Question

N is a tuxedo rental company for the most high-end occasions. 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 3.2% on its marketable securities and requires a total of $10,000,000 in cash each year to maintain its level of operations. Transactions costs are $100 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.

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

(a) What is the company’s optimum cash order quantity?

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

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

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

Answer 1

a.

Annual requirement of cash (A)=10000000

fixed cost of cash transfer (O)=$100

Annual Return of funds (C)=3.2%

Formula for optimal Cash quantity = √(2*A*O/C)

√(2*10000000*100/3.2%)

=250000

So company's optimum cash order quantity is $250000

b.

Optimum number of securities liquidation = annual demand for cash/optimum cash order quantity

=10000000/250000

=40

So optimum number of securities liquidations for cash per year is 40

c.

Optimum number of days between order for cash = 365/number of orders per year

=365/40

=9.125

So the optimum number of days between orders for cash is 9 days

d.

If make transfer as per optimal cash Quantity

Average cash = optimum cash quantity/2

=250000/2

=125000

Total holding or carrying cost= Average cash * rate of return of funds

=125000*3.2%

=$4000

Total ordering cost = number of order per year * order cost per liquidation

=40*100

=4000

Total cost associated with Optimum cash level = Total carrying cost + total ordering cost

=4000+4000

=8000

So the minimum total cost associated with obtaining and maintaining cash balances is $8000