**In a previous article we looked at how to calculate the cost of goods sold (COGS) and now we’re going to build on that understanding to consider mark-ups and margins. **

I also wrote an article on study tips which included percentages and covered the basic numerical skills we need to successfully calculate mark-ups and margins. So if you missed either of those, they would be worth a quick read before you carry on.

Let’s start with what margins and mark-ups are and their similarities, then we’ll look at their differences.

## Margins and mark-ups are sales and profits

They are the difference between the cost of a product or service (COGS) and it’s selling price, in effect the profit, however they are expressed as a percentage rather than a figure. Put another way, a sales figure is made up of both COGS and profit.

All three of these components can be quantified as values or as percentages but margins and mark-ups are specifically the percentage related to the profit component.

As well as knowing what they are, the other fundamental bit of knowledge we need is:

- when calculating mark-ups, COGS equals 100%
- but when calculating margins, sales equals 100%.

## Sales, COGS and Profit

This is typically a challenging topic so we’re going to use a table to help us understand it:

As you can see the table has the three component parts, a column for values and a column for percentages. We’re unlikely to have all the information we need to complete it but if we understand the relationship between the three components, we can use percentages and remember which component equals 100%, then we only need some of the information and we’ll be able to work out the rest.

## Let’s start by looking at mark-ups

Imagine you are a manufacturer and you buy raw materials, make them into a product and then need to sell them at a price which covers the COGS and generates a profit.

Let’s say we manufacture hinges and it costs us £17 to make one.

If we want to make 40% profit we can use a mark up to calculate the selling price. Using the table, we can complete the two boxes we have figures for and use our knowledge to identify that COGS represent 100%:

In order for the sales to include both the COGS and the required profit it must represent 140%.

Now that we have all the percentages, we can calculate the missing values.

The easiest method to use is to calculate 1% first and then scale that up to 40% to tell us how much profit we will make, and to 140% to calculate the required selling price.

So in this case we need to sell each hinge for £23.80 in order to have enough money to cover the £17’s worth of manufacturing costs and make 40% profit which is £6.80.

## Now let’s consider margins

Even though they’re similar to mark-ups, margins are calculated differently and must not be confused.

The difference in the calculations from a mark-up stems from which of the three components represents 100%. Remember, for a mark-up it’s the COGS but with a margin it’s the sales figure.

Let’s imagine we work for a company who made £256,000 worth of sales and have a target of achieving a 25% margin.

The information we have, and our fundamental understanding, allows us to partially complete the table:

As the sales figures includes both the profit and COGS, then COGS must represent 75%. Once we have all the percentages, we can calculate the missing values, being careful to use the right figures to calculate the initial 1%.

Therefore, in order to achieve a 25% profit of £64,000 the company’s COGS must be £192,000.

Once we understand the similarities and differences between margins and mark-ups we can use this theory to check our calculations to see if the figures look reasonable.

As a mark-up is a percentage added to the COGS, the percentage that represents sales should always be more than 100%. However, as a margin expresses the profit as an amount included in the sales figure, then the COGS percentage and the profit percentage should always add up to 100% but never exceed it.

In both instances though, once we’ve calculated the values of the components, it’s reasonable to expect that the sales figure should be more than the COGS. If it isn’t, we won’t be in business for much longer.

## So how do mark-ups and margins help with an incomplete set of records?

Those of you who read the COGS article before starting this one, will recognise this table:

And that we went on to calculate that the missing figure for the closing inventory is £7,364. We weren’t told where the £97,906 COGS figure came from in the first place. So, let’s suppose that this company had generated sales of £122,382.50 and operates with a 25% mark-up.

Now we can combine the top section of the profit and loss statement (SPL) with the table we’ve been using to help us with mark-ups and margins. Put in the figures we have, then we can use our knowledge to work out the correct percentages, as COGS is 100% when calculating mark-ups:

Now we can work out the values:

Finally, we need to check our figures to see if they ‘look reasonable’ given all the knowledge and understanding we have and the skills we have applied.

## In summary

As we have constructed our SPL out of order, we can re-work our figures to check that the opening inventory, plus the purchases, less the closing inventory does give the same COGS figure and that the gross profit is the same amount if we deduct the COGS from the sales.

Read more on Final Accounts Preparation:

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**
Gill Myers is a self-employed accounts consultant. She has taught AAT qualifications since 2005 and written numerous articles and e-learning resources.
**