| Net cash requirement | 8100000 |
| Fixed transaction cost | 30 |
| Return on marketable securities | 8% |
| Baumol's Model |
| Baumol's model is similar to the Economic Order Quantity for inventory. It assumes that cash and invetory are similar. |
| A transaction cost and opportunity cost are inevitable in holding a certain amount of cash. |
| Transaction cost is the cost of converting the securities to cash. |
| Holding cost is the opportunity cost incurred by not investing the cash in marketable securities. |
| a. Optimal transaction size for converting marketable securities to cash | |||
| Optimal transaction size | = | Squareroot ( 2 A B / I) | |
| where, | |||
| A - Annual cash requirement | |||
| B - Transaction cost of converting securities to cash | |||
| I - Opportunity cost of converting the securities | |||
| Optimal transaction size | = | Squareroot ( 2 X 8100000 X 30 / 0.08) | |
| = | $ 77,942.29 | (max. cash per transaction) | |
| b. Average cash balance | |||
| Average Cash balance | = | Optimal transaction size / 2 | |
| = | 77942.29 / 2 | ||
| = | $ 38,971.15 | ||
| c. Cost of maintaing the optimal average cash balance | |||
| Cost of optimal average cash balance | = | B X (A / C) + I (C / 2) | |
| where, | |||
| B - Transaction cost of converting securities to cash | |||
| A - Annual cash requirement | |||
| C - Optimal transaction size (as arrived above) | |||
| I - Opportunity cost of converting the securities | |||
| Cost of optimal average cash balance | = | 30 X (8100000 / 77942.29) + (0.08) X (77942.29 / 2) | |
| = | $ 6,235.38 | ||