Break-even analysis and margin of safety

The three formulas

$\text{Sản lượng hoà vốn}=\dfrac{\text{chi phí cố định}}{\text{lãi góp/đơn vị}}$

$\text{Doanh thu hoà vốn}=\text{sản lượng hoà vốn}\times\text{giá bán}$

$\text{Sản lượng cho lợi nhuận mục tiêu}=\dfrac{\text{chi phí cố định}+\text{lợi nhuận mục tiêu}}{\text{lãi góp/đơn vị}}$

Margin of safety

$\text{Biên an toàn}=\text{sản lượng hiện tại}-\text{sản lượng hoà vốn}$, often expressed as a percentage of current output. It answers the question a manager actually asks: how far can sales fall before we start losing money?

Reading the chart

Fixed cost is the horizontal line; total cost starts at the fixed cost level and slopes up by the variable cost per unit; revenue starts at the origin. Where revenue crosses total cost is break-even; the vertical gap between the two lines is loss to the left and profit to the right.

What changes what

A rise in fixed costs shifts break-even output up and does not change the slope. A rise in variable cost per unit reduces contribution, so break-even rises and the total cost line becomes steeper. A price rise raises contribution and lowers break-even — but only if volume holds, which is exactly the assumption that makes the model fragile.

The assumptions, which carry the evaluation marks

The model assumes selling price is constant at all volumes, costs split cleanly into fixed and variable, everything produced is sold, and the product mix does not change. In reality bulk discounts, stepped fixed costs and multiple products all break these. Break-even is a planning guide, not a prediction.