Lockbox Question

Hey guys, taking a corporate finance class and I need to figure out the following problem. Of course, I want to get the right answer, but I am more concerned with figuring out the logic so I can apply to other problem sets.

I’ve figured out the first 2 parts. I need some help w/ the last 2 parts, c1 & c2.

Any help you can lend would be greatly appreciated.

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It takes Cookie Cutter Modular Homes, Inc., about six days to receive and deposit checks from customers. Cookie Cutter’s management is considering a lockbox system to reduce the firm’s collection times. It is expected that the lockbox system will reduce receipt and deposit times to three days total. Average daily collections are $127,000, and the required rate of return is 6 percent per year. Assume 365 days per year.

a. What is the reduction in outstanding cash balances as a result of implementing the lockbox system?

_ This one is pretty simple – 3 days x $127,000 = $381,000 _

b. What is the daily dollar return that could be earned on these savings? (Round your answer to 2 decimal places. (e.g., 32.16))

First, figure the average daily rate: (1+r)^(1/365)-1 = 1.06^(1/365)-1 = .000159654

_ Now multiply: $381,000 x .000159654 = $60.828, or $60.83 rounded _

c1. What is the maximum monthly charge Cookie Cutter should pay for this lockbox system if the payment is due at the end of the month? (Round your answer to 2 decimal places. (e.g., 32.16))

c2. What is the maximum monthly charge Cookie Cutter should pay for this lockbox system if the payment is due at the beginning of the month? (Round your answer to 2 decimal places. (e.g., 32.16))

Never mind, I figured it out.

First, you need to convert the annual rate to a monthly rate: (1+r)^(1/12)-1 = 1.06^(1/12)-1 = 0.0048676

For c1 use the perpetuity formula to solve:

PV = c / r 381,000 = c / .0048676 381,000*.0048676 = c 1854.5368 = c

Or rounded, $1854.54

For c2, use the perpetuity due formula to solve:

c = (PV * r) / (1+r) c = (381,000*.0048676) / 1.0048676 c = 1845.5534

Or rounded, $1845.55

Thanks, this helped me a lot!