Question

You serve 3,000 commercial patients and 1,000 hmo members. your fixed costs are $50,000, and your incremental cost is $50. you currently charge private-pay patients $75 and hmo members $60. which of the following statements is true?

A. this line of business is profitable.
B. profits would increase if you stopped serving hmo members.
C. you should stop serving hmo members if fixed costs increased to $60,000.
D. all of the above

Answer 1

The correct answer is that the line of business is profitable, with total revenues exceeding total costs, resulting in a profit of $35,000 after accounting for both fixed and incremental costs.

Step-by-step explanation:

The correct answer is option A: this line of business is profitable. To determine profitability, we must calculate total revenue and subtract both fixed and variable costs. The revenue generated from commercial patients is 3,000 patients × $75 = $225,000.

Revenue from HMO members is 1,000 members × $60 = $60,000. Thus, the total revenue equals $285,000. The total variable costs (incremental costs) are ($50 × 3,000) + ($50 × 1,000) = $200,000.

Subtracting the variable costs and the fixed costs of $50,000 from the total revenue yields a profit of $35,000. Options B and C are incorrect because they both suggest actions that would lead to a reduction in the number of patients and therefore a potential reduction in profits without providing enough information to quantitatively support those actions.

To determine whether a line of business is profitable, we can calculate the contribution margin. The contribution margin equals the selling price minus the variable costs.

For the commercial patients, the contribution margin is $75 - $50 = $25. For the HMO members, the contribution margin is $60 - $50 = $10. Since both contribution margins are positive, it indicates that the line of business is profitable.