Question

A mail-order firm processes 4,300 checks per month. Of these, 60 percent are for $33 and 40 percent are for $65. The $33 checks are delayed two days on average; the $65 checks are delayed three 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 5 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. Average daily collection flot =[(4300*60%) (33*2) +( 4300*40% *65*3)]/30

=( 2580* 66+ 1720* 195)/30

=( 170280+ 335400)/30

= 16856

A2. Total collection =(4300*60%) (33) +( 4300*40% *65*]

= 2580*33 + 1720*65

= 85140+ 111800= 196940

On average, 16856 is uncollected and not available to firm.  

B.1 Weight average delay = average daily flot * number of days / total collection

=16856*30/196940

=2.567686 or 2.57

A. 2. Average daily flot = weighted average delay*Total collection/number of days

= 2.567686*196940/30

= 16856

C. Maximum average daily float = 16856

D. Daily cost of float = average daily float * Rate

(1+0.05)= (1+r)^1/days

(1+r)= (1+.05)^1/365

(1+r)= 1.00013368

r=1.00013368-1

r=0.013368%

=16856*0.013368%

= 2.25

e. New Average daily float=weighted average float * total collection / number of days

=1.50*196940/30

=9847