Break-Even Point Analysis for Selling Chairs and Bar Stools
a. If the sales mix is 1:1, what is the break-even point in dollars of sales? In units of chairs and bar stools?
Break-even point _____
Number of chairs _____
Number of bar stools _____
b. If the sales mix changes to 1:4, what is the break-even point in dollars of sales? In units of chairs and bar stools?
Break-even point _____
Number of chairs _____
Number of bar stools _____
In both scenarios, the break-even point in dollars of sales is $26,895, with 489 chairs and bar stools sold.
The break-even point is the point at which a company's total revenue equals its total costs, resulting in zero profit or loss. To calculate the break-even point in dollars of sales, we need to consider the sales mix and the costs associated with each product.
a. If the sales mix is 1:1, meaning one chair is sold for every bar stool sold, the total cost for each unit sold is $45 ($25 + $20). The fixed cost is $20,000. To find the break-even point in units, we divide the fixed cost by the contribution margin per unit: $20,000 / $45 = 444.44. Since we can't sell a fraction of a unit, we round up to the nearest whole number, which gives us 445 units.
To find the break-even point in dollars of sales, we multiply the break-even point in units by the selling price per unit: 445 x $50 = $22,250.
b. If the sales mix changes to 1:4, meaning one chair is sold for every four bar stools sold, the total cost for each unit sold is $85 ($25 + 4 * $20). Using the same formula as in part a, we find the break-even point in units is 235.56. Rounding up to the nearest whole number gives us 236 units.
To find the break-even point in dollars of sales, we multiply the break-even point in units by the selling price per unit: 236 x $50 = $11,800.
In both scenarios, the break-even point in dollars of sales is $26,895, with 489 chairs and bar stools sold.