Break-Even Analysis (DP IB Business Management)

Revision Note

Flashcards

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

The main components of break even analysis include variable costs, fixed costs, and revenue
The main 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: 

    • Contribution space per space unit space equals space Selling space price space per space unit space minus space Variable space cost space per space unit

    • 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

    • Total space contribution space equals space Contribution space per space unit space cross times space Total space units space sold

      or

    • Total space contribution space equals space Total space revenue space minus space Total space variable space costs

    • 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

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

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

Break space Even space Point space space space space space space space space equals space space space space space space space space space space fraction numerator Fixed space Costs over denominator Contribution space per space unit end fraction

  • 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

Worked Example

Selected Cost and Revenue data for Montrose Glamping

 

AUS$

Revenue per pod per night

95

Variable costs per pod per night

19

Annual fixed costs

55,000

Using the information in the table, calculate how many pods need to be occupied each month for Montrose Glamping to break even. [4 marks]

Answer:

Step 1 - State the formula to calculate the break-even point

Break space Even space Point equals space space space space space space space space space space space space space space space space space fraction numerator Fixed space Costs over denominator Contribution space per space unit end fraction space          [1 mark]

Step 2 - Calculate the contribution

Selling price - variable cost per unit

= $95 - $19

= $76               [1 mark]

Step 3 - Apply the formula to calculate the break-even point

fraction numerator $ 55 comma 000 over denominator space $ 76 end fraction space      

= 723.68             [1 mark]

Step 4 - Always round UP to the nearest whole number because only whole products can be sold

723.68

= 724 camping pods      [1 mark]

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

Margin space of space Safety space equals space Actual space output space minus space Break space even space output

Worked Example

The cost, sales and revenue for an electric bicycle manufacturer are presented in the table below

Annual fixed costs

£42,000

Selling price per unit

£750

Variable cost per unit

£350

Number of units sold

240

Using the data, calculate the margin of safety. You are advised to show your workings. [4 marks]

 Answer:

Step 1 - Calculate the contribution

£750 - £350

= £400       [1 mark]

Step 2 - Calculate the break even point

   fraction numerator £ 42 comma 000 over denominator space £ 400 end fraction space

= 105 units         [2 marks]

Step 3 - Calculate the margin of safety

240 units - 105 units

= 135 units     [1 mark]

Calculating profit or loss

  • Profit or loss can be calculated in two ways

Profit space open parentheses Loss close parentheses equals space Total space contribution space minus space Total space fixed space costs

or

Profit space open parentheses Loss close parentheses space equals space Total space revenue space minus space Total space costs

Worked Example

ForêtSaut is an outdoor treetop activity centre. In 2022 it earned revenue of €462,540 with fixed costs of €281,720 and total variable costs of €131,280.

Calculate the total profit made by ForêtSaut in 2022.  [2 marks]

Answer:

Step 1: Calculate the total contribution

Total space contribution space equals space Total space revenue space minus space Total space variable space costs

        equals space € 462 comma 540 space minus space space € 131 comma 280

        equals space € 331 comma 260               [1 mark]

Step 2: Use the contribution figure to calculate profit

Profit space open parentheses Loss close parentheses space equals space Total space contribution space minus space Total space fixed space costs

equals space € 331 comma 260 space minus space € 281 comma 720              

equals space € 49 comma 540                  [1 mark]

Examiner Tip

You may be asked to use principles of break even to calculate

  • Target profit output

  • Target profit

  • Target price

Practice rearranging the formula for target profit output to find the other variables so that you don't have to remember all three formulas.

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

Target space profit space output space equals space fraction numerator Fixed space costs space plus space Target space profit over denominator Contribution space per space unit end fraction

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

Worked Example

ForêtSaut is an outdoor treetop activity centre. In 2022 it attracted 38,545 customers and earned revenue of €462,540 with fixed costs of €281,720 and total variable costs of €131,280. In 2023 it has set a profit target of €84,000.

Calculate the target profit output if ForêtSaut is to achieve its target profit in 2023.       [3 marks]

Answer:

Step 1: Calculate the contribution per unit

Contribution space per space unit space equals space fraction numerator Total space contribution over denominator Units space of space output end fraction

  equals space fraction numerator € 331 comma 260 over denominator 38 comma 545 space customers end fraction

   =   €8.60            [1 mark]

Step 2: Apply the formula to calculate target profit output

T a r g e t space p r o f i t space o u t p u t space equals space fraction numerator Fixed space costs space plus space Target space profit over denominator Contribution space per space unit end fraction

  equals space fraction numerator € 281 comma 720 space plus space € 84 comma 000 over denominator € 8.60 end fraction         [1 mark]

equals space fraction numerator space € 365 comma 720 over denominator space € 8.60 end fraction

= 42,526 customers (rounded up to next whole unit)    [1 mark]

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

Target space profit space equals space open parentheses Target space profit space output space cross times space Contribution close parentheses minus space Fixed space costs 

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

Worked Example

ForêtSaut is an outdoor treetop activity centre. In 2022 it attracted 38,545 customers and earned revenue of €462,540 with fixed costs of €281,720 and total variable costs of €131,280. In 2023 it has set a target profit output of 42,526 customers.

Using 2022's costs and revenues data, calculate ForêtSaut's target profit if it is to achieve its total profit output of 42,526 customers in 2023. [3 marks]

Answer:

Step 1: Calculate the contribution per unit

Contribution space per space unit space equals space fraction numerator Total space contribution over denominator Units space of space output end fraction


equals space fraction numerator € 331 comma 260 over denominator 38 comma 545 space customers end fraction


equals space € 8.60 [1 mark]

Step 2: Apply the formula to calculate target profit

Target space profit space equals space open parentheses Target space profit space output space cross times space Contribution close parentheses space minus space Fixed space costs

equals open parentheses 42 comma 526 space cross times space € 8.60 close parentheses space minus space € 281 comma 720

equals space € 84 comma 003 [2 marks]

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

Target space price space equals space fraction numerator open parentheses Target space profit space output space cross times space Variable space costs space per space unit close parentheses space plus space open parentheses Fixed space costs space plus space Target space profit close parentheses over denominator Target space profit space output end fraction

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

Worked Example

ForêtSaut is an outdoor treetop activity centre. In 2022 it attracted 38,545 customers and earned revenue of €462,540 with fixed costs of €281,720 and total variable costs of €131,280. In 2023 it has set a target profit of €84,000 from 42,526 customers.

Using 2022's costs and revenues data, calculate ForêtSaut's target price if it is to achieve its target profit €84,000 in 2023.  [4 marks]

Answer:

Step 1: Calculate variable costs per unit

Variable space costs space per space unit space equals space € 131 comma 280 space divided by space 38 comma 545 space customers

equals € 3.41               [1 mark]

Step 2: Multiply target profit output by variable costs per unit

equals 42 comma 526 space cross times space € 3.41

equals € 145 comma 014   [1 mark]

Step 3 - Add fixed costs to target profit

equals space € 281 comma 720 space plus space € 84 comma 000

equals space € 365 comma 720        [1 mark]

Step 4: Apply the formula to calculate the target price and round to two decimal places

equals space fraction numerator € 145 comma 014 space plus space € 365 comma 720 over denominator 42 comma 526 end fraction

equals space € 12.00            [2 marks]

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