2.2.3 Break-Even

Break-Even

Key Definitions

Break-Even: The comparison of a business's revenue with its fixed and variable costs to identify the minimum sales needed to cover costs. 

Fixed Costs: A cost that does not change depending on the change in the number of sales, such as rent or staff salaries.

Variable Costs: A cost that changes depending on the change in the number of sales, such as the cost of buying raw materials.

Contribution: The total revenue minus the variable costs, this is the money that the product contributes to the total revenue. 

Break-Even Graph: A line graph that shows the total revenue and total costs at all possible levels of output or demand for products from 0 to the maximum capacity. 

Margin of Safety: The amount of current output exceeding the level of output needed to break even with the costs. 

Key Formulae

The Break-Even Formula:  

                                       Break-Even =                            Fixed Costs                              

                                                               (Sales Price per Unit - Variable Cost per Unit)

The Contribution per Unit:

                                       Contribution per Unit = Selling Price - Variable Cost per Unit

The Margin of Safety:

                                       Margin of Safety = Sales Volume - Break-Even Output

The Total Contribution:

                                       Total Contribution = Contribution per Unit x Unit Sales

Calculating the Break-Even Point

Calculating the break-even point for a product requires information on both costs and prices, shown in the selling price of the product, the fixed costs, and the variable costs per unit produced. The fixed costs are the expenses that do not change in response to changing output or demand, such as rent and salaries. Variable costs change depending on changes in output or demand, meaning that if demand for a product doubled the variable costs would also double. 

The Break-Even Formula:  

                                       Break-Even =                            Fixed Costs                              

                                                               (Sales Price per Unit - Variable Cost per Unit)

Contribution

There are 2 types of contribution: unit contribution and total contribution. The sales price minus the variable cost is what calculates the unit contribution, and the unit contribution is then multiplied by the quantity sold to calculate the total contribution. The total contribution is then used as a quick way to calculate the profit by subtracting the fixed costs from the total contribution. 

Break-Even Graphs

A break-even graph is a line graph that shows the revenue and costs for a business at all levels of demand or output for the business.The break-even graph uses the horizontal axis to show the output per time period for the business, and the vertical axis is used to represent the costs and sales in the currency. An example break-even graph is shown in the image below:

Using Break-Even Graphs

Various pieces of information can be taken from break-even graphs, such as the one above. As well as the level of output needed to break even, the break-even graph also shows the level of profits and/or losses at every possible level of output. Many conclusions can be reached, such as:

• Any level of output lower than the break-even point would mean the product is making a loss for the business. The amount of the loss is shown in the vertical difference between the total cost and total revenue lines.
  
• Sales above the break-even point would be earning the business additional profits. If the company were to produce and sell an output above the break-even point they would be making enough profits to sustain a good level of growth.
  
• The margin of safety (the amount by which demand can fall before the company starts to make losses on their products) that the business's products have - this is shown by subtracting the break-even point from the sales. 

The Effects of Changes in Price, Output and Cost

A limitation of the break-even graph is that it is a static model - it ignores any changes in trends over time. However, when changes are planned it can be useful in showing what could potentially happen for the product in terms of sales. The main changes that need to be considered are:

• The impact on revenue, profits and break-even of a change in price
  
• The impact on revenue and profits of changes in demand - this could come about if the product has become more or less fashionable
  
• The effect of a rise or fall in variable costs, such as the raw materials
  
• The effect of a rise or fall in fixed costs - this could be due to a decision to downsize to a smaller, cheaper head office premise

Price Rise

If a company increases its prices its revenue line will rise more steeply than before. The line will start at the same point as before, but it will to a higher revenue point at maximum output. This steepening will increase the profit potential at each level and lower the break-even point - meaning that if more is charged less needs to be sold. 

A Rise or Fall in Demand

A change in demand has no impact on the lines in a break-even graph. It just means you need to draw a line vertically up from the new sales quantity. 

Rise in Variable Costs

If the variable costs were to increase this would make the line for the variable costs steeper. The total costs would also increase, making the line for the total costs steeper also. This would mean that more would need to be sold in order to break even. 

A Fall in Fixed Costs

If fixed costs were to decrease this would mean that the line for the fixed costs would become flatter and less steep. The decrease in fixed costs would also mean that the total costs would decrease, making the line for the total costs flatter also. This means that less would need to be sold in order to break even. 

Interpretation of Break-Even Graphs

Break-even analysis is particularly useful for small businesses where the managers may not be able to employ more sophisticated techniques. Businesses can use break-even to:

• Estimate the future level of output they will need to produce and sell in order to meet the given profit objectives
  
• Assess the impact of planned price changes upon profit and the level of output needed to break even
  
• Take decisions on whether to produce their own products or components, or whether to purchase them from external sources. 

Key factors in interpreting break-even graphs include:

• Understanding that profit can be estimated as the vertical difference between the revenue line and the total costs line at any single level of output
  
• Acknowledging that no company really has the same sales level per month or per year, despite this being what the break-even graph assumes - it is important to remember that the chart is just a 'snapshot' of a particular point in time when sales happen to be at a particular level

Limitations of Break-Even Analysis

The limitations of break-even analysis are as follows:

• The model is a simplification that assumes that the variable costs increase constantly, ignoring the benefits of bulk buying. If a firm negotiates lower prices for purchases of larger quantities of raw materials then its total cost line will no longer be straight.
  
• Similarly, break-even analysis assumes that the firm sells all of their goods at a single set price, whereas in reality firms frequently offer discounts for bulk purchases.
  
• A major flaw in the technique is that it assumes that all output is sold. In times of low demand a firm may have difficulty in selling all of its products.
  
• The most important limitation is the fact that it is a static model. It does not take sales trends into account, so it is only true in a particular point in time.