Question

Delaware Medical Center operates a general hospital. The medical center also rents space and beds to separately owned entities rendering specialized services, such as Pediatrics and Psychiatric Care. Delaware charges each separate entity for common services, such as patients’ meals and laundry, and for administrative services, such as billings and collections. Space and bed rentals are fixed charges for the year, based on bed capacity rented to each entity. Delaware Medical Center charged the following costs to Pediatrics for the year ended June 30, 20x1:

	Patient Days (variable)			Bed Capacity (fixed)
Dietary	$	550,000			—
Janitorial		—		$	78,000
Laundry		250,000			—
Laboratory		410,000			—
Pharmacy		350,000			—
Repairs and maintenance		—			31,000
General and administrative		—			1,400,000
Rent		—			1,530,000
Billings and collections		260,000			—
Total	$	1,820,000		$	3,039,000

During the year ended June 30, 20x5, Pediatrics charged each patient an average of $400 per day, had a capacity of 70 beds, and had revenue of $3 million for 365 days. In addition, Pediatrics directly employed personnel with the following annual salary costs per employee: supervising nurses, $26,000; nurses, $20,900; and aides, $8,600.

Delaware Medical Center has the following minimum departmental personnel requirements, based on total annual patient days:

Annual Patient Days	Aides		Nurses		Supervising Nurses
Up to 22,000	20		10		4
22,001 to 26,000	25		14		5
26,001 to 29,200	31		16		5

Pediatrics always employs only the minimum number of required personnel. Salaries of supervising nurses, nurses, and aides are therefore fixed within ranges of annual patient days.

Pediatrics operated at 100 percent capacity on 85 days during the year ended June 30, 20x1. Administrators estimate that on these 85 days, Pediatrics could have filled another 10 beds above capacity. Delaware Medical Center has an additional 10 beds available for rent for the year ending June 30, 20x2. Such additional rental would increase Pediatrics’ fixed charges based on bed capacity. (In the following requirements, ignore income taxes.)

Required:

Calculate the minimum number of patient days required for Pediatrics to break even for the year ending June 30, 20x2, if the additional 10 beds are not rented. Patient demand is unknown, but assume that revenue per patient day, cost per patient day, cost per bed, and salary rates will remain the same as for the year ended June 30, 20x1.

Answer 1

The break-even point is calculated as follows:

TOTAL FIXED COST
Medical center charges	3039000
supervising nurses (26000*4)	104000
Nurses (20900*10)	209000
Aids (8600*20)	172000
Total fixed cost	$ 3524000

contribution margin per day :
Revenue per patient day	$400
variable cost per patient day: (total revenue / revenue per patient days =$3000000/$400=7500 patient days) (total variable cost / patient days = $1820000/ 7500)	$243
Contribution margin per patient day	$ 157

Break even point in patient days = total fixed cost / contribution margin per patient day

= $3524000 / 157

= 22446 patient days