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

Optimal Cash Level =(3*Fixed Cost of a security transaction*daily cash variance/4*daily interest rate on marketable securities)^1/3 + Minimum Cash Balance

Daily Interest rate = 2.6/365 = 0.007

Now putting the details in the above formula

Optimum Cash Level =(3*390*3900/4*0.007)^(1/3) + 44000

= 546.22 + 44000

= 44546.22

Optimal Upper Cash Limit = (3*Cash)-2*Minimum Cash Balance

= (3*44546.22)-2*44000

= 45638.65

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