## Determining the Optimum Cash Balance
The Core Trade-off:
- Too little cash → Risk of default on obligations
- Too much cash → Opportunity cost (loss of interest/profit)
- Goal: Find the optimum cash level based on predictability of cash flows
### Classification of Cash Management Models
| Model Type | When to Use | Example |
|---|---|---|
| Inventory-type models | Predictable, steady cash flows | Baumol's EOQ Model |
| Stochastic models | Random, unpredictable cash flows | Miller-Orr Model |
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### Baumol's Economic Order Quantity (EOQ) Model
Applies the EOQ logic (from inventory management) to determine the optimal cash balance.
Assumptions: Cash usage is predictable and steady.
Formula:
$$C = \sqrt{\frac{2PU}{S}}$$
| Variable | Meaning |
|---|---|
| C | Optimal cash balance to be maintained |
| P | Cost per cash conversion (transaction cost) |
| U | Annual cash usage |
| S | Opportunity cost of holding cash (interest rate) |
Logic: Minimize total cost = Transaction cost + Opportunity cost
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### Miller-Orr Cash Management Model (1966)
Designed for random, unpredictable cash flows. Avoids daily monitoring.
Three Control Limits:
| Limit | Level | Action Triggered |
|---|---|---|
| Upper Limit (h) | High threshold | Cash exceeds h → Invest the excess |
| Lower Limit | 0 (or minimum) | Cash drops to 0 → Withdraw from investments |
| Return Point (z) | Target level | Cash is brought back to z after any transfer |
Advantage: Works well in fluctuating conditions; does not require daily decision-making.