**Break-even analysis**, in other words, cost-volume-profit analysis indicates how many units the firm has to produce and sell before it recovers its total costs. When a business achieves a break-even level of output and sales, it recovers all of its costs. To conduct the break-even analysis, it is essential to calculate the break-even level of output.

## Example problem and solution

How to calculate the break-even level of output?

There are two ways to calculate the break-even level of output:

1) Formula: $Breakeven=\frac{totalfixed\mathrm{cos}ts}{contibutionperunit}$

2) Break-even chart (including variable costs, fixed costs, total costs and revenue)

**Fixed costs** are costs that remain the same (in the short term) regardless of the number of units produced, for example, rent and rates.

**Variable costs** are costs that rise and fall in direct proportion to the number of units produced, for example, raw materials used in production or direct labour.

**Total costs** are fixed costs and variable costs added together.

**Contribution per unit **is **total revenue** from the sale of one unit. It is the selling price minus variable costs.

Company E produces e-bikes. A rental cost of a factory is £8,000 a month and the cost of heat and light there is £6,000 a month. The selling price per e-bike is £2,000. The cost of materials per e-bike is £400. How many e-bikes per month does the company have to produce and sell to reach the break-even level of output?

First, we need to calculate fixed costs.

$\pounds 8,000+\pounds 6,000=\pounds 14,000$

Then, contribution per unit.

$\pounds 2,000-\pounds 400=\pounds 1,600$

Finally, break-even level of output.

$\frac{\pounds 14,000}{\pounds 1,600}=8.75$

R = revenue

TC = total costs

FC = fixed costs

VC = variable costs

🔴 = break-even level of output

To create a break-even chart (see Figure 1), we need to plot both fixed costs (FC) and variable costs (VC). Then, adding them together, we arrive at total costs (TC). Lastly, we have to plot revenue according to the number of units produced (R). The point where the revenue and total costs lines cross is the break-even level of output.

This means that company E has to produce 9 e-bikes a month to reach the break-even level.

## Margin of safety

The margin of safety is the difference between the current level of output and the breakeven level of output. It considers the number of units produced and the number of units that need to be produced in order to achieve the break-even level of output. In other words, it is the amount sales can decrease before a company reaches the break-even level of output and fails to make a profit.

The formula for calculating the margin of safety is the following:

$marginofsafety=levelofoutput-breakevenlevelofoutput$

$15-9=6units$

The margin of safety can also be expressed as a percentage:

$\frac{6}{15}x100\%=40\%$

It means that company E produces and sells 6 units or 40% more than it has to in order to reach the break-even level.

## Target profit

The target profit is an expected amount of profit that the shareholders and/or managers of a business expect to achieve by the end of a specified accounting period. It states how many units a company needs to sell in order to achieve desirable profit.

The formula for calculating the target profit is the following:

$sales\left(units\right)=\frac{targetprofit+fixed\mathrm{cos}ts}{contributionperunit}$

(Based on company E and assuming that a target profit is £15,000)

$\frac{\pounds 15,000+\pounds 14,000}{\pounds 1,600}=18.13$

It means that company E has to produce and sell 18.13 units, or 19 units in total, in order to achieve the target profit of £15,000.

## Advantages and disadvantages of break-even analysis

Advantages | Disadvantages |

It provides a measurement of profit and losses at different levels of production and sales. | It assumes that sales prices are constant at all levels of output. |

It predicts the effect of changes in sales prices. | It assumes production and sales are the same. |

It analyzes the relationship between fixed and variable costs. | It may be time-consuming. |

It predicts the effect of cost and efficiency changes on profitability. | It can only apply to a single product or a single mix of products. |

## Break-Even and Profitability Analysis - Key takeaways

Break-even is a level of production at which the costs of production equal the revenues for a product.

The break-even level is calculated by dividing the total fixed costs of production by the contribution per unit. However, it can also be determined using a chart.

The margin of safety is the difference between the current level of output and the breakeven level of output.

Target profit is the expected amount of profit that the shareholders and/or managers of a business expect to achieve by the end of a specified accounting period.

The break-even analysis has advantages, such as being able to predict the effect of changes in sales prices and disadvantages, as it can only be applied to a single product or a single mix of products.

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##### Frequently Asked Questions about Break-Even Analysis

How do you solve break-even analysis problems?

The Break-even analysis problem is solved by dividing total fixed costs divided by contribution per unit.

What is break-even analysis with examples?

**Break-even analysis **indicates how many units the firm has to produce and sell before it recovers its total costs.

For example, if a business has a £200 break-even point, it must reach that level to cover its costs.

What is the formula for the break-even point?

Break-even = total fixed costs divided by contribution per unit.

Why do we use break-even analysis?

We use break-even analysis to determine the number of units to sell to cover the costs of a business.

What are the advantages and disadvantages of break-even analysis?

Profit/loss measurement, predicts the effect of changes in sales prices and analyzes the relationship between fixed and variable costs.

assumes that sales prices are constant at all levels of output, assumes production and sales are the same.

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