Donaldson Inc. spends $87,000 a week to pay bills and maintains a lower cash balance limit of $40,000. The standard deviation of the disbursements is $12,900. The applicable weekly interest rate is .042 percent and the fixed cost of transferring funds is $57. What is your optimal average cash balance based on the Miller-Orr model?

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Quizplus · Accepted Answer

The Miller-Orr model calculates the optimal cash balance by using the formula: $Z = L + \sqrt[3]{\frac{3 \times F \times \sigma^2}{4 \times i}}$, where $Z$ is the optimal cash balance, $L$ is the lower limit of cash balance, $F$ is the fixed cost of transferring funds, $\sigma^2$ is the variance of cash flows, and $i$ is the interest rate.Given:- $L = $40,000$- $F = $57$- $\sigma = $12,900$ (standard deviation, so $\sigma^2 = $12,900^2$)- $i = 0.042\% = 0.00042$ (weekly interest rate)Plugging these values into the Miller-Orr formula:$$Z = 40000 + \sqrt[3]{\frac{3 \times 57 \times (12900)^2}{4 \times 0.00042}}$$$$Z = 40000 + \sqrt[3]{\frac{3 \times 57 \times 166410000}{0.00168}}$$$$Z = 40000 + \sqrt[3]{\frac{28484100}{0.00168}}$$$$Z = 40000 + \sqrt[3]{16978630952.38}$$$$Z = 40000 + 2571.97$$$$Z \approx 74242$$Therefore, the optimal average cash balance based on the Miller-Orr model is approximately $74,242.