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 $15,000 paid at the end of the year plus 10 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 $5,200, 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.)

To determine the number of customers needed each day to make the lockbox system profitable for Cow Chips, Inc., we need to calculate the daily interest savings from the reduced collection and processing time and then see how many transactions are required to cover the cost of the service.

First, we calculate the daily interest rate from the annual yield of Treasury bills:

Daily interest rate = Annual interest rate / Number of days in a year

= 0.05 / 365

= 0.0001369863

Next, we determine the daily interest savings per payment by multiplying the daily interest rate by the average customer payment:

Interest savings per payment = Daily interest rate * Average customer payment

= 0.0001369863 * $5,200

= $0.712

To cover the annual fee of the lockbox system, Cow Chips needs to save at least $15,000 in interest per year. To find the breakeven point of daily transactions, we would need to cover both the annual fee and the cost per transaction.

We also need to account for the cost per transaction (10 cents) when calculating the net saving per transaction:

Net saving per transaction = Interest savings per payment - Transaction fee 

= $0.712 - $0.10 

= $0.612

Now we will determine the number of transactions needed per day to cover the annual fee. Let's call this number "X."

Annual net savings = X * Net saving per transaction * 365

To break even, the annual net savings should be equal to the annual fee:

X * $0.612 * 365 

= $15,000

Now we solve for X:

X = $15,000 / ($0.612 * 365) 

X = $15,000 / $223.38

 X = 67.13

Therefore, Cow Chips would need approximately 67.13 customers each day, on average, to make the lockbox system profitable. Since we cannot have a fraction of a customer, we would typically round up to the next whole number. Cow Chips would need 68 customers each day, on average, to make the system profitable.