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 =

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 =

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.