Cash Management Models: Baumol vs Miller-Orr

# Cash Management Models: Baumol vs Miller-Orr

Firms must decide how much cash to hold and when to move money between cash and marketable securities. Two classical models address this.

## William J. Baumol's Model (Deterministic / EOQ-style)

Based on the Economic Order Quantity logic. The optimum cash level is the point at which two costs balance out:

• Carrying cost — interest income foregone by holding cash instead of marketable securities.
• Transaction cost — clerical, brokerage, and registration costs incurred each time securities are converted to cash to plug a shortfall.

The optimum cash balance occurs where carrying cost equals transaction cost.

### Formula

$$C = \sqrt{\dfrac{2 \times U \times P}{S}}$$

Where:

• C = Optimum cash balance (per transaction conversion)
• U = Annual (or monthly) cash disbursements
• P = Fixed cost per transaction (per conversion of securities to cash)
• S = Opportunity cost of holding one rupee of cash p.a. (or p.m.)

The model assumes a constant, predictable rate of cash usage.

## Miller-Orr Model (Stochastic)

Designed for situations where net cash flows are random / unpredictable. It decides the timing and size of transfers between an investment account and the cash account.

Three control limits are set on the cash balance:

• h = Upper limit
• z = Return point (target level)
• 0 = Lower limit

### How it operates

### Inputs that determine h and z

• Fixed cost per securities transaction
• Opportunity cost of holding cash
• Degree of likely fluctuation (variance) in cash balances

The limits are chosen so that demands for cash are met at the lowest possible total cost.

## Quick Comparison