Given the information in the table below, how many units will be required to be sold to hit the break-even point?
| Fixed Cost | $120,000 |
|---|---|
| Variable Cost | $0.20 |
| Selling Price | $2.20 |
[?] units
Answer (2)
Define x as the number of units to be sold.
Express the total cost as the sum of fixed cost and variable cost: T o t a l C os t = 120000 + 0.20 x .
Express the total revenue as the selling price times the number of units: T o t a l R e v e n u e = 2.20 x .
Set total cost equal to total revenue and solve for x : x = 2 120000 = 60000 . The break-even point is 60000 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 reach the break-even point. The break-even point is where total revenue equals total costs (both fixed and variable).
Calculating Total Cost 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 can be expressed as: T o t a l C os t = F i x e d C os t + ( Va r iab l e C os t × x ) Substituting the given values, we have: T o t a l C os t = 120000 + 0.20 x
Calculating Total Revenue The total revenue is the selling price per unit times the number of units, which can be expressed as: T o t a l R e v e n u e = S e ll in g P r i ce × x Substituting the given values, we have: T o t a l R e v e n u e = 2.20 x
Setting Up the Equation To find the break-even point, we set the total cost equal to the total revenue: T o t a l C os t = T o t a l R e v e n u e 120000 + 0.20 x = 2.20 x
Solving for x Now, we solve for x :
2.20 x − 0.20 x = 120000 2 x = 120000 x = 2 120000 x = 60000
Final Answer Therefore, the number of units that must be sold to reach the break-even point is 60,000 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 ($10) and variable costs like lemons and sugar ($0.50 per cup). If you sell each cup for $1.50, calculating the break-even point tells you how many cups you need to sell to cover your costs before making a profit. This concept applies to larger businesses too, helping them make informed decisions about pricing, production, and investments. Knowing the break-even point helps businesses avoid losses and understand the sales volume needed for profitability.
To break even, 60,000 units must be sold. This is determined by equating total costs to total revenue, considering fixed and variable costs. The calculation shows that the company needs to reach this sales figure to cover all costs.
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