Solutions to Assignments
BCOE - 143 Fundamentals of Financial Management
Question No. 5
Explain Baumol’s Model and Miller and Orr’s Model of cash management.
1. Baumol’s EOQ Model of Cash Management:
William J. Baumol (1952) suggested that cash may be managed in the same way as any other inventory and that the inventory model could reasonably reflect the cost – volume relationships as well as the cash flows. In this way, the economic order quantity (EOQ) model of inventory management could be applied to cash management. It provides a useful conceptual foundation for the cash management problem.
In the model, the carrying cost of holding cash-namely the interest forgone on marketable securities is balanced against the fixed cost of transferring marketable securities to cash, or vice- versa. The Baumol model finds a correct balance by combining holding cost and transaction costs, so as to minimize the total cost of holding cash.
The optimum level of cash balance is found to be:
Where,
C = Optimum level of cash balance
A = Annual cash payments estimated
T = Cost per transaction of purchase or sale of marketable securities
I = Interest on marketable securities p.a. (i.e., carrying cost per rupee of cash)
According to the model, optimum cash level is that level of cash where the carrying costs and transaction costs are the minimum. The carrying costs refers to the cost of holding cash i.e. interest forgone on marketable securities. The transaction cost refers to the cost involved in getting the marketable securities converted into cash and vice versa.
Assumptions:
The Baumol’s model holds good if the following assumptions are fulfilled:
(a) The rate of cash usage is constant and known with certainty. The model has limited use in times of uncertainty and firms whose cash flows are discontinuous or bumpy.
(b) The surplus cash is invested into marketable securities and those securities are again disposed of to convert them again into cash. Such purchase and sale transactions involve certain costs like clerical, brokerage, registration and other costs. The cost to be incurred for each such transaction is assumed to be constant/fixed. In practice, it would be difficult to calculate the exact transaction cost.
(c) By holding cash balance, the firm is would incur the opportunity cost of interest forgone by not investing in marketable securities. Such holding cost per annum is assumed to be constant.
(d) The short-term marketable securities can be freely bought and sold. Existence of free market for marketable securities is a prerequisite of the Baumol model.
2. Miller-Orr Cash Management Model:
Miller and Orr model (1966) assumes that the cashflow of the firm is assumed to be stochastic, i.e. different amounts of cash payments are made on different points of time. It is assumed that the movements in cash balance occur randomly. Miller and Orr suggested a model with control limits, which sets control points for time and size of transfers between an Investment Account and Cash Account.
The model asserts that transfer money into or out of the account to return the balance to a predetermined ‘normal point whenever the actual balance went outside a lower or upper limit.
The lower limit would be set by management, and the upper limit and return points by way of formulae which assume that cash inflows and outflows are random, their dispersion usually being assumed to repeat a pattern exhibited in the past.
The model specifies the following two control limits:
h = Upper control limit, beyond the cash balance should not be carried.
0 = Lower control limit, sets the lower limit of cash balance, i.e. the firm should maintain cash resources atleast to the extent of lower limit.
z = Return point for cash balance
The Miller-Orr model, will work as follows:
(i) When cash balance touched the upper control limit (h), securities are bought to the extent of Rs. (h-z).
(ii) Then the new cash balance is z.
(iii) When cash balance touches lower control limit (o), marketable securities to the extent of Rs. (z-o) will be sold.
(iv) Then the new cash balance again return to point z.
Assumptions:
The basic assumptions of the model are:
(a) The major assumption with this model is that there is no underlying trend in cash balance over time.
(b) The optimal values of ‘h’ and ‘z’ depend not only on opportunity costs, but also on the degree of likely fluctuations in cash balances.
The model can be used in times of uncertainty and random cash flows. It is based on the principle that control limits can be set which when reached trigger off a transaction. The control limits are based on the day-to-day variability in cash flows and the fixed costs of buying and selling government securities.
