Question

SHOW WORK

A healthcare provider offers a single service to its patients, and the patients are covered by only two different third parties. Payer 1, Medicare, represents 45% of the patients and pays a fixed fee of $115 per patient. Payer 2, a Commercial Insurer, represents 50% of the patients and pays 70% of the provider's gross charge. The remaining patients are Charity Care patients who do not pay for their services. The provider treats 7,000 patients per month. The fixed costs of the provider each month is $475,000, and their variable cost per patient is $50. The provider desires to set its gross charge per patient to achieve a profit, or net income, of $80,000 for the month.

a. Set up an Algebraic expression, with "p" being the gross charge (price) of the service to each patient being seen in the month, to solve this problem. Show this expression on your spreadsheet.

b. Solve the problem finding the Gross Price to be charged to achieve the profit target.

c. How many charity patients does the organization treat per month? d. What is the grand total sum of payments that the Commercial Insurer pays for all its patients in a month? (Note, this is not the total for one patient, but instead it is the total for all their patients together in the month).

Answer 1

Let's first state and analyze the given data before delving into the questions.

Total Number of patients treated are 7,000 per month. However for the purpose of forming the algebraic equation, we will assume the number of patients to be equal to 'x' patients. Thus number of patients(n) = x

Fixed Cost per month (FC) = $475,000

Variable Cost per patient (VC) = $50

Profit (S) = $ 80,000

Let the gross charge(p) charged by the healthcare provider by $ p

Medicare patients

Total number of patients covered by medicare (n_m) = 45% of n = 45% * x = 0.45x patients

Fee paid per patient = (f_m) = $115

Commercial Insurer Patients

Total number of patients covered by commercial insurer (n_i) = 50% of n = 50% * x = 0.50x patients

Fee paid per patient (f_i) = 70% of Gross Charge (p) = 70/100 * p = 0.7p

Charity Care Patients

Total number of patients covered by charity care (n_c) = x - n_{m -} n_i = x - 0.45x - 0.5x = 0.05x patients

Fee paid per patient (f_c) = $ 0

Now let us answer the question :

a. We know that :

Revenues - Cost = Profit

Thus in case of the healthcare provider it would be :

Revenues from Medicare patients + Revenue from commercial insurer patient + Revenue from charity care patients - Fixed Cost - Total Variable Cost = Profit Expected

=> (n_m*f_{m) +} (n_i*f_{i) +} (n_c*f_c) - FC - (VC*n) = S

=> (0.45x * 115) + (0.5x * 0.7p) + (0.05x * 0) - 475,000 - (50 * x) = 80,000

=> 51.75x + 0.35px + 0 - 475000 - 50x = 80,000

=> 1.75 x + 0.35px - 475000 - 80,000 = 0

=> 1.75x + 0.35px - 5,55,000 = 0

This is the algebraic equation.

b. We know that the number of patients treated is 7000 per month. Substituing this to the equation evaluated in (a) we can get the value of gross charge (p).

Equation :

1.75x + 0.35px - 5,55,000= 0

=> 1.75 * 7000 + 0.35 * p * 7000 - 5,55,000 = 0

=> 12,250 + 2450p - 5,55,000 = 0

=> 2450p - 542,750 = 0

=> 2450p = 542,750

=> p = 542,750 / 2450

=> p = $ 221.53 (approx)

c. We have determined be the number of charity patients is 0.05x.

Substituting 'x' as 7000 patients, we get:

Number of charity patients treated = 0.05 * 7000 = 350 patients

d. Total number of commercial insurer patients( n_i) = 0.5x = 0.5 * 7000 = 3500 patient

Fee per patient paid by commercial insurer (f_i ) = 0.7p = 0.7 * 221.53 = $ 155.07 (approx)

Total sum of payments made by Commercial insurer = n_i * f_i

= 3500 * 155.07

= $ 542,745