Question

A company is considering implementing a lockbox system. There is an annual fee of $7,610 plus a transaction fee of $0.05 per payment. The average size of customer payments is $3,615, and there are 39 payments made daily on average. The company can earn an EAR of 3.81% on its cash balances. For the lockbox system to be adopted with a positive NPV, by how many days should the average collection time be reduced at a minimum? Fractional answers are OK. (Assume 365 days in a year.)

A) 1.55

B) 1.59

C) 1.63

D) 1.67

E) 1.71

Answer 1

Average daily collections = average size of payment × average number of payments

=3,615 × 39

=$140,985

The PV of the lockbox service is the daily payments multiplied by the number of days the collection is reduced.

Let the number of days of collection reduced be a .

PV = $140,985 × a

The PV of the cost is the daily cost (transaction fee * average number of payments) divided by the daily interest rate.

Daily cost = daily fee + annual fee/365

=0.05 × 39 + 7,610/365

=1.95 + 20.85

= $ 22.80

Interest rate = 3.81 %/365 = 0.01043835616

PV of cost = 22.80/0.01043835616%

=$218,425.20

The minimum days of average collection time to be reduced is when NPV is zero.

NPV = savings - PV of costs

0 = 140,985 × a - 218,425.20

a= 218,425.20/140,985

a = 1.549

a = 1.55

The average collection time be reduced at a minimum is 1.55 days.

The correct answer is option A i.e. 1.55 days

Cross verification :

With the reduction of 1.55 days in average collection time , the company will have positive NPV.

NPV = 140,985 × 1.55 - 218,425.20

=$(218,526.75 - 218,425.20)

=$101.55

The company will have positive NPV.