Break Even Analysis_v1.pdf

8/14/2019 Break Even Analysis_v1.pdf

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Break Even Analysis


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Break Even Analysis_v1 Dr. Harald Fien 2

Break Even Analysis

Break even

Break even is a level of output and sales where total costs equals

total revenue

At this point the firms is making neither profit nor loss

At output above break even the firm will be in profit

At output below break even the firm will be making a loss


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Break Even Analysis

Assumptions

All other variables remain constant

A single product is produced

Costs can be divided into fixed and variable elements There is a linear (straight line) relationship between output and total costs -

variable costs per unit remain unchanged

There is a linear relationship between output and sales revenue each unitis sold at the same price

All output can be sold at the given price The analysis applies to the relevant range only


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Break Even Analysis

Costs

Fixed costs

Do not rise with output

Examples

rent

rates

administrative costs

interest payments

Variable costs

Rise as output rises

Examples :

cost of materials

labour costs

Total costs = fixed costs + varable

costs


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Break Even Analysis

Total revenue

Also known as sales revenue or turnover

Total revenue = quantity sold x price per unit

This rises as sales rise

If we assume that price is uniform throughout then there is a linear

relationship between total revenue and sales volume


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Break Even Analysis

Graphical analysis

Salesand

cos

ts()

Sales / production (units)

Total fixed costs

Sales revenue

Total costs

Breakeven

point

Breakeven quantity

Breakeven

sales

Sales revenue less

Total costs

= profit

Variable costs

= total costs

less fixed costs


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Break Even Analysis

Notes on the break even graph (1)

Fixed cost are shown as horizontal straight line

Variable cost are added to the fixed costs

Hence total costs start part way up the vertical axis

Total sales revenue starts from the origin and rise in the form of a

straight line

Break even occurs at the intersection of total costs and total revenue We can read off both the break even quantity (horizontal axis) and

break even revenue (vertical axis)


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Break Even Analysis

Notes on the break even graph (2)

The triangles between the total cost and total revenue curves areareas of loss (to the left of break even point) or profit (to the right of

the break even point) The actual profit or loss can be read off as the vertical distance

between total cost and total revenue

The gap between current output and sales and break even output

and sales is known as the margin of safety


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Break Even Analysis

Contribution

Contribution is equal to Sales revenue minus variable costs

This is not the same as profit since so far only variable costs have

been taken into account Contribution per unit = revenue per unit (i.e. price) minus variable

cost per unit

Contribution per unit can be regarded as that units contribution to:

Fixed costs and

Profits

Once fixed costs have been covered the contribution is to profits


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Break Even Analysis

Break even formulae

Contribution per unit

= selling price minus variable costs per unit

Break even (qu)

= Fixed costs


Break even () =

Fixed costs x Price



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Break Even Analysis

Example

Given data

Fixed costs: 500k

Variable costs per unit: 13Selling price per unit: 19

Calculations

Contribution per unit: (19 - 13) 6

Break even quantity: 500k/6 = 83,334 unitsBreak even revenue: (500k/6) x 19 = 1,583,333

Note: for break output in quantity terms always round up to the nearest whole number.Never round down


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Break Even Analysis

Rise in selling price

As price rises the total revenue curve rises at a steeper angle

Break even occurs at a lower level of

Sales volume and

Sales revenue

Also at each quantity level profits will be higher than before

But we are assuming the customers are not deterred from buying asa result of the higher price


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Break Even Analysis

Rise in variable costs

The total cost curve starts at the some as before but rises at a

steeper angle

Break even occurs at a higher level of

sales volume

sales revenue

At each quantity level profits will be lower


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Break Even Analysis

Rise in fixed costs

The starting point for total revenue moves up the vertical axis

The new total cost curve is parallel with the old one but at a higher

level

Break even occurs at a higher level

sales volume

sales revenue

Profits are lower at each level of sales


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Break Even Analysis

Margin of safety

This is equal to current output minus break even output

Measures how far sales can fall before the business starts to make

a loss

Once break even output/sales is reached then the contribution on

each additional unit goes towards profit

As a result we can calculate profits as follows:

Profit = margin of safety x contribution per unit


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Break Even Analysis

Target rate of profit

We can adapt break even to calculate the level of sales needed to

reach a profit target

Treat the target level of profits as a kind of fixed cost

Therefore output and sales needed to reach the target level of

profits =

fixed costs + profit target

contribution per unit


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Break Even Analysis

Uses of break even analysis

A tool for use in planning

A new start up business can estimate the required level of sales

before it starts to make a profit

Similarly it can be used in new product development to estimate

sales needed to break even on a new product

Measures profit at different level of sales

It can be used in modelling what if scenarios

It helps identify the impact of price or cost changes


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Break Even Analysis

Limitations of break even analysis

Assumptions on which the analysis is based are not valid

No costs are truly fixed -the divide between fixed and variable costs

is not clear cut Cost curves are not necessarily linear. As output rises it does not

follow that there will be a proportionate increase in sales

Takes no account of economies of scale and bulk buying discounts

Production and sales are assumed to be the same but it is

unrealistic to assume that all output is sold at and at a uniform price It is a static model and needs to be reworked whenever there is a

change in anyone of the variables

The analysis is only as good as the information provided

It ignores outside variables such as the reaction of competitors


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Break Even Analysis

Lessons Learned

What is a break even analysis?

Show a principal graphical break even analysis.

What are uses of break even analysis?

What are limitations of break even analysis?

Break Even Analysis_v1.pdf

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