Cash flow optimization models. Models for calculating cash reserves without borrowed funds The Baumol model is used to determine

The process of managing an 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 of cash flow statement analysis is the calculation and interpretation of financial efficiency ratios cash flows(see table). This system 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 by calculating liquid cash flow (LCF) for express diagnostic purposes financial condition organizations:

LCF = (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 beginning of the analyzed period;

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

CASH 1, CASH 0 - funds held at the cash desk, in settlement and foreign currency accounts in banks at the end and beginning of the analyzed period.

Liquid cash flow is a measure of an organization's excess or deficit cash balance. 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 cash received from its own activities. He is internal indicator 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 determine the sources of funds and evaluate their use, as well as identify 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 sources of funds and the validity of expenses, the synchronicity of their occurrence, and determine the possible need for borrowed funds. A cash flow plan can be drawn up directly or indirectly.

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 interconnected. It completely covers the organization’s cash flow; makes it possible to link cash receipts and payments in cash and non-cash forms; allows you to ensure constant solvency and liquidity.

The payment calendar is being compiled financial service enterprises, while the cash flow budget targets are broken down by month 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 connection of cash receipts and upcoming expenses of the organization;

· formation information base about 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 available funds of the organization;

· analysis 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 about the organization’s cash flows, which includes: agreements with counterparties; acts of reconciliation of settlements with counterparties; invoices for payment of products; invoices; bank documents confirming the receipt of funds into accounts; money orders; product shipment schedules; payment schedules wages; status of settlements with debtors and creditors; legislatively deadlines payments for financial obligations to the budget and off-budget funds; internal orders.

To effectively draw up a payment calendar, a financial manager needs to monitor information about cash balances in bank accounts, funds spent, average balances per day, 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 presented in the specialized literature on financial management.

Balancing and synchronization of cash flows

The result of developing a cash flow plan can be either a deficit or 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 over time and optimizing the cash balance on the current account.

Both deficit and excess cash flow have a negative impact on the activity of the enterprise. The negative consequences of a deficit cash flow are manifested in a decrease in liquidity and the level of solvency of the enterprise, an increase in overdue accounts payable suppliers of raw materials and materials, increasing the share of overdue debts on received financial loans, delays in the payment of wages, an increase in the duration of the financial cycle, and ultimately a decrease in the profitability of using the company’s own capital and assets.

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 portion monetary assets in the field of short-term investment, which ultimately also negatively affects the level of return on assets and equity capital of the enterprise.

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

1) attracting additional own or long-term borrowed capital;

2) improving work with current assets;

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

4) reduction of the enterprise’s investment program;

5) cost reduction.

The volume of excess cash flow must 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 - alignment and synchronization. Alignment of cash flows is aimed at smoothing their volumes across individual intervals of the time period under consideration. This optimization method makes it possible to eliminate, to a certain extent, seasonal and cyclical differences in the formation of cash flows (both positive and negative), while simultaneously optimizing average cash balances and increasing the level of liquidity. The results of this method of optimizing cash flows over time are assessed using the standard deviation or coefficient of variation, which should decrease during the optimization process.

Cash flow synchronization is based on convariance positive and negative types. The synchronization process should ensure an increase in the level of correlation between these two types of cash flows. The results of this method of optimizing cash flows over time are assessed using the correlation coefficient, which should tend to the value “+1” during the optimization process.

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

Payment turnover is accelerated through the following measures:

1) increasing the amount of discounts to debtors;

2) reducing the term of trade credit provided to buyers;

3) tightening of 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, bill accounting, forfaiting;

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

Payment turnover can be slowed down by:

1) increasing the term of trade credit provided by suppliers;

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

3) transferring short-term loans to long-term ones;

4) reduction of cash payments to suppliers.

Calculation of the optimal cash balance

Cash as a type of current assets is characterized by certain characteristics:

· routine - cash used to pay off current financial obligations, therefore, there is always a time gap between incoming and outgoing cash flows. As a result, the enterprise is forced to constantly accumulate available funds in a bank account;

· precaution - the activities of the enterprise are not strictly regulated, so cash is necessary to cover unexpected payments. For these purposes, it is advisable to create a safety stock cash;

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

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

· timely payment of supplier bills, allowing you to take advantage of the discounts they provide on the price of goods;

· maintaining constant creditworthiness;

· payment of unforeseen expenses that arise during the process commercial activities.

