(Cash management) As CFO of Portobello Scuba Diving Inc. you are asked to look into the possibility of adopting a lockbox system to expedite cash receipts from clients. Portobello receives check remittances totaling $24 million in a year. The firm records and processes 10,000 checks in the same period. The National Bank of Brazil has informed you that it could provide the service of expediting checks and associated documents through the lockbox system for a unit cost of $0.35 per check. After conducting an analysis, you project that the cash freed up by the adoption of the system can be invested in a portfolio of near-cash assets that will yield an annual before-tax return of 6 percent. The company usually uses a 365-day year in its financial calculations.

a. What reduction in check collection time is necessary for Portobello to be neither better nor worse off for having adopted the lockbox system?

b. How would your solution to part (a) be affected if Portobello could invest the freed-up balances at an expected annual return of only 3 percent?

c. What is the logical explanation for the differences in your answers to part (a) and part (b)?