Question

Paper Submarine Manufacturing is investigating a lockbox system to reduce its collection time. It has determined the following:

Average number of payments per day 355
Average value of payment $ 945
Variable lockbox fee (per transaction) $ 0.30
Daily interest rate on money market securities 0.068 %.

The total collection time will be reduced by four days if the lockbox system is adopted. What is the PV of adopting the system?

Answer 1

Answer:

-1,185,282.35‬

Explanation:

The average daily collections are the average number of payments times the average value of a payment, so:

Average daily collections = =355 * 945

Average daily collections = $335,475

The present value of the lockbox service is the average daily receipts times the number of days the collection is reduced, so:

     PV = (4 day reduction)( $335,475)

     PV = $1,341,900‬

 The daily cost is a perpetuity. The present value of the cost is the daily cost divided by the daily interest rate. So:      

     PV of cost = (.3*355)/.00068

           PV of cost = $106.5/.00068= $156,617.65

     The firm should take the lockbox service. The NPV of the lockbox is the cost plus the present value of the reduction in collection time, so:

     NPV = $156,617.65 - 1,341,900

           NPV = -1,185,282.35‬

Answer 2

Answer:

$770,245

Explanation:

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

Average Value of collection for 4 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 = 355 x $945

Average daily cash receipts = $335,475

Reduction in collection time = 4

Average Value of collection for 4 days = $335,475 x 4

Average Value of collection for 4 days = $1,341,900

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

where;

Variable lockbox fee (per transaction) = $0.30

Lockbox fee per day = 355 x $0.30

Lockbox fee per day = $106.50

Annual Interest Rate = 0.068

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 = 0.068 / 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 = $106.50 / 0.0001863014

Present Value of Lock Box = $571,654

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 = $1,341,900 - $571,654

NPV of the Lock Box = $770,245

Since the value of NPV is positive, Paper Submarine Manufacturing, should consider using the lock box system.