As noted above, if there is a large money supply the organization faces opportunity costs (refusal to participate in any investment project). With a minimum reserve of funds, costs arise to replenish this reserve, the so-called maintenance costs (business expenses caused by the purchase and sale of securities, or interest and other expenses associated with borrowing to replenish the cash balance). Therefore, when solving the problem of optimizing the balance of money in a current account, it is advisable to take into account two mutually exclusive circumstances: maintaining current solvency and obtaining additional profit from investing free funds.

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 for managing liquidity (the balance of funds in a current account) is the Baumol-Tobin model, built on the conclusions reached by W. Baumol and J. Tobin independently of each other in the mid-50s. The model assumes that 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 work progresses, the level of liquidity decreases (cash is constantly spent over a certain period of time). The company invests all incoming funds in short-term liquid securities. As soon as the level of liquidity reaches a critical level, that is, it becomes equal to a certain specified level of security, the enterprise sells part of the purchased short-term valuable papers 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. Graph of changes in the balance of funds in 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 organization’s receipts and payments are considered constant, and therefore planned, which makes it possible to calculate net cash flow;

4) the level of costs associated with converting securities and other financial instruments into cash is calculable, as well as losses from lost profits in the form of interest on the proposed investment of available funds.

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

where C is the optimal amount of funds;

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

T - annual requirement for funds necessary to maintain current operations;

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

Example 1

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

Using 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 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 mitigated by the Miller-Orr model, which is an improved EOQ model. Its authors, M. Miller and D. Orr, use a statistical method when constructing the 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. Once this happens, it is necessary to purchase a sufficient number of liquid instruments in order to return the cash level to some normal level (the reversion point). If the cash reserve reaches the lower limit, then in this case it is necessary to sell liquid short-term securities and thus replenish the liquidity reserve to the normal limit (Fig. 2).

The minimum value of the cash balance on the current account is taken at the level of the safety stock, and the maximum - at the level of three times its size. However, when deciding on the range (the difference between the upper and lower limits of the cash balance), it is recommended to consider the following: if the daily variability of cash flows is large or fixed costs associated with the purchase and sale of securities are high, then the enterprise 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.

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

To determine the cusp point, the following formula is used:

where Z is the target cash balance;

δ 2 - dispersion of the daily cash flow balance;

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

L - lower limit of cash balance.

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

H = 3Z – 2L. (3)

The average cash balance is determined by the formula:

C = (4Z – L) / 3, (4)

Example 2

Let's calculate the optimal cash balance 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 cash - 0.0083%. The minimum cash balance is 2500 thousand rubles.

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

We determine the upper limit of the cash balance using formula (3):

N = 3 × 2558.17 – 2 × 2500 = 2674.5 thousand rubles.

We determine the average cash balance using formula (4):

The main disadvantage of the model is that the upper limit of the liquidity level corridor is set depending on the lower limit, but there is no clear methodology for establishing the lower limit. The manager who controls the liquidity level has to rely on common sense and experience in determining the lower limit, hence the subjectivity of the model’s assessments.

Stone's model

Stone's model complements the Miller-Orr model and is based on cash flow forecasts for the near future. Reaching the upper limit on the amount of funds in the current account will not cause their immediate transfer into securities if the organization is forecast to have relatively high payments in the coming days. This allows you to minimize the number of conversion operations and, therefore, reduce the associated 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 process of its production and economic activities, and increasing the degree of its financial and production flexibility.

E. G. Moiseeva,
Ph.D. econ. Sciences, Arzamas Polytechnic Institute

To ensure effective cash flow management in foreign practice, the Baumol model and the Miller-Orr model are most widely used.

The first was developed by W. Baumöl in 1952, the second by M. Miller and D. Orr in 1966. The direct application of these models in domestic practice is still difficult due to insufficient development of the securities market, therefore we will give only a brief theoretical description of these models.

Baumol's model

It is assumed that the enterprise begins to operate with the maximum and appropriate level of cash for it and then constantly spends it 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, i.e. becomes equal to zero or reaches a certain specified level of security, the company sells part of the securities and thereby replenishes the stock of funds to the original value. Thus, the dynamics of the balance of funds in the current account is a “sawtooth” graph.

Rice. 6.3.

