#### Cash Management Model # 1. **William J. Baumol’s Model:**

William J. Baumol developed a model (The Transactions Demand for Cash: An Inventory Theoretic Approach) which is usually used in inventory management but has its application in determining the optimal cash balance also. Baumol found similarities between inventory management and cash management.

As Economic Order Quantity (EOQ) in inventory management involves tradeoff between carrying costs and ordering cost, the optimal cash balance is the tradeoff between opportunity cost or cost of borrowing or holding cash and the transaction cost (i.e. the cost of converting marketable securities into cash etc.) The optimal cash balance is reached at a point where the total cost is the minimum. The figure below shows the optimum cash balance.

**Illustration 1:**

The annual cash requirement of A Ltd. is Rs 10 lakhs. The company has marketable securities in lot sizes of Rs 50,000, Rs 1, 00,000, Rs 2, 00,000, Rs 2, 50,000 and Rs 5, 00,000. Cost of conversion of marketable securities per lot is Rs 1,000. The company can earn 5% annual yield on its securities. You are required to prepare a table indicating which lot size will have to be sold by the company. Also show that the economic lot size can be obtained by the Baumol Model.

#### Cash Management Model # 2. Miller and Orr Model:

Baumol’s model is based on the basic assumption that the size and timing of cash flows are known with certainty. This usually does not happen in practice. The cash flows of a firm are neither uniform nor certain. The Miller and Orr model overcomes the shortcomings of Baumol model.

M.H. Miller and Daniel Orr (A Model of the Demand for Money) expanded on the Baumol model and developed Stochastic Model for firms with uncertain cash inflows and cash outflows.

**The Miller and Orr (MO) model provides two control limits-the upper control limit and the lower control limit along-with a return point as shown in the figure below:**

When the cash balance touches the upper control limit (h), markable securities are purchased to the extent of hz to return back to the normal cash balance of z. In the same manner when the cash balance touches lower control limit (o), the firm will sell the marketable securities to the extent of oz to again return to the normal cash balance.

**The spread between the upper and lower cash balance limits (called z) can be computed using Miller-Orr model as below:**

**Variance of Cash Flows = (Standard deviation) ^{2} or (s)^{2}:**

**Illustration 2:**

A company has a policy of maintaining a minimum cash balance of Rs 1, 00,000. The standard deviation in daily cash balances is Rs 10,000. The interest rate on a daily basis is 0.01%. The transaction cost for each sale or purchase of securities is Rs 50. Compute the upper control limit and the return point as per the Miller-Orr model.

**Illustration 3:**

A firm having an annual opportunity cost of 15 per cent is contemplating installation of a lock box system at an annual cost of Rs 3, 00,000. The system is expected to reduce mailing time by 4 days and reduce cheque clearing time by 3 days. If the firm collects Rs 4, 00,000 per day, would you recommend the system?

Thus, it is recommended that the proposed lock box system should be installed.

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