Question

Assume the managers of the Fort Winton Hospital are setting the price on a new outpatient service. Here are the relevant data estimates:

Variable cost per visit $5.000

Annual direct fixed costs $500,000

Annual overhead allocation $50,000

Expected Annual utilization 10,000 visits           

1.What per-visit price must be set for the service to break-even? To earn an annual profit of $100,000?

2.Repeat part a, but assume that the variable cost per visit is $10.

3.Return to the data given in the problem. Again, repeat part a, but assume that direct fixed costs are $1,000,000.

4. Repeat part a assuming both a $10 variable cost and $2,000,000 in direct fixed costs

Answer 1

a. Let per visit price for the service to break even be x

At break even point ,

Total contribution=Total fixed cost

10,000(x-5) =500,000+50,000

10,000x-50,000=550,000

x=$60

To earn desired profit of $100,000

Total contribution=Total fixed cost + desired profit

10,000(x-5) =500,000+50,000+100,000

x=$70

b)

At break even point ,

Total contribution=Total fixed cost

10,000(x-10) =500,000+50,000

10,000x-100,000=550,000

x=$65

To earn desired profit of $100,000

Total contribution=Total fixed cost + desired profit

10,000(x-10) =500,000+50,000+100,000

x=$75

c)

At break even point ,

Total contribution=Total fixed cost

10,000(x-5) =1,000,000+50,000

10,000x-50,000=1,050,000

x=$110

To earn desired profit of $100,000

Total contribution=Total fixed cost + desired profit

10,000(x-5) =1,000,000+50,000+100,000

x=$120

d)

Total contribution=Total fixed cost

10,000(x-10) =2,000,000+50,000

10,000x-100,000=2,050,000

x=$215

To earn desired profit of $100,000

Total contribution=Total fixed cost + desired profit

10,000(x-10) =2,000,000+50,000+100,000

x=$225