If fixed costs are $20,000,000, variable cost per inpatient day are $450, average length of stay is 3.3 days, and volume is 8,000, what revenue per patient day must the hospital make in order to make a profit of $500,000?
To find the revenue per patient day that the hospital must make in order to make a profit of $500,000, we need to calculate the total cost and then add the desired profit.
First, let's calculate the total cost:
Fixed costs are given as $20,000,000.
Variable cost per inpatient day is $450.
Average length of stay is 3.3 days.
Volume is 8,000.
To find the total variable cost, we multiply the variable cost per inpatient day ($450) by the average length of stay (3.3 days):
Total Variable Cost = Variable Cost per Inpatient Day x Average Length of Stay
Total Variable Cost = $450 x 3.3
Total Variable Cost = $1,485
Next, let's calculate the total cost by summing up the fixed cost ($20,000,000) and the total variable cost ($1,485 per patient):
Total Cost = Fixed Costs + Total Variable Cost
Total Cost = $20,000,000 + ($1,485 x 8,000)
Total Cost = $20,000,000 + $11,880,000
Total Cost = $31,880,000
Now, let's calculate the revenue per patient day. To do that, we divide the total cost plus the desired profit ($31,880,000 + $500,000) by the total inpatient days (8,000 x 3.3):
Revenue per Patient Day = (Total Cost + Desired Profit) / (Volume x Average Length of Stay)
Revenue per Patient Day = ($31,880,000 + $500,000) / (8,000 x 3.3)
Revenue per Patient Day = $32,380,000 / 26,400
Revenue per Patient Day ≈ $1,227.27
Therefore, the hospital must make approximately $1,227.27 in revenue per patient day to make a profit of $500,000.