Question
24. Arshadi Wineries is considering the purchase of lockbox services from First Bancorp. 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 5c per check in return for operating the lockbox system. Assume one-year T-bills yield 5%, and use a 360-day year (i) Calculate the daily rate of return. (ii) Should Arshadi Wineries purchase the system (i.e., is its NPV greater than 0?) (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 S36.000 (-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)? (ii) 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 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 $65. Suppose your firm's target cash balance, C* 68,830 (G) What lower cash balance limit (L) is consistent with this information. (ii) Find U*, the firm's implied maximum cash balance limit. the Miller-Orm model. The (ii) Find your firm's average cash balance held over time (iv)Using your answer to part (ii, find the average dollar cost incurred by the firm from holding cash over a two-week period.
Explanation / Answer
As per the instructions given by Chegg team, I can solve only the first question i.e. q24
i) The daily rate of return = 0.05/360 = 0.00012%
ii) After the lockup system is purchased,
amount collected in per day = number of checks* average amount per check = 300*150 = $45,000
The present value of daily benefit if the company purchases the system = $(45,000 * 0.00012) = $6.25
The present value of daily cost if the company purchases the system = $(5/100)*300 = $15 , note: 1 cent = 1/100 of a dollar
NPV = PV(benefit) - PV(cost) = $(6.25 - 15) = - $8.75 < 0
Therefore, the company should not purchase the system.
iii) Let the acceptable cost per check be x.
Then, for NPV to be greater than 0,
PV(benefit) - PV(cost) > 0
6.25 - (x*number of checks per day) >0
6.25 - (x*300) >0
x < 6.25/300
x< 0.021
i.e. the cost per check should be less than $0.021 for the lockup system to be acceptable.
