A mail-order firm processes 5,700 checks per month. Of these, 60 percent are for
ID: 2776650 • Letter: A
Question
A mail-order firm processes 5,700 checks per month. Of these, 60 percent are for $55 and 40 percent are for $80. The $55 checks are delayed two days on average; the $80 checks are delayed three days on average. Assume 30 days per month.
On average, there is $ that is (Click to select)uncollectedcollected and (Click to select)availablenot available to the firm.
What is the weighted average delay? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
How much should the firm be willing to pay to eliminate the float?
If the interest rate is 7 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))
How much should the firm be willing to pay to reduce the weighted average float by 1.5 days? (Do not round intermediate calculations.)
a-1. What is the average daily collection float? (Do not round intermediate calculations.)Explanation / Answer
a-1) no of checks=5700
No of $55 check=60%*5700=3420 and total amount= 3420*55=$1,88,100
Delay of $55 check=2 days
No of $80 check=40%*5700=2280 and total amount= 2280*80=$1,82,400
Delay of $80 check=3 days
Average daily Collection float=((188100*2)+(182400*3))/30=$30,780
a-2)On average, there is $ that is ($30780)uncollected/collected and not availableavailable to the firm.
b-1) Weighted average delay=((3420*2)+((2280*3))/5700= 2,4 days
b-2)
no of checks=5700
No of $55 check=60%*5700=3420 and total amount= 3420*55=$1,88,100
Delay of $55 check=2 days
No of $80 check=40%*5700=2280 and total amount= 2280*80=$1,82,400
Delay of $80 check=3 days
Average daily Collection float=((188100*2)+(182400*3))/30=$30,780
c) $30780*2,4=$73,872
d)daily cost of the float=(73872*7/100*1/365)=$14.167
e)for 2.4 days it is =$30782*2.4=$73872
reduced by 1.5 days means delay is(2.4-1.5)=.9 days
=30782*.9=$27703.8
maximum payment =$73872-27703.8=$46,168.2
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