Question

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 ​$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 through the lockbox system 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 10 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 ​percent?

Answer 1

Ans a.
Portobella Scuba Diving Inc.
Yearly check remittances received	$   28,000,000
No of checks received	15,000
Lockbox charge per check =	$0.30
Totl Annual Lockbox charge	$         4,500.0
Return from invested portfolio =10%
Check remittance received /day=$28M/365=	$     76,712.33
Assume the collection days are received by x days
So, Funds freed up =76,712.33*x
Annual Return from investing the freed up fund for x days @ 10% pa= 76,712.33*x*10%/365*x
The return from freed up fund should be =$4500 for indifference on Lockbox implementation
76,712.33*x*10%/365*x =4500
x=14.63
Therefore , the lockbox decision will have not positive or
negative impact if the collection days are reduced by 14.63 days
Ans b.
The expected annual return % is not given in the part b. of the question.
However, the given % return can be put in place of above equation
and the required reduction in collcetion days will come up .
We can compare the reduction against the previous reduction and comment.