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 $7,000 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, and there are 365 days per year.

If the average customer payment in this region is $6,500, how many customers each day, on average, are needed to make the system profitable for Cow Chips? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Let number of customers needed per day be N.

At break even, NPV =0

Reduction in processing time = 1 day

Savings due to lockbox = $6,500*1*N

Variable transaction cost = 0.05*N

Daily interest rate = 1.05^(1/365) - 1 = 1.000133681 - 1 = 0.000133681

Fixed annual transaction cost = $7,000

NPV = 0 = ($6,500 * 1 * N) - [($0.05 * N) / 0.000133681] - [$7,000/0.05]

0 = $6,500N - [$0.05N / 0.000133681] - $140,000

$140,000 = $6,500N - 374.03N

$140,000 = $6,125.97N

N = $140,000 / $6,125.97 = 22.85 customers