A mail-order firm processes 5,000 checks per month. Of these, 65% are for $50 and 35% are for $70. The $50 checks are delayed two days on average; the $70 checks are delayed three days on average.
a. What is the average daily collection float? How do you interpret your answer?
b.What is the weighted average delay? use the results to calculate the average daily float.
c. How much should the firm be willing to pay to eliminate the float.
d. If the interest rate is 7% per year, calculate the daily cost of the float.
e. How much should the firm be willing to pay to reduce the weighted average float by 1.5 days?

Solution Preview

a. What is the average daily collection float? How do you interpret this answer?

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 = [.65(5,000)($50)(2) + .35(5,000)($70)(3)]/30
Average daily float = $23,083
On average, there is $23,083 that is uncollected and not available to the firm.

b. What is ...

Solution Summary

The solution explains the calculation of the average daily float using the weighted average delay.

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