24. Arshadi ineries is considering the purchase of lockbox services from First c

Question

24. Arshadi ineries is considering the purchase of lockbox services from First corp. Currently, it takes 6 days to collect funds from customers; this would be reduced by 2 days with the lockbox system. The average number of payments received per day is 300 and the average check size is $150. First Bancorp will charge Se per check in return for operating the lockbox system. Assume one-year T-bills yield 5%, and use a 360-day year. an (i) Calculate the daily rate of return. (ii) Should Arshadi Wineries purchase the system (i.e., is its NPV greater than 02) (iii) What is the maximum acceptable cost per check that Arshadi Wineries could pay and still find the system acceptable? 25. Cindy's Toys has an average cash balance of $18.000 ( C/2) opportunity cost of carrying cash is 5%. Cindy replenishes with $36,000 (-c ) on the first of each month and the order cost is $25 (So, total cash needs for the year-C x 12 432000) (i) What are the total carrying (opportunity) costs under the current system? (ii) What are the total replenishment costs under the current system (C)? (iii) By looking at the results from parts (i) and (ii) above, state, in one, very short sentence, whether the firm is replenishing cash balances optimally. If not, find the firms optimal cash replenishment amount(C*). (iv) What are the costs savings (i.e. the difference between the total (carrying and replenishing) costs using the current system and total costs using C*? (v)When the firm replenishes cash optimally, how many times a year would it replenish? How frequently would it replenish (every 20 days, or 30 days, etc.)? 26. Your firm's management of its cash position is based on the Miller-Orr model. The weekely standard deviation of the disbursements is $8,.600. The applicable weekly interest rate is 0.054 percent and the fixed cost of transferring funds is S65. Suppose your firm's target cash balance, C 68,830 (i) What lower cash balance limit (L) is consistent with this information. (ii) Find U*, the firm's implied maximum cash balance limit. (iv)Using your answer to part (i), find the average dollar cost incurred by the firm from holding cash over a two-week period. (ii) Find your firm's average cash balance held over time

Explanation / Answer

Answer to question 34:

Daily rate of return = 5/360 % = 0.014 %

DAILY RATE OF RETURN = 0.014%

Annual yield ( 360 days ) = 5%

Therefore, daily yield percentage = 5/360

Daily value of perpetually locked up cash = 300 payments/ day x $ 150 / payment = $45000

Interest on 6 days basis under current system on $45,000

= 5/360 % x 6 days x $45,000

= $37.5

Interest on 2 days basis under lockbox system = 5/360 % x 2 days x $45,000 = $12.49

Amount to be paid to first Bancorp ( @ $0.05 perc check ) = 0.05 x 300 = 15

Hence,

Savings through purchase of new system

= Total cost in original system – Total cost in new system involving lockbox

= Interest on 6 days basis – ( Interest on 2 days basis + Amount to be paid to Frist Bancorp)

= 37.5 – ( 12.49 + 15)

= $ 10.01

SINCE THERE IS SAVING, ARSHAD MUST BUY THE SYSTEM

Let the maximum acceptable cost per check = $ C

Under this,

Total cost in old system = Total cost in new system

Or, 37.5 = 12.49 + 300 x C

Or, 300 x C = 25.01

Or, C = $ 25.01/300 = Cents 25.01/300 x 100 = Cents 8.33 ( Cents 8 rounded to nearest whole number )

MAXIMUM ACCEPTABLE COST PER CHECK = 8 CENTS

DAILY RATE OF RETURN = 0.014%

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