1. Float and Weighted Average Delay Your neighbor goes to the post office once a
ID: 2663576 • Letter: 1
Question
1. Float and Weighted Average DelayYour neighbor goes to the post office once a month and picks up checks, one for 17,000 and one for 6000. The larger check takes four days to clear after it is deposited, the smaller one takes five days.
a. What is the total float for the month?
b. What is the average daily float?
c. What is the average daily receipts and weighted average delay
2. Lockboxes and collections
It takes cookie cutter modular homes Inc about six days to receive and deposit checks from customers. Cooke Cutter’s management is considering a lock box system to reduce the firm collection times. It is expected that the lockbox system will reduce receipt and deposit times to three days total. Average daily collections are 145,000 and the required rate of return is 9 percent per year.
a. What is the reduction in outstanding cash balance as result of implementing the lockbox system?
b. What is the dollar return that could be earned on these savings?
c. What is the maximum monthly charge cookies cutter should pay for this lockbox system if the payment is due at the end of the month? What if the payment is due at the beginning of the month?
3. Size of Accounts Receivable
The Arizona Bay Corporation sells on credit terms o net 30. Its accounts are, on average, 8 days past due. If annual credit sales are 8.4 million, what is the company’s balance sheet amount in account receivable?
4. EQO
The Trektronics store begins each week with 300 phases in stock. This stock is depleted each week and reordered. If the carrying cost per phaser is 41 per year and the fixed order cost is 95, what is the total carrying cost? What is the restocking cost? Should Trektronics increase or decrease it order size? Describe an optimal inventory policy for Tretronics in terms of order size and order frequency.
Explanation / Answer
1)
a) The total float for the month is calculted as:
Cheque-1: Amount * Processing and availability delay
$17,000 * 4 = $68,000
Cheque-2: Amount * Processing and availability delay
$6,000 * 5 = $30,000
Total float = $68,000 + $30,000
= $98,000
b) Average Daily float = Total float / Total days
The total days in a month are 30days
Average daily float = $98,000 / 30
= $3266.67
So, on an average thers is $3266.67 that is uncollected and not available.
Average daily receipts is calculated as:
Average daily receipts = Total receipts / Total days
But total receipts = $17,000 + $6,000
= $23,000
Therefore, Average daily receipts = $23,000 / 30
= $766.67
Weighted average daily = (17,000 / $23,000) * 4days + ($6,000 / $23,000) * 5days
= (0.74 * 4) + (0.26 * 5)
= 2.96 + 1.3
= 4.26
Therefore, the weighted average daily receipts ia 4.26
2)
a) The collection time will be decreased by 3days , so the lockbox system will increase the collected bank balance by
Average daily collections * Number of days reduced
$145,000 * 3 = $435,000
In other words, the lockbox system releases $435,000 to the firm by reducing the collection time by 3days.
The reduction in the outstanding cash balance as a result of implementing the lockbox is ($435,000 - $145,000 = $290,000)
b) To calculate the dollar return that could be earned, we need to calculate the average daily interest rate
Average daily rate = (1+ Annual interest rate /365) - 1
= [(1+0.09)/365] - 1
= 0.000236 or 0.0236% per day
The daily dollar return is calculated as
$435,000 * 0.000236 = $102.72
Therefore,the dollar amount that could be earned is $102.66
c) We can use the daily interest rate from part-b, so the present value of savings is
PV of Savings = Average collections + Average collections(PVIFA %, n)
= $145,000 + $145,000(PVIFA0.0236% , 3)
= $145,000 + $145,000(2.9985)
= $145,000 + $434,782.5
= $579,782.5
PV of Savings = $579,782.5
As the lockbox payments occur at the end of the month, we need the effective monthly interest rate, which is:
Monthly interest rate = (1 + Annual Interest rate)/12 - 1
Monthly interest rate = (1.091/12) – 1
Monthly interest rate = 0.7207%
We are assuming the lockbox payments to occur at the end of the month, which are perpetuity:
PV = C/R
$579,782.5 = C / .007207
C = $4,178.5
The maximum monthly charge should be paid for the lockbox system is $3,134.35.
PV of perpetuity due is given by:-
PV = C + C / R
Solving for C:
C = (PV × R) / (1 + R)
C = (579,782.5 × .007207) / (1 + .007207)
C = $4,148.6
The payment due at the beginning of the month is $4,148.6
3) The size of the accounts receivables is calculated as
Accounts receivables = Credit sales per day * lenght of collection period
= ($8,400,000 / 30) * 8
= $2,240,000
Therefore, the size of accounts receivables is $2,240,000
4) The total cost is calculated as:
EOQ = Sqrt.[ (2 * Annual demand * ordering cost ) / Carrying cost per unit]
= Sqrt. [( 2 * 14400 * 95 ) / 41]
= Sqrt. (2,736,000 /41)
= 258
Total annual cost = Ch(Q/2) + Co (R/Q)
The weekly demand is given as 300
Monthly demand = 300* 4
= 1200
yearly demand = 1200 * 12
= 14,400
Total annual cost = $41 (300 /2) + $95 (14400 / 300)
= $6,150 + $4,560
= $10,710
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