) liquidity level for it. Next, as the level of liquidity is reduced, the level of liquidity is reduced (cash is permanently spent for a certain period of time). All incoming cash enterprises invest in short-term liquid securities. As soon as the level of liquidity reaches a critical level, it becomes equal to some specified security level, the company sells part of the purchased short-term securities and thereby replenishes the stock of funds before the initial value. Thus, the dynamics of the cash balance of the enterprise is a "saw-eyed" graph (Fig. 1).
Fig. 1. Schedule changes to the balance of funds at the current account (model Baumol-Tobin)
When using this model, a number of restrictions take into account:
1) on this segment of time the need for organizing in cash is constant, it can be predicted;
2) All incoming products from the sale of products are invested in short-term securities. As soon as the balance of cash drops to the unacceptable small level, the organization sells part of securities;
3) constant, and therefore, and the planned of the organization's receipts and payments are considered, which allows calculating the net cash flow;
4) Calculating the level of costs associated with the transformation of securities and other financial instruments into cash, as well as losses from the missed benefit in the form of interest for the alleged investments of free funds.
According to the model under consideration, it is possible to use the model of the optimal order batch (EOQ) to determine the optimal balance of money:
where C is the optimal amount of funds;
F - fixed costs of buying and selling securities or maintenance of the loan obtained;
T. - Annual need for cash required to maintain current operations;
r is an alternative income (interest rate of short-term market securities).
Example 1.
We define the optimal balance of cash according to the Baumol-Tobin model, if the planned volume monetary turnover amounted to 24,000 thousand rubles, the costs of servicing one cash replenishment operation - 80 rubles, the level of loss of alternative income during the storage of funds is 10%.
By formula (1), we calculate the upper limit of the balance of the organization:
The average cash balance will be 97.98 thousand rubles. (195.96 / 2).
The lack of the Baumol-Tobin model is the assumption of the predictability and stability of the cash flow. It also does not take into account cyclicity and seasonality peculiar to most cash flows.
Miller Orra model
The above disadvantages of the Baumol-Tobin model will level the Miller-Orra model, which is an enhanced EOQ model. Its authors M. Miller and D. Orr use when constructing a model by the statistical method, namely the Bernoulli process - a stochastic process in which the receipt and spending of cash in time are independent random events.
When managing liquidity level, the financial manager must proceed from the following logic: the cash balance is chaotically change until the top limit reaches. As soon as this happens, you need to buy a sufficient number of liquid tools in order to return the level of funds to some normal level (return point). If the cash supply reaches the lower limit, then in this case it is necessary to sell liquid short-term securities and thus replenish liquidity supply to a normal limit (Fig. 2).
The minimum value of the cash balance at the current account is made at the level of the insurance stock, and the maximum one at the level of its three-time size. However, when solving the issue of the range (difference between the upper and lower limits of the cash balance), it is recommended to take into account the following: if the daily variability of cash flows are large or constant costs associated with the purchase and sale of securities, high, then the enterprise should increase the variation and vice versa. It is also recommended to reduce the scope of the variation, if there is a possibility of receiving income due to the high interest rate on securities.
When using this model, it is necessary to take into account the assumption that the costs of buying and selling securities are fixed and equal to each other.
Fig. 2. Schedule Changes to the balance of funds at the current account (Miller-Orra model)
To determine the return point, the following formula is used:
where Z is the target balance of funds;
Δ 2 - dispersion of the flow of day cash flow;
r is the relative amount of alternative costs (per day);
L is the lower limit of the cash balance.
The upper limit of the cash balance is determined by the formula:
H \u003d 3z - 2L. (3)
The average cash balance is by the formula:
C \u003d (4z - L) / 3, (4)
Example 2.
Calculate the optimal balance of cash according to the Miller-Orra model, if the rms (standard) rejection of the monthly amount of money circulation is 165 thousand rubles, the costs of servicing one cash replenishment operation - 80 rubles, the average daily level of loss of alternative income when storing funds - 0.0083%. Minimum cash balance - 2500 thousand rubles.
By formula (2) we define the target balance of funds:
The upper limit of the cash balance determine by formula (3):
H \u003d 3 × 2558.17 - 2 × 2500 \u003d 2674.5 thousand rubles.
The average size of the cash balance is determined by formula (4):
The main disadvantage of the model is that the upper limit of the liquidity level corridor is set depending on the bottom, but there is no clear method of setting the lower boundary. A manager who controls the level of liquidity in determining the lower border has to be based on common sense and experience, hence the subjectivity of the model estimates.
Model Stone
Stone model complements the Miller-Orra model and is based on the forecasts of cash flow at the near future. Achieving the upper amount of cash values \u200b\u200bat the current account will not cause them immediately transfer to securities, if in the coming days of the organization, according to forecasts, are expected to relatively high payments. This allows you to minimize the number of conversion operations and, therefore, reduce the cost-related expenses.
It seems that the considered mechanism of cash flow management is quite effective, and its implementation will allow to support financial equilibrium of the enterprise in the process of its production and economic activities, increase its financial and production flexibility.
E. G. Moiseeva,
Cand. ECON. Sciences, Arzamas Polytechnic Institute
To ensure effective cash flow management in foreign practice, the Baumol model and Miller model - Orra were obtained the greatest distribution.
The first was developed by V. Bumol (W. Baumöl) in 1952, the second - M. Miller (M. Miller) and D. Orrome (D. Orr) in 1966. The direct use of these models in domestic practice is still difficult due to insufficient The development of the securities market, so we give only a brief theoretical description of these models.
Baumol model
It is assumed that the company begins to work, having the maximum and appropriate level of money and then constantly consumes them for a period of time. All incoming funds from the sale of goods and services enterprise invest in short-term securities. As soon as the stock of money is depleted, i.e. It becomes equal to zero or reaches some given level of security, the company sells part of the securities and thereby replenishes the stock of money to the original value. Thus, the dynamics of the balance of funds at the current account is a "saw-eyed" schedule.
Fig. 6.3.
