MD Groceries currently sets its initial cash balance at $5,000, which is depleted every four days. The current market rate of return is 4.5% per year. The firm pays $2.50 each time it replenishes its cash account. Use a 360-day year.

What is the optimal initial cash balance for MD using the BAT model?

Question

What is the optimal initial cash balance for MD using the BAT model?

Quizplus · Accepted Answer

The optimal initial cash balance can be calculated using the Baumol Model (also known as the BAT model), which is given by the formula: $C^* = \sqrt{\frac{2bT}{i}}$, where $C^*$ is the optimal cash balance, $b$ is the transaction cost per replenishment, $T$ is the total cash needed for the period, and $i$ is the interest rate per period.Given:- Initial cash balance depletes every 4 days, implying the firm needs to replenish its cash every 4 days in a 360-day year. This means the firm replenishes 360/4 = 90 times a year.- If the initial balance is $5,000, the total cash needed for the period (T) is 90 * $5,000 = $450,000.- The transaction cost ($b$) is $2.50.- The annual interest rate ($i$) is 4.5%, or 0.045 when expressed as a decimal. For the Baumol model, we need the interest rate per period, which in this case is per year, so we use 0.045.Plugging these values into the Baumol formula gives:$$C^* = \sqrt{\frac{2 * 2.50 * 450,000}{0.045}} = \sqrt{\frac{2,250,000}{0.045}} = \sqrt{50,000,000} = 7,071$$Therefore, the optimal initial cash balance for MD Groceries, according to the BAT model, is $7,071.

MD Groceries Currently Sets Its Initial Cash Balance at $5,000