Question

St. Mark’s Hospital contains 480 beds. The occupancy rate varies between 60% and 90% per month, but the average occupancy rate is generally 80%. In other words, on average, 80% of the hospital’s beds are occupied by patients. At this level of occupancy, the hospital’s operating costs are $35 per occupied bed per day, assuming a 30-day month. This $35 figure contains both variable and fixed cost elements. This average cost figure drops to $32 when the occupancy rate is 90% (typically during the months of July and August).

During June, the hospital’s occupancy rate was only 60% and a total of $384,000 in operating costs was incurred during the month.

Required:

1-a. Using the high-low method, estimate the variable cost per occupied bed on a daily basis. (Round your answer to 3 decimal places.)

1-b. Using the high-low method, estimate the total fixed operating costs per month. (Do not round intermediate calculations.)

1-c. Assume an occupancy rate of 70% per month. What amount of total operating cost would you expect the hospital to incur? (Do not round intermediate calculations. Round your answer to the nearest whole dollar amount.)

Answer 1

Beds at High level of activity (90%) = 480*90% =	432
Total operating cost at high level of activity = Beds High level of activity * Average rate per bed per day * days in a month = 432 * 32 * 30 =	414720
Beds at Low level of activity (60%) = 480*60% =	288
Total operating cost at low level of activity	384000

	Number of Beds	Total operating cost
High level of activity	432	414720
(-) Low level of activity	288	384000
Difference	144	30720

1-a.
Variable cost per bed per day = ( Difference in total operating cost / Difference in number of beds ) / Days in a month = ( 30720 / 144 ) / 30 =	7.111	per bed per day

1-b.
Let us calculate the fixed cost from the data of high level of activity
Total operating cost = Total fixed operating cost + ( Number of beds * Days in a month * Variable cost per bed per day )
414720 = Total fixed operating cost + ( 432 * 30 * 7.111 )
414720 = Total fixed operating cost + 92159
Total fixed operating cost = 414720 - 92159 =	322561

1-c.
Beds at 70% activity = 480*70% =	336
Total operating cost at 70% = Total fixed operating cost + ( Number of beds * Days in a month * Variable cost per bed per day )
Total operating cost at 70% = 322561 + ( 336 * 30 * 7.111 ) =	394240