Question

# B is a small privately-owned chain of hairstyling salons particularly targeted at celebrities preparing for special...

B is a small privately-owned chain of hairstyling salons particularly targeted at celebrities preparing for special occasions. The owner has determined that operating circumstances require the use of the Miller-Orr cash management model to manage the cash balances of the enterprise. The standard deviation of daily cash balances has been shown to be \$5,000, and the owner believes this figure also reflects future balance variability. The enterprise earns an average daily return of 0.3% on its marketable securities and incurs an average brokerage fee of \$160 each time it engages in a securities transaction. The owner has determined that it cannot permit the enterprise’s cash balance to fall below \$20,000.

Answer the following questions by filling in the blanks. Give your answers rounded to the nearest whole number in each case.

(a) What is the company’s “z” value?

(b) What is the company’s “return-to-point”?

(c) What is the company’s optimum maximum cash balance?

Please give a step-by-step answer and clearly explain the problem solving process.

Solution:

First of all we list all the given information

Standard deviation of daily cash balance = \$ 5000

Average daily return on marketable securities = .3 %

Average brokerage fee = \$ 160

Minimum cash balance = \$ 20000

Now in Miller orr model Return point = 33b2 / 4i + Lower limit

where b = transaction cost or brokerage fee = 160

= 5000 and 2 = 25000000

i = .3% or .003

Lower limit = 20000

Z= 3 * 33b2 / 4i = 3 * 10000 = 30000

Return point = 20000 + 1/3 Z = 30000

Upper limit = 3 * return point - ( 2 * 20000)

= 90000 - 40000 = 50000

Company optimum cash balance = (4 * z - lower limit ) /3

= (120000 -20000) /3

= \$ 33333 .33 or \$ 33333

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