Question

1. Downing Consulting, Inc. is an independent political consulting agency that specializes in providing advice to members of parliament in the U.K. The business owner has determined that its operating circumstances are quite suitable for use of the Baumol-Tobin cash management model. The business consistently earns an annual rate of return of 4.0% on its marketable securities and requires a total of $7,500,000 in cash each year to maintain its level of operations. Transactions costs are $60 each time it is necessary to liquidate marketable securities. Assume a 365-day year.

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 optimum cash order quantity? $.

(b) What is the optimum number of securities liquidations for cash per year? transactions.

(c) What is the optimum number of days between orders for cash? days.

(d) What is the minimum total cost associated with obtaining and maintaining cash balances? $

4.

Markert’s Markets is a small privately-owned chain of grocery stores. 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 $6,000, and the owner believes this figure also reflects future balance variability. The enterprise earns an average daily return of 0.2% on its marketable securities and incurs an average brokerage fee of $250 each time it engages in a securities transaction. The owner has determined that it cannot permit the enterprise’s cash balance to fall below $25,000.

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? $

Answer 1

Downing Consulting,Inc:

Baumol's Cash management model;

Given: Transactions Costs (T)= $60
Rate of Interest(r)= 4%
Total Cash (A)= $7,500,000

Formula:

where,

A= Annual Cash
T= Transaction Cost
r= rate of interest

Now,

a) optimum cash order quantity:

=

= 1,50,000

optimum cash order quantity is $ 1,50,000

b) optimum number of securities liquidations for cash per year:

= $7,500,000 / 1,50,000

= 50

optimum number of securities liquidations for cash per year is 50.

c) optimum number of days between orders for cash

=No. of working days per year / number of orders

= 365 / 50

= 7.3

optimum number of days between orders for cash is 7.3 days or 7 days (round off)

d) minimum total cost associated with obtaining and maintaining cash balances:

Total Costs= Transaction Costs + Interest Costs

Transaction Costs= number of transaction * transaction cost per transaction

= 50 * 60

= $3000

Interest Costs= ( 1,50,000 / 2 ) * 4%

= $3000

Total Costs= 3000+3000

= $6000

minimum total cost associated with obtaining and maintaining cash balances is $6000

Markert’s Markets

Miller-Orr cash management model :

Given; Standard deviation= $6,000 so, Variance = 3,60,00,000

Average daily return = 0.2% ( 0.2 / 100 = 0.002 )

Transaction Cost= $250

Minimum Cash Balance= $25,000

Formula:

Z =  

where,

T= transaction cost

V= variance of daily cash requirement

i= daily rate of interest

a) company’s “z” value:

Z=

Z= 9448.08

or 9448

company’s “z” value is $9448

b) the company’s “return-to-point:

R= Minimum cash balance + Z level

R= 25000+9448

R= $34,448

c) the company’s optimum maximum cash balance:

H=3Z+L

H= ( 3*9448 )+ 25000

H= $53,344

the company’s optimum maximum cash balance is $53,344