So, in accordance with the Baumol model, cash balances for the upcoming period are determined in the following sizes:
- a) the minimum cash balance is taken zero;
- b) the optimal (one maximum) residue is calculated by the formula
where DaMax is the maximum cash balance in the planned period; RK is the average amount of the cost of servicing one operation with short-term financial investments; Oda - total cash flow in the upcoming period; SPCFB - a percentage rate on short-term financial investments in the period under consideration;
c) The average balance of cash in accordance with this model is planned as half the maximum balance (DaMax: 2).
Miller model - Orra It is a more complex option for calculating the optimal amount of cash balances. The model is based on a certain unevenness of the receipt and consumption of funds, and, accordingly, their balance is also provided for the presence of an insurance reserve.
The minimum limit of the formation of the cash balance is made at the level of the insurance residue, and the maximum - three-time size of the insurance residue.
The logic of the actions of the financial manager for managing the balance of funds at the current account is presented in Fig. 6.4 And consists in the following - the balance of funds on the account is changing until the upper limit reaches. As soon as this happens, the company begins to acquire a sufficient amount of securities in order to return funds to some normal level (return point). If the cash supply reaches the lower limit, then in this case the company sells its securities and thus replenishes the stock of money to a normal limit.
Fig. 6.4.
When solving a question about the swing of variation (the difference between the upper and lower limits) is recommended to adhere to next policy: If the daily variability of cash flows are large or constant costs associated with the purchase and sale of securities, high, then the enterprise should increase the variation variation, and vice versa. It is also recommended to reduce the scope of the variation, if there is a possibility of receiving income due to the high interest rate on securities.
In accordance with the Miller model - Orra, cash balances for the upcoming period are determined in the following sizes in several stages.
- 1. The minimum amount of funds is established (it), which is advisable to constantly have at the current account.
- 2. According to statistical data, the variation of the daily receipt of funds for the current account is determined ( V.).
- 3. The costs of (PX) are defined on the storage of funds at the current account and expenses (RT) on mutual transformation of funds and securities.
- 4. The variation of the cash balance is calculated on the settlement account ( S.) according to the formula:
5. Determine the upper limit of funds at the current account (), if one is exceeded, part of the funds must be converted to short-term securities:
6. Find a return point (TV) - the value of the cash balance in the current account, to which it is necessary to return if the actual balance of funds at the current account goes beyond the boundaries of the interval ():
On the first The stage is regulated by the decada time spending time (in conjunction with their receipts), which allows you to minimize the balance of monetary assets within each month (quarter).
On the second Stage The size of the average balance of cash assets is optimized, taking into account the redundant reserve of these assets provided. At the same time, the maximum balance of monetary assets is determined, taking into account the unevenness of payments and the reserve, and then their average residue (half of the sum of the minimum and maximum balance of monetary assets).
The amount of cash assets in the process of adjusting the flow of payments is reinvested in short-term financial investments or other types of assets.
Ensuring the acceleration of the turnover of cash assets determines the need to search for reserves of such acceleration in the enterprise. The main of these reserves include:
- a) acceleration of collection of funds, in which the balance of monetary assets in the checkout is reduced;
- b) Cash Calculation Reduction (Cash cash payments increase the balance of cash at the checkout and reduce the use of its own cash for the period of passing payment documents of suppliers);
- c) Reducing settlements with suppliers with the help of letters of credit and checks, as they distract monetary assets from turnover for a long period due to the need for their reservation on special accounts in banks.
Ensuring the effective use of temporarily free cash balance can be carried out at the expense of the following events:
- a) coordination with the bank the conditions of current storage of the balance of funds with the payment of a deposit interest;
- b) the use of highly profitable short-term stock tools to accommodate a reserve of cash assets, but provided that they have sufficient liquidity on stock market.
Minimizing the losses of the funds used on inflation is carried out separately on funds in national and foreign currencies.
The anti-inflational protection of monetary assets is ensured if the rate of profitability according to the temporarily free to their residue is not lower than the inflation rate.
In 1952, William Baumolsm proposed a model for determining the target cash balance of the company. This model allows you to calculate the optimal amount of funds in the conditions of certainty when the company can accurately predict the outflows and cash flows. List the main prerequisites of the model:
- The demand for the company's money in each period is known and is located on one predicted level;
- All payment requirements are performed immediately;
- cash balances are used evenly;
- Transaction costs for the purchase and sale of securities or the transformation of assets in money are constant value.
So, the company can pre-predicting the need for cash for the coming period, which is most often considered one year. At his account, the company keeps not all this amount, because a large balance of cash has two opposite parties. With an increase in cash reserves, transaction costs are reduced because it is not required to receive a loan in a bank or sell securities. Negative side Cash extensions at the current account is that cash does not bring income, alternative costs arise. Cash could bring income as a percentage if they were put on the bank account. The optimal amount of funds in the Company's account is based on the requirement of minimizing transaction costs and alternative costs. We will try to determine what magnitude the company should sell securities or take a loan to maintain the optimal amount of cash on the account. This will be the target balance of the company's funds. The model assumes that the company can store a certain reserve of liquid securities, and when money ends in the account - to sell these securities, having received the required amount of money revenues.
Let at the time when the company has completed money, it replenishes them into the amount FROM. Since according to the prerequisites of the model, the cash is consumed evenly and in the initial period the amount of money is equal to C, and at the end of the period it is zero, then the average balance of cash will be the amount. Then we can determine the value of alternative costs as a magnitude
where FROM - the amount on which the company repleens its cash through the sale of liquid securities or as a result of obtaining a loan, r. - the relative amount of alternative costs of storage of cash.
If the overall need for the period (per year) in cash is the magnitude T, And the company comes over the amount of C, then the number of transactions selling securities or to get a loan will be. Since the company carries for each transaction transaction costs in the amount of F, then them total amount will be
where F - Permanent transaction costs for the sale of securities or a loan.
