According to the rule in the baumol model are calculated. Using the Baumol model in enterprise cash management. Initial provisions of the Baumol model

The process of managing the organization's cash flows is carried out in stages. We mentioned this earlier in the article "Company Cash Flows: Features of Management" (see Economist's Handbook No. 3, 2010). One of the most important stages in the analysis of the cash flow statement is the calculation and interpretation of financial ratios for the efficiency of using cash flows (see table). This system of indicators allows you to expand the traditional set of financial ratios, focusing on the analysis of the organization's cash flows.

You can also evaluate cash flow using the calculation of liquidity cash flow (LCF) for the purpose of express diagnostics of the financial condition of the organization:

LCF = (FL 1 + CL 1 - CASH 1) - (FL 0 + CL 0 - CASH 0),

where FL 1 , FL 0 - long-term credits and loans at the end and beginning of the analyzed period;

CL 1 , CL 0 - short-term credits and loans at the end and beginning of the analyzed period;

CASH 1 , CASH 0 - cash on hand, on settlement and currency accounts in banks at the end and beginning of the analyzed period.

Liquid cash flow is a measure of an organization's cash surplus or deficit. Its difference from other liquidity indicators is that liquidity ratios reflect the organization's ability to repay its obligations to external creditors, and liquid cash flow characterizes the absolute amount of funds received from its own activities. It is an internal indicator of the performance of the organization and is important for both creditors and investors.

Cash flow planning

One of the stages of cash flow management is the planning stage. Cash flow planning helps the financial manager to determine the sources of funds and assess their use, as well as to identify the expected cash flows, and therefore the growth prospects of the organization and its future financial needs.

The main task of drawing up a cash flow plan is to check the reality of the sources of funds and the validity of expenses, the synchronism of their occurrence, to determine the possible need for borrowed funds. The cash flow plan can be drawn up in a direct or indirect way.

In addition to the annual cash flow plan, it is necessary 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 of cash receipts and expenses for a certain period of time are calendar-related. It fully covers the cash flow of the organization; makes it possible to link receipts of funds and payments in cash and non-cash form; allows to ensure constant solvency and liquidity.

The payment calendar is compiled by the financial service of the enterprise, while the planned indicators of the cash flow budget are broken down by months and smaller periods. The terms are determined based on the frequency of the organization's main payments.

In the process of compiling a payment calendar, the following tasks are solved:

organization of accounting for the temporary docking of cash receipts and future expenses of the organization;

Formation of an information base on the movement of cash inflows and outflows;

daily accounting of changes in the information base;

analysis of non-payments and organization of measures to eliminate their causes;

calculation of the need for short-term financing;

Calculation of temporarily free funds of the organization;

· analysis of the financial market from the position of the most reliable and profitable placement of temporarily free funds.

The payment calendar is compiled on the basis of a real information base on the organization's cash flows, which includes: contracts with counterparties; acts of reconciliation of settlements with counterparties; invoices for products; invoices; bank documents on receipt of funds to accounts; money orders; product shipment schedules; payroll schedules; status of settlements with debtors and creditors; statutory deadlines for payments on financial obligations to the budget and extra-budgetary funds; internal orders.

To effectively draw up a payment calendar, a financial manager needs to control information about cash balances in bank accounts, funds spent, average daily balances, the state of the organization's marketable securities, planned receipts and payments for the coming period.

The methodology for compiling a payment calendar is widely represented in the specialized literature on financial management.

Balancing and synchronization of cash flows

The result of developing a cash flow plan can be both a deficit and an excess of cash. Therefore, at the final stage of cash flow management, they are optimized by balancing in volume and time, synchronizing their formation in time, and optimizing the cash balance on the current account.

Both deficit and excess cash flow have a negative impact on the activities of the enterprise. The negative consequences of a deficit cash flow are manifested in a decrease in the liquidity and solvency of an enterprise, an increase in overdue accounts payable to suppliers of raw materials and materials, an increase in the share of overdue debts on financial loans received, delays in paying wages, an increase in the duration of the financial cycle, and ultimately in a decrease in profitability use of own capital and assets of the enterprise.

The negative consequences of excess cash flow are manifested in the loss of the real value of temporarily unused funds from inflation, the loss of potential income from the unused part of monetary assets in the field of their short-term investment, which ultimately also negatively affects the level of return on assets and equity of the enterprise.

According to I. N. Yakovleva, the volume of scarce cash flow should be balanced by:

1) attracting additional equity or long-term debt capital;

2) improving work with current assets;

3) getting rid of non-core non-current assets;

4) reduction of the investment program of the enterprise;

5) cost reduction.

The amount of excess cash flow should be balanced by:

1) increasing the investment activity of the enterprise;

2) expansion or diversification of activities;

3) early repayment of long-term loans.

