Question

Use the following information for the next 3 questions. Metro Health & Spa offers three membership programs: Platinum, Gold and Silver. Metro incurs annual fixed costs of $19,200,000 Additional information about the programs is presented below Platinum Gold Silver 30,000 150,000120,000 $2,500 $1,000 $800 Variable cost per membership $1,000 $500 $200 Memberships sold Membership price 13. What is the weighted-average unit contribution margin? 14. Assuming that the sales mix of memberships remains constant, what is the total number of memberships that the company must sell to break even? 15. What is the break-even point (in memberships) for the "Gold" membership?

Answer 1

13.

	Platinum	Gold	Silver
Membership price (i)	$2,500	$1,000	$800
Variable cost per membership (ii)	$1,000	$500	$200
Contribution margin per membership (i) - (ii)	$1,500	$500	$600

Sales mix = Platinum 30,000:Gold 150,000:Silver 120,000

= 1:5:4

Weighted average contribution margin per membership = 1,500 x 0.1 + 500 x 0.5 + 600 x 0.4

= 150 + 250 + 240

= $640

14.

Break even point = Fixed costs/Weighted average contribution margin per membership

= 19,200,000/640

= 30,000

Number of memberships to be sold for break even = 30,000

15.

Break even point for Gold membership = Number of memberships to be sold for break even x Percentage of sale quantity of Gold membership

= 30,000 x 50%

= 15,000

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