Question

​(Cash receipts acceleration system​) Peggy Pierce Designs Inc. is a vertically​ integrated, national manufacturer and retailer of​ women's clothing.​ Currently, the firm has no coordinated cash management system. A​ proposal, however, from the First Pennsylvania Bank aimed at speeding up cash collections is being examined by several of​ Pierce's corporate executives. The firm currently uses a centralized billing​ procedure, which requires that all checks be mailed to the Philadelphia head office for processing and eventual deposit. Under this​ arrangement, all the​ customers' remittance checks take an average of 4 business days to reach the head office. Once in​ Philadelphia, another 2 days are required to process the checks for ultimate deposit at the First Pennsylvania Bank. The​ firm's daily remittances average ​$1.8 million. The average check size is ​$2 comma 000. Pierce Designs currently earns 8 percent annually on its​ marketable-securities portfolio. Under the proposed​ plan, First Pennsylvania said that they could reduce funds tied up by mail float to 2 ​days, and processing float will be eliminated. Funds would then be transferred twice each business day by means of automated depository transfer checks from local banks to the First Pennsylvania Bank. Each DTC costs ​$17. These transfers will occur all 270 business days of the year. Each check processed through the proposed cash collection system will cost ​$0.22.

a. What amount of cash balances will be freed up if Peggy Pierce Designs Inc. adopts the system suggested by First​ Pennsylvania?

b. What is the opportunity cost of maintaining the current banking​ setup?

c. What is the projected annual cost of operating the proposed​ system?

d. Should Pierce adopt the new​ system? Compute the net annual gain or loss associated with adopting the system.

Answer 1

Based on the information available in the question, we can calculate the following :-

Requirement a:-

Cash balance freed up.

Step 1:- Find the number of days freed because of the new proposal.

Particulars	Current	Proposed
Mail Float	4	2
Processing Float	2	0
Total Float	6	2
Step 2:- Calculate the cash balance freed
Reduction in float	4
Average daily remittance	1,800,000
Cash balance freed	7,200,000

Cash Balance freed = $7,200,000

Requirement b:-

The Opportunity cost of maintaining the current banking setup can be calculated as follows :-

Opportunity cost
Cash balance freed up	7,200,000
Interest on marketable sec	8%
Opportunity cost (Cash balance freed * Interest on Marketable Securities)	576,000

The Opportunity cost of maintaining the current banking setup = $576,000

Requirement c:-

The projected annual cost of operating the proposed system

Days of business	270
No.of times of transfer	2
Cost per transfer	17
Total DTC Cost(Days of business * Cost per transfer * No. of transfers)	9,180
Daily Remittance	1,800,000
Average check size	2,000
No.of checks	900
Cost per check	0.22
Total Check cost per day	198
No. of days	365	(Assuming that daily remittance average provided in the question is for 365 days)
Total Check cost	72,270
Total Operating cost	81,450

Requiremend d:-Please note that in calculating the average number of days for computing the check processing charges, we have assumed it to be 365. This way, we have also adopted the conservative strategy in calculating the gain/loss under the new system.

Total Opportunity cost - $576,000

Total Operating cost because of new processing system - $81,450

As can be seen, Peggy pierce Designs, Inc has an opportunity to earn $576,000 if the new system is adopted while it spends only $81,450 because of the new system. Therefore , there is a possibility for an annual gain of $494,550 ($576,000 - $81,450) in adopting the new system.

As such, it is beneficial for Peggy Pierce Designs, Inc to adopt the New system.

Note:- Please let me know if you have any questions/concerns through the comments section.