WHEN TOTAL REVENUE EQUALS TOTAL COSTS

Break – even Analysis

PLANNING AND FINANCING A BUSINESS – Financial PlanningUsing Break-Even Analysis to Make Decisions

Contribution per unitContribution per unit of production is the amount that producing and

selling that unit will contribute to Fixed Costs.  

 

Contribution per unit = selling price per unit – variable cost per unit  Using the previous data: 

Contribution per unit = selling price per unit – variable cost per unit

= £11.50 - £1.50 = £10.00 per unit

Calculations

Work out the following contributions.1.Selling Price is £18 and Variable costs is £4.2.VC is £19 and SP is £21.3.SP is £250 and VC is £129.4.VC is £1560 and SP is £2108.

Total Contribution This is what production output makes to cover the fixed costs - it is not

profit. Any surplus above the fixed cost amount is profit and any short-fall is a loss. If total contribution equals fixed costs then a break-even situation has arisen.

 

 Using the previous data:  Total Contribution = contribution per unit x production output

= £10.00 x 10,000 = £100,000

  Total Profit = total contribution – total fixed costs

= £100,000 - £85,000 = £15,000 (£15,000/10,000 = £1.50 profit per unit)

QUESTIONS

1. Work out the total contribution on a business making a 2000 units of a product which is selling at £11.50 and the Variable cost is £1.50.

2. If fixed costs are £5000 work out the total profit the business will make.

3. Now work out the profit per unit that it will make.4. A different business is selling products for £10 the variable

cost is £2. Work out the total contribution they are making when producing 4000 units.

5. Their fixed costs are £30,000 work out the total profit the business will make.

6. Now work out the profit per unit that it will make.7. A business is making 3500 units. The selling price is £9.80

and the variable cost £5 work out the total contribution.8. If fixed costs are £13800 work out the total profit the

business will make.9. Finally work out the profit per unit.

Formulae:  Contribution per unit = selling price per unit less variable

cost per unit 

Total Contribution = contribution per unit multiplied by total units produced

 

If total contribution exceeds fixed cost the excess is profit

If total contribution equals fixed cost then break-even has occurred

If total contribution falls short of fixed cost the shortfall is a loss

Construct a break-even chart from the following table:

UnitsProduced

Selling Price

Per Unit

Variable Cost

Per Unit

TotalVariable

Cost(Variable

CostPer unit

multiplied by Units

Produced)

Fixed Cost

Total Cost

(Fixed Cost plus

Total Variable

Cost)

Total Revenue(Selling

Price per unit

multiplied by Units

Produced)

Profit or

(Loss)(Total

Revenue

MinusTotalCost)

- £ £ £ £ £ £ £

100 5 3 300 600 900 500(400) Loss

200 5 3 600 600 1,200 1,000(200) Loss

300 5 3 900 600 1,500 1,500Break even

400 5 3 1,200 600 1,800 2,000200

Profit

500 5 3 1,500 600 2,100 2,500400

Profit

Break-even chart

Costs and Revenues (£) 

2,500 Total Revenue

 2,000

Break even point Total Cost

1,500  

1,000  Fixed Cost 500  

0 100 200 300 400 500 Units of Output

MARGIN 0F SAFETY

MARGIN OF SAFETY = CURRENT OUTPUT – BREAK – EVEN POINT

= 500 – 300

= 200 UNITS

This means the business can sell up to 200 fewer products before they start to lose money.

This allows businesses to make important decisions e.g. To increase it by lowering costs or increasing revenue

BREAK – EVEN ANALYSIS/TARGETS

Break – even is when TOTAL REVENUE EQUALS TOTAL COSTS. It is a good way for businesses to target how many units they need to produce to cover costs.

SELLING PRICE – VARIABLE COST = CONTRIBUTION

FIXED COST = BREAK – EVENCONTIRBUTION

e.g Nike are selling trainers for £45.oo. They cost £18.00 to make and the fixed costs for the store in Oxford Street is £250,000 a month.

Therefore 45 – 25 = 20. This means for every trainer sold £27.00 is contribution.

So 250,000 = 12,500 units a month. 20

Questions

Work out the break – even targets for the following questions.

1. SP £10 VC £4 and FC £1500.2. SP £15 VC £11 and FC £2000.3. The selling price is now £18 but VC remains at £11

and FC is £2000.4. Selling price reduces to £9 VC changes to £6 and

FC is still £2000.

Using Break-even analysis to make Decisions1. Complete the table below.

UnitsProduced

Selling Price

Per Unit

Variable Cost

Per Unit

ContributionPer Unit

TotalContribution

Fixed Cost

Profit or

(Loss)

- £ £ £ £ £ £

700 25

800

900 9,000

1,000 15

1,100

1,200

Using Break-even analysis to make Decisions 1. Complete the table below.

UnitsProduced

Selling Price

Per Unit

Variable Cost

Per Unit

Contribution

Per Unit

TotalContribu

tion

Fixed Cost

Profit or

(Loss)

- £ £ £ £ £ £

700 25 15 10 7,000 9,000 (2,000)

800 25 15 10 8,000 9,000 (1,000)

900 25 15 10 9,000 9,000Break even

1,000 25 15 10 10,000 9,000 1,000

1,100 25 15 10 11,000 9,000 2,000

1,200 25 15 10 12,000 9,000 3,000

Using Break-even analysis to make Decisions

2. Draw a break-even chart using the information in your table.

3. Explain what you understand by the term ‘Margin of Safety’. Why might a business wish to calculate the Margin of Safety?