Thus, in accordance with the Baumol model, cash balances for the coming period are determined in the following amounts:

a) the minimum cash balance is assumed to be zero;
b) the optimal (aka maximum) balance is calculated using the formula

where DAmax is the maximum cash balance in the planning period; Rk – average amount expenses for servicing one operation with short-term financial investments; Oda – total cash expenditure in the coming period; SPKfv – interest rate on short-term financial investments in the period under review;

c) the average cash balance in accordance with this model is planned as half of its maximum balance (DAmax: 2).

Miller–Orr model is a more complex option for calculating the optimal size of cash balances. The model is based on a certain unevenness in the receipt and expenditure of funds, and, accordingly, their balance, and also provides for the presence of an insurance reserve.

The minimum limit for the formation of the cash balance is taken at the level of the insurance balance, and the maximum limit is three times the amount of the insurance balance.

Logic of action financial manager for managing the balance of funds on a current account is shown in Fig. 6.4 and is as follows - the account balance changes chaotically until it reaches the upper limit. Once this happens, the company begins to purchase a sufficient amount of securities in order to return the cash reserve to some normal level (the point of return). If the cash reserve reaches the lower limit, then the company sells its securities and thus replenishes the cash reserve to the normal limit.

Rice. 6.4.

When deciding on the range of variation (the difference between the upper and lower limits), it is recommended to adhere to next policy: If the daily variability of cash flows is high or the fixed costs associated with buying and selling securities are high, then the company should increase the magnitude of the 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.

In accordance with the Miller-Orr model, cash balances for the upcoming period are determined in the following amounts in several stages.

1. The minimum amount of funds (He) is established, which it is advisable to constantly have in the current account.
2. Based on statistical data, the variation in the daily receipt of funds to the current account is determined ( V).
3. Expenses (Px) for storing funds in a current account and expenses (Pt) for the mutual transformation of cash and securities are determined.
4. The range of variation in the balance of funds on the current account is calculated ( S) according to the formula:

5. Determine the upper limit of funds in the current account (), if exceeded, it is necessary to convert part of the funds into short-term securities:

6. Find the point of return (TV) - the amount 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 boundaries of the interval ():

On first At this stage, ten-day terms for spending funds are regulated (in connection with their receipts), which allows minimizing the balance of monetary assets within each month (quarter).

On second stage, the size of the average balance of monetary assets is optimized taking into account the envisaged reserve stock of these assets. In this case, the maximum balance of monetary assets is first determined, taking into account the unevenness of payments and the reserve stock, and then their average balance (half the sum of the minimum and maximum balances of monetary assets).

The amount of monetary assets released 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 monetary assets determines the need to search for reserves for such acceleration in the enterprise. The main of these reserves include:

a) acceleration of cash collection, which reduces the balance of monetary assets in the cash register;
b) reduction of cash payments (cash cash settlements increase the balance of funds in the cash register and reduce the period of use of own funds for the period of processing supplier payment documents);
c) reducing the volume of settlements with suppliers using letters of credit and checks, since they divert monetary assets from circulation for a long period due to the need to pre-reserve them for special accounts in banks.

Security effective use The temporarily free balance of funds can be realized through the following activities:

a) agreeing with the bank on the conditions for the current storage of the balance of funds with the payment of deposit interest;
b) the use of high-yield short-term stock instruments to place a reserve of monetary assets, but subject to their sufficient liquidity in the stock market.

Minimization of losses of used funds from inflation is carried out separately for funds in national and foreign currencies.

Anti-inflation protection of monetary assets is provided if the rate of return on the temporarily free balance used is not lower than the inflation rate.

One of the most famous money management models is the Baumol model. It was developed in 1952 by William Baumol (W.J. Baumol) based on the inventory management model EOQ (Economic Order Quantity). Basic assumptions of the Baumol model:

1. The enterprise’s sustainable need for funds;

2. Everything cash receipts the company immediately invests in highly liquid securities;

3. The cost of converting investments into cash does not depend on the amount being converted (fixed for one transaction);

4. The company begins operations with maximum reasonable cash balances.

Baumol's model is applicable in cases where an enterprise can predict its cash needs with a sufficient degree of certainty. In this case, as already noted, it is assumed that the enterprise begins to operate with the maximum appropriate level of funds Q+m. Then the enterprise evenly (due to sustainable needs) spends these funds over a certain period of time (see Fig. 8.5).

