Childers, Inc. operates primarily in the Southeast but has a number of customers in Phoenix who remit about 8,000 checks a year. The average check is $2,400. It currently takes the Phoenix checks an average of seven days after mailing to clear into Childers' account. A Phoenix bank has offered Childers a lock box system for $2,400 a year plus $.22 per check. This will reduce the clearing time for the checks to four days. How much will the lock box system save Childers if it borrows at 11%?
A)$157,808
B)$13,199
C)$17,359
D)$4,160

Question

Childers, Inc. operates primarily in the Southeast but has a number of customers in Phoenix who remit about 8,000 checks a year.  The average check is $2,400.  It currently takes the Phoenix checks an average of seven days after mailing to clear into Childers' account.  A Phoenix bank has offered Childers a lock box system for $2,400 a year plus $.22 per check.  This will reduce the clearing time for the checks to four days.  How much will the lock box system save Childers if it borrows at 11%?
A)$157,808
B)$13,199
C)$17,359
D)$4,160

Quizplus · Accepted Answer

The lock box system will save Childers money by reducing the time it takes for checks to clear, thus reducing the amount of time Childers has to borrow money at an 11% interest rate. The calculation involves finding the value of having the money available three days sooner (7 days - 4 days = 3 days sooner) for all the checks, then subtracting the cost of the lock box system.First, calculate the total annual amount of checks from Phoenix: 8,000 checks * $2,400/check = $19,200,000.The daily interest rate is 11% annually, so: 11% / 365 = 0.0301% per day.The value of having $19,200,000 three days sooner is: $19,200,000 * 0.0301% * 3 days = $17,359.20.Then, calculate the total cost of the lock box system: $2,400 + ($0.22 * 8,000) = $4,160.Finally, subtract the cost of the lock box system from the value of having the money sooner: $17,359.20 - $4,160 = $13,199.20.Therefore, the lock box system will save Childers approximately $13,199 annually.