Question

15) 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.

15) Answer=29382.53

16) 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 3 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? 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.

17) 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 $13.95. By what amount will PRI’s optimal cash amount C* increase from what you calculated in problem 15? 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.

Answer 1

15). As per Baumol model, optimal cash balance is calculated as

C = (2*F*T/I)^(0.5)

		Current
F	Fixed cost of transaction	12.95
T	Total cash requirement for the period	1,500,000
I	Interest rate on marketable securities	4.50%
Formula	(2*F*T/I)^(0.5)	29,382.53

Optimal cash balance C* = 29,382.53

16). Total cost = trading cost + opportunity cost

= (T/C)*F + (C/2)*I

If withdrawals are made every three weeks, then number of withdrawals = number of weeks in a year/three weeks

= 52/3 = 17.33 or 18 withdrawals per year

Cash withdrawn C = 1,500,000/18 = 83,333.33

	Cash	Opportunity cost [A]	Trading cost [B]	Total cost
		(C/2)x I	(T/C)x F	[A] + [B]
Optimal cash (C*)	29,382.53	661.11	661.11	1,322.21
Present cash (C)	83,333.33	1,875.00	233.10	2,108.10
			Cash savings	785.89

Total cash cost saved if PRI transfers optimal cash amount = 785.89

Note: If number of withdrawals (17.33) is not rounded off but taken as it is, the cash amount will be 86,538.46 and total cost will then be 2,171.58 (cash savings of switching to C* will be 849.37)

17).

		Current	New
F	Fixed cost of transaction	12.95	13.95
T	Total cash requirement for the period	1,500,000	1,500,000
I	Interest rate on marketable securities	4.50%	3.25%
Formula	(2*F*T/I)^(0.5)	29,382.53	35,884.43

The optimal cash balance will increase by 35,884.43 - 29,382.53 = 6,501.90