Cash Management

CASH MANAGEMENT- MODELS While it is true that financial managers need not necessarily follow cash management models exactly but a familiarity with them provides and insight into the normative framework as to how cash management has to be conducted. There are three analytical models which helps in effective cash management. • Baumol model • Miller-orr model • Orgler’s model Baumol model: The purpose of this model is to determine minimum cost amount of cash that a financial manager can obtain by converting securities to cash, considering the cost of conversion and the counter-balancing cost of keeping idle cash balances which otherwise have been invested in the marketable securities. The total cost associated with cash management, according to this model, has two elements: 1. Cost of converting marketable securities into cash 2. The lost opportunity The conversion cost is incurred each time marketable securities are converted into cash. Symbolically, TOTAL CONVERSION COST PER PERIOD = Tb/C Where : b = cost of conversion which is assumed to be independent of Of size of transaction T = Total transaction cash needs for the period

C = Value of marketable securities sold at each conversion. The opportunity cost is derived from the lost/forfeited interest rate (i) that could have been earned on the investment of the cash balances. The total opportunity cost is the interest rate times the average cash balance kept by the firm. The model assumes a constant and certain pattern of cash outflows. At the beginning of each period, the firm starts with a cash balance which it gradually spends until at the end of the period it has a zero cash balance and must replenish its each supply to the level of cash

balance in the beginning. Symbolically, the

average lost opportunity cost.

i(C/2) Where i = interest rate that could have been earned c/2 = the average cash balance , that is the beginning cash (C) plus the ending cash balance of the period (0) divided by 2 The total cost associated with the cash management comprising total conversion cost plus opportunity cost of not investing cash until needed in interest- bearing instruments can be symbolically expressed as: I(C/2)+(Tb/C) To minimise the cost, the model attempts to determine the optimal conversion amount , that is, cash withdrawal that

costs the least. The reason is that the firm should not keep the total beginning cash balance during the entire period as it is not needed at the beginning of the period. For ex: if the period were one thirty day month, only one-thirtieth of the opening cash balance each day will be required. This means only required one-thirtieth money is withdrawn and the rest of the money will be invested in the marketable securities. Miller-Orr Model: The objective of cash management, according to miller-orr (MO) is to determine the optimum cash balance level which minimises the cost of cash management. Symbolically C = bE (N) /t + iE (M) b = the fixed cost per conversion E(M) = the expected no. of conversions t = the no. of days in the period i = the lost opportunity cost C = total cash management cost The MO model is to make the baumol model more realistic as regards the flow of cash. As against the assumption of uniform and certain levels of cash balances in the baumol model, the MO model assumes that cash balances randomly fluctuate between an upper bound, the firm has too much cash balances back to the optimal bound

(z). when the cash balance hit zero, the financial manager must return them to the optimum bound (z) by selling/converting securities into cash. According to the MO model, as in Baumol model, the optimal cash balance (z) can be expressed symbolically as

z=

3br 2

4i

r2 = the variance of the daily changes in cash balances Thus, in the baumols model there are economies of scale is cash management and the two basic cost of conversion and lost interest that have to be minimised. Orgler’s Model: According to this model, an option cash management strategy can be determined through the use of multiple linear programming model. The construction of the model comprises three section: (1) selection of the appropriate planning horizon, (2) selection of the appropriate decision variables and (3) formulation of the cash management strategy itself. The advantage of linear programming model is that it enables coordination of the optimal cash management strategy with the other opertions of the firm such as production and with less restrictions on working capital balances. The model basically uses one year planning horizons with twelve monthly periods because of its simplicity. It has four basic sets of decisions variables which influence cash management of a firm and which must be incorporated into the linear programming model of the firm. These are;

1. payment schedule 2. short-term financing 3. purchase and sale of marketable securities 4. cash balance itself The formulation of the model requires that the financial managers first specify an objective function and then specify a set of constraints. Orgler’s objective function is to ‘ minimise the horizon value of the net revenues from the cash budget over the entire planning period’. Using the assumption that all revenues generated are immediately re-invested and that any cost is immediately financed , the objective function represents the value of the net income from the cash budget at the horizon “ by adding the net returns ove the planning period”. Thus, the objective function recognises each operations of the firm that generates cash inflows or cash outflows as adding or subtracting profit opportunities from the firm from its cash management operations. An example for the linear programming model is as follows. Objective function: Maximise profit = a1 x1 + a 2 x2 The important feature of the model is that it allows the financial managers to integrate cash management with production and other aspects of the firm.