Then total costs (TC) to maintain cash balance on the account that are the sum of alternative costs and permanent transaction costs will be
To minimize these costs, differentiate the previous expression on FROM And equal to zero:
From here express FROM. Receive
where is the optimal amount of money that needs to be obtained from the sale of liquid securities or as a result of obtaining a loan in the bank. If the amount of cash on the company's account becomes zero, then the account replenishment must be made in the amount.
Example 12.2.Company Weekly spending 83,200 rubles. It is also known that the transaction costs for the transformation of assets in money are 512 rubles. If the company had placed money on the bank account, then would receive a yield of 16% per annum. Determine:
- a) target cash balance in the company's accounts;
- b) the number of transactions per year selling securities;
- c) the magnitude of the average cash balance on the account.
Decision
a) Since the company spends 83,200 per week., And in the year 52 weeks, the annual cash costs will be
Calculate the target balance of the company's funds:
If the company has completed cash on the account, it should replenish it in the amount of 166,400 rubles, selling securities or leaving a loan.
b) the number of transactions per year selling securities:
Making the calculation based on the data
we will find that transactions will be performed every 14 days, i.e. Once every two weeks.
c) the average cash balance will be
We highlight the influence of some parameters of the Baumla model on its results:
- Reducing transaction costs F. leads to a decrease in cash on the account. This is possible due to the development of new technologies, high-speed payments over the Internet, accelerating payments, so the company can more often replenish the score, but to a smaller value;
- With the increase in the company's need for cash and increasing parameter T. The target balance of money will not increase in the same scale. Increase value FROM* It will be less due to the nonlinear character of the specified parameters obtained in equation (12.2).
This model is actively used in macroeconomics to determine the demand for money. A significant disadvantage limiting the application of this model in practice is the prerequisite for the sustainability and predictability of the company's cash flows. In addition, the model does not take into account the seasonality of the business and the conditions for changing the phases macroeconomic cycles. The advantage of the model is to include alternative costs of cash storage.
- Baumol W. J. The Transactions Demand for Cash: An Inventory Theoretic Approach // Quarterly Journal of Economic. 1952. Nov. P. 545-556.
Foreign researchers in the field of stock management emphasizes the importance of calculating the optimal stock of funds developed by W. Bumolem and J. Tobin.
It is noted that W. Baumol first emphasized the similarity of the reserves of material assets and cash reserves and considered the possibility of applying stock management model to calculate the balance of cash of the company. In the Baumol model, as in the Miller model - Orra, the possibility of attracting borrowed funds is not taken into account.
1. Model Baumol - Tobin
W. Bumol fairly claims that the cash cash can be viewed as a stock of money, the owner of which is ready to exchange them for labor, raw materials and other types of material assets. Money cash is essentially not different from the reserves of shoes at the shoe-shoe-proclaser, which he is willing to exchange the retail merchant. Therefore, methods for determining the optimal size of reserves can be applied to calculate the stock of cash optimal for the company under existing costs.
W. Baumol model described in detail in the November issue of the magazine In 1952, 1811. The model developed by W. Baumo-Lem is based on the assumption that transactions are performed continuously and in a situation of complete certainty. Suppose the company is obliged to pay daily during the period T. Cash with shared volume R. The company has the ability to replenish the cash margin at the expense of money attracted to debt (by placing a bond loan) or in the stock market, selling securities. In any case, the Company bears debt service costs or alternative costs arising from the sale of securities and related to the refusal of the Company from securities revenue.
Consider the situation of the company of short-term financial investments In profitable securities, and then their subsequent sale to replenish the stock of cash. In this case, denote? d - profitability of financial investments in securities (reflective profits for each ruble embedded in securities), and b - Costs associated with the sale of securities selling. It is interesting to note that W. Bumol calls such expenses by the "brokerage fee", emphasizing that such a phrase should not be understood literally 181, p. 5461. Such costs include all costs associated with short-term financial investments, which are conventionally relying on the permanent for the accuracy of funds to attract funds (in this case, the sale of securities). Period T.divided at equal intervals t. The amount of money attracted evenly during the period T.to replenish the stock of cash, denote by S. Considering this amount, W. Bumol uses the term "seizure" ( withdrawal), Assuming cash is made from a financial investment by selling securities.
Thus, the total volume of transactions performed R predetermined, and values? D I. B - constant. The amount of cash with attached to replenish the supply of cash is declining evenly until the amount of money is fully exhausted, and the amount of money is rehasting again. Middle cash supply with Wed in the interval t. Raven
Then the alternative costs of the company from the termination of a financial investment during the time T. (In terms of stock management, such costs reflect the cost of storage for a certain time) will be
The number of securities selling transactions over time T.equally / Us, and the costs associated with the commission of the sale of securities make up B rubles for the transaction. It means that the total costs of attracting funds are equal
^, R.L \u003d * ?? (3.3)
Consequently, the total costs /% include the cost of storage and attracting funds will be
Full company costs when changing cash reserves over time T:
(3.4) where E - profitability of financial investments in securities per day;
T - Monetary reserve planning period, days.
Based on the fact that the company seeks to reduce the costs of attracting and storing the stock of cash, the optimal amount of cash balance with the Wholesale will correspond to the minimum full costs. Consider changing the stock of money over time T. When replenishing the stock for the optimal value from the wholesale at the time of time t V T 2 and g 3 with full cash spending by the time (Fig. 3.1).
We investigate the expression (3.4). The first term depends on with linearly and increases with an increase in the cash balance, and the second term, on the contrary, decreases with increasing C (Fig. 3.2).
From the graph, it can be seen that there is such an optimal value of the cash balance with the wholesale, in which E. Accept minimum value. Indeed, consider / 'as a function C and, equating the derivative from /' by zero, we get
Then, the optimal value of the cash stock
Fig. 3.1.
- 1, 3, 5, 7 - uniform spending of cash on payments in total R;
- 2, 4, 6 - replenishment of cash reserve at the expense of funds received from the sale of securities
Fig. 3.2.
The second derivative from 7 by with, equal
positive, we have at c \u003d with wholesale minimum.
