## Cash Management Models
Cash management models help decide how much cash to hold to:
- Avoid excessive idle cash, and
- Prevent cash shortages
| Model Type | Used When | Example |
|---|---|---|
| Inventory-type | Cash flows are predictable/certain | Baumol's EOQ Model |
| Stochastic | Cash flows are random/uncertain | Miller-Orr Model |
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## Baumol's EOQ Model
Applies the Economic Order Quantity (EOQ) logic from inventory management to cash.
Key Assumption: Cash is used at a steady, predictable rate.
Two costs being balanced:
- Transaction cost (cost of converting securities to cash each time)
- Opportunity cost (interest forgone by holding idle cash)
Formula:
$$C = \sqrt{\frac{2 \times P \times U}{S}}$$
| Symbol | Meaning |
|---|---|
| C | Optimal cash balance (amount to convert each time) |
| P | Cost per cash conversion (fixed transaction cost) |
| U | Annual cash usage/requirement |
| S | Opportunity cost = interest rate on marketable securities |
Logic: Just like EOQ finds the order quantity that minimizes total inventory cost, Baumol's model finds the cash balance that minimizes total cash management cost.
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## Miller-Orr Model (1966)
Designed for random, unpredictable cash flows — more realistic for most businesses.
Three Control Limits:
| Level | Definition | Action Triggered |
|---|---|---|
| Upper limit (h) | Maximum cash balance | If cash reaches h → invest excess, bring back to z |
| Return point (z) | Target/normal cash balance | Cash is always restored here after any transfer |
| Lower limit (0) | Minimum cash balance | If cash falls to 0 → liquidate investments, bring back to z |
How it works:
- Cash balance fluctuates randomly between 0 and h
- No action is taken as long as cash stays within the band
- Action (invest or liquidate) is only triggered at the limits
Advantages:
- Avoids the need for daily monitoring
- Works well in volatile, unpredictable environments
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### Model Comparison
| Feature | Baumol | Miller-Orr |
|---|---|---|
| Cash flow pattern | Certain, steady | Random, unpredictable |
| Based on | EOQ concept | Control limits |
| Monitoring needed | Periodic conversion | Only at limit breach |
| Complexity | Simpler | More realistic |