Cost-Volume-Profit Analysis for a Hospital

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.

The Pediatrics Departments activity/capacity is measured by patient days. If a patient occupies a bed for 1 day, it has 1 patent day. In case a patient occupies a bed for 30 days, it will be 30 patient days. Also, if each of 5 patents occupies a bed for 20 days, patient days will be 100.

Pediatrics has 60 rented beds. Assume that one year is 365 days throughout the case. Therefore, Pediatrics maximum capacity (capacity of fully utilizing all beds 100%) is 21,900 patient days (365 days*60 beds).

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 Year 1:

Variable (varying with patient Days) Dietary Laundry Laboratory Pharmacy Billings/collections Total

$600,000 300,000 450,000 350,000 300,000 $2,000,000

Fixed (relating to bed capacity) Janitorial Repairs and maintenance General and administrative Rent Total

$70,000 30,000 1,300,000 1,500,000 $2,900,000

During Year 1, Pediatrics charged $300 per patient day and had 20,000 patient days. Therefore, it had revenue of $6,000,000. In addition, Pediatrics directly employed personnel with the following annual salary costs per employee: supervising nurses, $25,000; nurses, $20,000; and aides, $9,000.

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

Annual Patient Days Up to 22,000 22,001 to 26,000

Aides 20 25

Nurses 10 14

Supervising Nurses 4 5

Total Salaries $480,000 $630,000

Salaries of supervising nurses, nurses, and aides are therefore step-fixed within ranges of annual patient days.

For Years 2 and 3, the Pediatrics Department assumes that revenue per patient day, variable cost per patient day, cost per bed, and salary rates will remain the same as those for Year 1.

In Year 2, Pediatrics will keep renting 60 beds. The department estimates that it will have 18,500 patient days for Year 2. In one of the meetings, the Department Head mentioned that Pediatrics hoped to generate an operating income of $500,000 for Year 2.

For Year 3, the Department will be able to exercise an option of increasing its capacity (currently, 21,900) by 2,400 extra patient days at a cost of $800,000.

Requirements:

To aid in the Departments profit planning for Years 2 and 3, you have been hired as a consultant by the Pediatrics Department. You are to prepare a report in the form of a memorandum to the Department that includes (but is not limited to) each of the following:

1. A pro-forma (budgeted) contribution format income statement for Year 2, in good form, which reflects the companys best estimates of operating results.

The income statement should be detailed enough to include all individual cost items.

- Treat bed capacity-related costs and salaries as fixed costs.

2. Computation of each of the following items for Pediatrics regarding Year 2.
   1. break-even point in terms of number of patient day
   2. break-even point in terms of revenue dollars
   3. safety margin
   4. operating leverage factor
   5. the number of patient days required to earn the target operating income
   6. Will Pediatrics be able to achieve the operating income level the Department Head hopes?

3. Income prospect for Year 3

The Department recognizes that the estimates/assumptions, particularly those regarding the number of patient days are subject change, given a great deal of uncertainty in operating environment. The uncertainty stemmed from the recent opening of another hospital in the area and also from an accelerated influx of people into the area. Ever-increasing costs of medical equipment, hiring nurses, medical supplies, etc. also have caused an upheaval in the medical service industry.

The operating environment becomes more chaotic each passing year. The Department is divided in opinion in estimating patient days for Year 3. One group has predicted that the number of patient days will change (increase or decrease) by 15% from the Year 2 estimate of 18,500. However, another group thinks that the change will be 25% (increase or decrease) from 18,500.

Note two things. (1) As shown above, salaries for employees are a step-fixed cost with respect to patient days; and (2) As stated at the beginning, currently Pediatrics maximum capacity is 21,900 patient days. The Department can obtain 2,400 additional patient days at a cost of $800,000 (this amount is additional Rent required to make the maximum capacity 24,300). The 2,400 additional days may require additional Salaries (figure out the amount by yourself). Assume that if the Department wishes to obtain additional patient days, it has to obtain exactly 2,400 additional patient days.

Answer for percent change in Pediatrics income from Year 2 to Year 3.

You may want to convert the percent increase in patient days below into the number of additional

patient days. Then, think hard and be very careful.

1. If patient days increase by 15%, operating income will increase/decrease by ___%.
2. If patient days increase by 25%, operating income will increase/decrease by ___%.

4. Right Decision

Assume that Year 3s expected demand is 23,125 patient days. However, the department can use its discretion to determine to what extent it will meet the demand. Without hurting its well-established reputation, it will be able to choose to provide any number of patient days between 18,500 (Expected demand in Year 2) and 23,125 (Expected demand in Year 3). This is possible by transferring or referring patients to other physicians/hospitals.

Note two things again. (1) As shown above, salaries for employees are a step-fixed cost with respect to patient days; and (2) As stated earlier, currently Pediatrics maximum capacity is 21,900 patient days. The Department can obtain additional 2,400 patient days at a cost of $800,000. (this amount is additional Rent required to make the maximum capacity 24,300). The 2,400 additional days may require additional Salaries (check out by yourself).

At this time, the department is to determine how many more patient days of service it will provide in Year 3 compared to Year 2s estimated demand of 18,500. An early decision is needed to make arrangements for personnel, equipments, supply procurements, and facilities in a timely manner.

1. Which of the following actions (in patient days) is the best in maximizing profit?

(i) 3,400 more patient days (increase from 18,500 to 21,900)

(ii) 3,500 more patient days (increase from 18,500 to 22,000)

(iii) 4,625 more patient days (increase from 18,500 to 23,125)

2. What makes your choice in (a) the right answer? Without resorting to computations, provide a reason intuitively.

5. Ex-Post Review

Pediatrics operated at 100 percent capacity on 90 days in a row during Year 1. Administrators estimate that in this 90-day period, Pediatrics could have taken more patients. Delaware Medical Center had an additional 20 beds available for rent for Year 1. If Pediatrics had rented another 20 beds, it would have filled these extra beds 100% for the 90 days. Such additional rental would increase Pediatrics Bed capacity-related fixed costs by $700,000.

In addition to planning for upcoming year, Pediatrics is also conducting an ex-post review.

In Year 1, the department decided not to rent 20 additional beds. Was that the right decision? If it had rented the beds, by how much Pediatrics would have been better-off or worse-off?

Use an incremental analysis to figure out income change in order to answer.

Note: Only need help on #3,4,5. I already got #1,2.