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 740
Average value of payment $690
Variable lockbox fee (per transaction) $ .20
Annual interest rate on money market securities 4.5%

What is the NPV of the new lockbox system?

-$434,544

Explanation:

The reduction in cash balances associated with implementing the system can be calculated as follows;

Average Value of collection for 1.5 days = Average daily cash receipts x Reduction in collection time

Where;

Average daily cash receipts = Average number of payments per day x Average value of payment

Average daily cash receipts = 740 x $690

Average daily cash receipts = $510,600

Reduction in collection time = 1.5

Average Value of collection for 1.5 days = $510,600 x 1.5

Average Value of collection for 1.5 days = $765,900

Lockbox fee per day = Average number of payments per day x Variable lockbox fee (per transaction)

where;

Variable lockbox fee (per transaction) = $0.20

Lockbox fee per day = 740 x $0.20

Lockbox fee per day = $148

Annual Interest Rate = 4.5% = 0.045

Since all the values are on a day basis, so let us find the value on interest per day, as follows;

Daily Interest Rate = Annual Interest Rate / No. of days in a year

Daily Interest Rate = 0.045 / 365

Daily Interest Rate = 0.0001232877

Hence, Present Value of the Lock Box can be calculated as follows;

Present Value of Lock Box = Lockbox fee per day / Daily Interest Rate

Present Value of Lock Box = $148 / 0.0001232877

Present Value of Lock Box = $1,200,444

Therefore the NPV of the Lock Box can be calculated as follows;

NPV of the Lock Box = Average Value of collection for 1.5 days - Present Value of Lock Box

NPV of the Lock Box = $765,900 - $1,200,444

NPV of the Lock Box = -$434,544

Since the value of NPV is negative, Bird's Eye Treehouses, Inc., should not consider using the lock box system offered by bank in Pittsburgh.

250 tickets needs to be sold.