HotFoot Shoes would like to maintain its cash account at a minimum level of $42,

Question

HotFoot Shoes would like to maintain its cash account at a minimum level of $42,000 but expects the standard deviation in net daily cash flows to be $3,700, the effective annual rate on marketable securities to be 2.8 percent per year, and the trading cost per sale or purchase of marketable securities to be $370 per transaction.

What will be its optimal upper cash limit? (Use 365 days a year. Do not round intermediate calculations and round your answer to 2 decimal places.)

PLEASE SHOW WORK,

THANKS

HotFoot Shoes would like to maintain its cash account at a minimum level of $42,000 but expects the standard deviation in net daily cash flows to be $3,700, the effective annual rate on marketable securities to be 2.8 percent per year, and the trading cost per sale or purchase of marketable securities to be $370 per transaction.

Explanation / Answer

Daily Interest Rate on Marketable Securities = 1.028^(1/365) - 1 = 0.000211 Optimal Cash Return Point (Z*) = [(3*F*S^2) / (4*i)] ^ (1/3) + L where, F = trading cost per sale or purchase of marketable securities S = standard deviation in net daily cash flows i = Daily Interest rate L = Minimum Cash Level Z* = [(3 * 370 * 3700^2) / (4 * 0.000211)] ^ (1/3) + 42000 or, Z* = 26214.86 + 42000 or, Z* = 68214.84 Upper Cash Limit (H*) = 3 x Z* - 2 x L = 3 * 68214.84 - 2 * 42000 = $120,644.58

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