Question

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.

Answer #1

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 = ^{3}3b^{2}
/ 4i + Lower limit

where b = transaction cost or brokerage fee = 160

= 5000 and
^{2} = 25000000

i = .3% or .003

Lower limit = 20000

**Z= 3 * ^{3}3b^{2}
/ 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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