Question

A hospital has an operating room used only for eye surgery. The annual cost of heat, rent, and electricity for the operating room and its equipment is $360,000 and the annual salaries for the people who staff this room total $540,000. Each surgery performed requires the use of $760 worth of medical supplies and drugs. Every patient receives a $30 bouquet of flowers the day after surgery. Also, one-third of the patients receive a $30 pair of dark glasses. 1a. Identify the annual fixed and variable costs for running the operating room. FC= $360,000 + $540,000 = 900,000 VC=760x + 30x + 1/3*x*30= 760x + 30x + 10x = 800x Let x be the number of patients having eye surgery in a year. Write the cost as a function of x : C(x)=900,000 + 800x 2a. The hospital receives $2,000 for each eye operation performed. Write the revenue function, in terms of the same variable x: R(x)= 2,000x 2b. Write the annual profit function for this hospital, in terms of the same variable x: P(x)= 2,000x - 800x - 900,000 = 1200x - 900,000 3. How many eye operations must the hospital perform each year in order to break even? Justify your answer! x = $900,000 / ($2,000 - $800) = $900,000 / $1,200 = 750 750 eye surgeries should be performed each year to break even. Contribution per unit = Revenue - Variable costs = $2,000 - 800 = $1,200 per unit Total Contribution from 750 units = $1,200 x 750 = $900,000 which is equal to the Annual Fixed Costs Fixed cost = Profit = $0, which is a break-even situation 4. Currently, the hospital averages 70 eye operations per month. There is a medical machine that would reduce the amount of medical supplies needed by $100 per patient; it can be leased for $100,000 annually. Keeping in mind the financial costs and benefits, advise the hospital on whether it should lease this machine. Justify completely your answer! The hospital currently averages 70 eye operations per month. The average eye operations per year = 70 x 12 months = 840 The medical machine would reduce the amount of medical supplies needed by $100 per patient, so the average of 840 patients per year, the savings in medical supplies would be = $100 per patient x 840 patients = $84,000 per year The annual cost of leasing the medical machine = $100,000 Hence, the benefit in terms of annual savings in amount of medical supplies needed of $84,000 would be less than the annual cost of leasing the machine of $100,000. I advise the hospital not to lease this machine 5. An advertising agency has proposed to the hospital administration that $30,000 per year be spent on advertising to persuade people to use the hospital. The agency estimates that this advertising would increase the business by 10 patients per month. If they are correct and if this increase is not big enough to affect variable costs or any other of the financial parameters, what impact would this advertising have on the hospital’s profits? (Hint: Compare the yearly profit without advertising with the profit using advertising.) 6. In case the advertising agency is overly optimistic, how many extra patients per year are needed to cover the cost of the proposed ads? Justify your answer! (Hint: Find the new break-even point given the additional cost of advertising and use the original break-even answer from part 3 to calculate the extra patients needed.) 7. If the ad campaign is approved and subsequently meets its projections, should the hospital purchase the machine mentioned earlier? Justify your answer! (Hint: Find a new profit function which includes advertising and the machine’s cost. Compare profits without the machine and with advertising with the profits with the machine and advertising.)

I need help with 5,6,7 since 1-4 are done Thank You

Answer 1

5. An advertising agency has proposed to the hospital administration that $30,000 per year be spent on advertising to persuade people to use the hospital. The agency estimates that this advertising would increase the business by 10 patients per month. If they are correct and if this increase is not big enough to affect variable costs or any other of the financial parameters, what impact would this advertising have on the hospital’s profits? (Hint: Compare the yearly profit without advertising with the profit using advertising.)

Solution:- The problem can be solved using marginal costing concept. By comparing the additional cost with the additional revenue, one can determine the viability of the advertising expense.

Assuming 10 patients add per month, Then additional profit= 10 X 12 month X 1200= $ 144,000

Additional Cost for advertisement= $30,000

Since the additional revenue is more than the additional cost, one must definitely go for advertising. However if there is no increase in the number of patients as such, the hospitals overall profit will reduce by $30,000/-

Note- Since fixed cost is already constant, while calculating marginal increment, fixed cost factor is not considered.

6. In case the advertising agency is overly optimistic, how many extra patients per year are needed to cover the cost of the proposed ads? Justify your answer! (Hint: Find the new break-even point given the additional cost of advertising and use the original break-even answer from part 3 to calculate the extra patients needed.)

Solution:-Extra patients required to cover the cost of $30,000 will be,

No of patients= Additional cost/ Contribution per patient= $30,000/1200= 25 patients per year.

7. If the ad campaign is approved and subsequently meets its projections, should the hospital purchase the machine mentioned earlier? Justify your answer! (Hint: Find a new profit function which includes advertising and the machine’s cost. Compare profits without the machine and with advertising with the profits with the machine and advertising.)

Solution:-Evaluating the purchase of machinery option after increment of 10 patients per month.

The hospital will have 70+10=80 eye operations per month.

The average eye operations per year = 80 x 12 months = 960

The medical machine would reduce the amount of medical supplies needed by $100 per patient, so the average of 840 patients per year, the savings in medical supplies would be = $100 per patient x 960 patients = $96,000 per year The annual cost of leasing the medical machine = $100,000

Thus still the machine won’t be able to recover its whole cost and thus the hospital should not lease the machinery.