It takes Cookie Cutter Modular Homes, Inc., about six days to receive and deposi

Question

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 $121,000, 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? Cash balance reduction $ 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)) Dollar return $ c-1 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)) Maximum monthly charge $ c-2 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)) Maximum monthly charge $

Explanation / Answer

a. Collection of 6 days= $ 121,000 * 6 = $ 726,000

Collection of 3 days= $ 121,000 * 3 = $ 363,000

Reduction in Outstanding balances as result of implementing lockbox system = $ ( 726,000 - 363,000 ) = $ 363,000.

b.  The dollar return that can be earned is the average daily interest rate times the cash balance reduction. The average daily interest rate is:

= (1+r)^(1/365)-1 = 1.06^(1/365)-1 = .000159654

Hence, the dollar return earned= Average Daily Interest Rate * Cash Balance Reduction

= .000159654 * 363,000 = 57.9544%= 57.95 % ( rounded off )

c-1 . Maximum monthly charge Cookie Cutter should pay for this lockbox system if the payment is due at the end of the month :

Conversion of annual required rate of return to monthly rate of return= (1+0.06)^(1/12)-1 = 0.0048676

Using perpetuity formula, maximum monthy charge to be paid at end of month= Cash Balance Reduction* Monthly Rate

PV = c / r

363,000= c / 0.0048676

c = $ 363,000 * 0.0048676 = $ 1,766.94 ( rounded off to 2 decimal places ).

c-2. Maximum monthly charge Cookie Cutter should pay for this lockbox system if the payment is due at the beginning of the month:

Using the perpetuity due formula ,

c = (PV * r) / (1+r)

c = (363,000*.0048676) / 1.0048676

c = 1,766.9388/ 1.0048676 = $ 1,758.38 ( approx. rounded off to 2 decimal places )

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