In the process of optimizing cash flows over time, two main methods are used - leveling and synchronization. Equalization of cash flows is aimed at smoothing their volumes in the context of individual intervals of the period under consideration. This optimization method eliminates, to a certain extent, seasonal and cyclical differences in the formation of cash flows (both positive and negative), while simultaneously optimizing the average cash balances and increasing the level of liquidity. The results of this method of optimizing cash flows over time are evaluated using the standard deviation or coefficient of variation, which should decrease during the optimization process.

Cash flow synchronization is based on convariations their positive and negative types. In the process of synchronization, an increase in the level of correlation between these two types of cash flows should be ensured. The results of this method of optimizing cash flows over time are evaluated using the correlation coefficient, which should tend to the value "+1" during the optimization process.

The tightness of the correlation increases due to the acceleration or deceleration of the payment turnover.

The payment turnover is accelerated by the following measures:

1) increasing the amount of discounts for debtors;

2) shortening the period of commodity credit provided to buyers;

3) tightening of the credit policy on the issue of debt collection;

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 of bills, forfeiting;

6) use of such types of short-term loans as overdraft and credit line.

The slowdown in the payment turnover can be carried out due to:

1) an increase in the term of a commodity loan provided by suppliers;

2) the acquisition of long-term assets through leasing, as well as the outsourcing of strategically less significant areas of the organization's activities;

3) transfer of short-term loans into long-term ones;

4) reduction of cash settlements with suppliers.

Calculation of the optimal cash balance

Cash as a type of current assets is characterized by some features:

Routine - funds are used to pay off current financial obligations, so there is always a time gap between incoming and outgoing cash flows. As a result, the company is forced to constantly accumulate free cash on a bank account;

precaution - the activity of the enterprise is not strictly regulated, so cash is needed to cover unforeseen payments. For these purposes, it is advisable to create an insurance cash reserve;

· speculative - funds are needed for speculative reasons, since there is always a small probability that an opportunity for profitable investment will suddenly appear.

However, cash itself is a non-profitable asset, so the main goal of the cash management policy is to maintain it at the minimum required level, sufficient for the effective financial and economic activities of the organization, including:

timely payment of suppliers' invoices, allowing them to take advantage of the discounts they provide on the price of goods;

maintaining a constant creditworthiness;

payment of unforeseen expenses arising in the course of commercial activities.

As noted above, if there is a large amount of money on the current account, the organization has the costs of missed opportunities (refusal to participate in any investment project). With a minimum stock of funds, there are costs to replenish this stock, the so-called maintenance costs(commercial expenses due to the purchase and sale of securities, or interest and other expenses associated with attracting a loan to replenish the balance of funds). Therefore, when solving the problem of optimizing the balance of money on the current account, it is advisable to take into account two mutually exclusive circumstances: maintaining current solvency and obtaining additional profit from investing free cash.

There are several basic methods for calculating the optimal cash balance: mathematical models of Baumol-Tobin, Miller-Orr, Stone, etc.

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 that W. Baumol and J. Tobin came to independently in the mid-1950s. The model assumes that a commercial organization maintains an acceptable level of liquidity and optimizes its inventory.

According to the model, the enterprise begins to operate with the maximum acceptable (expedient) level of liquidity for it. Further, as the work progresses, the level of liquidity decreases (money is constantly spent over a certain period of time). The company invests all incoming cash in short-term liquid securities. As soon as the level of liquidity reaches a critical level, that is, it becomes equal to a certain predetermined level of security, the company sells part of the purchased short-term securities and thereby replenishes the cash reserve to its original value. Thus, the dynamics of the company's cash balance is a "sawtooth" graph (Fig. 1).

Rice. 1. Schedule of changes in the balance of funds on the current account (Baumol-Tobin model)

When using this model, a number of limitations are taken into account:

1) at a given period of time, the organization's need for funds is constant, it can be predicted;

2) the organization invests all incoming funds from the sale of products in short-term securities. As soon as the cash balance falls to an unacceptably low level, the organization sells part of the securities;

3) the receipts and payments of the organization are considered constant, and therefore planned, which makes it possible to calculate the net cash flow;

4) the level of costs associated with the conversion of securities and other financial instruments into cash, as well as losses from lost profits in the form of interest on the proposed investment of free funds, can be calculated.

According to the model under consideration, to determine the optimal cash balance, you can use the optimal order lot (EOQ) model:

where C is the optimal amount of money;

F - fixed costs for the purchase and sale of securities or servicing the loan received;

T - annual need for cash needed to maintain current operations;

r - value of alternative income (interest rate of short-term market securities).

