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A company estimates that its fixed operating costs are \(\$ 500,000,\) and its variable costs are \(\$ 3.00\) per unit sold. Each unit produced sells for \(\$ 4.00 .\) What is the company's breakeven point? In other words, how many units must it sell before its operating income becomes positive?

Short Answer

Expert verified
The company's breakeven point is 500,000 units.

Step by step solution

01

Understand Fixed and Variable Costs

The fixed operating costs remain constant regardless of the number of units sold. Here, the fixed operating costs are \( \\(500,000 \). The variable costs depend on the number of units produced and sold, which is \( \\)3.00 \) per unit.
02

Determine Revenue per Unit

The revenue per unit, which is the selling price of each unit, is \( \$4.00 \). This is how much money the company makes from selling one unit.
03

Calculate Contribution Margin per Unit

The contribution margin per unit is the selling price minus the variable cost per unit. Calculate it as:\[ \text{Contribution Margin} = \\(4.00 - \\)3.00 = \$1.00 \]
04

Compute Breakeven Point in Units

The breakeven point in units is calculated by dividing the fixed costs by the contribution margin per unit. Use the formula:\[ \text{Breakeven Point} = \frac{\text{Fixed Costs}}{\text{Contribution Margin}} = \frac{\\(500,000}{\\)1.00} = 500,000 \text{ units} \]
05

Verify the Breakeven Point

Verify the calculation by considering that at 500,000 units, the total sales revenue equals the total costs (fixed plus variable), meaning the operating income is zero.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fixed and Variable Costs
In the realm of breakeven analysis, understanding costs is a key foundational step. Costs are typically divided into two categories: fixed costs and variable costs.

**Fixed Costs** are costs that do not change with the level of production or sales. For a company, these might include rent, salaries, or insurance. In the exercise, the fixed operating costs are stated as \(\\(500,000\). No matter how many units you produce or sell, these costs remain constant.

**Variable Costs**, on the other hand, vary with the volume of units produced. They are directly tied to production levels. In this exercise, the variable cost is \(\\)3.00\) per unit. This means for every additional unit sold, the cost increases by \(\$3.00\).

Understanding these costs helps in calculating the contribution margin and eventually the breakeven point, where the revenues cover all costs.
Contribution Margin
The contribution margin is a critical figure in breakeven analysis because it tells you how much each unit sold contributes to covering the fixed costs and generating profit.

It is calculated as:\[ \text{Contribution Margin per Unit} = \text{Selling price per unit} - \text{Variable cost per unit} \]
For the exercise given, each unit sells for \(\\(4.00\), and the variable cost is \(\\)3.00\). Thus, the contribution margin is \(\\(1.00\) per unit.

This means for every unit sold, \(\\)1.00\) is available to pay off fixed costs. Knowing the contribution margin is vital because it helps determine how many units need to be sold to achieve a positive operating income.
Operating Income
Operating income is the profit generated from the core business operations, excluding any income from investments or non-operating activities. It is calculated as total revenue minus total costs (both fixed and variable).
At the breakeven point, operating income is zero because total revenue is exactly equal to total fixed and variable costs.
Once a company surpasses the breakeven point in sales, any additional sales will contribute directly to the operating income.
Therefore, understanding the breakeven analysis is crucial to evaluating when a business will start being profitable.
Revenue per Unit
Revenue per unit, also known as the selling price, is the amount of money a company earns from selling one individual unit of its product. In the given exercise, this is specified as \(\$4.00\) per unit.
This revenue per unit is important because it directly influences the contribution margin.
  • When the selling price per unit increases, without a corresponding increase in variable costs, the contribution margin rises.
  • Conversely, if the revenue per unit decreases, the contribution margin shrinks, requiring more units to be sold to cover the fixed costs and reach the breakeven point.
Thus, maintaining an optimal price point is vital for profitability and achieving business goals. A proper understanding of revenue per unit helps businesses in strategic pricing decisions.

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