Question

Cow Chips, Inc., a large fertilizer distributor based in California, is planning to use a lockbox system to speed up collections from its customers located on the East Coast. A Philadelphia-area bank will provide this service for an annual fee of $14,000 paid at the end of the year plus 5 cents per transaction. The estimated reduction in collection and processing time is one day. Treasury bills are currently yielding 5 percent per year. If the average customer payment in this region is $5,300, how many customers are needed, on average, each day to make the system profitable for the company

Answer 1

The collections system requires annual fees of $14,000 and 5 cents ($0.05) per transaction. The estimated reduction in collection and processing time is 1 day.

The treasury bills currently yielding 5% per year. Thus, we will calculate the interest on customer payments for 1 day at 5% per year rate.

Let the number of customers be x.

Interest on customer payment for 1 day = 5,300 * x * 5% * 1/365

Interest on customer payment for 1 day = 0.7260x.

The collection service charges for 1 day are :-

Service charges per day = (14000/365) + 0.05*x

Service charges per day = 38.3562 + 0.05x.

(We convert the fixed annual payment of $ 14,000 into how much amount it is daily.)

We equate the cost and benefit from the new collection system to get the number of customer(x).

Interest on customer payment for 1 day = Service charges per day

0.7260x = 38.3562 + 0.05x

0.6760x = 38.3562

x = 56.74 customers per day

x = 20,709.22 customer per year

Thus, 56.74 customers are required daily to breakeven i.e, cost = benefit from the new collection system.

For the system to be profitable 57 customers are needed daily. i.e, 20710 customers in a year.