Example 1

Let us determine the optimal balance of funds according to the Baumol-Tobin model, if the planned volume of cash turnover amounted to 24,000 thousand rubles, the cost of servicing one cash replenishment operation was 80 rubles, and the level of losses of alternative income when storing funds was 10%.

According to formula (1), we calculate the upper limit of the organization's cash balance:

The average cash balance will be 97.98 thousand rubles. (195.96/2).

The disadvantage of the Baumol-Tobin model is the assumption of predictability and stability of the cash flow. It also does not take into account the cyclicality and seasonality inherent in most cash flows.

Miller-Orr model

The disadvantages of the Baumol-Tobin model noted above are eliminated by the Miller-Orr model, which is an improved EOQ model. Its authors M. Miller and D. Orr use a statistical method when building a model, namely the Bernoulli process - a stochastic process in which the receipt and expenditure of funds over time are independent random events.

When managing the level of liquidity, the financial manager must proceed from the following logic: the cash balance changes chaotically until it reaches the upper limit. As soon as this happens, it is necessary to buy enough liquid instruments in order to return the level of funds to some normal level (point of return). If the stock of funds reaches the lower limit, then in this case it is necessary to sell liquid short-term securities and thus replenish the stock of liquidity to the normal limit (Fig. 2).

The minimum value of the cash balance on the current account is taken at the level of the insurance stock, and the maximum - at the level of its triple size. However, when deciding on the range (the difference between the upper and lower limits of the cash balance), it is recommended to take into account the following: if the daily volatility of cash flows is large or the fixed costs associated with buying and selling securities are high, then the company should increase the range of variation and vice versa. It is also recommended to reduce the range of variation if there is an opportunity to generate income due to the high interest rate on securities.

When using this model, one should take into account the assumption that the costs of buying and selling securities are fixed and equal to each other.

Rice. 2. Graph of changes in the balance of funds on the current account (Miller-Orr model)

The following formula is used to determine the cusp point:

where Z is the target cash balance;

δ 2 - dispersion of the daily cash flow balance;

r is the relative value of opportunity costs (per day);

L - the lower limit of the cash balance.

The upper limit of the cash balance is determined by the formula:

H = 3Z - 2L. (3)

The average cash balance is found by the formula:

C \u003d (4Z - L) / 3, (4)

Example 2

Calculate the optimal balance of funds using the Miller-Orr model, if the standard deviation of the monthly volume of cash turnover is 165 thousand rubles, the cost of servicing one cash replenishment operation is 80 rubles, the average daily level of losses of alternative income when storing funds - 0.0083%. The minimum balance of funds is 2,500 thousand rubles.

According to formula (2), we determine the target cash balance:

The upper limit of the cash balance is determined by the formula (3):

H \u003d 3 × 2558.17 - 2 × 2500 \u003d 2674.5 thousand rubles.

The average amount of the cash balance is determined by the formula (4):

The main drawback of the model is that the upper limit of the liquidity level corridor is set depending on the lower one, but there is no clear methodology for setting the lower limit. The manager who controls the level of liquidity has to rely on common sense and experience in determining the lower limit, hence the subjectivity of the model estimates arises.

Stone model

The Stone model complements the Miller-Orr model and is based on near-term cash flow projections. Reaching the upper limit of the amount of funds in the current account will not cause their immediate transfer into securities if the organization is expected to have relatively high payments in the coming days, according to forecasts. This allows you to minimize the number of conversion operations and, consequently, reduce the associated withdrawal costs.

It seems that the considered cash flow management mechanism is quite effective, and its implementation will allow maintaining the financial balance of the enterprise in the course of its production and economic activities, increasing the degree of its financial and production flexibility.

E. G. Moiseeva,
cand. economy Sciences, Arzamas Polytechnic Institute

Federal Agency for Education of the Russian Federation

GOU VPO “SIBERIAN STATE

UNIVERSITY OF TECHNOLOGY"

Faculty: Chemical-technological ZDO

Department: Accounting and Finance

Discipline: Financial management

Test

Option number 15

Checked: N.I. Popova

(signature)

______________________

(estimate, date)

Completed:

stud. 5th course, spec. 060805ks

code K605115

N.V. Lazarevich

(signature)

Krasnoyarsk 2010

Theoretical part:

Give a description of the Baumol model……...………………………………3

Describe the indirect method for calculating cash flows………………………………………………….

Define the following terms:

Financial instruments …………………………………………………….... 7

Issue policy…………………………………………………………….. 7

Elasticity ……………………………………………………………………….. 7

Bibliographic list...…………………………………………………….. 8

Practical part (option No. 15):

Task #1

Task #2

Task #3

Theoretical part

1. Describe the Baumol model

The Baumol model is a model for changing the balance of funds on a current account, in which the enterprise invests all incoming funds from the sale of goods and services in securities, then, when the cash reserve is depleted, the enterprise sells part of the securities and replenishes the cash balance to its original value.

