# GMROI – 2 out of 3 ain’t bad!

I was working with a client recently who had a report which showed him the GMROI and the stock turn of various categories. He asked me to comment on it, but clearly, with just two of the three elements that make up GMROI showing I needed to be able to derive the third – Gross Margin % – to be able to make much sense of this.

Now, normally, finding the 3rd of three variables when two are already known is relatively easy, but this became more complicated because the 3rd variable appears twice in the equation here.

The formula for GMROI is:

GMROI = Gross Margin / (100- Gross Margin) x Annual Stock Turn

Being in a hurry and a bit rusty on my algebra, my immediate solution was Excel goal seeking, which worked well enough to get an immediate result, but I knew there was a better way.

Tom, my son, was doing ‘A’ level maths so, when I got home again, I poured myself a beer set him to earning his keep. Within a minute or so he came up with the answer.

Gross Margin % = GMROI/(GMROI+ Annual Stock Turn)

For the sake of completeness here is how to calculate all three variables of the equation with worked examples based on a Gross Margin of 60%, an annual stock turn of 2 and a GMROI of 3.

GMROI = Gross Margin / (100- Gross Margin) x Annual Stock Turn

Worked example: 3 = 60/40 * 2

Gross Margin % = GMROI/(GMROI + Annual Stock Turn) x 100

Worked Example: 60 = 3 / (3 + 2) x 100

Annual Stock Turn = GMROI/(Gross Margin % / (100-Gross Margin %))

Worked Example: 2 = 3 / (60/(100-60)

Note: Gross Margin % is expressed here as a whole number not a decimal