Vidhyamath Forum

Case based question of function

Student Apozee

Student

Southwest Hospital has an operating room used only for eye surgery. The annual cost of rent, heat, and electricity for the operating room and its equipment is $360,000. The annual salaries of the people who staff this room total $540,000.

Each surgery performed requires the use of $760 worth of medical supplies and drugs. To promote goodwill, every patient receives a bouquet of flowers the day after surgery. In addition, one-quarter of the patients require dark glasses, which the hospital provides free of charge. It costs the hospital $30 for each bouquet and $40 for each pair of glasses.

The hospital receives a payment of $2,000 for each eye operation performed. The hospital currently averages 70 eye operations per month.

One of the nurses informed the board that she has recently learned about a machine that would reduce the per-patient amount of medical supplies needed

for each operation by $100. The machine can be leased annually for $100,000.

a. Identify the revenue per case and the annual fixed and variable costs for running the operating room.

b. How many eye operations must the hospital perform each year in order to break-even?

c. Advise the hospital on whether it should lease the machine.

24 Dec, 2023

Replies (4)

Vidhyamath Online

Instructor

Let's break down the revenue per case and the annual fixed and variable costs for running the operating room.

Revenue per Case:
- The hospital receives $2,000 for each eye operation performed.
- Since there are two eyes, the revenue per case is $2,000 x 2 = $4,000.
Annual Fixed Costs:
- Rent, heat, and electricity: $360,000
- Salaries of the staff: $540,000
- Total Annual Fixed Costs: $360,000 + $540,000 = $900,000
Variable Costs per Case:
- Medical supplies and drugs: $760
- Bouquet of flowers: $30
- Dark glasses (for 1/4 of the patients): $40 (assuming one pair per patient, so $40 x 1/4 = $10 on average per patient)
- Total Variable Costs per Case: $760 + $30 + $10 = $800

b. Break-even Analysis:

Break-even point is reached when total revenue equals total costs.
Total Costs = Total Fixed Costs + (Variable Cost per Case x Number of Cases)
Break-even Equation: $4, 000 � = 900, 000 + (800 �)$
Solving for x (number of cases), we get: $3, 200 � = 900, 000$
$� = \frac{900, 000}{3, 200}$
$� \approx 281.25$

The hospital must perform approximately 282 eye operations per year to break-even.

c. Lease Decision:

The machine reduces the per-patient amount of medical supplies by $100.
Annual leasing cost for the machine: $100,000
The reduction in variable cost per case with the machine: $100
Net savings per case with the machine: $100 (reduction in variable cost) - $100,000 (leasing cost) = -$99,900

Since the net savings per case is negative, leasing the machine would increase costs rather than save money. Therefore, the hospital should not lease the machine.

25 Dec, 2023

Harit Thakuri

Instructor

a. Revenue, Fixed, and Variable Costs:

Revenue per case: $2,000
Fixed costs:
- Rent, heat, and electricity: $360,000
- Salaries: $540,000
- Total fixed costs: $900,000
Variable costs per case:
- Medical supplies and drugs: $760
- Flowers: $30
- Glasses (for 25% of patients): $40 * 0.25 = $10
- Total variable costs per case: $760 + $30 + $10 = $800

b. Break-Even Point:

To calculate the break-even point, we need to find the number of surgeries where total revenue equals total costs.

Total cost equation: Total cost = Fixed costs + (Variable cost per case * Number of cases)
Total revenue equation: Total revenue = Revenue per case * Number of cases

Setting these equations equal and solving for the number of cases:

$900,000 + ($800 * Number of cases) = $2,000 * Number of cases $900,000 = $1,200 * Number of cases Number of cases = 750

Therefore, the hospital must perform 750 eye operations per year to break even.

c. Decision on Leasing the Machine:

New variable cost per case with the machine: $760 - $100 = $660
New total variable cost per case: $660 + $30 + $10 = $700
New break-even point:

$900,000 + ($700 * Number of cases) = $2,000 * Number of cases $900,000 = $1,300 * Number of cases Number of cases = 692.31 (approximately 692)

Additional fixed cost: $100,000 (lease cost)
New total fixed costs: $900,000 + $100,000 = $1,000,000
New break-even point:

$1,000,000 + ($700 * Number of cases) = $2,000 * Number of cases $1,000,000 = $1,300 * Number of cases Number of cases = 769.23 (approximately 769)

Analysis:

Currently, the hospital performs 70 eye operations per month, or 840 per year, which is above the current break-even point of 750 surgeries.
Leasing the machine would reduce variable costs, but it would also increase fixed costs, resulting in a slightly higher break-even point (769 surgeries).
Since the hospital performs more surgeries than the new break-even point, leasing the machine would be beneficial, as it would reduce variable costs and potentially increase profits.

Recommendation:

The hospital should lease the machine. It will reduce variable costs and increase the hospital's profitability.

19 Dec, 2024

Harit Thakuri

Instructor

PLEASE CORRECT

Without the machine the hospital breaks even at 750 operations per year. With the macine the break even point increases to 769 operations per year.

Recommendation:

The hospital should not lease the machine. It will reduce variable costs and decreases the hospital's profitability.

19 Dec, 2024

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Case based question of function

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Replies (4)

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