Break-Even Analysis

Break-Even Analysis

Specific Learning Outcomes

• Define the term ‘break-even’.

• Use a numerical method to calculate break-even output.

• Define, calculate, and explain the importance of the margin of safety.

• Evaluate the usefulness of break-even analysis.

• If you don't break even, the business will start accumulating debt.

Understanding Break-Even Analysis

• Organizations need to know the costs of production for their goods and services.

• They also need to know how many products they have to produce and sell in order to cover all their costs.

• Break-even analysis helps organizations determine the costs of production and the required production or sales volume to cover all costs.

Definition of Break-Even Point

• The break-even point is the level of output at which total revenue equals total costs.

• At the break-even point, a business has neither made a profit nor incurred a loss.

• Formula: Total Revenue = Total Costs

Break-Even Formulas

1. Profit = Total Revenue - Total Costs

   • Profit = TR - TC

2. Total Revenue = Price x Quantity

   • TR = P \times Q

3. Total Costs = Fixed Costs + Variable Costs

   • TC = FC + VC

4. Break-even occurs when Total Costs = Total Revenue

   • BE: TC = TR

5. Break-even output = Fixed Costs / (Selling Price - Variable Costs)

   • BE = \frac{FC}{SP - VC}

   • Where (SP-VC) is Contribution

Key Cost Concepts

• Fixed Costs: Costs that do not vary with the level of output in the short term. These costs must be paid whether the firm produces anything or not.

• Total Costs: The sum of fixed costs and variable costs.

• Variable Costs: Costs that vary in direct proportion to output.

• Total Revenue: Obtained by multiplying selling price by output level.

• Fixed costs do not vary or depend on output, while variable costs vary based on output.

Graphical Representation of Break-Even Analysis

• The fixed-cost line is horizontal, indicating that fixed costs are constant at all output levels.

• The sales revenue line starts at the origin (0), as no sales result in no revenue.

• The variable-cost line starts from the origin (0), as no production results in no variable costs.

• The total-cost line begins at the level of fixed costs, with the difference between total and fixed costs being accounted for by variable costs.

• The point where the total-cost and sales-revenue lines cross is the break-even point (BE).

• Production levels below the break-even point result in a loss, while levels above result in a profit.

Example Calculation

• Samsons sells 300 items at a price of £3.50.

• Fixed costs are £500, and variable costs per unit are £1.00.

  • Calculate the total contribution.

  • Calculate the break-even quantity.

  • Calculate the profit/loss.

Example Question

• Given the following information, calculate the monthly break-even output:

  • Average fixed costs at full capacity: £12.50

  • Unit variable costs: £15.00

  • Price: £35.00

  • Maximum capacity: 12000

• The correct answer is 7500.

  • BE = \frac{FC}{Contribution (SP-VC)} = \frac{12.50 \times 12000}{35-15} = \frac{150000}{20} = 7500

Launching a New Product: An Example

• Davie Enterprises is launching a men’s cologne gift set and needs to determine the break-even point.

  • Variable production costs:

    • Direct materials: ₤5 per unit

    • Direct labor: ₤11 per unit

    • Variable overheads: ₤2 per unit

  • Planned selling price: ₤30 per unit

  • Fixed overheads specific to the new product: ₤20,000

• Calculate the break-even point:

  • BE = \frac{FC}{Contribution (SP-VC)} = \frac{20000}{30 - (5 + 11 + 2)} = \frac{20000}{12} = 1666.67 \approx 1667

Additional Examples

• Peter's window cleaning business:

  • Annual sales revenue: £126,550

  • Total annual variable costs: £77,290

  • Total contribution: £126,550 - £77,290 = £49,260

  • 9,000 customer visits each year.

  • Contribution per visit (unit): £49,260 / 9,000 = £5.473 per visit

  • Annual fixed costs: £10,560

  • Annual profit: £49,260 - £10,560 = £38,700

• Pat's Pastries:

  • Sales of 250 units

  • Sales revenue: £26,500

  • Total variable costs: £12,340

  • Total fixed costs: £4,600

  • Total contribution : 26500 - 12340= £14,160

  • Contribution per unit: £14,160 / 250 = £56.64

  • Profit: £14,160 - £4,600 = £9,560

• Krishna Inn:

  • Annual fixed costs: £150,000

  • Contribution per unit: £5

  • Break-even quantity: £150,000 / £5 = 30,000 units

Margin of Safety

• This measures the difference between the actual output and the break-even output.

