Cost-Volume-Profit Analysis

FINDING THE BREAK-EVEN POINT

At the zero volume of activity (zero sales), there is zero sales revenue. The profit (loss), which is the difference between sales revenue and total cost, for some volume of activity is the vertical distance between the total sales revenue line and the total cost line at that particular line of activity. Where the volume of activity is at break-even point (BEP), there is no vertical distance between these two lines (total sales revenue equals total costs) and so there is no profit or loss. That is, the activity, whatever it might be breaks even. In the company I worked for this basic procedure wasn’t carried out, hundreds of business unit were not assessed and were suffering varying degrees of loss. My particular branch was the subject of -£14,000 loss per quarter The volume of activity was below BEP, the business was incurring a significant loss, total costs were exceeding the sales revenue. After I got to grips with the team, got them working together creating unity, following my attitude and application the business operated at a volume of activity above the BEP, there was a profit because total sales revenue exceeded total costs. There was a complete change in fortunes a £36,000 turnaround in net profit. So the store was making a £22,000 net profit.  Remember, look at the figure, the further below BEP, the higher the higher the loss: the further above BEP, the higher the profit.

The sloping line at the zero represents the sales revenue at various volumes of activity. The point at which this finally catches up with the sloping total cost line, which starts at F, is the break-even point (BEP). Below this point a loss is made.

This can be a laborious business. However, since the relationships in the graph are linear that’s the lines are all straight, it’s easy to calculate the BEP.
We know that at BEP (but not at any other point):

Total sales revenue = Total costs

At all the other points except the BEP, either total sales revenue will exceed total cost or the other way round. Only at BEP are they equal.) That is,

Total sales revenue = Fixed costs + Total variable costs

If we call the number of units of output at BEP b, then
b x Sales revenue per unit = Fixed costs + (b x Variable costs per unit)
so:
b x (sales revenue per unit)- (b x variable costs per unit)=Fixed costs
and:
bx(sales revenue per unit- Variable costs per unit)=Fixed costs
giving the final, vital equation:
b=

Fixed costs

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Sales revenue per unit - Variable costs per unit

If you look at the break-even chart in the figure this is logical. The total cost line starts at point F, higher than the starting point for the total sales revenues line (zero) by amount F (the amount of the fixed costs). Because the sales revenue per unit is greater than the variable cost per unit, the sales revenue line will gradually catch up with the total cost line. The rate at which it will catch up is dependent on the relative steepness of the two lines and the amount it has to catch up (the fixed costs). bearing in mind that the slopes of the two lines are the variable cost per unit and the selling price per unit, the above equation looks perfectly logical. Though the BEP can be calculated quickly and simply, it does not mean that the graphical approach of the break-even chart is not without value. The chart shows the relationship between cost, volume and profit over a range of output and in a form that can easily be understood by non-financial managers. The break-even chart can therefore be a useful device for explaining this relationship.
Here is an example, Dappy Industries Ltd makes bar stools. The fixed costs of operating the warehouse for a month cost a total of £500. Each bar stool requires materials that cost £2. Each bar stool takes one hour to make, and the business pays the bar stool makers £10 an hour. The bar stool makers are all on contracts such that if they don’t work for any reason, they are not paid. The bar stools are sold to a wholesaler for £14 each.
What is the BEP for bar stool making for the business?
The BEP (in number of bar stools)

Fixed Costs

---

(Sales revenue per unit- Variable costs per unit)

£500

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£14-(£2+£10)

= 250 bar stools per month to break-even

REAL WORLD

BE at BA, Ryanair and easyJet

Commercial airlines pay a lot of attention to their BEPs and their ‘load factors’, that is, their actual level of activity. British Airways is a traditional airline. Ryanair and easyJet both ‘no frills’ carriers, which means that passengers receive lower levels of service in return for lower fares. All three operate flights within the UK and from the UK to other European destinations. Only BA operates flights beyond Europe. We can see that all three airlines are making operating profits as each has a load factor greater than it BEP.

The usefulness of being able to deduce the BEP is that it makes it possible to compare the planned or expected volume of activity with the BEP and so make a judgement about risk. Planning to operate only just above the volume of activity necessary in order to break even may indicate that it is a risky venture, since only a small fall from the planned volume of activity could lead to a loss. This  indicates to me that Ryanair make substantially more profit per unit.