# Question: HotFoot Shoes would like to maintain its cash account

## Description

Question:

HotFoot Shoes would like to maintain its cash account at a minimum level of \$28,000 but expects the standard deviation in net daily cash flows to be \$2,300, the effective annual rate on marketable securities to be 3.8 percent per year, and the trading cost per sale or purchase of marketable securities to be \$230 per transaction.

What will be its optimal upper cash limit?

Daily rate of interest on marketable securities =[(1 + 0.038)1/365] – 1

= [ (1.038)1/365 – 1 ]

= [ 1.0001022 – 1

= 0.0001022

Optimal cash return point = [(3 * 230 * 2300 * 2300) / (4 * 0.0001022) ]0.33333 + 28000

= [ 3650100000 / 0.0004088 ]0.33333 + 28000

= (8.928816e+12)0.33333 + 28000

= 20743.79 + 28000

= \$ 48743.79 (approx)

Optimal upper cash limit = (3 * 48743.79) – (2 * 28000)

= 146231.37 – 56000

= \$ 90231.37

Conclusion:- Optimal upper cash limit = \$ 90231.37 (approx).

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