Profitable Break-even Point Analysis
a. What is the break-even point in dollars of sales if the sales mix is 1:1? How many units of chairs and bar stools need to be sold to reach the break-even point?
Break-even point______
Number of chairs_____
Number of bar stools_____
b. How does the break-even point in dollars of sales change if the sales mix changes to 1:4? How many units of chairs and bar stools need to be sold in this scenario?
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. Break-even Point Calculation with 1:1 Sales Mix
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 $22,000. To find the break-even point in units, we divide the fixed cost by the contribution margin per unit: $22,000 / $45 = 488.89. Since we can't sell a fraction of a unit, we round up to the nearest whole number, which gives us 489 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: 489 x $55 = $26,895.
b. Break-even Point Calculation with 1:4 Sales Mix
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 $29 ($25 + 4 * $20). Using the same formula, we find the break-even point in units is 488.89. Rounding up to the nearest whole number gives us 489 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: 489 x $55 = $26,895.