5.5 Break even analysis

Question 1

contribution

Answer 1

refers to the money remaining after all direct and variable costs are taken away from the sales revenue. More specifically , contribution is the amount available to ‘contribute’ towards paying fixed costs of production once the variable costs has been deduced.

Question 2

what can contribution be used to calculate

Answer 2

to calculate how many products need to be sold in order to cover the firms’ costs.

Question 3

contribution per unit

Answer 3

contribution per unit refers to the difference between the selling price per unit and the variable cost per unit (or average variable cost)

Question 4

total contribution

Answer 4

can be calculated in two ways: by subtracting the total variable cost from the total sales revenue:
𝒕𝒐𝒕𝒂𝒍 𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏=𝑻𝑹−𝑽𝑪
Or :
𝒕𝒐𝒕𝒂𝒍 𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏=𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒑𝒆𝒓 𝒖𝒏𝒊𝒕∗𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒖𝒏𝒊𝒕𝒔 𝒔𝒐𝒍𝒅

𝒕𝒐𝒕𝒂𝒍 𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏=𝑸∗(𝑷−𝑨𝑽𝑪)

Question 4

contribution per unit formula

Answer 4

𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒑𝒆𝒓 𝒖𝒏𝒊𝒕=𝑷−𝑨𝑽𝑪

Question 5

contribution and unit

Answer 5

profit can be calculated after contribution has been established. To make this calculation we need to know the Total Fixed Cost (FC).
Hence the profit will be the difference between the total contribution and the total fixed cost, as follows:
𝑷𝒓𝒐𝒇𝒊𝒕=𝑻𝒐𝒕𝒂𝒍 𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 −𝑭𝑪 **
Following our example, what would the profit be?
𝑷𝒓𝒐𝒇𝒊𝒕=£𝟗,𝟎𝟎𝟎−£𝟓,𝟎𝟎𝟎=£𝟒,𝟎𝟎𝟎
** Note that this is an alternative way to calculate the profit.

Question 6

when does the break even point occur

Answer 6

when the total costs (TC) equals total revenue (TR)

Question 7

why is the break even point so important

Answer 7

At the break-even point the firm is not making a profit or a loss, it’s just covering all its costs.
Since the aim is to ‘make a profit’, the break-even point is very important for startup companies; since they need to calculate the minimum number or products they need to produce, to cover all their costs.
Hence, the production after the break-even point will determine the profit the firm will be making.

Question 8

a business can be in any of the following at any point in time

Answer 8

Loss – costs of production receding the revenues TC > TR
Break-even – when revenues of the firm equal the costs of production TC = TR
Profit – when revenues exceed the costs of production TR > TC

Question 9

what is the break even chart

Answer 9

is a graphical method that measures the costs and revenues of the firm against the level of output (sales).

Question 10

what needs to be considered when plotting a break even chart

Answer 10

1. Fixed Costs (FC) need to be paid no matter what level of output; hence they are constant.

2.Variable Cost (VC) will start from the origin, since at zero level of production there won’t be VC incurred. But as the output increases, so does the VC (generally, VC is not included in the Break-even chart)

3.The Total Cost (TC) starts where the FC line begins (since FC still must be paid even without output produced) – its parallel to the VC

4.With no output sold, there will be no revenue; so, the TR line begins from the origin. The greater the number of units sold the grater the revenue.

5.The break-even point will be where the TC line intersects with the TR one. This point shows both scenarios: break-even cost/revenue and break –even level of output.

6.The chart shows: the loss for the firm (the left side of the break-even point) and the profits made by the firm (the right side of the break-even point)

** for simplicity, the VC is generally NOT INCLUDED in de Break-even chart**

Question 11

margin of safety

Answer 11

refers to the difference between the break-even level of output and the actual level of output. This margin shows the actual profits the business is actually making.
The greater the difference between the break-even output and the actual output, the saver the firms will be (the greater the safety net).

𝑚𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦=𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑢𝑝𝑢𝑡−(𝑏𝑟𝑒𝑎𝑘−𝑒𝑣𝑒𝑛 𝑜𝑢𝑡𝑝𝑢𝑡)

Question 12

calculating break even quantity

Question 13

target profit output

Answer 13

the level of output needed to make profit
This basically refers to how many products you need to sell (i.e. 90 bicycles) to make a profit.

