Milwaukee Surgical Supplies, Inc., sells on terms of 3/10, net 30. Gross sales for the year are $1,200,000 and the collections department estimates that 30% of the customers pay on the tenth day and take discounts, 40% pay on the thirtieth day, and remaining 30% pay, on average, 40 days after the purchase. (Assume 360 days /year.)

1. Calculate the firm’s average collection period.

2. Calculate the firm’s current receivables balance.

3. Calculate the firm’s new receivables balance if Milwaukee Surgical toughened up on its collection policy, with the result that all non-discount customers paid on the 30th day.

4. Assuming the cost to the firm to carry receivables is 8% per annum, calculate the annual savings resulting from the toughened credit policy. (Assume the entire amount of receivables had to be financed.)

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To answer these questions, we need to follow a few steps.

1. Calculate the firm’s average collection period:
The average collection period is the average number of days it takes for customers to pay their bills. We can calculate this using the formula:

Average Collection Period = (Percentage of customers paying on the tenth day * Number of days for the discount)
+ (Percentage of customers paying on the thirtieth day * Number of days for the net 30 terms)
+ (Percentage of customers paying after 40 days * Number of days for payment after purchase)

In this case:
Percentage of customers paying on the tenth day = 30%
Number of days for the discount = 10 days
Percentage of customers paying on the thirtieth day = 40%
Number of days for the net 30 terms = 30 days
Percentage of customers paying after 40 days = 30%
Number of days for payment after purchase = 40 days

Substituting the values into the formula:
Average Collection Period = (30% * 10 days) + (40% * 30 days) + (30% * 40 days)
Average Collection Period = 3 days + 12 days + 12 days
Average Collection Period = 27 days

Therefore, the firm’s average collection period is 27 days.

2. Calculate the firm’s current receivables balance:
The receivables balance is the total amount of unpaid bills owed by customers. To calculate this, we can use the formula:

Receivables Balance = Gross Sales * (Percentage of customers paying on the thirtieth day + Percentage of customers paying after 40 days)

In this case:
Gross Sales = $1,200,000
Percentage of customers paying on the thirtieth day = 40%
Percentage of customers paying after 40 days = 30%

Substituting the values into the formula:
Receivables Balance = $1,200,000 * (40% + 30%)
Receivables Balance = $1,200,000 * 0.7
Receivables Balance = $840,000

Therefore, the firm’s current receivables balance is $840,000.

3. Calculate the firm’s new receivables balance if all non-discount customers paid on the 30th day:
In this scenario, all non-discount customers would pay on the thirtieth day. The formula to calculate the new receivables balance would be the same as in step 2, but with different percentages for the payment days:

Receivables Balance = Gross Sales * (Percentage of customers paying on the thirtieth day)

In this case:
Gross Sales = $1,200,000
Percentage of customers paying on the thirtieth day = 100%

Substituting the values into the formula:
Receivables Balance = $1,200,000 * 100%
Receivables Balance = $1,200,000

Therefore, the firm’s new receivables balance would be $1,200,000 if all non-discount customers paid on the 30th day.

4. Calculate the annual savings resulting from the toughened credit policy:
To calculate the annual savings, we need to compare the cost of financing the current receivables balance to the cost of financing the new receivables balance. The cost to the firm to carry receivables is given as 8% per annum. We can calculate the annual savings using the following formula:

Annual Savings = Current Receivables Balance * Cost to Carry Receivables
- New Receivables Balance * Cost to Carry Receivables

In this case:
Current Receivables Balance = $840,000
Cost to Carry Receivables = 8%
New Receivables Balance = $1,200,000

Substituting the values into the formula:
Annual Savings = $840,000 * 8% - $1,200,000 * 8%
Annual Savings = $67,200 - $96,000
Annual Savings = -$28,800

Therefore, the annual savings resulting from the toughened credit policy would be -$28,800 (negative value indicates a cost rather than savings).