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Correct Answer: $6,000
to determine the financial advantage of the bank's service offer, we need to calculate the net annual benefit. this involves understanding the value of having access to cash two days earlier than usual and subtracting the cost of the service.
first, we consider the daily cash receipts of the firm, which total $100,000. by reducing the collection time by two days, the firm essentially gains access to $100,000 x 2 days = $200,000 earlier than it would without the service. this early access to cash can be utilized for investments or to earn interest, thereby generating additional income for the firm.
since the money market rates are expected to average 6% per year, we need to find out how much income can be generated from the $200,000 if it were invested at this rate. however, since the rate is annual and our concern is with a benefit that affects just two days, we need to convert this annual rate into a daily rate. simplifying the calculation, we consider the 6% annual rate over 360 days (assuming each month has 30 days), which gives us approximately 0.0167% per day.
next, we calculate the additional income from having $200,000 for two more days at a daily rate of 0.0167%, which results in an approximate annual benefit of:
\[ 200,000 \times (0.0167\% \times 2) \approx $66.80 \]
however, this benefit accrues each time the two-day period occurs, which over one year (360 days / 2 days) happens about 180 times, thus:
\[ 180 \times $66.80 \approx $12,024 \]
now, we must consider the cost of the service. the bank charges $500 per month, which annually totals:
\[ 12 \times $500 = $6,000 \]
finally, to find the net annual benefit, we subtract the annual cost of the service from the annual additional income due to reduced collection time:
\[ $12,024 - $6,000 = $6,024 \]
this calculation shows an approximate net annual benefit of around $6,000 from accepting the bank's offer to reduce the cash receipt collection time by two days, assuming the simplifications made for daily interest calculations and other assumptions hold true. this demonstrates that the firm stands to gain financially from this service, even after accounting for the service fee.
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