Question

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 Memberships sold 30,000 150,000 120,000 Membership price $2,500 $1,000 $800 Variable cost per membership $1,000 $500 $200

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?

Thompson Company is considering the development of two products: Alpha and Beta. Regardless of which product is introduced, the anticipated selling price will be $50. Manufacturing cost information follows: Alpha Beta Annual fixed costs $200,000 $300,000 Variable cost per unit $30 $20 16. Which of the two products will be more profitable at a sales level of 20,000 units? a. Alpha b. Beta 17. Refer to the previous question. By what amount is the product (Alpha or Beta) more profitable? 18. At what volume level (i.e., number of units) will the profit for the two products be the same?

Answer 1

	Platinum	Gold	Silver	Total
Memberships sold	30,000	150,000	120,000	300,000
Membership Price	2,500	1,000	800
Variable cost	1,000	500	200
Contribution Margin per Membership	1,500	500	600
Total contribution margin	45,000,000	75,000,000	72,000,000	192,000,000
Weighted average Unit CM				640
14.Breakeven memberships = Fixed cost/Weighted average unit contribution margin
=19,200,000/640 = 30,000 meemberships
15.For gold = Break even memberships*Sales mix for Gold
=30,000*150,000/300,000 = 15,000 memberships
	Alpha	Beta
Fixed costs	200,000	300,000
Variable cost at 20,000 units	600,000	400,000
Total cost	800,000	700,000
Hence, beta will be more profitable
Amount = $100,000
Level of volume = Difference in fixed costs/Differenece in variable cost per unit
=100,000/10 = 10,000 units