To find the break-even point for Alexa's coffee shop, we need to calculate the fixed and variable costs and then determine how many cups of coffee and muffins must be sold to cover those costs.
1. Fixed Costs:
The fixed costs include monthly rental and advertising.
- Advertising: $36.00
- Monthly rental: $109.00
Total Fixed Costs = Advertising + Monthly Rental \[ \text{Total Fixed Costs} = 36 + 109 = 145.00 \]
2. Variable Costs:
The variable cost is the cost per cup of coffee and a muffin.
- Variable cost per cup of coffee and muffin: $5.50
3. Selling Price:
The selling price for a cup of coffee and muffin is:
- Selling price: $9.50
4. Contribution Margin:
The contribution margin per cup is the selling price minus the variable cost.
Contribution Margin = Selling Price - Variable Cost \[ \text{Contribution Margin} = 9.50 - 5.50 = 4.00 \]
5. Break-even Point:
To find the break-even point in units (number of cups of coffee and muffins), we use the formula:
Break-even Point (units) = Total Fixed Costs / Contribution Margin \[ \text{Break-even Point} = \frac{145.00}{4.00} = 36.25 \]
Since Alexa can't sell a fraction of a cup, we round up to the next whole number:
Break-even Point:
Alexa needs to sell 37 cups of coffee and muffins to break even.