Rice. 8.5. Changes in enterprise cash balances according to the Baumol model

As soon as cash balances fall to the minimum allowable safety stock m, the company sells part of its short-term investments and restores its cash reserve to its initial level.

In this case, it is assumed (see assumption 2) that the funds received by the enterprise as a result of the sale of products, goods, and services are transferred as received into short-term investments.

Let us introduce the following notation:

V- the projected total need for funds for the period (usually a year);

c- costs of converting short-term investments into cash ( transaction costs);

r- average annual return on short-term investments.

The number of conversions of securities into cash during the period will be .

Total enterprise costs TC related to cash management for the period will be:

where the first term represents transaction costs and the second term represents opportunity costs.

To determine the amount of replenishment of cash balances Q opt., with which TC minimally differentiate the function TC(Q) By Q:

Equating expression (8.2) to zero, we find the value Q, corresponding to the minimum of the function TS:

A graphical illustration of cost minimization using the Baumol model is presented in Figure 8.6.

Rice. 8.6. Minimizing costs according to the Baumol model.

Graphs in Fig. 8.6 built at following conditions: V= 2000 thousand rubles, c= 0.1 thousand rub., r= 5%, m= 50 thousand rub.

Calculation using formula (8.8.3) showed that Q opt≈ 89.44 thousand rubles. The same result can be obtained graphically with an acceptable degree of accuracy.

Miller-Orr model

In 1966, Merton Miller and Daniel Orr (M.H.Miller, D.Orr) developed a money management model that is much closer to reality than Baumol's model. It helps answer the question: how should a company manage its cash reserves if it is impossible to predict the daily outflow or inflow of cash? 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.

The basic premise of the Miller-Orr model is that the distribution of daily cash flow balances is approximately normal. The actual balance on any day may correspond to the expected value, be higher or lower. Thus, the cash flow balance varies randomly from day to day; no tendency for its change is envisaged.

The model is implemented in several stages [ Kovalev]:

1. The minimum amount of funds is established ( L), which it is advisable to constantly have in the current account (determined by experts based on the average need of the enterprise to pay bills, possible demands of the bank, creditors, etc.).

2. Based on statistical data, the variation in the daily receipt of funds to the current account (σ 2) is determined.

3. Opportunity costs are determined r- expenses for storing funds in a current account (usually they are taken into account in the amount of the bet daily income for short-term securities traded on the market) and expenses c on the mutual transformation of cash and securities (this value is assumed to be constant per transaction).

4. Calculate the range of variation in the balance of funds on the current account R according to the formula

5. Calculate the upper limit of funds in the current account H, above which it is necessary to convert part of the funds into short-term securities:

H=L+R (8.5)

6. Determine the return point ( Z) - the amount of funds balance on the current account, to which it is necessary to return if the actual balance of funds on the current account goes beyond the boundaries of the interval ( L, H):

An example of a graph depicting the dynamics of funds using the Miller-Orr model is presented in Fig. 8.7.

Rice. 8.6. Dynamics of enterprise cash balances using the Miller-Orr model [ Kovalev, s. 547].

At a moment in time t 1 there is a purchase of securities in the amount of ( H – Z), and at the moment t 2 securities are sold with net proceeds ( Z – L).

When using the Miller-Orr model, you should pay attention to the following points[ Brigham, Gapenski, p.312-313].

1. The target account balance is not the average between the upper and lower limits, since its value more often approaches its lower limit than its upper limit. Setting the target balance equal to the average between the limits will minimize transaction costs, but if it is set below the average, the result will be a reduction in opportunity costs. Based on this, Miller and Orr recommend setting the target balance in the amount if L= 0; this minimizes overall costs.

2. The size of the target cash balance and, therefore, the limits of fluctuation, increase with growth c and σ 2 ; increase c makes it more expensive to reach the upper limit, and a larger σ 2 leads to both being reached more often.

3. The target balance decreases as it increases r; because if the rate bank interest increases, then the value of opportunity costs increases and the firm seeks to invest funds rather than keep them in an account.

4. The floor does not have to be zero, but can be positive if the firm has to maintain a compensating balance or management prefers to maintain a safety stock of cash.

5. Experience in using the described model has shown its advantages over purely intuitive money management; however, if the company has several alternative options for investing temporarily free funds, and not the only one in the form of purchasing, for example, government securities, then the model ceases to work.