Thus, with permanent amounts of costs for the conclusion of transactions and returns securities, the amount of money is changed in proportion to the square root of the amount of payments that the company undertakes to produce for a certain period of time.
J. Tobin independently of W. Baumol developed a similar model of demand for money, showing that cash reserves intended to conclude transactions depend on the change in the interest rate 11021. The model J. Tobin comes from the premise that the company chooses between bonds and cash . At the same time, J. Tobin notes that bonds and cash are the same assets, with the exception of two differences. First, bonds are not a means of payment. Secondly, the bonds bring income, and cash yield is zero. Unlike W. Baumol, J. Tobin used a portfolio approach to proof its provisions.
Following the arguments of J. Tobin, the following options are possible to make transactions for the acquisition of bonds and their subsequent sale. For example, the company buys bonds not immediately, after receiving funds, but after a while, and sells bonds, without waiting for complete consumption of cash. This approach is not optimal for the company, since the postponement of the purchase of bonds leads to a percentage of interest on them. More rationally for the company to purchase bonds at once at the time of the receipt of funds in the logistics system and sell them later, due to the consolidation of funds. In this case, the company will get more high percent By bonds. .
W. Bumol used the idea of \u200b\u200bminimizing the total costs of design and storage of material reserves, considering alternative costs of storing funds and the costs of attracting financial resources. The basic idea of \u200b\u200bthe Baumol model lies in the fact that there are alternative costs of storage of money - interest income, which can be obtained by other assets. However, cash reserves reduces transaction costs. With an increase in the interest rate, the company will strive to reduce the amount of funds due to the growth of alternative costs of money storage. Based on the calculations carried out, Baumol and Tobin proposed a formula for calculating demand for
money ( M.), which is middle value Cash balance:
The resulting formula was called the rule of the square root 149, p. 762].
Example 3.1.
Suppose that the company has the ability to purchase securities yield 0.022% in the morning (8.03% per year). At the same time, the constant costs of making transactions by the company are equal to 1.2 thousand rubles. For each operation. We define the optimal balance of funds evenly spent during the quarter, given that the total amount of all payments of the company for the quarter is equal to 90,000 thousand rubles. Conducting calculations according to formula (3.6), we obtain from opt \u003d 3302.9 thousand rubles. (Fig. 3.3):
1 2-1.2 90 000 V 90 0.00022
3302.9 (thousand rubles).
At the same time, the minimum costs of the company, calculated by formula (3.4), are equal to 65.4 thousand rubles:
Those with і- + - 2 with
- 1,2-90 000 3302,9
- 90 0,00022-3302,9 - ! --+
65.4 (thousand rubles).
A cash supply, equal to 200 thousand rubles, will lead to the full cost of the company in the amount of 542 thousand rubles, and if the company will keep a cash supply in the amount of 10,000 thousand rubles, then its full cost will amount to 110 thousand rubles. The company will be able to minimize its full costs, forming a cash supply at the level of 3302.9 thousand rubles. (Table 3.2)
Table 3.2.
Changing the costs in the micrological system, depending on the monetary stock according to the Baumol model E. \u003d 0.022% per day, thousand rubles.
- - the total cost of the company;
- - costs of attracting funds;
- - costs of money storage
Fig. 3.3. Changing the cost of the company, depending on the balance of cash on the Baumol - Tobin model E \u003d. 0.022% per day, thousand rubles.
The value of funds of funds increases with increasing costs of operations with securities and payments, and decreases with an increase in the profitability of financial investments. If we substitute the profitability of securities less adopted in settlements and equal to 0.0137% per day (5% per year), and the constant costs of making transactions in the amount of 1.8 thousand rubles. The operation and the amount of payment of the company is 280,000 thousand rubles. Quanttern, you can draw the following conclusion:
Cash supply in the amount of 200 thousand rubles. will lead to the full cost of the company, equal to 2521 thousand rubles, and in the amount of 12,000 thousand rubles. - to total costs 116 thousand rubles; The company's minimum cost is achieved in the range between 6,000 thousand and 10,000 thousand rubles. The Baumol model based on the data provided allows you to calculate a cash supply that minimizes the company's total costs (111 thousand rubles). Thus, the optimal stock of money is 9042 thousand rubles.
The model of calculating the optimal balance of Baumol's cash - Tobin is deterministic, which limits its use in practice.
2. Model Miller and Orra
Bernell K. Stone 11011 should be accepted that it is possible to distinguish two completely different logistics approaches to cash reserves management: a model in conditions of complete certainty proposed by W. Baumolem, and a model for calculating funds in the situation of uncertainty, developed by American economists, Merton Miller (Merton N. Miller) and Daniel Orrome (Daniel OPT) and published in the issue of magazine Quarterly Journal of Economics For August 1966. Based on the later publication of M. Miller and D. Orra, which contains additional evidence of the applicability of a stochastic model of cash reserves management, one can generally formulate the similarities and difference between these models. M. Miller and D. Orr, as well as W. Bumol, emphasize that the stock of the company depends on the alternative costs of cash storage and the cost of making securities purchase and sale transactions. However, in contrast to the Baumol model, Tobin stochastic model involves a probabilistic nature of the company's cash flow behavior.
The stochastic model of Miller - Orra is based on three major assumptions. At the same time, the first assumption repeats the assumptions of developers of deterministic models.
- 1. Similarly, assumptions previously discussed in U. Baumol models and debt accumulation, M. Miller and D. Orr, theoretically admit that the company uses two types of assets ( bank deposits, securities and cash) concludes transactions to translate one type of asset to another without a delay in time and consumes a permanent amount independent of the transaction.
- 2. There is a minimum level of cash reserve that the company seeks to maintain. Practically, the company follows the terms of the contract with the Bank, stipulating the company's responsibility, do not reduce the amount of funds at the current account below a certain amount.
- 3. Unlike the Baumol model - Tobin, the stock of money changes randomly, since the amounts of cash flows cannot be predicted on the basis of previous values.
