Question

A mail-order firm processes 4,500 checks per month. Of these, 60 percent are for $35 and 40 percent are for $67. The $35 checks are delayed two days on average; the $67 checks are delayed three days on average. Assume 30 days per month. a-1. What is the average daily collection float? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) a-2. How do you interpret your answer? b-1. What is the weighted average delay? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b-2. Calculate the average daily float. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) c. How much should the firm be willing to pay to eliminate the float? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) d. 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 answer to 2 decimal places, e.g., 32.16.) e. How much should the firm be willing to pay to reduce the weighted average float by 1.5 days? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Answer 1

Mail order Firm Requirement a 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 = [.60(4,500)($35)(2) +.40(4,500) ($67)(3)]/30 Average daily float = $18,360 On average, there is $18,360 that is uncollected and not available to the firm. Requirement b 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 = .60(4,500) ($35) +.40(4,500) ($67) Total collections = $215,100 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 = 2[.60(4,500) ($35)/$215,100] +3[.40(4,500)($67) /$215,100) Weighted average delay = 2.560669 days 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 = 2.560669 ($215, 100/30 days) Average daily float = $18,360 Requirement The most the firm should pay is the total amount of the average float, or $18,360. Requirement d The daily cost of float is the average daily float times the daily interest rate, so: Daily cost of the float = $18,360.000192) Daily cost of the float = $3.52 Requiremente 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($215, 100/30) New average daily float = $10,755