It takes Cookie Cutter Modular Homes Inc about six days to r

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 $123,000, and the required rate of return is 4 percent per year. Assume 365 days per year. What is the reduction in outstanding cash balances as a result of implementing the lockbox system? What is the daily dollar return that could be earned on these savings? (Round your answer to 2 decimal places, (e.g., 32.16)) Dollar return 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))

Solution

b. We need to find the daily rate:

The avearge daily rate is (1+r)^(1/365)-1 =1.04^(1/365) -1 = 0.00010746

Daily savings = 369,000 * 0.00010746 = $39.65

c1: First, you need to convert the annual rate to a monthly rate: (1+r)^(1/12)-1 = 1.04^(1/12)-1 = 0.00327374

For c1 use the perpetuity formula to solve:

PV = c / r
369,000 = c / 0.00327374
369,000*.00327374 = c
1208.01006 = c

Or rounded, $1,208.01

c2: For c2, use the perpetuity due formula to solve:

c = (PV * r) / (1+r)
c = (369,000*.00327374) / 1.00327374
c = 1204.068

Or rounded, $1,204.07