Omega System Services, a member of the Omega Health Foundation operates a free-standing ambulatory care center that averages $60 in charges per patient. Variable costs are approximately $10 per patient, and fixed costs are about $1.2 million per year. Using this data, how many patients must be seen each day, assuming a 365-day operation, to reach the break- even point?
To determine the break-even point, we need to calculate the number of patients that must be seen each day to cover the fixed and variable costs.
First, let's calculate the total variable cost per patient:
Total Variable Cost = Variable Cost per Patient * Number of Patients
In this case, the variable cost per patient is $10.
Next, let's calculate the total fixed costs:
Total Fixed Cost = $1.2 million
To find the break-even point, we need to determine the total cost, which includes both variable and fixed costs:
Total Cost = Total Variable Cost + Total Fixed Cost
Now, since we already know the average charge per patient, we can express the total variable cost as a percentage of the total charges:
Total Variable Cost = (Variable Cost per Patient / Average Charge per Patient) * Total Charges
To find the break-even point, we need to set the total cost equal to the total charges:
Total Cost = Total Charges
Now, let's substitute the previous formulas and solve for the number of patients:
(Variable Cost per Patient / Average Charge per Patient) * Total Charges + Total Fixed Cost = Total Charges
Simplifying the equation, we get:
(Variable Cost per Patient / Average Charge per Patient) * Total Charges = Total Charges - Total Fixed Cost
Next, let's isolate the variable "Total Charges" by dividing through by the coefficient of the variable:
(Variable Cost per Patient / Average Charge per Patient) = (Total Charges - Total Fixed Cost) / Total Charges
Finally, we can solve for the total charges and use that to compute the number of patients:
Total Charges = Total Fixed Cost / (1 - (Variable Cost per Patient / Average Charge per Patient))
Number of Patients = Total Charges / 365
Let's plug in the given values:
Variable Cost per Patient = $10
Average Charge per Patient = $60
Total Fixed Cost = $1.2 million
Total Charges = $1.2 million / (1 - ($10 / $60)) = $1.2 million / (1 - 1/6) = $1.2 million / (5/6) = $1.2 million * (6/5) = $1.44 million
Number of Patients = $1.44 million / 365 = 3945.205
Therefore, approximately 3,946 patients must be seen each day to reach the break-even point.