Question 14

target profit output formula

Answer 14

𝑇𝑎𝑟𝑔𝑒𝑡 𝑝𝑟𝑜𝑓𝑖𝑡 𝑂𝑢𝑡𝑝𝑢𝑡 (𝑇𝑃𝑂)=(𝐹𝐶+𝑇𝑎𝑟𝑔𝑒𝑡 𝑃𝑟𝑜𝑓𝑖𝑡(𝑇𝑃))/(𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡)

Question 15

target price

Answer 15

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

Question 16

target profit

Answer 16

is the amount (value) of profit that a firm aims to earn within a given time period. The target profit for each level of output can been seen in a break-even chart by comparing the total cost and total revenue lines.
The company determines the TP

Question 17

target price is calculated by

Answer 17

𝑇𝑎𝑟𝑔𝑒𝑡 𝑃𝑟𝑖𝑐𝑒 =𝐴𝐹𝐶+𝐴𝑉𝐶
= (𝐹𝐶/𝑄)+AVC

Question 18

target profit is calculated by

Answer 18

using the formula for the TPO and solving for the target profit:
𝑇𝑃=(𝑇𝑃𝑂×𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡)−𝐹𝐶

Question 19

Besides helping managers with BE levels of productions and margins of safety; BE techniques can also help managers to make other decisions.

Answer 19

Basically, comparing the ‘actual situation’ with a ‘potential new situation’. However, this needs to be done very carefully since forecast and predictions have to be made.
Specifically, the different situations may affect either the price (hence the revenue) or the cost (either fixed or variable).

Question 20

Before analysing the effect of the changes, it is important to remember the following formula:

Answer 20

𝑇𝐶=𝐹𝐶+𝑉𝐶
𝑇𝐶=𝐹𝐶+𝐴𝑉𝐶∗𝑄
Mathematically, this is ‘just’ a linear function:
𝑌=𝑎+𝑏𝑋
Where:
a = intercept
b = slope
Hence:
FC = intercept
AVC = slope

Question 21

changes in price

Answer 21

an increase in price, for example, will help to make a ‘marketing decision’. The price increase will directly affect the Total Revenue (since TR = P*Q)
Using of our linear function, in this case the intercept of the TR will be equal to 0, making P the slope. Hence, the TR will just change its slope .
This means that the sales revenue increased (at any level of output) and the firm will break even at a lower level of output (lower BEQ) with higher profits and an increase in the firms’ margin of safety.

Question 22

changes in costs

Answer 22

the changes could be either on the fixed costs or the variable costs, and the results will lead to different charts.

Question 23

increase in fixed costs

Answer 23

this could happen for example when the firm needs to pay a higher rent. Using the linear function, we can observe that in this case is the ‘intercept’ (FC) that is changing. Therefore, the TC will be affected as well. However, in this case both curves are going to ‘shift’ upwards.
The final outcome will be a decrease in profits (at all levels of output), an increase in the BEQ and a decrease in the margin of safety.

Question 24

increase in variable cost

Answer 24

if for example wages increase, or the price of raw materials increase, these will lead to an increase in the firms’ variable costs (VC).
Using our linear function again, the change in VC will affect the slope of the TC. Therefore, the TC curve will shift (only changing its gradient).
This leads to an increase in the BEQ and a reduction of the margin of safety.

Question 25

benefits of break even analysis

Answer 25

• provides a quick graphical focus on cost and revenue structures in different scenarios (ie. helps quickly visualise the impact of changes in crisis)
• helps make realistic predictions since calculations are great for making quick estimates
• measure profit and losses at different levels of production and sales
• predict the effect of changes in sales prices
• analyse the relationship between fixed and variable costs
• predict the effect of cost and efficiency changes on profitability

Question 26

BEA is particularly beneficial for businesses that

Answer 26

Produce and/or sell a single product
Operate in a single market
All output is sold

Question 27

limitations of break even analysis

Answer 27

• assumes that all costs functions are linear which, in reality, are not. (FC and variable costs can actually change)
• does not include semi-variable costs. If it did the analysis will be more complex.
• Assumes production and sales are the same. It can’t cope with ‘sudden’ changes in technology, price or cost.
• may be time consuming to prepare.
  It can only apply to a single product or single mix of products. It is very difficult to calculate a multiproduct BEA.
• Some factors like “staff working overtime” are ignored in the BEA but do affect the cists and revenues of the firm.
• assumes that all the output is sold with no possibility of stocking products. In reality, most of the business that can stock produce twill do it (i.e. For sudden changes in demand).