Question

Bird's Eye Treehouses, Inc., a Kentucky company, has determined that a majority of its customers are located in the Pennsylvania area. It therefore is considering using a lockbox system offered by a bank located in Pittsburgh. The bank has estimated that use of the system will reduce collection time by 1.5 days. Assume 365 days a year. Average number of payments per day 890 Average value of payment $ 840 Variable lockbox fee (per transaction) $ .15 Annual interest rate on money market securities 4.8 % a. What is the NPV of the new lockbox system? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. Suppose in addition to the variable charge that there is an annual fixed charge of $5,000 to be paid at the end of each year. What is the NPV now? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

(a). NPV for the lockbox system = Present Value of benefits - Present Value of costs

Present Value of benefits:

Average collection/day = Average number of payments/day * Average value of payment = 890*840 = 747,600

Present Value = (1.5 days reduction)*(747,600) = 1,121,400 ----(a)

Present Value of costs:

Daily interest rate = annual interest rate/365 = 4.8%/365 = 0.0132%

The daily cost is a perpetuity so Present Value of daily cost = daily cost/daily interest rate = (890*0.15)/0.0132% = 1,015,156.25 ----(b)

NPV = (a) - (b)

= 1,121,400 - 1,015,156.25 = 106,243.75 (Answer)

(b). Present Value of annual fixed charge = annual fixed charge/annual interest = 5,000/4.8% = 104,166.67

Present Value of total cost = 1,015,156.25 + 104,166.67 = 1,119,322.92

NPV = 1,121,400 - 1,119,322.92 = 2,077.08 (Answer)