Assume that the managers of fort winston hospital are setting the price on a new outpatient service. here are the relevant data estimates:

variable cost per visit: $5

annual direct fixed costs: $500,000

annual overhead allocation: $50,000

expected annual utilization: 10,000 visits

a.) what per visit price must be set for the service to break even? to earn an annual profit of $100,000?

b.) repeat part a, but assume that the variable cost per visit is $10.

c.) return to the data given in the problem. again repeat part a, but assume that the direct fixed costs are $1,000,000.

d.) repeat part a assuming both a $10 variable cost and $1,000,000 in direct fixed costs.

(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) = 1,000,000 + 50,000

10,000x - 100,000 = 1,050,000

x = $115

To earn desired profit of $100,000

Total contribution = Total fixed cost + desired profit

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

x = $125

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