Break-Even Point (BEP) is the level of sales or output at which total revenue equals total costs, resulting in zero profit and zero loss. It is a critical financial metric used in cost-volume-profit (CVP) analysis to determine the minimum level of sales needed to cover all fixed and variable costs.

🔹 Definition:

Break-Even Point is the point at which Total Revenue = Total Cost, and the business makes no profit, no loss.

🔹 Formula:

There are two main formulas to calculate the BEP:

1. In Units:

BEP (Units)
= Fixed Costs / [Selling Price per Unit − Variable Cost per Unit]
=Fixed Costs​ / Contribution per Unit

2. In Sales Value:

BEP (Sales ₹) = Fixed Costs / P/V Ratio

🔹 Key Concepts:

• Fixed Costs: Costs that do not change with the level of production (e.g., rent, salaries).

• Variable Costs: Costs that change in proportion to the output (e.g., raw materials).

• Contribution per Unit: Selling Price – Variable Cost per unit.

• P/V Ratio: Contribution / Sales × 100

🔹 Example:

Let’s assume:

• Fixed Costs = ₹1,00,000

• Selling Price per unit = ₹50

• Variable Cost per unit = ₹30

• Contribution per unit = ₹20

BEP (Units) = ₹1,00,000 / ₹20​ = 5,000 units.

So, the company must sell 5,000 units to break even.

🔹 Graphical Representation:

In a Break-Even Chart:

• The X-axis represents the number of units or sales value.

• The Y-axis represents revenue and costs.

• The Break-Even Point is where the Total Cost Line intersects the Total Revenue Line.

🔹 Importance of Break-Even Analysis:

1. Profit Planning: Identifies the minimum performance needed to avoid losses.

2. Pricing Decisions: Helps determine the effect of pricing on profitability.

3. Cost Control: Aids in managing and reducing fixed and variable costs.

4. Investment Evaluation: Assesses the viability of launching a new product or entering a new market.

5. Margin of Safety Calculation: Tells how much sales can drop before incurring a loss.

🔹 Margin of Safety (MOS):

Once the break-even point is crossed, every additional sale contributes to profit. The margin of safety shows how much sales exceed the break-even point:

$$\text{MOS}=\text{Actual Sales }-\text{Break-Even Sales}$$

✅ Final Summary:

The Break-Even Point is a foundational financial metric that tells a business the exact volume of sales required to cover all costs and begin making profit. It plays a vital role in decision-making, risk analysis, and strategic planning.

Law of Diminishing Returns

✅ Definition

The Law of Diminishing Returns, also called the Law of Diminishing Marginal Returns, states that:

As additional units of a variable input (e.g., labor) are added to a fixed input (e.g., land or capital), the marginal product of the variable input will eventually decline, holding all other inputs constant.

In simpler terms, after a certain point, adding more of one input while keeping others fixed results in smaller and smaller increases in output.

✅ Assumptions

1. Only one input is variable (e.g., labor); all others are fixed (e.g., land, machinery).

2. Technology remains constant.

3. Input units are homogeneous (each additional unit is of the same quality).

4. It applies in the short run, where at least one factor is fixed.

✅ Graphical Representation

In a production graph:

• The Total Product (TP) curve increases, but at a decreasing rate.

• The Marginal Product (MP) curve rises initially, reaches a peak, then declines and may become negative.

✅ Conclusion

The Law of Diminishing Returns highlights an important constraint in production: when one input is increased while others are fixed, there comes a point when the productivity of the added input begins to fall. Recognizing this helps businesses allocate resources more efficiently and avoid wasteful input use.