According to the Baumol model, it is assumed that the enterprise begins to work with the maximum and expedient level of funds for it, and then it is constantly spent over a certain period of time. The company invests all incoming funds from the sale of goods and services in short-term securities.

Figure 1- Graph of changes in the balance of funds on the current account

The optimal cash balance is determined by the formula.

where Q is the optimal cash balance;

F is the projected need for funds in the period (year,

quarter, month);

c - one-time expenses for converting cash into valuable

d - acceptable and possible interest income for the enterprise on

short-term financial investments.

The average stock of cash is Q /2, and the total number of transactions for the conversion of securities into cash (K) is equal to:

The total cost (CT) of implementing this cash management policy would be:

The first term in this formula is direct costs, the second is the lost profit from keeping funds in a current account instead of investing them in securities.

2. Describe an indirect cash flow calculation method

indirect method is based on the identification and accounting of cash flow transactions and the consistent adjustment of net income, i.e. the starting point is profit.

The essence of the indirect method is to convert the amount of net profit into the amount of cash. At the same time, it is assumed that in the activities of each enterprise there are separate, often significant types of expenses and incomes that reduce (increase) the profit of the enterprise without affecting the amount of its cash. In the process of analysis, the amount of the specified expenses (income) is adjusted for the amount of net profit so that the items of expenses that are not associated with the outflow of funds and the items of income that are not accompanied by their inflow do not affect the amount of net profit.

The indirect method is based on the analysis of balance sheet and income statement items, and:

allows you to show the relationship between different types of activities of the enterprise;

establishes the relationship between net profit and changes in the assets of the enterprise for the reporting period.

When analyzing the relationship between the obtained financial result and the change in cash, one should take into account the possibility of obtaining income reflected in the accounting of real cash receipts.

The indirect method of analysis is based on adjustments to the net profit of the reporting period, as a result of which the latter becomes equal to the net cash flow (increase in the cash balance). Such adjustments are conditionally divided into three groups according to the nature of business transactions:

1. Adjustments related to the discrepancy between the time of recording income and expenses in accounting records with the inflow and outflow of cash from these operations.

2. Adjustments related to business transactions that do not directly affect the formation of profits, but cause cash flows.

3. Adjustments related to transactions that have a direct impact on the calculation of the profit measure, but do not give rise to cash flows.

To carry out calculations, it is necessary to use the data of the turnover sheet for accounting accounts, as well as separate analytical records.

The procedure for the adjustment value for accounts receivable is to determine the increment in the balance for the analyzed period for accounts receivable. The financial result of the analyzed period will be adjusted by the amount of this increment. If the increment is positive, then the amount of profit must be reduced by this amount, and if it is negative, it must be increased.

Profit adjustments in connection with the calculation of depreciation are made for the amount of accrued depreciation for the analyzed period (credit turnover on accounts 02, 05), while the amount of profit increases.

The mechanism for calculating the adjustment of net profit in accordance with the indirect method of cash flow analysis is presented in Table. one.

Table 1

Mechanism for calculating net income adjustment based on the indirect method of cash flow analysis

The indirect method of cash flow analysis allows you to determine the impact of various factors of the financial and economic activities of the organization on the net cash flow.

The indirect method helps to detect negative trends in time and take adequate measures in a timely manner to prevent possible negative financial consequences.

To solve the problem of linking two "net" resulting indicators: net profit and net cash flow, an indirect method of analysis is used.

The indirect method allows:

Control the correctness of filling out the forms of accounting financial statements No. 1, No. 2, No. 4 by docking net cash flow and net profit;

Identify and quantify the causes of deviations of financial performance indicators calculated by different methods from each other (net cash flow and net profit);

To identify in the composition of the assets of the balance sheet those that could initiate an increase or decrease in cash;

Track the impact of changes in passive items on the value of the cash balance;

Consider the depreciation factor as the cause of the gap between net income and net cash flow;

Explain to the manager the reasons why the organization's profit is growing, and the amount of money in the current account is decreasing.

When evaluating the results of the analysis, it should be borne in mind that a growing successful business is characterized by:

Inflows - own capital (profit of the reporting year and contributions of participants), loans and borrowings, as well as accounts payable;

Outflows - non-current assets, inventories and receivables, that is, inflows from the liability of the balance sheet and outflows from the asset.

3. Define the following concepts: financial instruments, emission policy, elasticity

financial instrument- a financial document (currency, security, monetary obligation, futures, option, etc.), the sale or transfer of which ensures the receipt of funds. This is, in fact, any contract, the result of which is the appearance of a certain article in the assets of one party to the contract and an article in the liabilities of the other party to the contract.

