Question

2-6Hospital Patient Mix Study Appendix 2A. Hospitals measure their volume in terms of patient-days. We calculate patient- days by multiplying the number of patients by the nurhber of days that the patients are hospitalized. Suppose a large hospital has fixed costs of $54 million per year and variable costs of $600 per patient- day. Daily revenues vary among classes of patients. For simplicity, assume that there are two classes: (1) self-pay patients (S) who pay an average of $1,000 per day and (2) non-self-pay patients (G) who are the responsibility of insurance companies and government agencies and who pay an average of $800 per day. Twenty percent of the patients are self-pay, 1. Compute the break-even point in patient-days, assuming that the hospital maintains its planned mix of patients. 2. Suppose that the hospital achieves 225,000 patient-days but that 25% of the patient-days were self-pay (instead of 20%). Compute the net income. Compute the break-even point.

Answer 1

Solution :

FIxed Cost = $ 54,000,000

Variable Cost = $ 600 per patient day

Average revenue from patient = (20% * 1000) + (80%* 800) = $ 840 per patient day

Contribution per patient day = 840-600 = $ 240

PV Ratio = 240/840 * 100 = 28.57 %

Break even point ( in $) = Fixed Cost / PV Ratio

= $ 54,000,000 / 28.57%

= $ 189,000,000

Break even Point ( in patient days ) = $ 189 ,000,000 / $ 840

= 2,25,000 patient days

2. In case 25% are self and 75% are non self

Average revenue per day = (25% * 1000) + (75%* 800)    

= $ 850

  Contribution per patient day = 850-600 = $ 250

PV Ratio = 250/850 * 100 = 28.57 % =29.41%

Break even point ( in $) = Fixed Cost / PV Ratio

= $ 54,000,000 / 29.41%

= $ 183,600,000

  Break even Point ( in patient days ) = $ 183 ,600,000 / $ 850

= 216,000 patient days