• It indicates how much sales could fall without the firm incurring a loss.

• A higher margin of safety indicates a lower risk of loss.

• Margin of safety: The amount by which the sales level exceeds the break-even level of output.

• Example: If actual output is 150 units and the break-even level of output is 100 units, the margin of safety is 50 units.

• Knowing the margin of safety can help a business assess the impact on profits of a change in output or the break-even level.

Margin of Safety - Cat's Cookies Example

• Financial forecasts for a new business, Cat's Cookies, during the first six months:

  • Fixed costs: £50,000

  • Selling price: £6.50

  • Variable cost per unit: £2.50

  • Sales capacity: 15,000

• Calculations:

  • Break-even quantity: \frac{50000}{(6.5 - 2.5)} = 12500

  • Profit (loss) at a sales volume of 10,000: 65000 - 50000 - (2.5 \times 10000) = -10,000

  • Profit (loss) at a sales volume of 15,000: 97500 - 50,000 - (2.5 \times 15,000) = 10,000

  • Margin of safety at a sales volume of 15,000: 15000 - 12500 = 2500

Benefits of Break-Even Analysis

• Highlights the required output or total sales.

• Aids decision-making.

• Shows different levels of profit arising from various levels of output and sales.

• Calculations are quick and relatively easy to complete, saving time.

• Break-even diagrams are easy to view, understand, and interpret.

Drawbacks of Break-Even Analysis

• The information may be unreliable as it based on forecasts, and costs can change.

• It ignores economies of scale as it assumes variable costs remain constant.

• Prices may change due to discounts or changes in demand.

• There is no certainty that goods will be sold.

• Break-even analysis should be seen as a planning aid rather than a decision-making tool.

Advantages of Break-Even Analysis

• Easy to do: If you can plot figures on a graph accurately, you can do break-even analysis.

• Quick: Managers can see the break-even output and margin of safety immediately, enabling them to take quick action to cut costs or increase sales if they need to increase their margin of safety.

• Break-even charts let businesses forecast how variations in sales will affect costs, revenue, and profits, and, most importantly, how variations in price and costs will affect how much they need to sell.

• Businesses can use break-even analysis to help persuade sources of finance to give them money.

• Break-even analysis influences decisions on whether new products are launched or not - if the business would need to sell an unrealistic volume of products to break even, they would probably decide not to launch the product.

Disadvantages of Break-Even Analysis

• Break-even analysis assumes that variable costs always rise steadily. This isn't always the case - e.g. a business can get discounts for buying in bulk so costs don't go up in direct proportion to output.

• Break-even analysis is simple for a single product - but most businesses sell lots of different products, so looking at the business as a whole can get a lot more complicated.

• If the data is inaccurate, then the results will be wrong.

• Break-even analysis assumes the business sells all the products, without any wastage. But, for example, a restaurant business will end up throwing away food if fewer customers turn up than they're expecting.

• Break-even analysis only tells you how many units you need to sell to break even. It doesn't tell you how many you're actually going to sell.

Margin of Safety Question

• The difference between the actual output and the break-even level is known as the margin of safety

Limitations of Breakeven Analysis

• A limitation of the usefulness of break-even analysis is that variable costs may fall over time

Reducing Breakeven Point

• An option for a firm looking to reduce its break-even point is to reduce its selling price.

Calculating Actual Output

• If the margin of safety is 7,500 units and break-even output is 12,200 units, what is actual output?

• Margin of Safety = Actual Output - Break Even Output -> 7500 = A - 12,200

• A = 7500 + 12,200 = 19700 units

Break-Even Chart

• On a break-even chart, a horizontal line represents fixed cost.d fixed costs.

Gift Shop Example

• John is thinking of opening a gift shop in a tourist area.

• Rent and other costs: £200 per week.

• Wage for himself: £100 per week.