Issuing policy- a set of long-term rules that determine the procedure for issuing and repurchasing the company's own shares. the main performance indicators of SKB OJSC ... description, systematization, grouping or classification, characteristics material (qualitative, quantitative) in accordance with...

This model assumes that the organization starts operating with a maximum level of cash that is constantly spent over a certain period of time. As soon as the stock of funds reaches a certain limit, the organization replenishes them.

This model is used in case of stability of receipts and expenditures of funds, taking into account the fact that the storage of all monetary assets is carried out in the form of short-term financial investments and the change in the balance of funds occurs from the maximum amount to zero.

Calculation of the maximum and average balance is carried out according to the formula:

R o

Software up to- the planned volume of cash turnover;

P d

If there is a very large amount of money in the account, the organization has the cost of unused opportunities or lost profits. These costs are also called forced costs. If the stock of cash is too small, the organization incurs costs to replenish this stock, which are also called maintenance costs or maintenance costs of a cash replenishment transaction.

Taking into account these types of costs, an optimization model is built that determines the frequency of replenishment and the optimal size of the cash balance, at which the total costs will be minimal.

Miller-Orr model

In the Miller-Orr model, receipts and expenditures of funds are stochastic, i.e. independent random events. The main feature of this model is the presence of a certain insurance stock of funds, at the level of which the minimum amount of cash balance is set. The maximum amount of cash balance is set at the level of three times the size of the insurance stock.

The cash balance changes until it reaches the upper limit. In this case, the excess cash is withdrawn and invested, for example, in short-term financial instruments. If the cash balance reaches the lower limit, then cash is replenished by selling a part of short-term instruments.

The range of fluctuations in the cash balance between the minimum and maximum levels is calculated by the formula:

KO- the range of fluctuations in the balance of cash;

R o– expenses for servicing one cash replenishment operation;

d2- standard deviation of the daily volume of money turnover;

P d- the level of loss of alternative income during the storage of funds (average% rate for short-term financial investments).

The calculation of the maximum and average balance is carried out according to the formulas:

Despite the clear mathematical apparatus for calculating the optimal amounts of cash balances, both of the above models (the Baumol Model and the Miller-Orr Model) are still rarely used in domestic financial management practice, in particular, for the following reasons:

· a chronic shortage of current assets does not allow organizations to form the balance of funds in the required amount, taking into account their reserve;

· the slowdown in the payment turnover causes significant (sometimes unpredictable) fluctuations in the amount of cash receipts, which, accordingly, is reflected in the amount of the balance of monetary assets;

· a limited list of circulating short-term stock instruments and their low liquidity make it difficult to use indicators related to short-term financial investments in calculations.

3. Differentiation of the average balance of monetary assets in the context of national and foreign currencies. Such differentiation is carried out only by organizations that conduct foreign economic activity. The purpose of such differentiation is to isolate their currency part from the general optimized need for monetary assets in order to ensure the formation of the currency funds necessary for the organization. The basis for the implementation of such differentiation is the planned volume of spending funds in the context of internal and external economic operations in the course of operating activities. In the calculations, formulas are used to determine the need for operating and insurance balances of monetary assets with their differentiation by type of currency.

4. The choice of effective forms of regulation of the average balance of monetary assets. Such regulation is carried out in order to ensure the constant solvency of the organization, as well as to reduce the estimated maximum and average need for cash balances.

The main method of regulating the average balance of monetary assets is to adjust the flow of upcoming payments (postponement of the term of individual payments upon prior agreement with counterparties). This adjustment is carried out in the following steps.

At the first stage on the basis of the plan (budget) for the receipt and expenditure of funds in the coming quarter, the range of fluctuations in the balance of the organization's monetary assets in the context of individual decades is studied. This range of fluctuations is determined in relation to the minimum and average indicators of the balances of monetary assets in the forthcoming period.

At the second stage ten-day periods for spending funds (in relation to their receipts) are regulated, which allows minimizing the balance of cash assets within each month and for the quarter as a whole. Optimality criterion This stage of regulation of the flow of forthcoming payments is the minimum level of the root-mean-square (standard) deviation of the ten-day values ​​of the balance of the organization's monetary assets from their average size.

At the third stage the values ​​of the balances of monetary assets obtained as a result of regulation of the flow of payments are optimized taking into account the envisaged size of the insurance balance of these assets. First, the maximum and minimum balances of monetary assets are determined, taking into account the new range of their fluctuations and the size of their insurance stock, and then their average balance (half the sum of the minimum and maximum balances of monetary assets).

The amount of monetary assets released during the ten-day adjustment of the flow of payments is reinvested in short-term financial instruments or in other types of assets.

