Assume that a certain nursing home has two categories of payers. Medicaid pays $

Question

Assume that a certain nursing home has two categories of payers. Medicaid pays $60.00 per day and private pay patients pay the established per diem, but approximately 10 percent of private-pay charges are not collected. If 50 percent of the patients are Medicaid and 50 percent are private pay, what rate must be set to generate $150,000 in profit? Variable costs are $45.00 per day and fixed costs are expected to be $1,000,000. Expected volume is 50,000 patient days. Using this data and assuming that the nursing home charges $100 per day, what would be the nursing home’s required volume (inpatient days) in order to make $150,000 profit? Medicaid pays $60 per day

Explanation / Answer

Lets say x be the required patientdays

Revenue from Medicaid=60*x*50%=30x

Revenue from private patients=100*50%*(1-10%)*x=45x

Total revenue=45x+30x=75x

Total costs=x*45+1000000=1000000+45x

So, profit=revenue-cost=75x-45x-1000000

Given ,required profit=150000

So, 75x-45x-1000000=150000

So, 30x=1150000

hence, x=115000/3=38333.33

So, number of patientdays required=38334

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