The Income Statement & Break-Even Analysis

You’ll be able to

Explain the structure of the income statement from revenue to net income
Calculate the break-even point in units
Interpret how price and costs affect break-even

The income statement

The income statement (profit-and-loss statement) reports financial performance over a period — a quarter or a year. It starts with revenue (total sales), subtracts the cost of goods sold to get gross profit, then subtracts operating expenses (rent, salaries, marketing) to reach operating income, and finally accounts for interest and taxes to arrive at net income — the "bottom line." Net income is the profit that remains after all costs, the clearest measure of whether the business made money.

Break-even analysis

Break-even analysis finds the sales level at which total revenue exactly equals total costs, so profit is zero. Below it the firm loses money; above it, it earns profit. Because each unit sold contributes its contribution margin (price minus variable cost per unit) toward covering fixed costs, the break-even quantity is simply the fixed costs divided by that per-unit contribution. It tells an entrepreneur the minimum they must sell to survive.

What moves the break-even point

Three levers change the break-even point. Raising price or cutting variable cost per unit increases the contribution margin, so fewer units are needed to break even. Lowering fixed costs also reduces the units required. Conversely, higher fixed costs or a thinner margin raise the break-even point. Managers use this to test decisions: "If I raise price by $2, how many fewer units must I sell to break even?"

Break-even point (units)

Break-Even Units = Fixed Costs ÷ (Price per Unit − Variable Cost per Unit)

The denominator is the contribution margin per unit. Each unit sold contributes that amount toward fixed costs; once fixed costs are fully covered, the firm reaches break-even.

Worked example

A company has fixed costs of $12,000 per month. It sells a product for $20 per unit, with a variable cost of $8 per unit. How many units must it sell each month to break even, and what happens to that number if it raises the price to $24?

1.Find the contribution margin per unit: Price − Variable Cost = $20 − $8 = $12.
2.Apply the break-even formula: Break-Even Units = Fixed Costs ÷ Contribution Margin = $12,000 ÷ $12.
3.Compute: $12,000 ÷ $12 = 1,000 units per month.
4.Now raise the price to $24: new contribution margin = $24 − $8 = $16, so break-even = $12,000 ÷ $16 = 750 units.

Answer: At a $20 price the firm must sell 1,000 units per month to break even. Raising the price to $24 lifts the contribution margin to $16 and lowers the break-even point to 750 units — a higher margin means fewer units are needed to cover fixed costs.

Checkpoint

A firm has fixed costs of $30,000, sells each unit for $50, and has a variable cost of $20 per unit. What is its break-even point in units?

Watch out

The break-even denominator is the contribution margin (price − variable cost), not the price. A common error is dividing fixed costs by the selling price, which ignores the variable cost each unit still incurs.

Checkpoint

All else equal, which change will lower a company’s break-even point (the number of units it must sell)?

On the exam

For break-even problems, compute the contribution margin first, then divide fixed costs by it. If asked how a price or cost change affects break-even, recompute the margin — the exam loves these "what if" follow-ups.

Answer the 2 checkpoints as you read.