Given the information in the table below, how many units will be required to be sold to hit the break-even point?
| Fixed Cost | $225,000 |
|---|---|
| Variable Cost | $0.20 |
| Selling Price | $1.20 |
[?] units
Answer (2)
Define x as the number of units to be sold.
Express total cost as Fixed Cost + (Variable Cost × x ) = 225 , 000 + 0.20 x .
Express total revenue as Selling Price × x = 1.20 x .
Set total cost equal to total revenue and solve for x : 225 , 000 + 0.20 x = 1.20 x , which gives x = 225000 .
Explanation
Problem Analysis Let's analyze the problem. We are given the fixed costs, variable costs, and selling price of a product. We need to find the number of units that must be sold to cover all costs, which is the break-even point.
Defining Total Cost and Revenue Let x be the number of units to be sold. The total cost is the sum of the fixed costs and the variable costs, which can be expressed as:
Total Cost = Fixed Cost + (Variable Cost × Number of Units)
Total Cost = $225,000 + ( 0.20 \times x$)
The total revenue is the selling price per unit multiplied by the number of units sold:
Total Revenue = Selling Price × Number of Units
Total Revenue = 1.20 \times x$
Setting up the Equation At the break-even point, the total cost equals the total revenue. Therefore, we set the total cost equal to the total revenue and solve for x :
225 , 000 + 0.20 x = 1.20 x
Solving for x Now, we solve for x :
Subtract 0.20 x from both sides of the equation:
225 , 000 = 1.20 x − 0.20 x
225 , 000 = 1.00 x
x = 225 , 000
Final Answer Therefore, the number of units that need to be sold to reach the break-even point is 225,000 units.
Examples
Understanding break-even points is crucial for businesses. For example, if you're starting a small business selling handmade jewelry, knowing your fixed costs (like studio rent and equipment), variable costs (like materials), and selling price helps determine how many pieces you need to sell to cover all your expenses. This calculation guides pricing strategies, production planning, and overall financial viability, ensuring your business can sustain itself before making a profit. It's a fundamental concept in business planning and financial management.
To reach the break-even point of covering fixed and variable costs, 225,000 units need to be sold. This is calculated by ensuring total revenue equals total costs. Therefore, the break-even point requires selling 225,000 units.
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