Management of monetary assets. Baumol and Miller-Orr model. See pages where the term Baumol model is mentioned Cash flow planning

Cash is vital to the operation of any business and is an integral part of its working capital. At the same time, the following features are characteristic of cash:

• loss of purchasing power due to inflation;
• ability to generate income.

Due to the above features, there is an objective need to justify the optimal balance of funds, which will not be excessive and at the same time will be sufficient to maintain solvency. allows you to calculate its value, subject to certain provisions.

Initial provisions of the Baumol model

• cash flows are not subject to fluctuations, that is, it is initially assumed that cash is spent evenly;
• spending of funds is carried out to zero balance;
• there is some uncertainty in the flow of funds;
• the possibility of using a credit line or overdraft is not expected;
• the opportunity cost of maintaining a cash balance does not change;
• surplus funds are invested in liquid securities;
• when buying and selling liquid securities into cash, certain transaction costs arise.

Calculation of the optimal cash balance

The value of the optimal cash balance, according to the Baumol model, depends on two factors: the cost of one cash replenishment transaction and the opportunity cost of maintaining it. In this case, the total cost function can be represented as follows:

where C- cash balance;

F– transaction costs of replenishing the balance of funds;

T- annual need for cash;

k– the opportunity cost of maintaining the cash balance (the interest rate on liquid securities).

From the resulting equation, we can express the optimal cash balance ( English Optimal Cash Balance, OCB):

Graphically, these dependencies can be expressed as follows:

Example. The company's need for cash is 75,000 USD. per week, transaction costs for the purchase and sale of securities are 800 USD, and the interest rate on liquid securities is 9% per annum.

The company's annual cash requirement is $3,900,000. (75000*52). In this case, the optimal cash balance in accordance with the Baumol model will be 263,312.24 c.u.

Interpretation of the Baumol model

Provided that the initial provisions of the Baumol model are met, the resulting optimal cash balance is sufficient to maintain the solvency of the business. When the condition of uniform spending of funds is met, there is no need to maintain the insurance balance, so their minimum balance will be equal to 0.

Since the expenditure of funds to zero balance is carried out over a certain period of time, all receipts received should be invested in liquid securities. When the cash balance reaches zero balance, it is necessary to replenish it to the optimal one by converting liquid securities.

Cash balance optimization (Baumol model)

One of the main tasks of managing cash resources is to optimize their average balance. We are talking about the total balance in bank accounts and on hand). First of all, the question arises: why does cash remain free, and is not used in full, for example, for the purchase of securities that generate income in the form of interest. The answer is that cash has absolute liquidity compared to securities.

The financial manager is faced with the task of determining the size of the cash reserve, based on the fact that the price of liquidity does not exceed the marginal interest income on government securities.

Thus, the model policy for absolutely liquid assets in a market economy is as follows. The company must maintain a certain level of free cash, which is supplemented for insurance by a certain amount of funds invested in liquid securities, that is, in assets that are close to absolutely liquid. If necessary or with some frequency, securities are converted into cash; when excess amounts of cash are accumulated, they are either invested on a long-term basis or in short-term securities, or paid out in the form of dividends.

From the standpoint of the theory of investment, cash is one of the special cases of investing in inventory. Therefore, the general requirements apply to them:

A basic cash reserve is needed to perform current calculations;

Some funds are needed to cover unforeseen expenses.

It is advisable to have a certain amount of free cash to ensure a possible or predictable expansion of their activities.

The complexity of optimizing the level of the average cash balance of an organization is due to the dialectical contradictory unity of its goals, which consists in the need to simultaneously maintain high business activity and a stable financial position.

The essence of this contradiction is also manifested in the contradictory unity of requirements for the optimal level of cash balance in the short and long term.

In the short term, from a liquidity standpoint, it is necessary to maximize cash balances (to maintain solvency); from the standpoint of business activity - minimization (money must change its physical form into a commodity one, then it becomes capital and can make a profit). With this approach, it is clear that in the long run, liquidity and business activity are inseparable. Sufficient business activity is the reason for generating a financial result, which means an increase in the balance of funds, hence solvency. Only sufficient solvency makes it possible to finance a continuous production process in a timely manner and in the required amount.

In the theory of financial management, there are two methods for determining the optimal amount of cash: the Baumol model and the Miller-Or model. We will consider the Baumol model.

Under the Baumol model, it is assumed that the enterprise starts working with the maximum and expedient level of funds for it, and then constantly spends them over a certain period of time. The company invests all incoming funds from the sale of goods and services in short-term securities.

As soon as the cash reserve is depleted, that is, it becomes equal to zero or reaches a certain predetermined level of security, the company sells part of the securities and thereby replenishes the cash reserve to its original value.