• Stock cost: £2 per unit.

• Selling price: £5.00 per unit.

  • Calculate his annual fixed costs.

  • How much profit will he make per year if he sells 150 units per week?

  • Calculate his break-even output.

  • How will break-even analysis help John to decide whether to open the shop? Will he need any further information?

Gift Shop Example - Answers

• Annual Fixed Costs:

  • (£200 + £100) * 52 = £15600

• Annual Variable Costs at 150 units:

  • 2 * 150 * 52 = £15600

• Annual Revenue at 150 units:

  • 5 * 150 * 52 = £39000

• Annual Profit:

  • 39000 - (15600 + 15600) = £7800

• Break-Even Output:

  • Fixed costs / contribution

  • = 15600 / (5 - 2)

  • = 5200 per year or 100 per week.

• John will be able to use this information to make an estimate of how well his business is likely to perform.

• He will also need some idea of how many sales he is going to make so that he can see whether his business will be profitable. As long as sales are likely to be above 100 per week, the business will be profitable.

• He might need to think about whether his sales are seasonal, as is often the case in tourist areas. If they are then he will have some weeks when sales are well below his break-even point but in the tourist season they will be much higher.

• He should also consider how accurate his estimates of costs are likely to be and whether there will be changes in these over time.

• Overall, the calculation will give him an idea of how well he is likely to do but there are a number of factors he will need to consider which will cast some doubt over his calculations.

• Break-even makes assumptions about the linear behavior of cost and revenue without output. Some candidates may challenge these assumptions. Better candidates will consider both the advantages and disadvantages.

Driving Instructor Example

• Jason is planning to start his own business as a driving instructor.

• He will be a sole trader.

• Jason plans to charge £20 per lesson.

• Jason has estimated that the variable costs per lesson will be £4 and total annual fixed costs will be £16,000.

• Jason estimates that he will average sales of 30 lessons per week.

• He plans to work for 46 weeks per year.

• Jason is not sure how best to promote his new business in his local town.

Jason would take all the profit and has full control of the business.

• Break-even number of lessons per year: \frac{16,000}{(20-4)} = 1000

• Forecast annual margin of safety: (30 * 46)=1380 ->1380-1000=380 lessons

Toy Company Example

• A business has annual fixed costs of £35,000.

• It sells wooden toys for £5 each.

• The direct cost of each toy is £2.50.

• Maximum capacity is 20,000 toys, and last year it made and sold 16,000.

  • Calculate the break-even level of production.

  • Calculate the margin of safety.

  • Calculate the profit at maximum capacity.

Additional Company Numbers

• A company sold 35000 units of output in 2017.

• Total fixed costs in 2017 were £450,000, and the average contribution per unit was £15.

  • Calculate the margin of safety for 2017.

Lawnmower Business Example

• Peter wants to start a lawnmower business.

• Cost of each mower from the distributor (the variable cost) = £50.

• Fixed costs (including loan repayment, additional insurance, business rates, heating etc) = £2,000

• He decides to draw a break-even chart to see if he could make a profit if he sold the mowers for £80 each.

• He thinks that the most he would sell in the year is 100 mowers.

  • Calculate the company’s break-even.
    BE = \frac{FC}{CONTRIBUTION : PER : UNIT (SP-VC)}
    = \frac{2000}{(80-50)}
    = \frac{2000}{30}
    = 67 : Units

Missing Figures Example

• BE = FC/CONTRIBUTION PER UNIT (SP-VC)

• = 2000/(80-50)

• = 2000/30

• = 67

*Question A7
The price of a product is calculated using a 250% mark-up on cost. The cost of [1]
making 100 units of product X is £250. The selling price of product X is:
£8.75.

Question A7
The total cost of producing one unit of product X is £12.00. Fixed costs are [1]
allocated to product X on the basis of £5000 per 2000 units. The selling price
of product X is £20.75. The contribution per unit for product X is:
B. £11.25

Question A10
A business has total annual fixed costs of £150,000. The unit variable cost of
production is £4.00. The average price per unit is £10.00.
a) Calculate the annual break even output.
a) = 25,000 whits
b) Explain the importance of margin of safety.