Consider a details of the third assumption. In the model of Miller - Orro, it is assumed that an increase or decrease in cash reserve for a certain amount (t) For a short period of time (1 / g of the working day) can be considered as the appearance of a certain event when p Independent repeated tests according to Bernoulli scheme (P - Number of days). If the probability of increasing funds in value t. rubles equal r, then the probability of reducing the stock for the same value t. calculated as q. = 1 -R. Then the distribution of the company's pure cash flow (the difference between the influx and outflow) will have the average p P. and dispersion a 2 " equal
p / 7 \u003d nTM (P-Q), O 2 N \u003d 4NTPQM 2.
M. Miller and D. ORR go to consider the case of equal probabilities of inflows and cash outflows:
ya \u003d o, 0 ^ \u003d / 7d7 2 /,
In this case
o 2 \u003d ^ \u003d t 2 g (3.10)
Thus, cash flows are standardly distributed with zero medium and constant dispersion.
At the same time, the model of Miller - Orra overcomes the lack of a Baumol - Tobin model associated with the assumption of uniform spending of funds during the planned period (Fig. 3.1). Indeed, the most often occurred uneven cash flow in the period T. (Fig. 3.4).
If the receipts exceed the cash outflows, the stock of funds with increases, on the contrary, in case of exceeding cash outflow over the influx, the value with decreases. The reserve of funds with decreases and is increasing irregularly, but when reaches the upper point from the TAX at the end of the interval., The company implements a short-term financial investment, reducing excess cash. At the end of the interval / 2, when the stock of money becomes minimal
Fig. 3.4.
1 - Implementation of short-term financial investment in securities worth M. 2 - sale of securities in order to replenish cash reserves M.
with T1P, the company replenishes the balance of cash, selling securities.
In accordance with the Miller model - Orra, the stock of funds varies within the limits established by the upper boundary from the tach and the lower boundary with T1P. At the same time, as the lower boundary, the zero value of the stock of money is considered, and in some positive value, which is the result of the calculation of the model. Reasoning M. Miller and D. Orra on the random wandering of the amount of cash in set limits Based on the findings of V. Feller on the theory of random wandering and the task of ruin.
According to the classical task of ruining the player wins or loses money with probabilities r and c. respectively. Under the condition of the task of the player's initial capital is equal g. And he plays against an opponent with initial capital but-1 . Therefore, the total capital of two players is equal but. The game continues until the player's capital is either but, either will not decrease to zero, i.e. Before the moment when one of the two players does not go broke. Unknowns in the task are the likelihood of the ruin of the player and the distribution of probabilities for the duration of the game. V. Feller leads an analogy using the concepts of a wandering point emerging from the initial position of r and performing single jumps in a positive or negative direction at an equal interval intervals. If the tests stop when the point first reaches either the value but, Either 0, they say that the point makes a random wandering with absorbing screens at points with the values \u200b\u200bof O and 0. Modification of the classical ruin task is the task in which the absorbing screen is replaced by reflective. In gaming terminology, this is consistent with the agreement, according to the terms of which the player who losses the last ruble, this ruble returns to him by the enemy, which makes it possible to continue the game.
It can be concluded that the Miller - Orra model is the task of wandering the amount of the company's pure cash flow with two absorbing screens: the top with the tach and the bottom with TЕ1. If the return point is to designate with wholesale, then mathematical expectation M (c) The duration of the change of stock with the touch of one of the screens (upper or lower) is equal
M (c) \u003d From wholesale (with tah - from 0t), (3.11)
if condition (3.9) is satisfied.
The target function in the model is the expected value of complete costs.
Lt 2 1 e th (x + 2c)
- (3.12)
- * \u003d With tah ~ S.
The first term in (3.12) reflects the costs of attracting funds, and the second is alternative costs of storage of cash.
After finding private derivatives E (P) by SI h. and equalizing them zero, get
E. HER) _ Oh 2 12e y. DS ~ C 2 x + 3
- (3.13)
- (3.14)
Er? (/ D)? T 2 g E.
---- \u003d - ~ -n-- \u003d and
Eh x 2 S. 3
(Yate 2 1 33
- 4? I am
- (3.16)
- (3.17)
h "" Tah ~ ^ wholesale in
However, expressions (3.16) - (3.17) are valid if the minimum monetary residue is zero: With t [n \u003d 0. Otherwise (if from 1\u003e 0) the values \u200b\u200bfrom the Wholesale and the TAC should be determined as follows:
FROM \u003d S. +
- ( Kommersant 2 ^
G ote 2 ^
Consequently, expressions (3.16) - (3.17) are a special case (at the zero lower limit of the cash supply) of the general case described (3.18) - (3.19) for C.\u003e 0.
The managerial impact of the company on the value of the stock of funds for a general case can be formulated as follows (Fig. 3.5):
1) if the amount of the money supply in will increase to the top limit from the TAX, then the company should invest over cash in short-term financial investments at the end of the period in the amount C -S. (rub.);
Fig. 3.5.
- 1 - the implementation of short-term financial investments in the amount of TAX - from 0s; 2 - sale of securities in order to replenish cash reserves by the value of the wholesale - with T; P
- 2) If the value of the reserve with will decrease to the lower limit C min, then companies should be replenished with money supply, selling securities at the end of the period t 2. in volume with wholesale - C MIN. (rub.).
Example 3.2.
Suppose that the dispersion of a planned daily money turnover is 70 thousand rubles, the minimum balance of funds under the terms of the contract with the bank - 200 thousand rubles, and the annual profit rate of securities and the constant costs of making securities transactions are the same as In the previous example. We define the optimal balance of money and the upper limit of the cash supply.
According to formulas (3.18) - (3.19), we obtain from opt \u003d 265.9 thousand rubles, and from TAX \u003d 397 '7 thousand RU 6 "
from = from +
"" "" Wholesale "" "PPP 1
f ъ bm 2 t ^
3-1,2-70 4 0,00022
265.9 (thousand rubles),
C \u003d. FROM +3
"" "TAX ^ TT 1 ^
Mr. 2 ^
3-1,2-70 4 0,00022
397.7 (thousand rubles).
