Baumol vs Miller-Orr Cash Management Models

## Baumol vs Miller-Orr — A Comparison

### Baumol's Model (EOQ for Cash)

#### Concept

The optimum cash level is that level where carrying costs and transaction costs are minimised.

#### Two Costs Trade Off

• Carrying cost: Interest forgone on marketable securities held as cash.
• Transaction cost: Cost of converting marketable securities to cash (clerical, brokerage, registration).

#### Optimum Cash Balance Formula

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

Where:

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

#### Assumption

Cash usage is steady and predictable (like inventory EOQ).

### Miller-Orr Model

#### Concept

A stochastic (random) cash flow model. Uses control limits (h, z, 0) — see separate Miller-Orr lesson.

#### Behaviour

• When cash hits h → invest (h − z) in securities.
• When cash hits 0 → liquidate z worth of securities.
• Between limits → no action.

### Side-by-Side Comparison