Question

Your firm has an average receipt size of $135. A bank has approached you concerning a lockbox service that will decrease your total collection time by one day. You typically receive 7,300 checks per day. The daily interest rate is .016 percent. The bank charges a lockbox fee of $125 per day.

a.	What is the NPV of accepting the lockbox agreement? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What would the net annual savings be if the service were adopted? (Use 365 days a year. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The average daily collections =average receipt × checks received per day

: Average daily collections = $135(7,300)

Average daily collections = $985500

Savings of the lockbox service = average collection * time saved

Savings= 1*($985500)

Savings= $985500

PV of cost = Lock box fee /interest

PV of cost = $125/0.00016

PV of cost = $781250

The NPV =savings - PV of cost

NPV = 985500 -781250

NPV = 204250

Annual savings = Savings × (1+I)^365 - Savings

Annual savings = 985500(1+0.016%)^365 - 985500 = 59262.07

Annual cost = $125 (FVIFA365,.016%)

Or125* (1+I)^n-1)/I)

= 125*(1+0.016%)^365-1)/0.016)

=125*375.8376

Annual cost = 46979.70

annual savings = annual saving - annual cost = 59262.07- 46979.70= 12282.37