Break even analysis

Well this is an interesting question…

So it’s obviously 50% – 8% = 42%
But why and how?

So let’s break the Gross profit on sales formula

SALES
LESS COST OF SALES
———————————-
= GROSS PROFIT
———————————–

Now let’s break up the formula for finding Contribution

SALES
LESS VARIABLE COSTS
————————————
=CONTRIBUTION
————————————

Now if you look closely and compare the two formulae they obviously relate by the SALES figures

Now look at the costs figures… In order to understand
Let me ask what does COST OF SALES represent?
Cost of sales are eventually costs that relate directly to sales. (as obvious by the name)

So then what does VARIABLE COSTS represent?
Variable costs are costs that vary with the sales units so it won’t be wrong saying that variable sales are directly related to sales.

So can you strike the similarity between cost of sales and variable costs??

Now if we adjust and combine the above formulae we can see:

SALES
LESS COST OF SALES
———————————-
= GROSS PROFIT
LESS VARIABLE COSTS
————————————
=CONTRIBUTION
————————————

So let’s take an example
For the month of March the
sales are $4000
Cost of sales are $1000
And variable costs are $500
What is the total contribution?

4000
– 1000
= 3000 (this is gross profit)
– 500
= $ 2500 (the total contribution)

So that’s according to your question
Gross profit on sales – other expenses
= contributions ratio

50% – 8% = 42%

The key in the question is that they have mentioned “ON SALES” for both gross profit and other expenses… Showing they are directly related to Sales.

I hope you have understood this cuz I think this a tricky question and honestly i have never come across like this before!

And i dont know how it might be explained in your book.

This the approach i would have taken though you could also do this with the Ratios formulae but I find the above easier.

Hope this helps

@johnmoffat said:
Although what Jetavi has answered is correct, I must add something to avoid any confusion.

Gross profit is sales less all costs of production (both variable and fixed costs).

Contribution is sales less all variable costs (both production and non-production variable costs).

There is no choice in this question but to assume that there are no fixed costs, and therefore the gross profit is the sales less the variable production costs.

To get the contribution we need to subtract any other variable costs, and the ‘other expenses’ must be variable (and will be selling and distribution expenses), and therefore the contribution must be 50% less 8% = 42%.

Oh… Never actually thought about both the variable cost and fixed cost element within cost of production.

These are the things that we must make sure not to miss out during exams… Though obvious, easy to forget under exam pressure.

Thank you very much sir!

@akshaykopite19 said:
So what should be done according to the question that I have written above?

So,
Contribution = Fixed Cost + Profit
Contribution =23,250 + 58,800 = £82,050

We also know the contribution ratio as 42%

From what i see, this is contribution to sales ratio (since both the % figures given in question are to sales) so in that case

Total Contribution ÷ total sales revenue = C/S ratio

Hence,

82,050 ÷ sales revenue = 0.42

Total sales revenue = 82,050 ÷ 0.42 = £195,357.14

As i mentioned earlier, i have never come across such a question so I am not 100% sure about the answer but this is the approach i would have taken.

So do check the answer key.

Hope this helps.