If we substitute in the model under consideration, a smaller amount of profitability of securities is 5% per year, and the constant costs of making transactions by the company to receive in the amount of 1.8 thousand rubles. The transmission of the planned daily money turnover is 8100 thousand rubles. and the minimum balance of funds under the terms of the contract with the Bank are 45,000 thousand rubles, the control effects of the micro-abstract system on the amount of money supply should be formulated as follows:
- 1) in case of reserves of cash of maximum values \u200b\u200bfrom TAX 46,292 thousand rubles. Companies should be purchased with securities in the amount of 861 thousand rubles, the difference between the maximum value of the reserve (46,292 thousand rubles) and the point of returning the amount of the cash supply from the Wholesale (45,431 thousand rubles), i.e. perform action 1 at the end of the period
- 2) If the company's cash supply reaches a minimum value with T1P, equal to 45,000 thousand rubles, then the company must, on the contrary, sell securities, seeking to increase the money supply from the value (45,000 thousand rubles) to the return point of the magnitude cash reserve by 431 thousand rubles, i.e. Make action 2 at the end of the period 2.
Thus, M. Miller and D. Orr, taking into account the company's desire to reduce the total costs, including the costs of attracting and alternative cash storage costs, proposed an approach to cash management, fully opposite to the deterministic approach of W. Baumol. Limitation practical application Miller - Orra models are associated with theoretical assumptions of the model, for example, with complete unpredictability of cash flows. Such an assumption means that the company does not have the opportunity with a sufficient degree of certainty to plan tributaries and cash outflows, which is not always true. Companies are known exact terms of dividend payments, wages, payments to creditors, tax payments. In addition, the model does not take into account the seasonal fluctuations in the demand for products and services of the company. Consequently, consideration of the behavior of the company's pure cash flow as a random wandering of a certain point between the absorbing screens should be recognized not completely reliable, but to some extent approximate to reality.
Expansion of the Miller - Orra model, involving the possibility of predicting the company's pure cash flow, proposed by the Associate Professor of Magistracy Trade and Industry and government controlled Cornell University Bernell K.
Stone (Bernell K. Stone). Unlike the considered stochastic model of calculating the optimal balance, model B. Stowan involves the possibility of predicting cash flow with a sufficient degree of certainty.
3. Improved Miller Model - Orra
The converted model of Miller - Orra to plan the stock of funds in the conditions of the transition economy is proposed by E.Yu. Krizhevskaya 1391. In conditions high inflation and absence state guarantees for investment in investment funds Krizhevskaya is recommended to invest free cash on currency market. Alternative cash storage costs are the loss of the company from cash depreciation, therefore in the model under consideration instead of profitability of short-term financial investments E A. Used the tempo of inflation E and.
In the model under consideration, the company's constant costs for conclusion of transactions b. Replaced on the costs of converting ruble cash in currency values? . expressed as a percentage of the amount
^ - ^ con (sleeping servants) ^^ CONSE
Unlike the model of Miller - Orro, the shelf life of funds in financial instruments is limited to family working days, i.e. Conversion costs increase three times compared with formula (3.20) and equal
L \u003d 6E COP with wholesale. (3.21)
Then, in accordance with the cash management model in the conditions of their depreciation, the Miller model - the Orra, discussed earlier, we formulate as follows:
FROM =3 FROM
^ tah - ^ whole
where E - the cost of converting funds in rubles in currency values; O is the standard deviation of the cash flow from the average value calculated by the formula (3.10), from where it follows
o \u003d l // l 2 /.
Companies with stable net cash flow in the planned period, it is recommended to place free cash on a deposit to the bank, and in the process of calculating with the Wholesale to use the following formula:
where E. - profitability of cash investment in the bank to the currency deposit, and the cost of converting ruble cash in currency values? KO | 1 is calculated by formula (3.20).
When applying this model, it should be remembered that alternative costs of cash storage are estimated in the amount of the highest profitability of the financial investment, from which the company refuses. In the model of Miller - Orro, such alternative costs are calculated on the basis of the profitability of short-term financial investments. E. Therefore, the addition of a percentage rate per currency deposit may be not sufficiently substantiated. E. To the inflation rate E I. In the denominator, the fracted expression under the sign of a square root in (3.24).
Note that the model under consideration has the following disadvantage. In the process of converting the formula Miller - Orro permanent and independent of the volume of transactions of the Company's costs for conclusion of transactions B Replaced with conversion costs expressed as a percentage of the transaction amount. However, the full cost formula underlying the reasoning of M. Miller and D. Orra is the amount of costs of attracting funds and alternative costs for storing cash. At the same time, the costs of attracting cash are equal to the work of the company's constant costs for conclusion of transactions B On the number of transactions performed. Therefore, it is not possible to withdraw the converted formula (3.22), if they substitute (3.12) instead of constant costs of conclusion of transactions B Variable costs for converting ruble cash in currency values? Con (pronounced as a percentage of the transaction amount). Consequently, the replacement of constant cost percentage should be justified.
It can be concluded that the improved model of Miller - Orra for the transition economy is a special case of an approach formulated by M. Miller and D. Orrome, for practical use in conditions of high inflation and FROM . = 0.
1. Baumol models and Miller-Orra Monetary Residue Management on the Settlement Account
Calculation of the optimal cash balance
Cashs as a type of current assets are characterized by some features:
routine - cash is used to repay current financial liabilities, therefore there is always a break in time between incoming and outgoing cash flows. As a result, the enterprise is forced to constantly accumulate free funds at the bank account;
precautions - the company's activities are not rigidly regulated, so cash cash is necessary for covering unforeseen payments. To this end, it is advisable to create a cash supply of cash;
speculativity - cash is necessary for speculative considerations, since there is a permanent probability that the opportunity will suddenly appear for profitable investment.
