Question

1. Suppose a hospital unit wants to offer a new service. The service has a fixed cost of $200,000. The service has three DRGs. The number of patients for a specific DRG, their average variable costs per unit, and their average price per unit are given in the table below.

	No. of Patients	Variable cost Rate $	Price Rate $
DRG1	200	300	450
DRG2	400	1200	1500
DRG3	350	900	1150

            

1. Find the break-even volume.
2. What is the assumption here about the product-mix, going forward into the future?
3. At the break-even volume, compute the expected volumes for individual DRGs.

Answer 1

a) First we will calculate product mix

Weight of a DRG = Percentage of patients with a DRG = No of patients with a DRG / total patients

Total patients = Sum of patients all DRGs = 200 + 400 + 350 = 950

WE get the following product mix

Weight of DRG1 = No of patients with DRG1 / Total patients = 200 / 950 = 21.05%

Weight of DRG2 = No of patients with DRG2 / Total patients = 400 / 950 = 42.11%

Weight of DRG3 = No of patients with DRG3 / Total patients = 350 / 950 = 36.84%

Contribution margin for DRG1 = Price per unit for DRG1 - Variable Cost per unit for DRG1 = 450 - 300 = 150

Contribution margin for DRG2 = Price per unit for DRG2 - Variable Cost per unit for DRG2 = 1500 - 1200 = 300

Contribution margin for DRG3 = Price per unit for DRG3 - Variable Cost per unit for DRG3 = 1150 - 900 = 250

Weighted Average contribution margin = Weight of DRG1 x Contribution margin for DRG1 + Weight of DRG2 x Contribution margin for DRG2 + Weight of DRG3 x Contribution margin for DRG3 = 21.05% x 150 + 42.11 x 300 + 36.84% x 250 = 31.575 + 126.33 + 92.10 = 250.005 = 250.00 (rounded to two decimal places)

Breakeven Volume = Fixed Cost / Weighted average contribution margin = 200000 / 250 = 800 patients

b. Assumption about the product mix:

The product mix of three DRG's will remain constant in near future irrespective of the volume or total number of patients. It implies that percentage of patients with each DRG or weight of each DRG will remain constant. DRG1, DRG2 and DRG3 will have 21.05%,42.11% and 36.84% of total patients respectively in future at the all levels of volume.

c. Expected volume of DRG1 = Weight of DRG1 x Breakeven volume = 21.05% x 800 = 168.40 = 168 (rounded to nearest whole number)

Expected volume of DRG2 = Weight of DRG2 x Breakeven volume = 42.11% x 800 = 336.88 = 337 (rounded to nearest whole number)

Expected volume of DRG3 = Weight of DRG3 x Breakeven volume = 36.84% x 800 = 294.72 = 295 (rounded to nearest whole number)