There are other forms of operational regulation of the average balance of monetary assets, providing both an increase and a decrease in its size. These forms are considered as part of the organization's cash flow management.

5. Ensuring profitable use of the temporarily free balance of monetary assets. At this stage of the formation of the monetary asset management policy, a system of measures is developed to minimize the level of losses of alternative income in the process of their storage and anti-inflationary protection. The main activities include:

· coordination with the bank that provides settlement services to the organization, the conditions for the current storage of the balance of monetary assets with the payment of deposit interest on the average amount of this balance (for example, by opening a checking account with a bank);

· the use of short-term monetary investment instruments (first of all, deposits in banks) for temporary storage of insurance and investment balances of monetary assets;

· the use of highly profitable stock instruments for investing the reserve and the free balance of monetary assets (government short-term bonds; short-term bank certificates of deposit, etc.), but subject to sufficient liquidity of these instruments in the financial market.

6. Construction of effective systems of control over the organization's monetary assets. The object of such control is the aggregate level of the balance of monetary assets that ensure the current solvency of the organization, as well as the level of efficiency of the formed portfolio of short-term financial investments - cash equivalents of the organization.

Monetary assets play a decisive role in the process of ensuring solvency for two types of financial obligations of the organization - urgent (with a maturity of up to one month) and short-term(with a deadline of up to three months); Current responsibility with a maturity of up to one year are provided mainly by other types of current assets. Control over the aggregate level of the balance of monetary assets while ensuring the solvency of the organization should be based on the following criteria:

· urgent liabilities ≤ balance of monetary assets

· current liabilities ≤ cash balance + net realizable value of current receivables

Control over the level of efficiency of the formed portfolio of short-term financial investments - cash equivalents of the organization should be based on the following criteria:

· the level of profitability of the portfolio as a whole and its individual instruments ≥ the average market level of profitability of short-term investments with an appropriate level of risk

· rate of return of each investment instrument > inflation rate

1. Models of Baumol and Miller-Orr of managing the cash balance on the current account

Calculation of the optimal cash balance

Cash as a type of current assets is characterized by some features:

routine - cash is used to pay off current financial obligations, so there is always a time gap between incoming and outgoing cash flows. As a result, the company is forced to constantly accumulate free cash on a bank account;

precaution - the activity of the enterprise is not strictly regulated, therefore, cash is necessary to cover unforeseen payments. For these purposes, it is advisable to create an insurance cash reserve;

speculative - funds are needed for speculative reasons, since there is always a small probability that an unexpected opportunity for profitable investment will appear.

However, cash itself is a non-profitable asset, so the main goal of the cash management policy is to maintain it at the minimum required level, sufficient for the effective financial and economic activities of the organization, including:

timely payment of suppliers' invoices, allowing you to take advantage of the discounts they provide on the price of the goods;

maintaining a constant creditworthiness;

payment of unforeseen expenses arising in the course of business activities.

As noted above, if there is a large amount of money on the current account, the organization has the costs of missed opportunities (refusal to participate in any investment project). With a minimum supply of cash, there are costs to replenish this stock, the so-called maintenance costs (sales expenses due to the purchase and sale of securities, or interest and other costs associated with raising a loan to replenish the balance of funds). Therefore, when solving the problem of optimizing the balance of money on the current account, it is advisable to take into account two mutually exclusive circumstances: maintaining current solvency and obtaining additional profit from investing free cash.

There are several basic methods for calculating the optimal cash balance: mathematical models of Baumol-Tobin, Miller-Orr, Stone, etc.

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 that W. Baumol and J. Tobin came to independently in the mid-1950s. The model assumes that a commercial organization maintains an acceptable level of liquidity and optimizes its inventory.

According to the model, the enterprise begins to operate with the maximum acceptable (expedient) level of liquidity for it. Further, as the work progresses, the level of liquidity decreases (money is constantly spent over a certain period of time). The company invests all incoming cash in short-term liquid securities. As soon as the level of liquidity reaches a critical level, that is, it becomes equal to a certain predetermined level of security, the company sells part of the purchased short-term securities and thereby replenishes the cash reserve to its original value. Thus, the dynamics of the company's cash balance is a "sawtooth" graph (Fig. 1).

Rice. 1. Schedule of changes in the balance of funds on the current account (Baumol-Tobin model)

When using this model, a number of limitations are taken into account:

1) at a given period of time, the organization's need for funds is constant, it can be predicted;

2) the organization invests all incoming funds from the sale of products in short-term securities. As soon as the cash balance falls to an unacceptably low level, the organization sells part of the securities;

3) the receipts and payments of the organization are considered constant, and therefore planned, which makes it possible to calculate the net cash flow;

4) the level of costs associated with the conversion of securities and other financial instruments into cash, as well as losses from lost profits in the form of interest on the proposed investment of free funds, can be calculated.

