BOGO Shoes would like to maintain their cash account at a minimum level of $100,000, but expects the standard deviation in net daily cash flows to be $7,000; the effective annual rate on marketable securities to be 6.5 percent per year; and the trading cost per sale or purchase of marketable securities to be $175 per transaction. What will be their optimal cash return point?
A) $107,000
B) $133,374.63
C) $144,266.52
D) $101,859.65

Question

Quizplus · Accepted Answer

The optimal cash return point can be calculated using the Baumol model, which is designed to determine the optimal cash balance by minimizing the total cost associated with holding cash and transferring funds between cash and marketable securities. The formula for the optimal cash return point (or the optimal conversion amount) is given by:$$ C^* = \sqrt{\frac{2FB}{i}} $$Where:- $ C^* $ = Optimal cash conversion amount- $ F $ = Fixed cost of transferring funds (trading cost per sale or purchase)- $ B $ = Annual cash requirements (in this case, we use the standard deviation in net daily cash flows as a proxy for variability in cash needs, although the actual annual cash requirements might be calculated differently in a comprehensive analysis)- $ i $ = Interest rate per period (effective annual rate)Given:- $ F = $175 $- $ B = $7,000 $ (although this is a daily figure, it's used directly in the formula for illustrative purposes; in practice, an annual figure would be needed)- $ i = 6.5\% = 0.065 $ (as a decimal)Plugging these values into the Baumol model formula:$$ C^* = \sqrt{\frac{2 \times 175 \times 7000}{0.065}} $$$$ C^* = \sqrt{\frac{2450}{0.065}} $$$$ C^* = \sqrt{37692.30769} $$$$ C^* = 194.147 $$This calculation does not directly match any of the provided options, suggesting a misunderstanding in the application of the formula or the interpretation of the question's data. The correct approach involves calculating the optimal cash balance that minimizes costs, but the specific values and interpretation provided here seem to have led to a miscalculation. The correct answer, based on the standard formula and typical interpretation of such a scenario, would involve calculating the square root of the product of twice the fixed transaction cost, the total cash requirement, and the reciprocal of the interest rate. However, without recalculating with the correct annual cash requirements or adjusting for the daily standard deviation properly, the precise answer from the provided options cannot be accurately determined based on the calculation shown. The correct approach should involve using the Baumol model formula accurately with the appropriate annual figures for cash requirements and adjusting the interpretation of the standard deviation in net daily cash flows as it relates to annual cash needs.

BOGO Shoes Would Like to Maintain Their Cash Account at a Minimum