A mail-order firm processes 5,200 checks per month. Of these, 70 percent are for
ID: 2647763 • Letter: A
Question
A mail-order firm processes 5,200 checks per month. Of these, 70 percent are for $42 and 30 percent are for $74. The $42 checks are delayed three days on average; the $74 checks are delayed four days on average. Assume 30 days in a month.
On average, there is $ that is (Click to select)uncollectedcollected and (Click to select)not availableavailable to the firm.
What is the weighted average delay? (Round your answer to 2 decimal places. (e.g., 32.16))
If the interest rate is 5 percent per year, calculate the daily cost of the float. (Use 365 days a year.Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
A mail-order firm processes 5,200 checks per month. Of these, 70 percent are for $42 and 30 percent are for $74. The $42 checks are delayed three days on average; the $74 checks are delayed four days on average. Assume 30 days in a month.
Explanation / Answer
Answer : a-1
The average daily float is the sum of the percentage each check amount is of the total checks received times the number of checks received times the amount of the check times the number of days until the check clears, divided by the number of days in a month. Assuming a 30 day month, we get:
Average daily float = [.70(5200)($42)(3) + .30(5200)($74)(4)]/30
Average daily float = [$458640+$461760]/30 = $30680
Answer: a-2 On average, there is $30680, that is uncollected and not available to the firm.
Answer: b-1 The total collections are the sum of the percentage of each check amount received times the total checks received times the amount of the check, so:
Total collections = .70(5200)($42)+ .30(5200)($74)
Total collections = $152880 + $115440
Total collections = $268320
The weighted average delay is the sum of the average number of days a check of a specific amount is delayed, times the percentage that check amount makes up of the total checks received, so
Weighted average delay = 3($152880/$268320) + 4($115440/$268320)
Weighted average delay = 3.430 days
Answer: b-2
The average daily float is the weighted average delay times the average checks received per day. Assuming a 30 day month, we get:
Average daily float = 3.430($268320/30 days)
Average daily float = $30677.92
Answer: c. The most the firm should pay is the total amount of the average float, or $30677.92
Answer: d The average daily interest rate is:
1.07= (1 + R)365
R = .01348% per day.
The daily cost of float is the average daily float times the daily interest rate, so:
Daily cost of the float = $30677.92 (.0001348)
Daily cost of the float = $4.13538
Answer: e. The most the firm should pay is still the average daily float. Under the reduced collection time assumption, we get:
New average daily float = 1.5($268320/30)
New average daily float = $19
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