Lawyers are wordsmiths not mathematicians who, when working on a deal, often leave the complex math to the bankers and accountants. Some of us decided to go to law school because of our dread of math; finance and the sciences were out for us.
This leads to my topic today, what is the difference between a Percent and a Percentage Point and why do we care?
It only takes a brief look at their linguistic roots to make it painfully obvious. My British colleagues write “percent” as two words “per cent” which evokes the Latin origins of the word meaning “by the hundred”. Percent tells us how much out of 100 something is. It can tell us what fraction something is out of a whole (e.g., saying gross margin are 80% means $80 are left out of every $100 of sales after deducting cost of goods sold) or it can tell us how much something has increased (e.g., revenue is up 10% this year means for every $100 of revenue last year we have made $110).
Percentage point is different. Percentage point tells the difference between two percentages. It is a more natural way of discussing percentages and you probably use it without even knowing.
Here is an hypothetical example from wikipedia:
In 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. By what percent did smoking drop from 1980 to 1990?
Stop and think about it. It seems simple, and the math looks easy: 40% less 30% is 10%, so smoking fell by 10% from 1980 to 1990. Right? Wrong. Smoking in fact fell in this example by 25%. In this context 40% means 40 out of 100 people and 30% means 30 out of 100%. So 10 less people out of a base of 40 (the number in 1980) smoke and 10 out of 40 is 25%.
Alternatively, you could have said smoking fell by 10 percentage points because 40% less 30% is 10 percentage points.
So why does this matter for M&A lawyers?
In a recent transaction I was a part of there was a term sheet which set out that an earn out would be based on 4% of the maximum earn out payment for every 1% that revenue increased above a target up to a maximum. The target was 75% of the maximum. The intent was to ratchet up the earn out until the maximum was paid.
The draft agreement provided to us said the earn would be calculated as actual revenue divided by the target multiplied by 4. It effectively put the words of the term sheet into the agreement, but due to confusing percent and percentage point, the intent of the parties was not expressed.
It should have been drafted as the percentage point difference between the percent actual revenue was of the maximum and target percentage (or in this case 75%).
Some numbers may help.
- Say the maximum is $100 and actual is $80, what is the earn out? Using the initial language, the target is $75, $80 is 6.6% more (80/75) so 4% of the maximum for every percent above target is $25.4. Using the correct language, $80 is 80% of the maximum, 80% less 75% is 5 percentage points and the earn out is $20.
- Now say the maximum is $100 and actual is $95, what the earn out? Using the initial language, the target is $75, $95 is 26.6% more so 4% of the maximum for every percent above target is $106.4. More than the $100 maximum. Clearly something is wrong. Using the correct language, $95 is 95% of the maximum, 95% less 75% is 20 percentage points and the earn out is $80.
The point is percents and percentages are different. As lawyers, we may not know the nuances of the Black-Scholes model or the quadratic equation, but linguistics is our thing. We live in the nuance and using terminology incorrectly causes confusion and may result in unnecessary errors.
The author would like to thank Andrew Bigioni, articling student, for his assistance in preparing this legal update.