Break even analysis - help please

I don’t understand break even!

Salaams sis try this InshaAllah.

https://articles.bplans.com/break-even-analysis/

All the best! .

Break even is the point where business gets no profit and no loss which means the business gets zero profit.

I dont understand how to create a graph

Cost on y-axis, units produced on x-axis.

Two graph lines intersecting at break-even point.

First line is cost of production comprising:

a) fixed costs - summed to include one off start up costs like product design, machine purchase, installation, office equipment, patent applications etc. NB the sum of these costs is the point on the y- axis where the first graph line starts.

b) variable costs - for each unit produced these costs are summed and plotted as a straight line with a gradient starting from the y-axis at a) above. Variable costs materiels, electricity, wages, taxes, distribution etc.

Second line is the total sale price per unit plotted as a straight line with a gradient, starting from the origin.

At some point, the two graph lines will intersect. This is the break even quantity. Before this point, the company runs at an overall loss having paid more money than taken in sales. After this point, the company makes a profit where revenues from sales exceed the costs of getting to that point.

So its meant to look like this..?

Exactly that

I honestly still dont get it

OK. Let's do an example:

Say you decide you want to set up a small business making and selling scented candles.

You don't want to turn your bedroom into a factory so you decide to run the operation from a small shed you will erect in your garden. To make the candles, you need a small shed, a table, a chair, a good lamp, a small stove to heat the candle wax, an electric extension cable you can run from the house to the shed and a sturdy saucepan to put the wax in. Your mum is bit mean and says you must pay her for any electricity you use in the shed.

The materials you need to make the candles are glass jars, candle wax, candle wicks and boxes to pack the finished candle in.

a) Fixed Costs.

Before you even make a single candle, you must purchase from your savings:

1) Garden shed, £300
2) Table, £30
3) Plastic chair, £15
4) Small electric stove, £50
5) Table lamp, £20
6) 20 metre extension cable, £20
7) Enamel saucepan, £15

Total = £450

This is the start up fixed cost and is point B on the graph.

b) Variable Costs.

These are the materials you need to make the candles. The costs are directly related to how many candles made.

i) Glass jars cost £20 in boxes of 40. Each jar therefore costs £20/40 = £0.50p for each candle made.
ii) Candle wax costs £15 per 10 litres and can fill 50 glass jars. Candle wax therefore costs £15/50 = £0.30p for each candle made.
iii) Candle wick string costs £4 for 10 metre lengths and can make 200 candle wicks. Candle wicks therefore cost £4/200 = £0.02p for each wick.
iv) Packing boxes cost £20 for 100. They therefore cost £20/100 = £0.20p per box.
v) Heating the candle wax uses £1 of electricity per saucepan which fills 10 glass jars. Electricity therefore costs £0.10p per candle made.

This means the materials and electricity will mean variable costs for each candle are: 50p + 30p + 2p + 20p + 10p = £1.12p per candle. i.e. a gradient of £112/100

This cost line gradient is plotted on the graph from point B and passes through point C which can be any quantity as long as the gradient is correct.

c) Revenue.

You decide that you will sell the finished candles for the price of £4 each.

i.e. the revenue line starts at the origin O and has a gradient of £400/100.

Putting all of this together:

If you only ever made and sold one candle, it would have cost £450 + £20 + £15 + £4 + £20 + £1 = £510 (because you needed to by and use all of those items at the start).

You sold one candle at £4 therefore you made a loss of £4 - £510 = -£506.

If however you made 200 candles and sold them all at £4, it would have cost £450 + (200 x £1.12) = £674

You sold 200 candles at £4 = £800 revenue. You therefore make a profit of £800 - £674 = £126. i.e. £126/200 = £0.63p profit per candle.

BREAK EVEN

This is the number of candles you must make in order for the revenue from your sales to equal the total cost of manufacture for that number sold.

That quantity and cost is where the two graph lines meet at P.

Mathematically this can b solved using simultaneous equations.

Straight line graphs y = mx + C are used.

For the costs line: y = 1.12x + 450

For the revenue line y = 4x

Equating:

4x = 1.12x + 450

x(4 - 1.12) = 450

x = 450 / (4 - 1.12) = 156.25

(costs = £625 and sales = £625)

i.e. This is the number of candles made where cost = revenue

No profit is made, but also no loss is incurred.