8. As of the beginning of the quarter, you have a cash balance of $250. During the quarter, you
pay your suppliers $310. Your accounts receivable collections are $420. You also pay an interest payment of $30 and a tax bill of $180. In addition, you borrow $75. What is your cash balance at the end of the quarter?
Solution: Computation of the Cash balance
Cash balance $ 250
Add: Cash collections $ 420
Total Receipts $ 670
Paid Supplies $ 310
Interest paid $ 30
tax paid $ 180
Cash net changes $ 150
Add; Borrowings $ 75
Cash Balance at the end $ 225
Hence the Cash balance is $225
9. Your firm has an average receipt size of $108. A bank has approached you concerning a lockbox service that will decrease your total collection time by two days. You typically receive 8,500 checks per day. The daily interest is .016 percent. If the bank charges a fee of $225 per day, should the lockbox project be accepted? What would be the net annual savings be if the service were adopted?
a. The average daily collections are the number of checks received times the average value of a check, so:
Average daily collections = 108(8,500)
Average daily collections = 918,000
The present value of the lockbox service is the average daily receipts times the number of days the collection is reduced, so:
PV = (2 day reduction)(918,000)
PV = 1,836,000
The daily cost is a perpetuity. The present value of the cost is the daily cost divided by the daily interest rate. So:
PV of cost = 225/0.00016
PV of cost = 1,406,250
The NPV of lockbox is 1,836,000-1,406,250 = 429,750
The firm should take the lockbox service.
The net annual savings excluding the cost would be the future value of the savings minus the savings, so:
Annual savings = 1,836,000(1.00016) ^ 365 – 1,836,000
Annual savings = 110,406
And the annual cost would be the future value of the daily cost, which is an annuity, so:
Annual cost = 225(FVIFA365,.016%)
Annual cost = $84,576.99
So, the annual net savings would be:
Annual net savings = 110,406- $84,576.99
Annual net savings = $25,829 Approx
10. No More Pencils, Inc., disburses checks every two weeks that average $93,000 and take seven days to clear. How much interest can the company earn annually if it delays transfer of funds from an interest-bearing account that pays .015 percent per day for those seven days? Ignore the effects of compounding interest.
0.015% can be written as .00015. Therefore, .00015*7*93000*26 shows the interest rate over 7 days times the principal times the number of times this can happen annually. This comes to: $2538.90
11. Cow Chips, Inc., a large fertilizer distributor based in California, is planning to use a lockbox system to speed up collections from its customers located on the East Coast. A Philadelphia-area bank will provide this service for an annual fee of $20,000 plus 10 percent per transaction. The estimated reduction in collection and processing time is one day. If the average customer payment in this region is $5,300, how many customers are needed, on average, each day to make the system profitable for Cow Chips? Treasury bills are currently yielding 5 percent per year.
NPV =0 =(5300*1*n)-(0.10*n)/0.000134-20000/0.05
N = 87.87
12. If 25% of the customers pay on day 10 and 75% pay on day 30, the average collection period is:
A. 15 days.
B. 20 days.
C. 25 days.
D. 30 days.
E. 40 days.
Solution: Average collection period assuming no of customers are 10 = 2.5*10+7.5*30
=25+225 = 250/10 = 25 Days
13. Collegiate Tuxedo rents apparel throughout the year. They have experienced non-payment by about 15% of their customers with an average loss of $200. Collegiate wants to stem their losses by using an instant electronic credit check on the customer. These checks will cost them $7 on each of the 1,000 customers. The opportunity cost is 1.5% for the credit period. Should they pursue the credit check?
A. No, because the $7000 cost is too high.
B. No, because a $200 loss is minor.
C. Yes, because the net gain is $30,000.
D. Yes, because the net gain is $23,000.
E. Yes, because the net gain is $193,000.
Expected loss from non-payment = 1000*15%*200 = $30000
Cost of Credit Check = 1000*7 = $7000
Opportunity cost = $7000*1.5% =$105
Hence Net Gain = 30000 -7000 -105 = $22895
14. If 20% of the customers pay on day 10 and 80% pay on day 30, the average collection period is:
A. 10 days.
B. 15 days.
C. 22.5 days.
D. 24 days.
E. 26 days.
Solution: Average collection period assuming no of customers are 10 = 2*10+8*30
=20+240 = 260/10 = 26 Days