Question

Sales Mix and Break-Even Sales

Dragon Sports Inc. manufactures and sells two products, baseball bats and baseball gloves. The fixed costs are $437,500, and the sales mix is 70% bats and 30% gloves. The unit selling price and the unit variable cost for each product are as follows:

Products	Unit Selling Price		Unit Variable Cost
Bats	$70		$50
Gloves	180		110

a. Compute the break-even sales (units) for the overall enterprise product, E.
? units

b. How many units of each product, baseball bats and baseball gloves, would be sold at the break-even point?

Baseball bats	units
Baseball gloves	units

Answer 1

Question A

Contribution Margin per Unit = Sales Price per Unit - Variable Costs per Unit

For Bats

Contribution Margin per Unit = 70 - 50

Contribution Margin per Unit = $ 20

For Gloves

Contribution Margin per Unit = 180 - 110

Contribution Margin per Unit = $ 70

Ratio of Sales of Bats to Gloves is 7:3 which means that for every 7 bats sold there are 3 gloves sold.

Contribution Margin on Sale of 7 Bats = 7 * $ 20 per Unit = $ 140

Contribution Margin on Sale of 3 Gloves = 3 * $ 70 per Unit = $ 210

Total Contribution on Sale of 7 Bats and 3 Gloves = 140 + 210 = $ 350

Break Even Point in Units for Enterprise = Total Fixed Costs / Weighted Average Contribution Margin per Unit

Total Fixed Costs = $ 437,500

Weighted Average Contribution Margin per Unit = Total Contribution Margin on Sale of 7 Units of Bats and 3 Units of Gloves / 10 Units

Weighted Average Contribution Margin per Unit = 350 / 10 = $ 35 per Unit

Break Even Point in Units for Enterprise = 437,500 / 35

Break Even Point in Units for Enterprise = 12,500 Units

Question B

Break Even Units for Bats = Break Even Units for Enterprise * 7 / 10

Break Even Units for Bats = 12,500 * 7 /10

Break Even Units for Bats = 8,759 Units

Break Even Point in Units for Gloves = Break Even Point in Units for Enterprise * 3 / 10

Break Even Point for Gloves = 12,500 * 3 / 10

Break Even Point in Units for Gloves = 3,750 Units