Respuesta :
Answer:
NPV is -$434,544.44
Explanation:
By using the new lockbox system there would benefits in terms of savings recorded as a result of 1.5 days reduction in collection time
savings =1.5*average number of daily payments*average value of payment
savings=1.5*740*$690
savings=$765,900
However there is additional cost for using the lockbox system which is computed thus:
cost=variable lockbox fee*average number of payments per day
average lockbox fee is $0.20 per transaction
average number of payments per day is 740
cost=$0.20*740
cost=$148
the cost is meant to be incurred daily forever,hence the actual cost of the lockbox system is PV of $148 in perpetuity.
PV(perpetuity)=cash flow/(interest rate/365 days)
in order to write down the interest rate to a daily rate
cash flow is $148
interest rate is 4.5%
PV=$148/(0.045/365)
PV=$148/0.000123288
PV=$1,200,444.44
NPV=PV of inflows-PV of ouflow
NPV=$765,900 -$1,200,444.44
NPV=-$434,544.44
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
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.
