Explain Baumol’s model of cash management.

**Baumol’s Model of Cash Management**

Baumol’s model of cash management, developed by economist William Baumol in 1952, is a technique used by companies to determine the optimal cash balance to hold for transactions. The model is based on the trade-off between the costs of holding cash (opportunity cost) and the costs of converting securities into cash (transaction cost).

**Assumptions of Baumol’s Model:**

1. The company has a known and constant cash outflow rate for transactions.
2. The company can invest excess cash in interest-bearing securities.
3. The company incurs a fixed cost for each transaction to convert securities into cash.

**Formula for Baumol’s Model:**

The optimal cash balance (C*) can be calculated using the formula:

\[ C^* = \sqrt{ \frac{2 \times T \times F}{i} } \]

Where:
– \( C^* \) = Optimal cash balance
– \( T \) = Total cash needed over the period
– \( F \) = Fixed cost per transaction
– \( i \) = Interest rate on marketable securities

**Explanation of the Model:**

– The model assumes that cash is used to pay for transactions, and any excess cash can be invested in interest-bearing securities.
– The company needs to balance the costs of holding too much cash (missed opportunity to earn interest) and too little cash (frequent transactions to convert securities into cash).
– By calculating the optimal cash balance using the formula, the company can minimize the total cost of holding cash and converting securities into cash.

**Example:**
Let’s consider a company that needs $1,000,000 in cash over a year for its transactions. The fixed cost per transaction is $50, and the interest rate on marketable securities is 5%.

\[ C^* = \sqrt{ \frac{2 \times \$1,000,000 \times \$50}{0.05} } \]
\[ C^* = \sqrt{ \$100,000 } \]
\[ C^* = \$10,000 \]

In this example, the company should maintain an optimal cash balance of $10,000 to minimize its total cash management costs.

**Conclusion:**
Baumol’s model of cash management provides a useful framework for companies to determine the optimal cash balance for transactions. By balancing the costs of holding cash and converting securities into cash, companies can improve their cash management efficiency and reduce overall costs.