6. The model can be supplemented with the assumption of seasonal fluctuations in revenue. In this case, cash flows will not follow a normal distribution, but will take into account the likelihood of an increase or decrease in the balance of funds, depending on whether the company is experiencing a period of decline or recovery. Under these assumptions, the target cash balance will not always be between the upper and lower limits.

Stone's model

Stone's model, unlike the Miller-Orr model, places more emphasis on managing the target residue rather than defining it; at the same time, they are similar in many ways [ Brigham, Gapenski, p. 313-314]. The upper and lower limits of the account balance are subject to change depending on information about cash flows expected in the next few days. The concept of Stone's model is presented in Fig. 8.7. Just like in the Miller-Orr model, Z represents the target account balance that the firm strives for, and H And L- the upper and lower limits of its fluctuations, respectively. In addition to those indicated, Stone’s model has external and internal control limits: N And L- external, and ( H – X) And ( L + x) - internal. Unlike the Miller-Orr model, where immediate action is taken when control limits are reached, this does not always happen in the Stone model.

Rice. 8.7. Dynamics of cash balances using the Stone model [ Brigham, Gapenski, p. 313].

Let's assume that the account balance has reached the outer upper limit (point A in Fig. 8.7.) at the moment of time t. Instead of automatic translation quantities ( H– Z) from cash into securities, the financial manager makes a forecast for the next few days (in our case, five). If the expected balance at the time ( t+ 5 ) will remain above the internal limit ( H– x), for example its size is determined at the point IN, then the sum ( H– Z) will be converted into securities. Further dynamics of the cash balance in this case will correspond to the thick line starting at the time t.If the forecast shows that at the moment ( t+ 5 ) the cash balance will correspond to the point WITH, then the firm will not buy securities. Similar reasoning is true for the lower limit.

Thus, the main feature of Stone's model is that the company's current actions are determined by its forecast for the near future. Therefore, reaching the cap will not trigger an immediate transfer of cash into securities if relatively high cash outflows are expected in the coming days; thereby minimizing the number of conversion operations and, consequently, reducing costs.

Unlike the Miller-Orr model, the Stone model does not specify methods for determining target cash balances and control limits, but they can be determined using the Miller-Orr model, and x and the period for which the forecast is made - with the help of practical experience.

Significant advantage This model is that its parameters are not fixed values. This model can take into account seasonal fluctuations, since the manager, making a forecast, evaluates the characteristics of production in individual periods.

The disadvantage of Stone's model is the emergence of subjectivity. If the manager makes a mistake with the forecast, the company will incur storage costs. excess amount funds (in the case of an upper limit) or will lose liquidity for a short period of time (in the case of a lower limit). However, correct short-term forecasting of the size of the cash balance can reduce transaction costs.

Simulation modeling

Simulation modeling is the most accurate of the models considered, but at the same time the most labor-intensive. The modeling technique is described by Brihgem and Gapenski ([ Brigham, Gapenski, p. 314-316].

Modeling begins with drawing up a preliminary cash flow budget. After this, an assumption about the probabilistic nature of the indicators is introduced into the forecasting methodology.

It is expected to calculate the volume of monthly sales ( S) random variable with normal distribution. Let us denote the coefficient of variation of the volume of monthly sales as CV, and its standard deviation is as s S. We will also assume that over time the relative variability of sales volume is constant.

Then the standard deviation of sales volume for i The th month will be equal to:

Where S i- volume of sales i month.

The receipt of revenue from sales is associated with the actual, and not with the expected volume of sales, that is, the payment receipt scheme is based on information about actual sales that took place in the past.

The essence of the Monte Carlo method is based on studying the operation of a model of a system when it receives random input data that has specified characteristics (type of distribution, dispersion, etc.) and restrictions. In our case, it is necessary to model (at a given level of significance) the value of the enterprise's possible cash shortage by month and plan the corresponding values as the target balance. The key indicator here is the significance level set by the manager - the probability with which the results obtained (target remainder) are statistically significant. The recommended level is around 90%.

Brigham and Gapensky emphasize that it is possible to introduce the assumption that monthly sales volumes are dependent on each other; that is, for example, if the actual implementations in i-month will be below their expected level, this should serve as a signal of a decrease in sales revenue in the following months. In this case, the uncertainty of cash flows will increase and, therefore, to ensure the desired level of security, it is necessary to set the target cash balance at a relatively higher level [ Brigham, Gapenski, p. 316].

