Break-even Analysis (DP IB Business Management)

An Introduction to Break Even Analysis

• Break Even analysis is a financial tool used to determine the point at which the business revenue equals its expenses, resulting in neither profit nor loss
  

• It helps businesses understand the minimum level of sales or output they need to achieve in order to cover all costs

  • This helps business managers make informed decisions about pricing and production volumes

• Break Even analysis takes into account three main components

Diagram: the components of break even analysis

• Fixed costs are costs that do not change regardless of the level of production or sales

  • E.g. rent, salaries and insurance 

• Variable costs are costs that vary with the level of production or sales

  • E.g. raw materials, direct labour costs, packaging and shipping costs 

• Sales revenue is the money gained from selling products/service and is calculated as follows

Sales revenue = number of items sold x selling price

Total Contribution Versus Contribution per unit

• Contribution refers to the amount of money that the sale of a particular product contributes towards paying off the fixed costs of a business

• Once the fixed costs are paid, the contribution becomes profit

• Contribution can be calculated on a per unit basis or as an aggregate

Contribution per unit

• Contribution per unit is a measure by which selling price of a unit exceeds the cost of making the unit

• It is calculated using the formula: 
  

  • 
    

  • E.g. If a product sells for $50 per unit and the variable cost of production is $30 per unit, the contribution per unit would be $20 ($50 - $30)

Total contribution

• Total contribution is a measure of the combined profit per unit generated from the sale of each goods/services

• It can be calculated in one of two ways
  

  • 
    

    or
    

  • 
    

  • E.g if 1,000 units of a product are sold, and the contribution per unit is $20, the total contribution would be $20,000 ($20 × 1,000)

• Total contribution is not the total profit made by the business because it does not take into account the fixed costs of the business

Interpreting Break Even Charts

• A break even chart is a visual representation of the break even point and is used to identify the following:

  • Fixed costs, total costs and revenue over a range of output

  • The break even point - where total costs are equal to revenue

  • Profit or loss made at each level of output

  • The margin of safety

Diagram: break even chart

Diagram analysis 

• Fixed costs do not change as output increases

  • A2B's fixed costs are £8,000 and these do not change whether the business produces 0 units or 500 units 

• Total costs are made up of fixed and variable costs

  • At 0 units of output, they are made up exclusively of fixed costs

  • At 500 units the total variable costs equate to £11,800

  • This line slopes upwards because total variable costs increase as output increases 

• The revenue line also slopes upwards

  • At 0 units of output, the revenue is £0

  • At 500 units the total revenue equates to £11,800

  • Revenue will increase with the output

  • The line will slope more steeply than the total costs and will cross the total costs line at some point 

• The point at which the total costs and the revenue lines cross is the break even point

  • The break even level of output for A2B is 324 units

• The margin of safety can be identified as the difference on the x-axis between the actual level of output (in this case 450 units) and the break even point
  

• The profit made at a specific level of output can be identified as the space between the revenue and total costs lines

  • In this instance the profit made at 450 units of output is £14,400 - £11,250 = £3,150

Calculating the Break Even Point

• The Break Even Point occurs where the total revenue earned for a product is exactly equal to its total costs

• At the break even point the business is making neither a profit nor a loss

• The contribution per unit value is used to calculate the Break Even Point

• The break even point is expressed as units (e.g. the number of scented candles)
  

• Identifying the break even point allows a business to understand how many items it needs to produce and sell to cover all costs before it starts to make a profit

  • Each subsequent unit sold past this point will generate profit for the business

The margin of safety

• The margin of safety is the difference between the actual level of output of a business and its break even level of output
  

• The margin of safety can be calculated using the following formula

Calculating profit or loss

• Profit or loss can be calculated in two ways

or

Calculating the target profit output

• Break even analysis can also be used to calculate the level of output needed to earn a target level of profit
  

• The target profit output can be calculated using the formula

• This calculation helps a business plan the resources required, such as stock, machinery and workers

Calculating the target profit

• The target profit output formula can be rearranged to calculate the target profit and the target price
  

• The target profit is the profit a business should expect to achieve at the target profit output level
  

• It is calculated using the formula

• This calculation can help a business with financial planning including forecasting cash flow

Calculating the target price

• The target price is the price at which a product should be sold in order to achieve the target profit

• It is calculated using the formula

• This calculation can help a business with its marketing planning, in particular its pricing strategy and sales promotions