BullsNBears, a purveyor of financial databases, estimates it they disburses $440,000 monthly in order to pay bills. The firm's opportunity rate is 5%. The fixed cost of transferring money is $25 per transfer. Based on historical data, the standard deviation of monthly cash flows is $15,000 and the lower cash balance limit is $20,000. For Miller-Orr model questions, assume the interest rate is 0.5% per month. Using the BAT model, what is the optimal average cash balance?

A) $34,495
B) $36,332
C) $37,195
D) $45,619
E) $53,227

The optimal average cash balance using the Baumol Model (BAT model) can be calculated using the formula: $C^{\ast }=\sqrt{\frac{2bT}{i}}$ , where $C^{\ast }$ is the optimal cash balance, $b$ is the fixed cost per transaction, $T$ is the total cash requirement for the period, and $i$ is the opportunity cost of holding cash. Plugging in the given values: $C^{\ast }=\sqrt{\frac{2\times 25\times 440,000}{0.05}}=\sqrt{\frac{22,000}{0.05}}=\sqrt{440,000}\approx 663.32$ . However, since none of the provided options match this calculation, it appears there may have been a misunderstanding in the application of the formula or the interpretation of the question's data. The correct approach for the BAT model involves the total disbursement and the cost per transfer, but the given answer suggests a different calculation might have been intended or a different model's formula was mistakenly applied. The correct formula for the BAT model indeed involves the square root of the product of 2, the transaction cost, the total disbursement, divided by the interest rate, but the calculation provided does not align with the options given, indicating a possible error in the calculation or a misunderstanding of the question's requirements.