Question

Sales Mix and Break-Even Sales

Dragon Sports Inc. manufactures and sells two products, baseball bats and baseball gloves. The fixed costs are $620,000, and the sales mix is 40% bats and 60% gloves. The unit selling price and the unit variable cost for each product are as follows:

Products	Unit Selling Price		Unit Variable Cost
Bats	$90		$50
Gloves	105		65

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

Concepts and reason

Marginal cost: Marginal cost is the change in the cost of production as output is changed. It is the cost altered by adding a single unit of goods or involving change in the service provided. Thus, the total cost of production is changed.

CVP analysis: Cost volume profit analysis is generally termed as CVP analysis. It determines the effect of operating income and net income due to a change in the cost and output. In CVP, variable cost per unit is constant and total fixed cost is constant.

Cost: Cost is any value spent to produce a product or to render any service. The types of costs are fixed cost and variable cost.

Fundamentals

Selling price: Selling price is the price at which products are sold in the market. It includes the total cost incurred on the product and profit.

Contribution margin: The balance when the sales are deducted by the variable costs is known as contribution margin. The management uses contribution margin to develop the weight of sales mix for multiple products. The contribution margin signifies the profit earned before deducting the fixed costs.

Break-even point: Break-even point is the stage where the income earned and expense incurred is equal. Thus, the net income at break-even point remains zero.

Sales mix: Sales mix is calculated by the proportion or ratio of products sold. It is essential as the products involved may differ in their profitability. Sales mix and profits of a product are mutually dependent.

Fixed cost: Fixed cost is the cost that remains the same, irrespective of the increase or decrease in the value of goods or any services rendered. It is the cost paid by a company that does not depend on the activities concerned with the business.

Variable cost: Variable cost is the cost that varies according to the output produced or any service rendered. It is the cost paid by a company that depends on the activities concerned with the business.

a)

Calculate the break-even units in the sale of Product E:

Therefore, the break-even unit in the sale of Product E is 15,500 units.

Working notes:

Calculate the contribution margin for bats and gloves:

Therefore, the contribution margin of bats is $40 and the glove is $40.

Calculate the overall contribution margin:

Therefore, the overall contribution margin is $40.

b)

Calculate the units sold at the break-even point:

Therefore, the unit sold at the break-even point for baseball bats is 6,200 units and baseball gloves are 9,300 units.

Ans: Part a

The break-even unit in the sale of Product E is 15,500 units.

Part b