To determine the break-even point, we need to calculate how many espresso machines need to be sold for the firm to cover both its fixed and variable costs.

Formula for break-even point:

$\text{Break-even point (units)} = \frac{\text{Fixed cost}}{\text{Selling price per unit} - \text{Variable cost per unit}}$

Given dataTo determine the break-even point, we need to calculate how many espresso machines need to be sold for the firm to cover both its fixed and variable costs.

Formula for break-even point:

$\text{Break-even point (units)} = \frac{\text{Fixed cost}}{\text{Selling price per unit} - \text{Variable cost per unit}}$

Given

• Fixed cost (FC) = $1,450,220
• Variable cost per machine (VC) = $86
• Selling price per machine (SP) = $332

Substituting values into the formula:

$\text{Break-even point (units)} = \frac{1,450,220}{332 - 86}$

First, calculate the difference between the selling price and the variable cost:

$332 - 86 = 246$

Now, compute the break-even point:

$\text{Break-even point (units)} = \frac{1,450,220}{246} \approx 5,895$

Conclusion:

The firm needs to sell approximately 5,895 espresso machines to break even.

Do you want more details or have any questions?

Here are some related questions for deeper understanding:

1. What is the total cost of producing 5,895 espresso machines?
2. How much profit will the firm make if they sell 6,500 machines?
3. What happens to the break-even point if the variable cost increases?
4. How would a change in the selling price impact the break-even point?
5. What are the benefits of reducing fixed costs in this scenario?

Tip: Understanding break-even analysis helps businesses decide pricing strategies and cost management approaches.