Your firm spends $150,000 a week to pay bills and maintains a lower cash balance limit of $45,000. The standard deviation of your disbursements is $10,000. The applicable interest rate is 6 % and the fixed cost of transferring funds is $35. What is your opportunity cost of holding cash based on the BAT model?

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The opportunity cost of holding cash based on the Baumol-Tobin (BAT) model is calculated using the formula: $$OC = \frac{1}{2} \times T \times C + \frac{F}{T} \times B$$ where $T$ is the optimal cash transfer size, $C$ is the annual cost of holding one unit of cash (opportunity cost), $F$ is the fixed cost per transfer, and $B$ is the average cash balance. The optimal cash transfer size $T$ is given by $\sqrt{\frac{2FB}{C}}$.Given:- Weekly disbursements = $150,000- Lower cash balance limit = $45,000- Standard deviation of disbursements = $10,000 (not directly needed for the BAT model calculation)- Annual interest rate = 6% or 0.06 (as the opportunity cost of holding cash)- Fixed cost of transferring funds = $35First, convert the weekly disbursements to an annual figure to match the annual interest rate: $150,000 * 52 = $7,800,000.The annual opportunity cost of holding one unit of cash (C) is the interest rate: 0.06.The optimal cash transfer size $T$ is calculated as: $$T = \sqrt{\frac{2 \times 35 \times 7,800,000}{0.06}}$$$$T = \sqrt{\frac{546,000}{0.06}} = \sqrt{9,100,000} \approx 3016.62$$The opportunity cost (OC) is then: $$OC = \frac{1}{2} \times 3016.62 \times 0.06 + \frac{35}{3016.62} \times 7,800,000$$$$OC = 90.50 + 2,771.50 \approx 2,862$$Therefore, the opportunity cost of holding cash based on the BAT model is approximately $2,862.

Your Firm Spends $150,000 a Week to Pay Bills and Maintains