According to the Baumol model:

1) the minimum balance of monetary assets is assumed to be zero:

2) the optimal (aka maximum) balance is calculated by the formula:

where V is the projected need for funds in the period (year, quarter, month);

c - expenses for converting cash into securities;

r - acceptable and possible interest income for the enterprise on short-term financial investments, for example, in government securities.

For the enterprise, the optimal balance of funds is the amount of 220857 rubles.

Thus, the average stock of cash is Q/2,

The total number of transactions for the conversion of securities into cash is equal to:

The total cost of implementing such a 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 checking account instead of investing them in securities.

ST \u003d 13785 * 104 + 13 * 110428.5 \u003d 1433640 + 1435570.5 \u003d 2869210.5 rubles

The costs of implementing this policy amounted to 2,869,210.5 rubles.

The disadvantage of the model is that it poorly describes the situation of return of funds from short-term financial investments.

There is no single way to determine the optimal cash balance. The compromise solution depends on the money management strategy. With an aggressive strategy, the priority is business activity, and with a conservative one, a sufficient value of indicators of financial condition characterizing liquidity, solvency and financial stability.

Baumol's model is simple and quite acceptable for enterprises whose cash costs are stable and predictable. In reality, this rarely happens - the balance on the current account changes randomly, and significant fluctuations are possible.

Introduction

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

2. Practical part

Conclusion

Bibliographic list

Introduction

In modern economic conditions, many enterprises are placed in conditions of independent choice of strategy and tactics of their development. Self-financing by the enterprise of its activities has become a priority.

In conditions of competition and an unstable external environment, it is necessary to quickly respond to deviations from the normal activities of the enterprise. Cash flow management is the tool with which you can achieve the desired result of the enterprise - making a profit.

The cash flow of a firm is a continuous process. For each direction of use of funds, there must be an appropriate source. Broadly speaking, a firm's assets represent the net use of cash, while liabilities and equity are net sources. There is no real starting and ending point for a running enterprise. The final product is the total cost of raw materials, fixed assets and labor, ultimately paid for in cash. The products are then sold either for cash or on credit. Selling on credit entails receivables, which are eventually collected and turned into cash. If the selling price of a product exceeds all expenses (including depreciation of assets) for a certain period, then a profit will be made for this period; there is no mudflow - a loss. The amount of cash fluctuates over time depending on the production schedule, sales volume, collection of receivables, capital expenditures and financing.

On the other hand, stocks of raw materials, work in progress, stock; finished goods, receivables and commercial credit payable fluctuate depending on the sales, production schedule and policy in relation to major debtors, inventory and commercial credit outstanding. The Cash Statement is the method by which we study the net change in cash between two points. These moments correspond to the start and end dates of the financial report, no matter what period the study refers to - quarter, year or five years. The Statement of Sources and Uses of Cash describes the net rather than the total changes in financial position at different dates. Total changes are all changes that occur between two reporting dates, and net changes are defined as the result of total changes.

The purpose of this work is to study the methodology of enterprise cash management.

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 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 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.

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 starts operating with the maximum and appropriate level of cash for it, and then 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 indicated expenses (income) is adjusted for the amount of net profit in such a way 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 changes 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 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 profit, but do not result in 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 interconnection between 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, specifications material (qualitative, quantitative) in accordance with...

[Kovalev, 1999]. The essence of these models is to give recommendations on the range of variation of the balance of funds, going beyond which involves either the conversion of funds into liquid securities, or the reverse procedure.

NB The average inventory value can be calculated using the Baumol model

The most popular theory of demand for money, which considers it from the point of view of optimizing money reserves, is based on the conclusions reached independently by William Baumol and James Tobin in the mid-1950s. Today this theory is commonly known as the Baumol-Tobin model. They pointed out that individuals maintain stocks of money in the same way that firms maintain stocks of goods. At any given moment, a household is holding a portion of its wealth in the form of money for future purchases.

At the same time, it is possible to obtain an algebraic expression for the demand for money in the Baumol-Tobin model. This equation is interesting because it allows you to represent the demand for money as a function of three key parameters of income, interest rate and fixed costs.