The main advantage of simulation modeling is the relatively high accuracy of the results obtained.

However, it should be noted that the use of this method for financial forecasting in practice is almost impossible without the use of a computer. In addition, to obtain reliable results, it is advisable to have information on the company's cash flows for at least two previous years to obtain a representative sample of the initial data.

Accounts receivable management.

Accounts receivable, or accounts receivable, are one of the most important and significant specific gravity elements of the enterprise's current assets. Modern trading practices increasingly rely on the buyer obtaining deferred payments for delivered products, which results in the creation of significant accounts receivable for the seller (supplier).

The level of receivables of an enterprise is determined by:

· Type of products sold

· Degree of market saturation with this type of product

· Payment system adopted at a particular enterprise

General economic factors

Accounts receivable management is a classic example of a trade-off between risk and return: the optimal level of accounts receivable is determined based on the trade-off between increased sales volume and, as a result, profits as a result of lower credit requirements for customers, and the parallel increasing costs of financing the increasing level of accounts receivable and an increase in probable losses on bad debts. At the same time, the basic laws of financial management are clearly followed: the expected profitability changes in inverse proportion to the liquidity of the asset (in this case, accounts receivable) and in the same direction as the risk. At the same time, attempts popular in the domestic literature to classify debts for shipped products as the object of accounts receivable management, which in their urgency significantly exceed the industry average for the period of circulation of receivables, or even a period of 12 months, are obviously untenable: such a “ accounts receivable"can no longer be considered as component current assets.

An important element of accounts receivable management is the ranking of accounts receivable according to the timing of their occurrence (compiling a so-called “aging register” of accounts receivable), as well as monitoring its turnover (turnover of funds in settlements). The latter is carried out on the basis of a number of turnover indicators, which are discussed in the corresponding section of the course.

A very popular tool for monitoring receivables is to compare the average repayment period with the average repayment period of debt on supplier accounts (accounts payable). Despite all the conventions of such a comparison (due, in particular, to the different nature of obligations and in some cases different volumes), it can show whether the enterprise is a net creditor financing investments in working capital its customers, or, conversely, a net borrower using the funds of its counterparties. It should be noted here, however, that the popular arguments among many domestic theorists about the management of receivables based on an analysis of the operating and financial cycles of an enterprise2, in practice, face significant limitations. The operating cycle of an enterprise is, as is known, equal, on the one hand, to the sum of the duration of the production process3 and the average repayment period (circulation period) of receivables, and on the other hand, to the sum of the duration of the financial cycle and the average repayment period (circulation period) of debt on supplier accounts (accounts payable ). If we approach the problem of managing receivables “mechanically”, then the task of minimizing the duration of the financial cycle4 (namely, for this period the enterprise’s funds are diverted from circulation and the enterprise has to use financing through own funds or attract a loan) can be solved in two ways5. On the one hand, it is possible to tighten the conditions for the sale of products on credit, which should reduce the period of circulation of receivables, but at the same time reduce the volume of sales (profit). On the other hand, you can “delay” the payment of supplier bills. Within certain limits, this may “work”, but if this technique is abused, the supplier will be objectively forced to reconsider the terms of delivery or simply include the cost of financing its increased receivables in the delivery price. The result is increased costs and decreased profits. The art of management here consists precisely in avoiding, if possible, both dangers.

From a practical point of view, the most important tool for managing receivables of an enterprise is its credit policy, represented by two interrelated activities: providing deferred payments and debt collection.

The credit policy of an enterprise involves making decisions on five main issues [ Levy, Sarnat]:

1. Determination of the period for which payment is expected to be deferred;

2. Determination of lending instruments, i.e. legal form processing a commercial loan;

3. Formation credit standards- a set of criteria and procedures for determining “good” and “bad” in terms of providing a deferment on customer payments;

4. Collection policy - certain procedures for monitoring receivables and procedures for action in cases of delays in payments must be established;

5. Incentives that can be offered to customers to speed up payment of bills (usually discounts).

In conditions developed countries the seller will rely on knowledge credit history client, for study financial statements client, etc. In domestic conditions, the main sources of information about the creditworthiness of clients are

· Own experience companies

· Information from confidential sources - for example, a bank where a potential client is served.

· Information from supplier companies that have already worked with this client.

For large contracts it is possible to carry out special investigations security service.

