Beware the lure of percentages as a metric.

Let’s say you are selling widgets for $100 each, to the tune of a million units per year. You are grossing $100 million in sales annually. Let’s assume your margin is 20%, making your net profit $20 million annually. So far, so good, right? (I mean, if you’re taking the time to read this, you’re probably not making that kind of bank – and if you are, then you should definitely hire me!)

Your customer comes to you with “the deal of the century”. They are trying to start a rebate program to encourage sales companies to push more product. In exchange for you paying them a 35% rebate for unit, they are willing to give you 50% more per unit than you are currently receiving. Would you take the deal?

Let’s hope not.

A 50% increase per unit means your sales price per unit is now $150/unit – making your gross $150 million in sales. Your investors will love it! Well, until they realize it’s time to make the rebate payment. 35% of your gross means you are paying your customer a rebate of $52.50 per unit – which means your margin per unit went from $100 each to $97.50 each. That may not sound like a big hit, but when you look at your overall net, it’s a reduction of a whopping 12.5% – that’s $2.5 million a year less profit!

I hope you have a great golden parachute, because your shareholders are ticked off and the board has just shown you the door. Better luck at your next gig. (See – I told you that you should’ve hired me!)

All jokes aside, it’s common to think that equivalent percentages will offset one another when one is negative and the other is positive. This was a common theme in investment articles after the market crash in 2008.

Check the math with a 25% gain followed by a 25% loss:

x*(1+.25)*(1-.25) = .9375x

Math’s Transitive Property tells us that the inverse is also true.

x*(1-.25)*(1+.25) = .9375x

Again, check the math – a mere 20% loss will offset a 25% gain.

x*(1+.25)*(1-.2) = x

Far too often, people will put trend graphs showing a month-to-month or year-to-year percent growth trend, and people will ignore the few dips in favor of the larger number of period with gains. It’s human nature to look at it and think the entire trend is upward – it may not be upward at all. While percentages can be extremely valuable analysis tools, it is key to remember that all of them are relative – the raw attribute to which the percentage is applied is just as important (if not more so) than the percentage being applied.