Question

Part 1)

Assume that XYZ lab has the following cost structure:

Fixed Costs = $450,000

Variable cost per test = $20

Charge per procedure = $100

1. What volume is required to break even?
2. What volume is required to generate a profit of $300,000?

Part II)

1. Using the data in Part I above, assume that Aetna proposes a 25% discount from charges, what volume would then be required to break even? Hint: Discount the charge per test before entering it into the formula.
2. Given the 25% discount from each charge per test, and a new variable cost per test which is $25, what volume would then be required to generate a profit of $300,000. Hint: Use the previously discounted charge per test to input into the formula.

Part III)

XYZ lab is planning to offer a unique test with an estimated volume of 20,000 tests per year.

1. Given the following additional data, what price should be set to obtain the $200,000 in profits?

Fixed Costs = $450,000

Variable cost per test = $20

Answer 1

Solution a
	Sale revenue	$                                              100.00
	Variable cost	$                                                20.00
	Contribution per bag (Sale less variable cost)	$                                                80.00
	Fixed cost	$                                            450,000
	Break-even point=	Fixed cost/contribution per bag
	Break-even point=	=450000/80
	Break-even point=	5625	Units
Solution b
	Sale revenue	$                                              100.00
	Variable cost	$                                                20.00
	Contribution per bag (Sale less variable cost)	$                                                80.00
	Fixed cost	$                                            450,000
	Profit	$                                            300,000
	Total	$                                            750,000
	Sale required=	(Fixed cost+Profit)/contribution per bag
	Sale required=	=(450000+300000)/80
	Sale required=	9,375	Units

Solution ii.a
	Sale revenue	$                                                75.00	100*75%
	Variable cost	$                                                20.00
	Contribution per bag (Sale less variable cost)	$                                                55.00
	Fixed cost	$                                            450,000
	Break-even point=	Fixed cost/contribution per bag
	Break-even point=	=450000/55
	Break-even point=	8,182	Units
Solution ii.b
	Sale revenue	$                                                75.00
	Variable cost	$                                                25.00
	Contribution per bag (Sale less variable cost)	$                                                50.00
	Fixed cost	$                                            450,000
	Profit	$                                            300,000
	Total	$                                            750,000
	Sale required=	(Fixed cost+Profit)/contribution per bag
	Sale required=	=(450000+300000)/50
	Sale required=	15,000	Units

Solution iii
	Variable cost per unit	$                                                20.00
	Units to be sold	20000
	Total variable cost	$                                      400,000.00	20000*20
	Fixed cost	$                                      450,000.00
	Profit required	$                                      200,000.00
	Total sale value required	$                                   1,050,000.00
	No of untis	20,000
	sale price per unit required	$                                                52.50	1050000/20000