Answer:
-$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
<em>Where;
</em>
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)
<em>where;
</em>
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.
