## Break-Even Analysis

##### Key Points
• In the linear Cost-Volume-Profit Analysis model, the break-even unit of sales can be directly computed in terms of total revenue and total costs.
• Unit contribution margin is the marginal profit per unit, or alternatively the portion of each sale that contributes to fixed costs.
• Break-even analysis is a simple and useful analytical tool, yet has a number of limitations as well.

##### Terms
• Break-even point - The point where total costs equal total revenue and the organization neither makes a profit nor suffers a loss.
• Opportunity costs - The costs of activities measured in terms of the value of the next best alternative forgone (that is not chosen).

##### Break-Even Analysis

In economics and business, specifically cost accounting, the break-even point is the point at which costs or expenses and revenue are equal - there is no net loss or gain, and one has "broken even".

A profit or a loss has not been made, although opportunity costs have been "paid", and capital has received the risk-adjusted, expected return. For example, if a business sells fewer than 200 tables each month, it will make a loss. If the business sells more, it will make a profit. With this information, the business managers will then need to see if they expect to be able to make and sell 200 tables per month. If they think they cannot sell that many, to ensure viability they could:

• Try to reduce the fixed costs (by renegotiating rent for example, or keeping better control of telephone bills or other costs)
• Try to reduce variable costs (the price it pays for the tables by finding a new supplier)
• Increase the selling price of their tables

In the linear Cost-Volume-Profit Analysis model, the break-even point - in terms of Unit Sales (X) - can be directly computed in terms of Total Revenue (TR) and Total Costs (TC) as: where TFC is Total Fixed Costs, P is Unit Sale Price, and V is Unit Variable Cost. The quantity (P - V) is of interest in its own right, and is called the Unit Contribution Margin (C). It is the marginal profit per unit, or alternatively the portion of each sale that contributes to Fixed Costs. Thus the break-even point can be more simply computed as the point where Total Contribution = Total Fixed Cost:

Break-Even Analysis Using Contribution Margin
A break-even quantity can also be found using contribution margin.

Break-Even Calculation
We can derive the calculation for the break-even quantity from the relation of total revenue to total costs.

##### Break-Even and Pricing Decisions

The break-even point is one of the simplest analytical tools in management. It helps to provide a dynamic view of the relationships between sales, costs, and profits. A better understanding of break-even, for example, is expressing break-even sales as a percentage of actual sales. This can give managers a chance to understand when to expect to break even (by linking the percent to when in the week/month this percent of sales might occur). In terms of pricing decisions, break-even analysis can give a company a benchmark quantity of goods to be sold. This quantity can then be used to derive the average fixed and variable costs, the sum of which can be used as the basis for markup pricing, et cetera. Some limitations of break-even analysis include:

• It is only a supply-side (costs only) analysis, as it tells you nothing about what sales are actually likely to be for the product at these various prices.
• It assumes that fixed costs (FC) are constant. Although this is true in the short run, an increase in the scale of production is likely to cause fixed costs to rise.
• It assumes average variable costs are constant per unit of output, at least in the range of likely quantities of sales (linearity).
• It assumes that the quantity of goods produced is equal to the quantity of goods sold.
• In multi-product companies, it assumes that the relative proportions of each product sold and produced are constant (the sales mix is constant).

Source: Boundless