However, funds themselves are an unprecedented asset; therefore, the main goal of the policy of management of them is maintaining them at the minimum necessary level sufficient to implement the effective financial and economic activities of the organization, including:
timely payment of accounts of suppliers, allowing to use the discounts provided by them from the price of goods;
maintaining permanent creditworthiness;
payment of unforeseen expenses arising in the process of commercial activities.
As noted above, if there is a large cash mass on the organization at the current account of the organization, the costs of missed opportunities arise (refusal to participate in a non-investment project). With minimal funds of funds, costs of replenishing this stock, the so-called maintenance costs (commercial expenses caused by buying securities, or interest and other expenses associated with attracting a loan to replenish cash balances). Therefore, solving the problem of optimizing the balance of money at the current account, it is advisable to take into account two mutually exclusive circumstances: maintaining current solvency and additional profit from the investment of free funds.
There are several basic methods for calculating the optimal balance of cash: Mathematical models of Baumol-Tobin, Miller-Orra, Stone, etc.
Baumol-Tobin model
The most popular liquidity management model (cash balance at the current account) is the Baumol-Tobin model, built on the conclusions to which W. Bumol and J. Tobin came independently of each other in the mid-50s. The model assumes that a commercial organization supports an acceptable level of liquidity and optimizes its commodity reserves.
According to the model, the enterprise begins to work, having the maximum acceptable (appropriate) liquidity level for it. Next, as the level of liquidity is reduced, the level of liquidity is reduced (cash is permanently spent for a certain period of time). All incoming cash enterprises invest in short-term liquid securities. As soon as the level of liquidity reaches a critical level, it becomes equal to some specified security level, the company sells part of the purchased short-term securities and thereby replenishes the stock of funds before the initial value. Thus, the dynamics of the cash balance of the enterprise is a "saw-eyed" graph (Fig. 1).
Fig. 1. Schedule changes to the balance of funds at the current account (model Baumol-Tobin)
When using this model, a number of restrictions take into account:
1) on this segment of time the need for organizing in cash is constant, it can be predicted;
2) All incoming products from the sale of products are invested in short-term securities. As soon as the balance of cash drops to the unacceptable small level, the organization sells part of securities;
3) constant, and therefore, and the planned of the organization's receipts and payments are considered, which allows calculating the net cash flow;
4) Calculating the level of costs associated with the transformation of securities and other financial instruments into cash, as well as losses from the missed benefit in the form of interest for the alleged investments of free funds.
According to the model under consideration, it is possible to use the model of the optimal order batch (EOQ) to determine the optimal balance of money:
F - fixed costs of buying and selling securities or maintenance of the loan obtained;
T - the annual need for cash required to maintain current operations;
r is an alternative income (interest rate of short-term market securities).
Miller Orra model
The above disadvantages of the Baumol-Tobin model will level the Miller-Orra model, which is an enhanced EOQ model. Its authors M. Miller and D. Orr use when constructing a model by the statistical method, namely the Bernoulli process - a stochastic process in which the receipt and spending of cash in time are independent random events.
When managing liquidity level, the financial manager must proceed from the following logic: the cash balance is chaotically change until the top limit reaches. As soon as this happens, you need to buy a sufficient number of liquid tools in order to return the level of funds to some normal level (return point). If the cash supply reaches the lower limit, then in this case it is necessary to sell liquid short-term securities and thus replenish liquidity supply to a normal limit (Fig. 2).
The minimum value of the cash balance at the current account is made at the level of the insurance stock, and the maximum one at the level of its three-time size. However, when solving the issue of the range (difference between the upper and lower limits of the cash balance), it is recommended to take into account the following: if the daily variability of cash flows are large or constant costs associated with the purchase and sale of securities, high, then the enterprise should increase the variation and vice versa. It is also recommended to reduce the scope of the variation, if there is a possibility of receiving income due to the high interest rate on securities.
When using this model, it is necessary to take into account the assumption that the costs of buying and selling securities are fixed and equal to each other.
Fig. 2. Schedule Changes to the balance of funds at the current account (Miller-Orra model)
To determine the return point, the following formula is used:
where Z is the target balance of funds;
Δ2 - dispersion of the flow of day cash flow;
r is the relative amount of alternative costs (per day);
L is the lower limit of the cash balance.
The upper limit of the cash balance is determined by the formula:
The average cash balance is by the formula:
C \u003d (4z - L) / 3
Miller Orra model. The model developed by M. Miller and D. Orrome is a compromise between simplicity and everyday reality. It helps to answer the question of how companies should manage their cash supply, if it is impossible to accurately predict everyday outflow or cash flow. Miller and Orr used when constructing the model Bernoulli - a stochastic process in which the receipt and consumption of money from the period by the period are independent random events. Their main prerequisite is that the distribution of the daily cash flow is approximately normal. The actual value of the balance in any of the days can correspond to the expected value, be higher or lower. Thus, cash flow balance varies by randomly day; A kind of trend of its change is not provided.
The logic of the actions of the financial manager for managing the balance of funds at the current account is as follows. The balance of funds on the account is changing until the top limit reaches. As soon as this happens, the company begins to buy highly liquid securities in order to return the stock of funds to some level (return point). If the cash supply reaches the lower limit, the company sells accumulated securities accumulated, raging money supply to a normal level.
When solving a question about the rotation of the variation (the difference of the upper and lower limits), it is recommended to adhere to the rule: if the daily variability of cash flows are high or constant costs associated with the purchase and sale of securities, high, then the enterprise should increase the variation variation, and vice versa. It is also recommended to reduce the scope of the variation, if there is a possibility of receiving income due to the high interest rate on securities.
The implementation of the model is carried out in several stages.
Stage 1. . Set the minimum amount of money (FROM MIN.) which is advisable to constantly have at the current account. It is determined by the expert path, based on the average need of the company to pay for accounts, the possible requirements of the bank, creditors, etc.
Stage 2. . According to statistical data, it is determined by the variation of the daily receipt of funds for the settlement account (Var).
