## Break-even

Let's start at the beginning: **Profit** is what is left from revenue after **expenses** are covered. **Break-even** is the point where revenue equals expenses and profit is zero. **Break-even analysis** is a tool businesses use to see whether selling/producing a proposed product or service can at least reach the break-even point. This in turn lets the business know whether the proposed product or service should be part of the company's product mix and business model.

We start from the base income formula:

- Revenue – Expenses = Profit

Since break-even is the point where revenue equals expenses and profit is zero, the base formula becomes:

- Revenue = Expenses

Let's look at each component.

## Revenue

**Revenue** is income from sales and is determined by multiplying the selling price by the quantity sold. Revenue usually increases in a linear manner from zero at no sales, and stays directly proportional to sales unless you give quantity discounts, which we will ignore for this exercise. (Learn more about the different types of discounts.)

Revenue = (Price per unit) x (Quantity)

Revenue = P x Q

## Expenses

Expenses can be categorized into either Fixed Costs, Variable Costs, or Mixed costs (some of both). Expenses don't start from zero, because unless you are out of business, there are some expenses even if you aren't making or selling anything. These expenses with no production are all fixed costs. Expenses then go up in proportion to sales because of variable costs. (See our article on Fixed Costs and Variable Costs, how to identify them, and how to split Mixed costs into their fixed and variable components.)

Expenses = Fixed Costs + Variable Costs

Expenses = F + V

Variable Costs are the cost per unit times the quantity

Variable Costs = Unit Cost x Quantity

V = C x Q

Expenses = F + (C x Q)

Now lets do a little algebraic substitution to combine these components to determine the formulas for break even.

Revenue = Expenses

P x Q = F + (C x Q)

Now we solve for Q (the quantity at which break even occurs).

P x Q = F + (C x Q)

(P x Q) – (C x Q) = F

Q(P -C) = F

Q = F/(P – C)

If you know the variable costs of production, the fixed costs of the business, and the selling price for the product or service, you can determine the quantity of sales that are required to cover all costs and break even. Sales beyond break even then result in profit to the extent that selling price exceeds the variable cost.

## Example

Let's work an example:

Price is $25 (P)

Variable Cost is $10 per unit (C)

Fixed Cost is $900,000 (F)

Right off, we can see it will take a bunch of sales to make up $900,000 in fixed costs when we only clear $15 per unit sold. (Price of $25 minus Cost of $10 means we clear $15 per unit; this concept is related to marginal cost and marginal revenue.)

Let's plug this into our formula.

Q = F/(P – C)

Q = $900,000/($25 – 10)

Q = $900,000/($15)

Q = 60,000

In this example, the company needs to sell 60,000 units to break even. In comparing this to their sales projections and overall marketing plan, they can thus determine whether it makes financial sense for them to do so.