Given the information in the table below, how many units will be required to be sold to hit the break-even point?
| | |
| :---------- | :---------- |
| Fixed Cost | $572,000 |
| Variable Cost | $0.20 |
| Selling Price | $11.20 |
[?] units
Answer (2)
Define x as the number of units to be sold.
Express total cost as the sum of fixed cost and variable costs: T o t a lC os t = F i x e d C os t + ( Va r iab l e C os t × x ) .
Express total revenue as the product of selling price and the number of units: T o t a lR e v e n u e = S e ll in g P r i ce × x .
Set total cost equal to total revenue and solve for x : $x = \frac{Fixed Cost}{Selling Price - Variable Cost} = \frac{$572,000}{$11.20 - 0.20} = 52,000 . The break-even point is 52000 units.
Explanation
Understanding the Problem 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 Total Revenue Let x be the number of units to be sold. The total cost is the sum of the fixed cost and the variable cost per unit times the number of units, which is given by: T o t a lC os t = F i x e d C os t + ( Va r iab l e C os t × x ) In our case: Total Cost = $572,000 + ($0.20 \times x) The total revenue is the selling price per unit times the number of units, which is given by: T o t a lR e v e n u e = S e ll in g P r i ce × x In our case: Total Revenue = $11.20 \times x
Setting Total Cost Equal to Total Revenue At the break-even point, the total cost equals the total revenue. Therefore, we set the total cost equal to the total revenue: $572,000 + ($0.20 \times x) = $11.20 \times x
Solving for the Break-Even Point Now, we solve for x :
$572,000 = $11.20 \times x - $0.20 \times x $572,000 = $11.00 \times x x = \frac{$572,000}{$11.00} x = 52 , 000 Therefore, 52,000 units must be sold to reach the break-even point.
Final Answer The number of units required to be sold to hit the break-even point is 52,000 units.
Examples
Understanding break-even points is crucial in business. For example, if you're starting a lemonade stand, you have fixed costs like the pitcher and sign ($5) and variable costs like lemons and sugar ($0.50 per cup). If you sell each cup for $1, knowing your break-even point tells you how many cups you need to sell to cover your initial expenses and start making a profit. This concept extends to larger businesses, helping them make informed decisions about pricing, production, and investment. Calculating the break-even point helps businesses understand the relationship between costs, revenue, and sales volume, which is essential for financial planning and profitability.
To hit the break-even point, 52,000 units must be sold. This calculation is based on fixed costs of $572,000, a variable cost of $0.20 per unit, and a selling price of $11.20. At this point, total revenue will equal total costs, allowing the business to cover expenses without making a loss.
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