The financial manager of JAC Cosmetics is considering opening a lock box in Pittsburgh. Checks cleared through the lock box will amount to $300,000 per month. The lock box will make cash available to the company three days earlier than is currently the case.

a. Suppose that the bank offers to run the lock box for a $20,000 compensating balance. Is the lock box worthwhile?

b. Suppose that the bank offers to run the lock box for a fee of $.10 per check cleared instead of a compensating balance. What must the average check size be for the fee alternative to be less costly? Assume an interest rate of 6 percent per year.

c. Why did you need to know the interest rate to answer (b) but not to answer (a)?