According to the model under consideration, to determine the optimal cash balance, you can use the optimal order lot (EOQ) model:

F - fixed costs for the purchase and sale of securities or servicing the loan received;

T - the annual need for funds necessary to maintain current operations;

r - value of alternative income (interest rate of short-term market securities).

Miller-Orr model

The disadvantages of the Baumol-Tobin model noted above are eliminated by the Miller-Orr model, which is an improved EOQ model. Its authors M. Miller and D. Orr use a statistical method when building a model, namely the Bernoulli process - a stochastic process in which the receipt and expenditure of funds over time are independent random events.

When managing the level of liquidity, the financial manager must proceed from the following logic: the cash balance changes chaotically until it reaches the upper limit. As soon as this happens, it is necessary to buy enough liquid instruments in order to return the level of funds to some normal level (point of return). If the stock of funds reaches the lower limit, then in this case it is necessary to sell liquid short-term securities and thus replenish the stock of liquidity to the normal limit (Fig. 2).

The minimum value of the cash balance on the current account is taken at the level of the insurance stock, and the maximum - at the level of its triple size. However, when deciding on the range (the difference between the upper and lower limits of the cash balance), it is recommended to take into account the following: if the daily volatility of cash flows is large or the fixed costs associated with buying and selling securities are high, then the company should increase the range of variation and vice versa. It is also recommended to reduce the range of variation if there is an opportunity to generate income due to the high interest rate on securities.

When using this model, one should take into account the assumption that the costs of buying and selling securities are fixed and equal to each other.

Rice. 2. Graph of changes in the balance of funds on the current account (Miller-Orr model)

The following formula is used to determine the cusp point:

where Z is the target cash balance;

δ2 - dispersion of the daily cash flow balance;

r is the relative value of opportunity costs (per day);

L - the lower limit of the cash balance.

The upper limit of the cash balance is determined by the formula:

The average cash balance is found by the formula:

C \u003d (4Z - L) / 3

Miller-Orr model. The model developed by M. Miller and D. Orr is a compromise between simplicity and everyday reality. It helps answer the question of how a company should manage its cash supply if it is not possible to accurately predict cash inflows or outflows on a daily basis. Miller and Orr used the Bernoulli process to build the model, a stochastic process in which the receipt and expenditure of money from period to period are independent random events. Their basic premise is that the distribution of daily cash flow balances is approximately normal. The actual value of the balance on any day may correspond to the expected value, be higher or lower than it. Thus, the cash flow balance varies by day randomly; no trend is foreseen.

The logic of actions of the financial manager to manage the balance of funds on the current account is as follows. The account balance fluctuates randomly until it reaches the upper limit. As soon as this happens, the company begins to buy highly liquid securities in order to return the stock of cash to a certain level (point of return). If the cash reserve reaches the bottom limit, then the company sells the previously accumulated securities, replenishing the cash reserve to a normal level.

When deciding on the range of variation (the difference between the upper and lower limits), it is recommended to follow the rule: if the daily volatility of cash flows is large or the fixed costs associated with buying and selling securities are high, then the company should increase the range of variation, and vice versa. It is also recommended to reduce the range of variation if there is an opportunity to generate 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 cash (WITHmin) , which it is advisable to always have on the current account. It is determined by an expert, based on the average need of the company to pay bills, the possible requirements of the bank, creditors, etc.

Stage 2 . According to statistical data, the variation of the daily receipt of funds to the current account is determined (VAR).

Stage 3 . Determine the cost of keeping funds in the current account (Zs) (usually they are taken as a sum of daily income rates on short-term securities circulating in the market) and expenses for the mutual transformation of cash and securities (Z). It is assumed that the value Z constant; an analogue of this type of expenses, which takes place in domestic practice, are, for example, commissions paid at currency exchange offices.

Stage 4 . Calculate the range of variation of the cash balance on the current account (R) according to the formula:

Stage 5 . Calculate the upper limit of cash on the current account ( Withmax), above which it is necessary to convert part of the funds into short-term securities:

Cmax= Cmin+R.

Stage 6. Define a cusp (WITHr ) - the value of the balance of funds on the current account, to which it is necessary to return if the actual balance of funds on the current account goes beyond the interval:

Cr = (Cmin+ 1 / 3Cmax).

The following data necessary to optimize the company's cash balance was taken as initial data:

minimum cash reserve (WITHmin) - 10,000 thousand tenge;

costs of converting securities (Z)- 25 thousand tenge;

· interest rate: r= 11.6% per year;

· standard deviation per day - 2,000 thousand tenge.

