5.5 Break-even Analysis

Question 1

5.5.1 Total Contribution VS Contribution per Unit (A02)

Define ‘Break-even Analysis’

Answer 1

A business management tool used to determine the level of sales volume needed to cover all the costs associated with the output of a particular good or service.

Question 2

5.5.1 Total Contribution VS Contribution per Unit (A02)

Define the terms:
1. Break-even Point (BEP)
2. Break-even Quantity (BEQ)

Describe the structure of a Break-even Analysis Graph

Answer 2

Break even point: A condition/point where a firm’s sales revenues cover/equal all of its production costs.

Break-even Quantity/Point (BEQ) - the level/amount of output where a business does not make either a profit or a loss.

TOP TIP:
When calculating the break-even quantity, if the answer is not a whole number (e.g. 132.4 cars) then make sure you round up (e.g. 133 cars)

BEQ = Fixed Costs/ Selling Price - Average Variable Cost

Description of a Break-even Chart:
- X Axis = Sales Quantity
- Y Axis = Costs and Revenues
- Total Fixed Costs = Horizontal Line above the X Axis
- Total Revenue = Diagonal Line originating from the origin
- Total Costs = Diagonal Line originating from the start of the TFC line
- Break Even Point = where the TR and TC intersect (to the left it is a loss, to the right of this intersection is a profit (should be in the triangles) )
- Break Even Quantity = the BEP point dragged to the X Axis
Break-even Revenue = the BEP point dragged to the Y Axis

Question 3

5.5.1 Total Contribution VS Contribution per Unit (A02)

Define the terms:
1. Contribution per unit
2. Total Contribution

State the common mistake that students make

Answer 3

Contribution per unit : the amount of money earned from each unit of the product sold to customers.

Formula : Selling Price - Average Variable Cost

Total Contribution: the unit contribution (P – AVC) multiplied by the quantity sold (Q), i.e. (P – AVC) × Q. This is the amount used to pay fixed costs; any surplus that remains becomes profit for the firm.

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

Question 4

5.5.2 Aspects of Break-Even Analysis (A02)(A04)

Define the ‘Margin of Safety’ and make clear when a business has a positive or negative margin of safety.

Answer 4

Margin of Safety/ Safety Margin (MOS) - the numerical difference between how much a business sells and how much it needs to sell (BEQ) to reach break-even.

Formula:
Sales Volume - BEQ

If the firm sells more than its break-even quantity (BEQ), it will earn a profit. This also means it has a positive margin of safety

Question 5

5.5.2 Aspects of Break-Even Analysis (A02)(A04)

Define the terms and state each of their formulas:
1. Target Profit Output/Quantity
2. Target Price
3. Target Profit

Answer 5

1. Target Profit Output : quantity of sales required to reach the firm’s target profit.

TOQ = (Fixed cost + Target profit) / (Price – Average Variable Cost)

2. Target Price: the amount customers need to pay per unit in order for the firm to break-even or to reach a particular target profit.

To reach break-even formula:

Average Fixed Cost + Average Variable Cost

To reach a target profit/ point beyond break-even:

(Target profit + Total cost) / Quantity of output

Target Profit : the value of profit that a firm aims to earn within a given time period.

TP = Total revenue – Total cost

Question 6

5.5.3 Changes in Price and Costs (A02, A04)

Explain what happens in to Break-even Analysis in the following Changes in Price and Costs:

1. INCREASE IN SELLING PRICE
2. HIGHER COSTS OF PRODUCTION

Answer 6

INCREASE IN SELLING PRICE:
1. Reduces Break even Point (if sales quantity/demand remains the same). This results in a higher gradient of the Total Revenue line.
2. Reduces the Break-even Quantity.
3. Raise in the Margin of Safety (if sales quantity/demand remains the same)

VICE VERSA FOR A REDUCTION IN PRICE.

INCREASE IN COSTS OF PRODUCTION (be they fixed and/or variable costs):
1. Raise Break-even Quantity. This will make a steeper if only variable costs increase or be shifted upwards if there is an increase in the firm’s fixed costs.

THE OPPOSITE CAN BE SAID FOR A REDUCTION IN THE COSTS OF PRODUCTION.

Question 7

5.5.4 Limitations of Break-even Analysis as a decision-making tool

State and Explain three DISADVANTAGES/LIMITATIONS of Break-even Analysis

Answer 7

1. Prices are assumed to be constant (the linear Total Revenue line is shown to have a constant gradient) but in reality many businesses offer price discounts to loyal customers and those who buy large quantities.
2. Break-even analysis is ideal for businesses that sell a single good or service. It can be difficult to calculate break-even for businesses that sell a large range of goods and services, as prices and production costs differ.
3. As with all quantitative tools, the effectiveness of break-even analysis relies on the accuracy of the cost and revenue data used to make the predictions. Any inaccuracies and/or deliberate bias in the use of the quantitative data will invalidate the results of the break-even analysis.