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Contribution analysis

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  • Old course (N23)/
  • Unit 3/
  • 3.3 Break-even analysis/
  • Contribution analysis
3.3 Contribution analysis (AO2)

Oyster vendor at Greenwich Market, London, UK

This section of the IB Business Management syllabus looks at the difference between total contribution and contribution per unit (AO2).

Break-even exists when a firm’s sales revenues cover all of its production costs.

The break-even quantity (BEQ) is the level of output where a business does not make either a profit or a loss.

The formula for calculating the BEQ is:

This can be demonstrated by using the numerical example below for a seller of oysters at a market stall in Greenwich Market, London, UK:

  • The average price of each oyster is £1.25
  • The variable cost of each oyster is £0.45
  • The vendor’s rent (its only fixed costs) is £200 per week
  • So, the BEQ = £200 ÷ (£1.25 – £0.45) = 250 oysters to reach break-even
  • At this level of output, the total revenue = £1.25 × 250 = £312.50
  • If the firm sells 250 oysters, the total costs = £200 + (£0.45 × 250) = £200 + £112.50 = £312.50
  • Hence, the firm will break even at 250 units (250 oysters), when the TR = TC = £312.50.

This can be represented by the break-even diagram below:

 

The difference between a firm’s price and its average variable cost is known as the unit contribution (or contribution per unit). This represents the amount of money earned from each unit of the product sold to customers.

The formula for calculating contribution per unit is: P – AVC, where P = price and AVC = average variable cost.

  • In the above example, for each oyster sold, the market vendor earns £1.25 – £0.45 = £0.80
  • So, for each oyster sold, the vendor earns £0.80 (80 pence) towards paying the firm's fixed costs
  • The market stall vendor will need to sell 250 oysters in order to pay for the weekly rent of £200, i.e. £0.80 × 250 = £200.

The positive difference between a firm’s selling price and its average variable cost is used to pay (or contribute to) its fixed costs. Hence, break-even occurs when a firm’s total contribution equals it total fixed costs.

  • Total contribution is simply the unit contribution (P – AVC) multiplied by the quantity sold (Q), i.e. Total contribution = (P – AVC) × Q.
  • Total contribution is used to calculate profit or loss by taking away fixed costs from total contribution, i.e. Profit = [(P – AVC) × Q] – TFC.
Common mistake

Contribution is not the same as value added, although the two terms are often confused by students:

  • Unit contribution = Price minus Average variable cost, i.e. P – AVC
  • Value added per unit = Price minus Average total costs, i.e. P – ATC

This means that value added considers both variable and fixed costs of production, whereas unit contribution only considers the cost of goods sold (COGS) or the variable costs.

Exam Practice Question 1 - Heather Manetta's Hotdogs

Heather Manetta is a hotdog vendor. She sells hotdogs for $10 each and has unit variable costs of $6. She pays $2,000 rent per month. On average, she sells 1,500 hotdogs per month.

(a).

Calculate Heather Manetta's contribution per unit.

[2 marks]

(b).

Calculate Heather Manetta's total contribution per month.

[2 marks]

(c).

Calculate Heather Manetta's break-even quantity.

[2 marks]

(d).

Calculate Heather Manetta's average profit per month.

[2 marks]

 Teacher only box

Answers

For each question, award 1 mark for the correct answer and 1 mark for showing appropriate working out.

(a).  Calculate Heather Manetta's contribution per unit.  [2 marks]

$10 – $6 = $4 contribution per unit.

(b).  Calculate Heather Manetta's total contribution per month.  [2 marks]

$4 × 1,500 hotdogs = total contribution of $6,000 per month

(c).  Calculate Heather Manetta's break-even quantity.  [2 marks]

BEQ = $2,000 / ($10 – $6) = 500 hotdogs per month

(d).  Calculate Heather Manetta's average profit per month.  [2 marks]

Profit = Total contribution – Fixed costs = $6,000 – $2,000 = $4,000

Exam Practice Question 2 - Mayer's Doughnuts

Vicky Mayer is the owner of Mayer's Doughnuts. The business has variable costs of $0.25 per doughnut and Vicky sells these for $1.50 each. Her fixed costs are $10,000 per month. She sells an average of 9,500 doughnuts each month.

(a).

Calculate the unit contribution for Mayer’s Doughnuts.

[2 marks]

(b).

Calculate the number of doughnuts the firm has to sell each month in order to reach break-even.

[2 marks]

(c).

Calculate the monthly safety margin for Mayer’s Doughnuts.

[2 marks]

(d).

Use the above answers to plot the break-even chart for Mayer’s Doughnuts.

[5 marks]

 Teacher only box

Answers

(a).  Calculate the unit contribution for Mayer’s Doughnuts.  [2 marks]

The formula for contribution per unit is selling price minus variable cost per unit (P – AVC).

Given that P = $1.50 and AVC = $0.25, the contribution per unit is $1.25

Award 1 mark for the correct working out and 1 mark for the correct answer with the correct unit of measurement ($).

(b).  Calculate the number of doughnuts the firm has to sell each month in order to reach break-even.  [2 marks]

The formula for break-even is fixed costs divided by unit contribution, i.e. TFC ÷ (P – AVC). Hence, BEQ = $10,000 ÷ $1.25 = 8,000 doughnuts per month.

Award 1 mark for the correct working out and 1 mark for the correct answer with the correct unit of measurement (doughnuts).

(c).  Calculate the monthly safety margin for Mayer’s Doughnuts.  [2 marks]

The safety margin is calculated by finding the difference between actual sales and the break-even quantity

Hence, the safety margin = 9,500 – 8,000 = 1,500 doughnuts

Award 1 mark for the correct working out and 1 mark for the correct answer with the correct unit of measurement (doughnuts).

(d).    Use the above answers to pot the break-even chart for Harvey’s Doughnuts.  [5 marks]

Break-even chart for Harvey’s Doughnuts

Award 1 mark for each of the following, up to the maximum of 5 marks:

  • Correctly plotting and labelling the total sales revenue (TR) line
  • Correctly plotting and labelling the total cost (TC) line
  • Clearly identifying the break-even output at 8,000 doughnuts
  • Clearly identifying the margin of safety of 1,500 doughnuts
  • Correctly labelling of both axes.

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