Question

Your firm has an average receipt size of $145. A bank has approached you concerning a lockbox service that will decrease your total collection time by one day. You typically receive 7,100 checks per day. The daily interest rate is .017 percent. The bank charges a lockbox fee of $135 per day. What is the NPV of accepting the lockbox agreement? What would the net annual savings be if the service were adopted?

Answer 1

The net present value of accepting the lockbox is equal to present value of savings minus present value of cost.

Average daily collections = average receipt size * checks received per day.

Average daily collections = 145 * 7100

Average daily collections = $1,029,500

Savings of the lockbox service = average daily collection * time saved

Savings= 1,029,500 * 1

Savings= $1,029,500

PV of cost = Lock box fee /interest

PV of cost = $135/0.00017

PV of cost = $794,117.647

The NPV = savings- PV of cost

NPV = 1,029,500 - 794,117.647

NPV = $235,382.3529

The net annual savings is equal to annual savings minus annual cost.

So,the annual savings is equal to,

S = savings * (1+interest rate)^365 - Savings

Annual savings = 1,029,500(1+0.017%)^365 - 1,029,500 = 65898.2259

Annual cost = $135 * (FVIFA365,.016%)

= 135* (1+interest rate)^n -1)/interest rate

= 135*(1+0.017%)^365 -1)/0.017/100)

= 135 * 376.529

Annual cost = $50831.417

Net annual savings = annual saving - annual cost

= 65898.2259 - 50831.417

= $15066.808