There are theories of the demand for money that emphasize such a function of money as a medium of exchange. These theories are called transactional demand theories for money. In them, money plays the role of a subordinate asset, accumulated only for the purpose of making purchases. Thus, the Baumol-Tobin model analyzes the benefits and costs of holding cash. The benefit is that there is no need to visit the bank for each purchase (transaction). The total costs are determined by the shortfall in interest on possible savings accounts (d), and the client's time to visit the bank based on his earnings (F). If Y is the amount of annual spending on purchases planned by the individual, then at the beginning of the year this amount will be equal to Y, at the end of the year - 0, and its average annual value - Y / 2. If an individual visits the bank not once a year, but N times, then the average annual value of the amount of cash in his hands will be Y / (2xN). The interest not received by him will be (rxU) / (2x.N), and the costs of visiting the bank will be equal to FxN. The greater the number of visits to the bank (N), the higher the costs associated with this, but the smaller the amount of lost interest.

Baumol model. According to W. Baumol, the balance of funds on the account is in many respects similar to the balance of inventory, therefore, the model of the optimal batch of the order can be used to optimize it. The optimal amount of funds in the account is determined using other variables C - the amount of cash in liquid securities or as a result of a loan C / 2 - the average balance of funds in the account C - the optimal amount of cash that can be received from the sale of liquid securities or loan C /2 - the optimal average balance on the account F - transaction costs for the purchase and sale of securities or servicing the loan received for one operation T - total

So, in accordance with the Baumol model, the balances of DA for the coming period are determined in the following amounts

The most widely used for this purpose is the Baumol Model, which was the first to transform the previously considered EOQ Model for cash balance planning. The starting points of the Baumol Model are the constancy of the cash flow, the storage of all reserves of monetary assets in the form of short-term financial investments and the change in the balance of monetary assets from their maximum to a minimum equal to zero (Fig. 5.17.)

Figure 5.17. formation and spending of the balance of funds in accordance with the Baumol Model.

Taking into account the losses of the two types considered, an optimization Baumol Model is constructed, which allows determining the optimal frequency of replenishment and the optimal size of the cash balance, at which the total losses will be minimal (Fig. 5.18.)

The mathematical algorithm for calculating the maximum and average optimal cash balances in accordance with the Baumol Model has the following form

An example is to be determined on the basis of the Baumol Model, the average and maximum amount of cash balances based on the following data, the planned annual volume of the company's cash turnover is 225 thousand conventional units. den. eg. the cost of servicing one operation of replenishment of funds is 100 conventional units. den. eg. the average annual interest rate on short-term financial investments is 20%.

In accordance with the Baumol model,

Baumol's model is simple and quite acceptable for enterprises whose cash costs are stable and predictable. In reality, this rarely happens, the balance of funds on the current account changes randomly, and significant fluctuations are possible.

What is the fundamental difference between the Baumol model and the Miller-Orr model?

The Baumol model is an algorithm that allows you to optimize the size of the average balance of the company's cash assets, taking into account the volume of its solvent turnover, the average interest rate on short-term financial investments and the average amount of costs on short-term investment operations.

Baumol model. Suppose that the organization has a certain amount of cash, which is constantly spent on paying supplier bills, etc. In order to pay bills on time, a commercial organization must have a certain level of liquidity. As a price for maintaining the required level of liquidity, the possible income from investing the average cash balance in government securities is taken. The basis for this decision is the assumption that government securities are risk-free (that is, their degree of risk can be neglected). Cash received from the sale of products (goods, works, services), a commercial organization invests in government securities. At the moment when the funds run out, there is a replenishment of the stock of funds to the initial value.

When a household takes the entire required amount with the help of one large-scale withdrawal M = P x Q, they are provided with their own needs, but interest is lost. In the Baumol-Tobin model, we can obtain an algebraic expression for the demand for money MD = M/2. The peculiarity of the equation is that it allows us to represent the demand for money (in terms of one visit to the bank) as a function consisting of three key parameters of fixed costs Pb, income Q, interest rate r

The Baumol model assumes that when an excess of money appears in the account in excess of the calculated amount of the optimal stock, it uses it to buy short-term securities in order to generate income, and when the stock of money decreases, it sells some of these securities, increasing the stock of money to the optimal level.

The Baumol model is suitable for stable predictable cash expenditures and receipts, it does not take into account seasonal or random fluctuations, i.e., it simplifies the real situation. Later, other models were developed that take into account the daily variability of cash flows (for example, the Miller-Orr model, 1966). However, all formalized models have certain limitations, therefore, in the practice of cash management, they are used as auxiliary to establish the optimal amount of cash.

Let us turn to the analysis of the properties of the transaction demand function for money obtained from the Baumol-Tobin model. First, as follows from formula (4), the demand for money depends negatively on the interest rate. This is because an increase in the interest rate leads to an increase in forgone interest payments and thus encourages the individual to go to the bank more often and hold less cash.

In addition to the two traditional factors discussed above that affect the demand for money, we can single out one more parameter that, according to the Baumol-Tobin model, affects

Thus, the velocity of circulation of money depends positively on