Break-even Analysis (HL IB Business Management)

• Break-even analysis is a financial tool used to determine the number of units a business must sell to reach a point where the business revenue equals its expenses (no 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 to make informed decisions about pricing and production volumes
     

Diagram with the Three main Components of a Break-even Analysis

Variable costs,, fixed costs and sales revenue are all used in calculating the break-even point
 

• 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

• 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

• 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
     

The break even chart for A2B Limited shows that at 324 units the total revenue = the total costs  

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

• The Break Even Point occurs where the total revenue earned for a product is exactly equal to its total costs and where 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 such as stock, machinery and workers required

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