Using the Miller-Orr model, it is necessary to determine the policy for managing funds on the company's current account.

Decision

1. Calculation Zs . :

Zs = r / 365 = 11.6 / 365 = 0.03% per day.

2. Calculation of daily cash flow variation (VAR) (thousand tenge):

VaR = (2000) 2 = 4 000 000.

3. Calculation of the range of variation (R) (thousand tenge):

4. Calculation of the upper limit of cash and the point of return (thousand tenge):

Withmax = 10 000 + 18 900 = 28 900.

Withr = 10 000 + 1 / 3 X 18 900 = 16 300.

Thus, the balance of funds on the company's current account should vary in the range of 10,000,000 - 28,900,000 tenge); when going beyond the interval, it is necessary to restore funds on the company's current account in the amount of 16,300,000 tenge.

As already noted, Western experts have developed other approaches to managing the target balance of funds, in particular, the Stone model, which is a development of the Miller-Orr model, has gained some popularity.

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 that W. Baumol and J. Tobin came to independently in the mid-1950s.

Using the Baumol-Tobin model, one can determine the optimal amount of a company's cash that it should keep under certainty. The Baumol-Tobin model relies heavily on the assumption that a possible alternative to holding money is the use of marketable securities and/or interest-bearing deposits.

According to the model, the company starts operating with the maximum acceptable (expedient) level of liquidity. Further, as the work progresses, the level of liquidity decreases (money is constantly spent over a certain period of time). The company invests all incoming cash in short-term liquid securities. As soon as the level of liquidity reaches a critical level, that is, it becomes equal to a certain predetermined level of security, the company sells part of the purchased short-term securities and thereby replenishes the cash reserve to its original value. Thus, the dynamics of the company's cash balance is like a "sawtooth" graph.

The Baumol-Tobin model is used when there is a high level of certainty that a company may need cash.

Suppose you want to determine how much cash the company should have. At the same time, the total costs should be minimized, which consist of conversion costs and costs that arise due to the fact that the company refuses part of the income from marketable securities, since it keeps funds in cash.

When building the model, it is assumed that for some time (for example, a month) the company has a stable need and demand for cash. At the same time, cash is received by selling marketable securities. When cash runs out, the company sells marketable securities to raise cash.

The total costs can be represented as:

Total costs =B x (T / C) + r x (C / 2),

where B X (T/C) are the total transaction costs for the period, while AT– total costs associated with the sale of securities (transaction costs); T/C- the number of transactions for the sale of marketable securities (equal to the ratio of the total demand for cash in the period ( T) to the cash balance ( With);

r X (S/2)- the amount of income that the company refuses, keeping its funds in cash, while r– interest rate on marketable securities; ( C / 2) is the average cash balance.

On the one hand, the more cash, the higher the income that the company refuses, simply by keeping its funds in cash or on current accounts. On the other hand, the higher the cash balance, the fewer transfers into marketable securities are needed and the lower the conversion costs.

In accordance with the Baumol-Tobin model, the company's costs for the sale of securities in the case of keeping part of the funds in highly liquid securities are compared with the lost profit that the company will have if it refuses to hold funds in securities, and therefore will not have interest and dividends on them. The model allows you to calculate the amount of money that would minimize both transaction costs and lost profits. The calculation is carried out according to the formula:

C = √2 x B x T / r.

The disadvantage of the Baumol-Tobin model is the assumption of predictability and stability of the cash flow. In addition, it does not take into account the cyclical and seasonal nature of most cash flows.

Let's determine the optimal cash balance according to the Baumol-Tobin model, if the planned volume of the company's cash turnover is 50 million tenge, the cost of servicing one cash replenishment operation is 400 tenge, the level of losses of alternative income when storing cash is 10%.

Using the formula, we calculate the upper limit of the company's cash balance (thousand tenge):

C=√2 X 0,4 X 50 000 / 0,1 = 632,46.

Thus, the average cash balance will be 316.23 thousand tenge (632.46 / 2).

Let's assume that the company's cash expenses during the year will be 1,500 million tenge. The interest rate on government securities is 8%, and the costs associated with each of their sale is 25,000 tenge.

Calculate the upper limit of the company's cash balance (million tenge):

C=√2 X 1 500 X 0,025 / 0,08 = 30,62.

The average amount of funds on the current account is 15.31 million tenge (30.62 / 2).

The total number of transactions for the transformation of securities into cash for the year will be (million tenge):

1 500 / 30,62 = 49.

Thus, the company's policy on managing cash and cash equivalents is as follows: as soon as the funds on the current account run out, the company sells part of its liquid securities in the amount of approximately 30 million tenge. This operation is performed approximately once a week. The maximum amount of funds on the current account will be 30.62 million tenge, the average - 15.31 million tenge.

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