Question

# Paradise Retailers, Inc. (PRI) determined that \$1,500,000 is needed for cash transactions made during the next...

Paradise Retailers, Inc. (PRI) determined that \$1,500,000 is needed for cash transactions made during the next year. Each time PRI deposits money in its checking account, a charge of \$12.95 is assessed to cover clerical costs. If PRI can hold marketable securities that yield 4.5%, and then convert these securities to cash at a cost of only the \$12.95 deposit charge, what is the optimal cash amount C* to transfer from marketable securities to the checking account according to the Baumol Model? Enter your answer rounded to two decimal places. Do not enter \$ or comma in the answer box. For example, if your answer is \$12,300.456 then enter as 12300.46 in the answer box.

Use the data from problem 15, PRI’s financial managers have not been following the Baumol Model. Instead, they have been transferring cash from marketable securities less frequently, namely, transferring cash every 2 weeks. What total cash cost including holding costs and transactions costs could PRI save by transferring the optimal cash amount C* rather than this larger transfer amount?

Using the data from problem 15, PRI’s financial managers are adjusting their optimal cash amount C* from the Baumol Model to respond to changing market conditions. Interest rates have declined so that their marketable securities now yield 3.25% and their bank raised its deposit charge from \$12.95 to \$14.95. By what amount will PRI’s optimal cash amount C* increase from what you calculated in problem 15?

Solution:

A)

Optimal cash Amount = (2*1,500,000*12.95/0.045)1/2

= \$29,382.53

B)

Total cost = A*O/money converted + Money converted*c/2

At Baumol level = 1,500,000*12.95/29,382.53 + 29,382.53*0.045/2 = 661.11 + 661.11 = \$ 1,322.22

Presently cash transferred = 1,500,000*2/52 = \$57,692.3

Total cost at this level = 1,500,000*12.95/\$57,692.3 + \$57,692.3*0.045/2

= 336.7 + 1298.08

= 1,634.78

savings = 1,634.78 - \$ 1,322.22 = 312.56

C)

Optimal cash Amount = (2*1,500,000*14.95/0.0325)1/2 = \$37,148.35

Increase in cash = \$37,148.35 - \$29,382.53 = \$7,765.82

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