17-1. (Cost of services) As CFO of Portobello Scuba Diving Inc. you are asked to

Question

17-1. (Cost of services) As CFO of Portobello Scuba Diving Inc. you are asked to look into the pos- sibility 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 S0.25 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 8 percent. The company usually uses a 365-day year in its procedures. a. What reduction in check collection time is necessary for Portobello to be neither better nor b. How would your solution to part (a) be affected if Portobello could invest the freed-up bal- c. What is the logical explanation for the differences in your answers to part (a) and part (b)? worse off for having adopted the lockbox system? ances at an expected annual return of only 4 percent?

Explanation / Answer

The per instrument cost of the bank is $0.25. Assuming uniform cheque value, the 24 million remittances across 10000 cheque will mean per cheque value of 2400. If this amount can be invested at 8% p.a., then daily investment income will be approx = 2400 * 8% /365 = $ 0.526

Now for the company to jus about cover the cost of the cheque processing, the time should reduce by (assuming fractional time in days is possible) 0.25/0.526 = 0.48 days

Now if the interest that can be earned reduces to 4%, the average daily interest will also reduce to $0.263. At this level, the time required to cover the cost should reduce by 0.95 days

The difference is simply because the opportunity cost in terms of alternate usage of funds has decreased for the company.

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