# "All You're Ever Gonna be is Mean - But Which One?"

In an effort to be down with the kids, this month's title comes from a Taylor Swift hit single - a big step from my normal classic rock comfort zone, but apropos none the less!

**Warning** - This month's topic could easily swing into total math nerd territory. I'll try and keep it under control as much as possible. The takeaway is to beware of how seemingly standard use of mathematics can inflate the value of a company.

One method of valuing a company is the market method in which we search for sales of similar companies to our subject company. We then analyze the transactions we find to determine a multiple of revenues or earnings to the sale price of the companies which were sold and then apply that multiple to the revenues or earnings of the subject company to get an indication of value.

For example, assume we find the following four comparable transactions:

** Transaction # Enterprise Value Earnings Multiple**

1 $2,500,000 $250,000 10

2 $3,000,000 $400,000 7.5

3 $1,500,000 $550,000 2.7

4 $4,250,000 $800,000 5.3

The average (or **arithmetic** mean) of the multiples is 6.4. Assuming our subject company had earnings of $500,000, this might suggest a starting point valuation of $3,200,000 (i.e. $500,000 x 6.4).

"Not so fast!" the statisticians cry. The argument goes that when trying to determine an average of a set of **ratios** (which is what the multiple of enterprise value to earnings is), the appropriate measure is the **harmonic **mean. Using the arithmetic mean tends to overweight the larger multiples in the sample. The formula to calculate the harmonic mean can be found easily online and the function is included in Excel so I won't set it out here. The important thing to note is that the harmonic mean is **always **lower than the arithmetic mean. In the case of the multiples set out above, the harmonic mean is 5.1 which would suggest a starting point valuation of $2,500,000, a drop of 20% from the value based on the arithmetic mean.

We often see the arithmetic mean being used, probably because it's a measure most people are familiar with, (rather than ascribing any nefarious motives to the user). However, just because it's easy to understand, doesn't mean it its right!

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