Question

A firm is selling two products-chairs and bar stools-each at $55 per unit. Chairs have a variable cost of $25, and bar stools $20. Fixed cost for the firm is $20,000 a. If the sales mix is 1:1 (one chair sold for every bar stool sold), what is the break even point in dollars of sales? In units of chairs and bar stools?

Answer 1

The break even point in dollars of sales is $110,000. The break even point in terms of units is 2000 chairs and 2000 bar stools.

Step-by-step explanation:

To calculate the break even point, we need to determine the total fixed costs and the contribution margin per unit.

Fixed costs for the firm are $20,000.

The contribution margin per unit is calculated by subtracting the variable cost from the selling price of each product. For chairs, the contribution margin is $55 - $25 = $30. For bar stools, the contribution margin is $55 - $20 = $35.

Since the sales mix is 1:1, we can assume that the number of chairs sold is equal to the number of bar stools sold.

Let's assume the number of units sold is x. Therefore, the total revenue is $55x.

At the break even point, the total revenue equals the total costs. Therefore, we can equate the total revenue to the total fixed costs plus the variable costs:

$55x = $20,000 + ($30 + $35)x

Simplifying the equation,

$55x = $20,000 + $65x

Subtracting $65x from both sides,

$55x - $65x = $20,000

Combining like terms, -$10x = $20,000

Dividing both sides by -$10, we get

x = -($20,000)/10 = 2000

The break even point in terms of dollars of sales is given by the number of units sold, which is x. Therefore, the break even point in dollars of sales is $55 x 2000 = $110,000.

Since the sales mix is 1:1, the break even point in terms of units is also 2000 chairs and 2000 bar stools.