Stage 3. . Determine the costs of storage of funds at the current account (Z. S.) (Usually they are taken in the amount of daily income rate on short-term securities circulating in the market) and the costs of mutual transformation of funds and securities (Z). It is assumed that the value Z. constant; Analogue of this type of costs that has a place in domestic practice is, for example, commissions paid at currency exchange offices.
Stage 4. . Calculate the scope of variation of cash balance at the current account (R) according to the formula:
Stage 5. . Calculate the upper limit of cash at the current account ( FROM Max), if you have been exceeded, part of the funds are required to convert into short-term securities:
C. Max\u003d C. MIN.+ R.
Stage 6. Determine the return point (FROM R. ) - the amount of cash balance at the current account, to which it is necessary to return if the actual balance of funds at the current account is out of the interval boundaries:
CR \u003d (C MIN.+ 1/3 C Max).
The following data required to optimize the cash balance of the company are adopted as source.
· Minimum cash supply (FROM MIN.) - 10,000 thousand tenge;
· Securities conversion costs (Z) - 25 thousand tenge;
· interest rate: r. \u003d 11.6% per year;
· Average quadratic deviation per day - 2,000 thousand tenge.
It is necessary using the Miller-Orra model to determine the means of managing funds at the company's current account.
Decision
1. Calculation Z. S. . :
Z. S. \u003d R / 365 \u003d 11.6 / 365 \u003d 0.03% per day.
2. Calculation of daily cash flow variations (Var) (thousand tenge):
Var \u003d (2 000) 2 = 4 000 000.
3. Calculation of variations (R) (thousand tenge):
4. Calculation of the upper limit of funds and return points (thousand tenge):
FROM Max = 10 000 + 18 900 = 28 900.
FROM R. = 10 000 + 1 / 3 h. 18 900 = 16 300.
Thus, the balance of funds at the company's current account should vary in the range of 10,000,000 - 28,900,000 tenge); When leaving the interval, it is necessary to restore funds on the company's current account in the amount of 16,300,000 tenge.
As noted by Western experts, other approaches to the management of the target cash balance were also developed, in particular certain fame received the Stone model, which is the development of the Miller-Orra model.
Baumol-Tobin model. The most popular model of liquidity management (cash balance on the current account) is the Baumol-Tobin model, built on the conclusions, to which W. Baumol and J. Tobin came independently from each other in the mid-50s of the last century.
With the help of the Baumol-Tobin model, you can determine the optimal amount of the company's funds, which should be stored in conditions of certainty. The Baumol-Tobin model is significantly based on the condition that the possible alternative to the storage of money is the use of market securities and / or interest deposits.
According to the model, the company begins to work, having the most acceptable (appropriate) liquidity level. Next, as the level of liquidity is reduced, the level of liquidity is reduced (cash is permanently spent for a certain period of time). All incoming money company invests in short-term liquid securities. As soon as the level of liquidity reaches a critical level, that is, it becomes equal to some specified security level, the company sells part of the purchased short-term securities and thereby replenishes the stock of funds before the initial value. Thus, the dynamics of the cash balance of the company represents a "saw-eyed" schedule.
The Baumol-Tobin model is used under conditions when there is a high level of confidence that companies may need cash.
Suppose you need to determine how much cash should have a company. It should be minimized by the total costs that consist of costs of conversion and costs that are formed due to the fact that the company refuses a part of income on market securities, as it stores funds in cash.
When building a model, it is assumed that for some time (for example, month), the company has a stable need and demand for money. At the same time, cash receives, selling market securities. When funds are completed, the company sells market securities to cash.
Total costs can be represented as:
Total costs \u003dB x (t / c) + r x (C / 2),
where B. h. (T / C) - General transaction costs for the period, while IN - total costs associated with the sale of securities (transaction costs); T / S. - the number of operations for the sale of market securities ( equal to relation total demand for cash in the period ( T.) to the cash balance ( FROM);
r. h. (C / 2) - the amount of income from which the company refuses, keeping its funds in cash, while r. - interest rate on market securities; ( C / 2.) - Middle cash balance.
On the one hand, the more funds, the higher the income from which the company refuses, simply keeping its funds in cash or on the current accounts. On the other hand, the higher the balance of the cash, the less you need transfers to market securities and the less conversion costs.
In accordance with the Baumol-Tobin model, the company's costs for the implementation of securities in the case of storage of a part of funds in high-liquid papers are compared with the missed benefit that the company will have in the event that it refuses to store funds in securitiesAnd therefore, there will be no interest and dividends on them. The model allows you to calculate such a value of cash that minimized the costs of transactions and the missed benefits. The calculation is carried out by the formula:
C \u003d √2 x b x T / R.
The lack of the Baumol-Tobin model is to assume the predictability and stability of the cash flow. In addition, it does not take into account cyclicity and seasonality characteristic of most cash flows.
We define the optimal balance of funds according to the Baumla-Tobin model, if the planned amount of money turnover is 50 million tenge, the costs of servicing one cash replenishment operation - 400 tenge, the level of loss of alternative revenues when storing funds - 10%.
By the formula, we calculate the upper limit of the cash balance of the company (thousand tenge):
C \u003d √ 2 h. 0,4 h. 50 000 / 0,1 = 632,46.
Thus, the average balance of funds will be 316.23 thousand tenge (632.46 / 2).
Suppose that the company's cash spending during the year will amount to 1,500 million tenge. The interest rate on state securities is 8%, and the costs associated with each implementation are 25,000 tenge.
Calculate the upper limit of the cash balance of the company (million tenge):
C \u003d √ 2 h. 1 500 h. 0,025 / 0,08 = 30,62.
The average cash amount at the current account is 15.31 million tenge (30.62 / 2).
The total number of transformation transformations in cash for the year will be (million tenge):
1 500 / 30,62 = 49.
Thus, the policy of managing money and their equivalents is: as soon as the funds are completed at the current account, the company sells part of its liquid securities in approximately 30 million tenge. Such an operation is performed about once a week. The maximum amount of cash at the current account will be 30.62 million tenge, the average - 15.31 million tenge.
