HotFoot Shoes would like to maintain its cash account at a minimum level of $44,

Question

HotFoot Shoes would like to maintain its cash account at a minimum level of $44,000 but expects the standard deviation in net daily cash flows to be $3,900, the effective annual rate on marketable securities to be 2.6 percent per year, and the trading cost per sale or purchase of marketable securities to be $390 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.)

HotFoot Shoes would like to maintain its cash account at a minimum level of $44,000 but expects the standard deviation in net daily cash flows to be $3,900, the effective annual rate on marketable securities to be 2.6 percent per year, and the trading cost per sale or purchase of marketable securities to be $390 per transaction.

Explanation / Answer

Daily interest rate = (1+2.6%)1/365 - 1

= 0.00703%

Optimal cash return point = [3 * $390 * ($3,900)2 / (4 * 0.00703%)]1/3 + $44,000

= $83,845.72

Optimal upper cash limit = 3 * $83,845.72 - 2 * $44,000

= $163,537.15

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