16-2. (Cost of services) As CFO of Portobello Scuba Diving Inc. you are asked to
ID: 2664268 • Letter: 1
Question
16-2. (Cost of services) 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 $0.25 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 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 4 percent?
c. What is the logical explanation for the differences in your answers to part a and part b?
(Keown. Foundations of Finance: The Logic and Practice of Financial Management, 6th Edition. Pearson Learning Solutions p. 511).
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Explanation / Answer
a. What reduction in check collection time is necessary for Portobello to be neither better nor worse off for having adopted the lockbox system?
$24,000,000
Average Check size = ------------------- = $2,400 per check
10,000 checks
Daily opportunit cost of carrying cash = 0.08 / 365 = 0.0002192 per day
Days saved in collection process can be expressed as :
Added Cost = Added Benefits
P = (D) x (S) x (i)
0.25 = $2,400 x 0.0002192 x D
D= 0.25 / 0.52608 = 0.4752 days
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 4 percent?
Daily opportunit cost of carrying cash = 0.04 / 365 = 0.0001096 per day
P = (D) x (S) x (i)
0.25 = $2,400 x 0.0001096 x D
D= 0.25 / 0.26304 = 0.9504 days
c. What is the logical explanation for the differences in your answers to part a and part b?
The break even cash acceleration period of 0.9504 days is more than the 0.4752 days calculated in part (a) for yield at 8%. Alternative rate of return on freed-up cash is lower in (b). As such more funds required to be invested to cover the cost of operating the National Bank of Brazil lock system.
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