Dr. Huckvale, of and Huckvale & Associates, LLP, is examining how overhead costs behave as a function of monthly physician contact hours billed to patients. The historical data are as follows:
Total Overhead Costs Physician Contact Hours Billed to Patients
$92,000 170
112,000 220
113,000 270
127,000 270
139,000 370
152,000 420
Compute the linear cost function, relating total overhead costs to physician contact hours, using the representative observations of 220 and 270 hours. Plot the linear cost function. Does the constant component of the cost function represent the fixed overhead costs of Huckvale and Associates? Why? What would be the predicted total overhead costs for 170 hours and 420 hours using the cost function estimated in requirement 1? Plot the predicted costs and actual costs for 170 and 420 hours. Dr. Huckvale had a chance to do some school physicals that would have boosted physician contact hours billed to patients from 220 to 270 hours. Suppose Dr. Huckvale, guided by the linear cost function, rejected this job because it would have brought a total increase in contribution margin of $10,000, before deducting the predicted increase in total overhead cost, $15,000. What is the total contribution margin actually forgone?
Dr. Huckvale of Huckvale & Associates, LLP is conducting an analysis to understand how overhead costs are related to monthly physician contact hours billed to patients. This examination is essential for making informed decisions regarding cost management and resource allocation. The goal is to establish a linear cost function that connects total overhead costs with physician contact hours, assess the significance of the fixed overhead costs, predict overhead costs for specific contact hours, and evaluate a decision made by Dr. Huckvale.
To establish a linear cost function, we’ll use the representative observations of 220 and 270 hours. These two data points are (220, $112,000) and (270, $113,000), where the physician contact hours are the independent variable (x) and the total overhead costs are the dependent variable (y). We can use these data points to compute the slope (variable cost per hour) and intercept (fixed cost component) of the linear cost function.
The linear cost function can be represented as follows: y = mx + b where: y represents total overhead costs, x represents physician contact hours, m is the slope (variable cost per hour), and b is the intercept (fixed cost component).
Using the two data points, we can calculate the values of m and b. Substituting these values into the equation, we can formulate the linear cost function relating total overhead costs to physician contact hours.
The constant component of the cost function (b) represents the fixed overhead costs of Huckvale & Associates. Fixed overhead costs are those costs that do not vary with changes in the level of activity, in this case, physician contact hours. These costs include items like rent, insurance, and salaries of permanent staff. The fixed cost component remains constant within the relevant range of activity. Therefore, it’s a significant factor to consider when planning and budgeting.
With the linear cost function established, we can predict total overhead costs for both 170 hours and 420 hours of physician contact. By substituting these values into the cost function, we can calculate the estimated overhead costs for these scenarios.
Suppose Dr. Huckvale rejected a job opportunity that would have increased physician contact hours from 220 to 270. According to the linear cost function, this job would bring a total increase in contribution margin of $10,000. However, the predicted increase in total overhead cost for this change was $15,000. Therefore, Dr. Huckvale made a decision based on a predicted net loss of $5,000.
The total contribution margin forgone by Dr. Huckvale can be calculated by subtracting the predicted net loss from the initial increase in contribution margin. In this case, it would be $10,000 – $5,000 = $5,000.
The analysis of overhead costs and physician contact hours for Huckvale & Associates, LLP has provided insights into the relationship between these variables. The establishment of a linear cost function helps in predicting and understanding cost behavior, while the fixed cost component represents the unchanging overhead costs.
Dr. Huckvale’s decision to reject a job opportunity based on the linear cost function demonstrates a commitment to effective cost management. The decision, guided by predicted outcomes, led to a calculated forgone contribution margin of $5,000, which serves as a practical example of cost-benefit analysis in action.
Understanding the cost structure and its implications can aid in making informed decisions and optimizing resources for Huckvale & Associates, ultimately contributing to the financial health and success of the practice.
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