Question

(Cash management​) As CFO of Portobello Scuba Diving​ Inc., you are asked to look into the possibility of implementing a system to expedite cash receipts from clients. Portobello receives check remittances totaling ​$28 million in a year. The firm records and processes 15, 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 for a unit cost of $ 0.30 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 9 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 proposed​ 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 5 ​percent?

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

Answer 1

Part a.

Please refer to the calculations in screenshot below:

So the collection time must reduce by 0.65 days.

Part b.

So, in this case, the average reduction in collection time must be at least 1.17 days per check.

Part c.

The reason for differences in these answers is simply the opportunity cost of capital. If the company can earn a higher interest rate on freed up cash, it makes sense to pay the additional cost of check processing even if the reduction in collection time is less because the cost will be easily compensated by the high return on investments. On the other hand, when the investment opportunity rate is lower, the reduction in collection time must be substantial so that larger cash can be freed up which in turn can earn enough returns to cover the additional costs.