Question

ptimal Cash Transfer. Barenbaum Industries projects that cash outlays of $5.4 million will occur uniformly throughout the year. Barenbaum plans to meet its cash requirements by periodically selling marketable securities form its portfolio. The firm’s marketable securities are invested to earn 6%, and the cost per transaction of converting securities to cash is $15. (5 pts)

a. Use the Baumol model to determine the optimal transaction size for transfers from marketable securities to cash.

​​​​​​b. What will be Barenbaum’s average cash balance? ​​​​​​​

c. How many transfers per year will be required?

​​​​​​​d. What will be Barenbaum’s total annual cost of maintaining cash balances?

​​​​​​​​​​​​​​e. What would the total cost be if the company maintained an average cash balance of $40,000 or of $0 (it deposits funds daily to meet cash requirements, using 360 days)?

Answer 1

Baumol cash management model:

Baumol noted that cash balances are very similar to inventory levels and developed a model based on the Economic Order Quantity (EOQ)

C=under root of 2*T*F/RR

Where c= optimal cash level

T= demand for cash over the entire period considered (year)    =$54,00,000

F-fixed costs of cash transfer =$15

R-alternative cost of maintaining cash =6%

This formula comes from from the fact that if the level of cash is to be optimal, then following equality must exist KA=KT, the alternative cost must equal the transaction costs . These, in tum are calculated as follows

KA=C*R/2

KT=T*F/C

Computation of C at $40000 or $0

Average cash balance =c/2

Therefore C=average cash balance *2

At 40000=$40000*2=$80000

At 0, C=0

ANS	particulars			formula		formula substitution		amount
a	optimal transaction size		C=under root of 2*T*F/R	under root of 2*5400000*15/0.06		51961.52
b.	average cash balance		=	C/2			51961.52/2		25980.76
c	Transfers per year		=	T/C			5400000/51961.52		103.9231

computation of total annual cost
	particulars	formula	ans d	ans e(i)	ans e(ii)
C			51961.52	80000	0
a.	Annual cost of transaction	KA=C*R/2	1558.846	2400	0
b.	Annual alternative cost	KT=T*F/C	1558.846	1012.5	NA
c,	Total cost c=a+b		3117.691	3412.5

notes

assumed $5.4 million is the annual cash distribution

Annual cost at $0 there will nnot be any transaction cost or alternative cost as daily funds are deposited a and when required

also $40000 can be taken as C itself or can use $80000 as defined above