Break-Even Analysis

Objective: Calculate Break-Even Output

Break-even analysis is a crucial tool for businesses to understand the relationship between costs, revenue, and profit. It helps determine the point at which total revenue equals total costs, meaning the business is neither making a profit nor a loss. This section focuses on calculating the break-even output.

Understanding the Concepts

There are two main types of costs involved in break-even analysis:

• Fixed Costs: These costs do not change with the level of output. Examples include rent, salaries, and insurance.
• Variable Costs: These costs change directly with the level of output. Examples include raw materials and direct labor.

The break-even point is where the total revenue is equal to the total costs.

Formula for Break-Even Output

The formula to calculate the break-even output is:

$$ \text{Break-Even Output (in units)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} $$

Alternatively, this can be expressed as:

$$ \text{BEP (units)} = \frac{FC}{P - VC} $$

Where:

• FC = Fixed Costs
• P = Selling Price per Unit
• VC = Variable Cost per Unit

Steps to Calculate Break-Even Output

1. Identify Fixed Costs: Determine the total fixed costs incurred by the business over a specific period.
2. Determine Selling Price per Unit: Find the price at which each unit of the product is sold.
3. Determine Variable Cost per Unit: Calculate the cost of producing each individual unit.
4. Apply the Formula: Use the break-even output formula to calculate the number of units that need to be sold to cover all costs.

Example Calculation

A company has the following costs:

• Fixed Costs = $20,000
• Selling Price per Unit = $10
• Variable Cost per Unit = $4

Using the formula:

$$ \text{BEP (units)} = \frac{20000}{10 - 4} $$ $$ \text{BEP (units)} = \frac{20000}{6} $$ $$ \text{BEP (units)} = 3333.33 $$

Therefore, the company needs to sell approximately 3334 units to break even.

Table Summary

Item	Value
Fixed Costs	$20,000
Selling Price per Unit	$10
Variable Cost per Unit	$4
Break-Even Output (in units)	3334