Question

Bright Eyes manufactures and sells two products. The first product is a disposable contact lens set that lasts about 4 months. The second product is a wetting solution. Customers of the first product use one bottle of solution each month. As a result, bottles of solution outsell lens by a 4:1 ratio. Lens sell for $42 per set, and have a contribution margin ratio of 60%. The solution sells for $8 per bottle, but only generates variable costs of $2. The company's total fixed costs are $12,400,000.

(a) What level of total sales is necessary to achieve break even?

(b) If a competitor began selling a wetting solution that forced Bright Eyes to reduce the price for its

solution to $6 (to maintain market share and the 4:1 ratio of solution to lens), what level of total sales is necessary to achieve break even?

Answer 1

a)Let the number of Contact lens set be Y, then number of solution sets = 4 Y,

Contribution on Lens = 60% of 42 = $ 16.8 per lens set and Solution Contribution = 8 - 2 = $6 per bottle

Total Contribution = 16.8 * Y + 6 * 4 Y = 40.8 Y

For a fixed cost of 12400000 ; total units required to be sold to break even = Fixed Cost /Contribution per Set

= 12400000 / 40.8 Y such that y = 303922

Hence we need to sell 303922 contact lens set and 303922 * 4= 1215688 solution bottles to break even.

Total Sales for break even = 303922 * 42 + 1215688 * 8 = 22490228

b)When price of solution is reduced to 6, new contribution = 6 - 2 = 4

Total Contribution per set = 16.8 Y + 4 * 4 Y = 32.8 Y

New Break even sets required = 12400000 / 32.8 = 378049

Hence 378049 units of lens sets are required to be sold along with 378049 * 6 = 2268294 bottles of solution to break even.