Analysis current situation in Russia shows that spontaneously, based on the interaction of market factors, domestic enterprises develop their own credit policy, already quite comparable with that which has developed in countries with developed market economy. The result is the establishment of a certain balance between sales on prepayment terms, with payment upon delivery and with deferred payment - a balance, the violation of which in one direction leads to a drop in sales volume, in the other direction to an unjustified increase in the risk of non-receipt of payment.

Inventory Management

Enterprise inventory management is the responsibility of the production manager rather than the financial manager. However, due to certain traditions, as well as the fact that many small and medium-sized firms simply do not have inventory management specialists, this function is often assigned to the financial manager. In addition, even in the presence of an advanced inventory management service at the enterprise, the financial manager is left with an extremely important and non-trivial side of the problem - assessing the cost of investments in inventory. It is the accounting of the cost of investments in inventories that fundamentally distinguishes modern models of their management from traditional rationing procedures.

From the point of view of financial management, the management of investments in inventories has certain specifics compared to the management, for example, of investments in fixed assets. These features, in particular, are expressed in the following [ Levy, Sarnat]:

· In practice, as a rule, it is impossible to unambiguously assess the profitability of investments in inventories; as a result, the main goal of inventory management is to minimize the costs of maintaining them;

·Decisions related to inventory management are repetitive; these decisions determine how often And how much stocks must be renewed.

The decision regarding the optimal inventory level must be based on a trade-off between the costs of carrying unreasonably high level inventories and the risk of downtime and delays in production and sales of products due to their depletion.

Without intending to provide a review existing methods and inventory management models (this is the subject of a separate course), we will focus on the classification of costs associated with inventories and formalize the most well-known management model.

The first group includes costs that increase with increasing inventory volume:

· Cost of financing investment in reserves;

· Cost of storage;

· Processing costs (moving, delivery to places of sale, etc.);

· Inventory insurance;

· Property tax;

· Obsolescence and loss of value.

Costs that decrease with increasing inventory volume (per unit of inventory) can be summarized into three subgroups:

· Costs of placing an order (fixed per order);

· Loss of discounts provided depending on the volume of purchases;

· Costs of possible depletion of reserves.

The most well-known inventory management model that implements the compromise formulated above is famous model EOQ(Wilson formula), according to which the optimal order size Q* is

Q* = 2SC 2 (8.8)

In formula (8.8) through S indicates the annual demand for reserves (in units), through C 1– variable costs per unit of inventory, through C 2– fixed costs per order.

Literature

1. Brigham Y., Gapenski L. Financial management: Full course. In 2 volumes. T.2 /Trans. from English edited by V.V. Kovaleva. - St. Petersburg: Economic school, 1997.

2. Van Horn J. Fundamentals of financial management: Trans. from English / Ed. I.I. Eliseeva. - M.: Finance and Statistics, 2000.

3. Kovalev V.V. Introduction to financial management. - M.: Finance and Statistics, 2004.

4. Financial management: theory and practice: Textbook / Ed. E.S. Stoyanova. - 5th ed., revised. and additional - M.: Publishing house "Perspective", 2000.

5. Cheng F. Li, Joseph I. Finnerty. Corporate finance: theory, methods and practice. Per. from English - M.: INFRA-M, 2000.

6. Shim Jay K., Siegel Joel G. Financial management / Translation from English. - M.: Information and Publishing House "Filin", 1996.

7. Levy H., Sarnat M. Principles of Financial Management. – Prentice Hall, Englewood Cliffs, 1988.

Introduction

1. Baumol and Miller-Orr control models cash balance on the current account

2. Practical part

Conclusion

Bibliography

Introduction

IN modern conditions In business management, many enterprises are placed in conditions of independent choice of strategy and tactics for their development. The enterprise's self-financing of its activities has become a top 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 desired result activities of the enterprise - making a profit.

A firm's cash flow is a continuous process. For each direction of use of funds there must be a corresponding source. Broadly speaking, a firm's assets represent its net use of cash, while its liabilities and equity– clean sources. For a running enterprise, there really is no starting point and ending point. 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. Credit sales generate accounts receivable, which are eventually collected and converted into cash. If selling price products exceed 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. Cash levels fluctuate over time depending on production schedules, sales volumes, accounts receivable collections, capital expenditures, and financing.