 4. Assuming that maximum production capacity is 2,500 units

and the break-even production level is 900 units, calculate the Margin of Safety at 90% capacity.

Using Break-even analysis to make Decisions – answer2. Draw a break-even chart using the information in your table.

Costs and Revenues £00030 Total Revenue

25 Break-even Point Total Cost

20 15

10 Fixed Cost

5 Margin of Safety

0 700 800 900 1,000 1,100 1,200 Units of Output

Using Break-even analysis to make Decisions 3.Explain what you understand by the term ‘Margin of Safety’.

Why might a business wish to calculate the Margin of Safety?  

The Margin of Safety is the quantity of goods that a business can afford not to sell/produce before they get into a loss-making situation. It can be calculated by the following formula:

 Margin of Safety = given production level less break-even output.

  A business may wish to calculate the Margin of Safety as it can help

them plan for any disruption to production output. By calculating the Margin of Safety the business will know the level of non-production it can sustain before it starts to make losses.

Using Break-even analysis to make Decisions – answer

4. Assuming that maximum production capacity is 2,500 units and the Break Even

production level is 900 units, calculate the Margin of Safety at 90% capacity.

 Production capacity at 100% = 2,500 unitsProduction capacity at 90% = 2,500 x 0.9 = 2,250 units 

Margin of Safety = Production capacity at 90% less Break even output

= 2,250 - 900 = 1,350 units. 

Using Break-even analysis to make Decisions

5. Explain what you understand by the term ‘Contribution per Unit’.

6. Using the Contribution concept calculate:  • The profit made by producing and selling 1,500 units with the

selling price being £25, the variable cost per unit £15 and fixed costs are £9,000.

 

Using Break-even analysis to make Decisions

5. Explain what you understand by the term ‘Contribution per Unit’. Contribution per unit is the amount each unit produced contributes towards the fixed costs.  Contribution per unit is calculated by the following formula: Selling Price per unit - Variable Cost per unit.

Using Break-even analysis to make Decisions – answer

6. Using the Contribution concept calculate:  The profit made by producing and selling 1,500 units. Units produced and Sold: 1,500 Contribution per unit = Selling Price per unit less Variable Cost

per unit = £25 - £15 = £10

 Total Contribution = Contribution per unit multiplied by Number

of units produced= £10 x 1,500= £15,000

 Profit = Total Contribution minus Fixed Cost

= £15,000 - £9,000 = £6,000

Using Break-even analysis to make Decisions7. With reference to Question 1 re-calculate the break-even point if:  

• The Fixed Cost increased to £10,000 and the Variable Cost per unit increased to £20, the Selling Price per unit remaining the same at £25.

 • The Fixed Cost decreased to £5,000 and the Variable Cost per unit

decreased to £9, the Selling Price per unit remaining the same. 

 

Using Break-even analysis to make Decisions – answer• 7. The Fixed Cost increased to £10,000 and the Variable Cost

per unit increased to £20, the Selling Price per unit remaining the same.

Fixed Cost = £10,000 Variable Cost per unit = £20 Selling Price per unit = £25

Contribution per unit = Selling price per unit - Variable Cost per unit = £25 - £20 = £5 per unit

Break-even point in units = Fixed Cost ÷ Contribution per unit = £10,000 ÷ £5 =2,000 units

Using Break-even analysis to make Decisions – answer

• The Fixed Cost decreased to £5,000 and the Variable Cost per unit decreased to £9, the Selling Price per unit remaining the same.

 

Fixed Cost = £5,000Variable Cost per unit = £9Selling Price per unit = £25

 Contribution per unit = Selling price per unit - Variable Cost

per unit = £25 - £9 = £16 per unit   Break-even point in units = Fixed Cost ÷ Contribution

per unit = £5,000 ÷ £16

= 312.5 units 

Advantages of using break-even analysis• It can be used to show relevant costs and revenues in diagrammatic form.

•It’s quick – managers can see the break – even point and margin of safety immediately so they can take quick action to cut costs or increase sales if they need to increase there margin of safety

• Businesses can use it to help persuade banks to give them a loan.

• It can influence 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 may not launch the product.

• It is a relatively easy concept to understand and is recognised by most businesses as a simple decision making tool to put into operation. For example, ‘you’ need to produce and sell 500 units of your product before you start to make a profit! Can you do this? 

Disadvantages of using break-even analysis•  It assumes that variable costs always rise steadily. This isn’t always the case – a business may buy in bulk and therefore get discounts so costs would not go up in proportion to output 

•It is limited in scope insofar as it can only relate to a single product. As many businesses have a multiple product portfolio a break-even analysis would have to be carried out on each product as each product would have its own cost and revenue structure.  

• Its effectiveness as a management decision making tool is limited by the accuracy and dependability of the primary or secondary data used in the analysis. Therefore if data is wrong then the results will be wrong

•Its analysis is based on the assumption that all goods produced are sold. This may be a false assumption in a dynamic business environment where consumers ‘shop around’ and competitors take advantage of this.