Martin Inc.is considering a lockbox system that will increase its check processing cost by $.20 per check.The company estimates an average check size of $900 and expects any funds freed up by the new lockbox system can be invested in an account that earns 4% per year before taxes.What reduction in collection time is necessary for the lockbox to be beneficial to Martin Inc.?
A) 1.96 days
B) 2.03 days
C) 1.73 days
D) 2.15 days

Question

Quizplus · Accepted Answer

First, we need to calculate the opportunity cost of holding onto checks instead of investing them immediately. The opportunity cost is:

($900 check size) x (4% APY) / 365 days per year = $0.04 per day

Next, we need to calculate the additional cost of the lockbox system:

$0.20 per check

To determine the breakeven point, we need to divide the additional cost by the opportunity cost:

$0.20 / $0.04 = 5 days

This means that if the lockbox system can reduce collection time by more than 5 days, it will be beneficial. To be more precise, we can calculate the exact number of days using the following formula:

(Cost of lockbox system) / (Opportunity cost per day x Check size) = Breakeven collection time

($0.20 per check) / ($0.04 per day x $900 check size) = 0.5556 days

Therefore, the reduction in collection time necessary for the lockbox to be beneficial is:

5 days - 0.5556 days = 4.4444 days or approximately 4.45 days

The closest answer choice is B) 2.03 days.