Cow Chips Inc. can install a lockbox system to speed up collections by two days for an annual fee of $17,000 plus 21 cents per transaction. The average customer payment is $11,480. Treasury bills are currently yielding 3.5 percent per year. Assume a year has 365 days. Approximately how many customers each day, on average, are needed to make this installation profitable for Cow Chips?

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To determine the profitability of the lockbox system, we calculate the daily benefit of speeding up collections by two days. The daily interest rate is $3.5\% / 365 = 0.009589\%$. The daily benefit per $11,480 payment is $11,480 \times 0.00009589 = 1.1006$. To cover the annual fee of $17,000 with this daily benefit, we need $17,000 / (1.1006 \times 2) = 7,723.91$ annually, or approximately $7,723.91 / 365 = 21.16$ daily. However, this calculation does not account for the 21 cents per transaction cost. To find the break-even point including the transaction cost, we set up the equation for annual savings equal to the annual cost:$$365 \times n \times (1.1006 + 0.21) = 17,000$$Solving for $n$ gives the average number of customers needed daily. The correct calculation should factor in both the daily benefit from the interest savings and the per transaction cost, aiming to find the number of transactions that equal the annual cost of the system. The provided calculation and choice do not directly align with the correct methodology, which involves calculating the net benefit per transaction (including the transaction cost) and comparing it to the annual cost to find the break-even number of daily transactions. The correct approach should calculate the daily transactions needed to offset both the fixed annual fee and the variable cost per transaction, using the interest savings per day per transaction as the basis for comparison.