Question

A mail-order firm processes 5,000 checks per month. Of these, 70 percent are for $40 and 30 percent are for $72. The $40 checks are delayed three days on average; the $72 checks are delayed four days on average. Assume 30 days in a month.

a-1.	What is the average daily collection float? (Do not round intermediate calculations.)

a-2.	How do you interpret your answer? (Do not round intermediate calculations.)

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.)

c.	How much should the firm be willing to pay to eliminate the float? (Do not round intermediate calculations.)

d.	If the interest rate is 6 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 to 1.5 days? (Do not round intermediate calculations.)

Answer 1

a-1). Average daily collection float = (number of checks of $40*check amount*number of days of delay + number of checks of $72*check amount*number of days of delay)/number of days in a month

= (70%*5,000*40*3 + 30%*5,000*72*4)/30 = 28,400

a-2). On an average, the firm has an uncollected amount of $28,400 per day which it cannot use.

b-1). Collection of $40 check = 70%*5,000*40 = 140,000

Collection of $72 check = 30%*5,000*72 = 108,000

Total collection = 140,000+108,000 = 248,000

Weighted average delay = sum of [number of days of delay*collection amount/total collection]

= 3*140,000/248,000 + 4*108,000/248,000 = 3.44 days

b-2). Average daily float = weighted average delaY*total collection/number of days in a month

= 3.44*248,000/30 = 28,400

c). The maximum amount which the firm should be willing to pay is the average daily float of 28,400.

d). Effective daily interest rate = [(1+APR)^(1/365] -1 = [(1+6%)^(365)]-1 = 0.015965%

Daily cost of the float = effective daily interest rate*average daily float

= 0.015965%*28,400 = 4.53

e). If weighted average float is reduced to 1.5 days then reduction in float = 3.44 - 1.5 = 1.94 days

Average daily float for 1.94 days = 1.94*total collection/30 = 1.94*248,000/30 = 16,000