On the other hand, raw materials inventories, work in progress, inventories; finished products, accounts receivable and trade credit payable fluctuate depending on sales, production schedule and policies regarding major debtors, inventories and outstanding balances. commercial loan. The cash flow statement is a method by which we examine the net change in funds between two points in time. These moments correspond to the start and end dates financial report, no matter what period the study relates to - a quarter, a year or a five-year period. The statement of sources and uses of funds describes net rather than total changes in financial situation for different dates. Total changes are all changes that occur between two reporting dates, and net changes are defined as the result general changes.

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

1. Baumol and Miller-Orr models for managing the cash balance on a current account

Calculation of the optimal cash balance

Cash as a type of current assets is characterized by certain characteristics:

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 enterprise is forced to constantly accumulate available funds in a bank account;

precaution - the activities of the enterprise are not strictly regulated, so cash is needed to cover unexpected 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 unexpectedly arise.

However, cash itself is a non-profitable asset, therefore 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 supplier bills, allowing you to take advantage of the discounts they provide on the price of goods;

maintaining constant creditworthiness;

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

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

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 for managing liquidity (the balance of funds in a current account) is the Baumol-Tobin model, built on the conclusions reached by W. Baumol and J. Tobin independently of each other in the mid-50s. 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 work progresses, the level of liquidity decreases (cash is constantly spent over a certain period of time). The company invests all incoming funds in short-term liquid securities. As soon as the level of liquidity reaches a critical level, that is, it becomes equal to a certain specified level of security, the enterprise 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. Graph of changes in the balance of funds in 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;

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

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

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

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

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

Miller-Orr model

The minimum value of the cash balance on the current account is taken at the level of the safety stock, and the maximum - at the level of three times its size. However, when deciding on the issue of the range (the difference between the upper and lower limits of the cash balance), it is recommended to consider the following: if the daily variability of cash flows is large or the fixed costs associated with the purchase and sale of securities are high, then the enterprise 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.

William Baumol (W.J. Baumol) was the first to propose and publish in 1952 in his monograph “The Transaction Demand for Cash: An Inventory Theoretical Approach” the hypothesis that the cash balance in the account is in many ways similar to the balance of inventory, so the model is optimal The order quantity (EOQ) can also be used to determine the target cash balance.

It is assumed that the enterprise begins to operate with the maximum and appropriate level of funds for it, and then gradually 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 specified level of safety, the company sells part of the securities and thereby replenishes the cash reserve to its original value. Thus, the dynamics of the balance of funds on the current account is a “sawtooth” graph (Fig. 13).

Fig. 13 - Graph of changes in the balance of funds on the current account

(Baumol model)

The replenishment amount (Q) is calculated using the formula:

, (10.8)

Where - forecasted need for funds in the period (year, quarter, month);

- expenses for converting cash into securities;

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

Thus, the average cash holding is , and the total number of transactions for converting securities into cash (K) is equal to:

, (10.9)

The total costs (OR) of implementing such a cash management policy will be:

, (10.10)

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

10.3.2 Miller–Orr model

Merton Miller (Miller M.H.) and Daniel Opp (Orr D.A.) created and first published in 1966 in the book “Model of the Demand for Money by Firms” a model for determining the target cash balance that takes into account the uncertainty factor cash payments and revenues.

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

The model developed by Miller and Orr represents a compromise between simplicity and reality. It helps answer the question: How should a business manage its cash reserves if it is impossible to predict the daily inflow or outflow of cash? Miller and Orr use 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.

The logic of the financial manager’s actions to manage the balance of funds in the current account is presented in the figure and is as follows. The account balance changes chaotically until it reaches the upper limit. As soon as this happens, the company begins to buy a sufficient amount of securities in order to return the cash reserve to some normal level (the point of return). If the cash reserve reaches the lower limit, then the company sells its securities and thus replenishes the cash reserve to the normal limit.

The concept of the Miller-Orr model is shown in Fig. 14.

Rice. 14 - Schedule of changes in the balance of funds on the current account

(Miller-Orr model)

When deciding on the range of variation (the difference between the upper and lower limits), it is recommended to adhere to the following policy: if the daily variability of cash flows is large or the fixed costs associated with buying and selling securities are high, then the enterprise should increase the range of variation and vice versa. It is also recommended to reduce the scope of variation if there is an opportunity to generate income due to high interest rate on securities.

The model is implemented in several stages.

, (10.11)

, (10.12)

, (10.13)

When using the Miller-Orr model, you should pay attention to the following points: