 # Equity Disclosures: Calculating Weighted Averages

August 13, 2021

Why does a simple average calculation not always fit the disclosure bill? When it comes to a company’s stock, the number of shares outstanding will usually fluctuate. These changes stem from a variety of reasons, such as:

• Issuances of new shares

• Share repurchases

• Retirement of existing shares

• Other instruments are converted to shares, such as from a stock option exercise

Because of these fluctuations, calculating a simple number of shares outstanding or a simple average price at a given point in time isn’t likely to paint a complete picture actual shares in play and the distribution of value among them. Some values matter more than others.

This where weighting comes into play, where more emphasis is given to certain values based on their weight or worth.  In the case of shares outstanding, the “weight” used can be the period of time the shares were actually outstanding.

If Company A started the year with 100,000 shares outstanding, and then issues an additional 25,000 shares halfway through the year, the 25,000 new shares don’t carry the same weight in the shares outstanding calculation as the original 100,000 shares. This is because those 25,000 shares weren’t outstanding for the entire year.

In this example, the company would use a time-based weight to arrive at a weighted shares outstanding figure for the year, which will be less than the actual 125,000 shares outstanding at year end.

Weighted averages are used in a variety of calculations – this is not unique to business disclosures. However, this blog will stick to business and equity compensation uses of weighted average.

## Weighted Averages for Equity Compensation

For stock compensation, weighted average calculations are commonly used in the following disclosure areas:

• Earnings per share (“EPS”)

• Financial statements

• Proxy reporting

• Section 16 reporting

## Weighted Average versus Simple Average Calculation – What’s the Difference?

So how are weighted averages calculated? The answer involves returning to grade school math. First, a revisit of simple average. A simple average is the sum of values, divided by the number of variables. For example:

Determine the simple average price of Company A’s outstanding stock option grants.

Company A’s Outstanding Grants

 Grant # # Stock Options Outstanding Price per Share 1 100 \$9 2 300 \$14 3 800 \$12 4 1,000 \$10 5 1,500 \$5

To calculate the simple average price, add up the prices in the “price per share” column, and then divide by the number of grants:

\$9 + \$14 + \$12 + \$10 + \$5 = \$50
\$50 total of per share prices / 5 grants = \$10 simple average price per share

## Calculating Weighted Average Price of Stock Options Outstanding

A simple average can present a distorted view of outstanding equity instruments, because the number of shares and prices vary. In using a weighted calculation, the largest items in the data set will have greater impact on the overall calculation. To calculate the weighted average of options outstanding, the following steps are used:

1. Calculate the total price of each outstanding grant by multiplying the number of outstanding shares by the price per share.

2. Add up the total price of each grant, to arrive at an overall total price of options outstanding.

3. Add up the stock option shares outstanding for all grants, arriving at a total number of options outstanding.

4. Divide the total price by the total number of option shares outstanding.

 Steps 1 & 2: Add up total price of stock options outstanding: 100 shares x \$9 = \$900300 shares x \$14 = \$4,200800 shares x \$12 = \$9,6001,000 shares x \$10 = \$10,0001,500 shares x \$5 = \$7,500 Total price of options outstanding: \$32,200

 Step 3: Determine total number of stock options outstanding:     100 shares   300 shares   800 shares1,000 shares1,500 shares Total shares outstanding: 3,700

 Step 4: Divide total price by total option shares outstanding:  \$32,200 ÷ 3,700 = \$8.70 weighted average price per share

In the weighted average price calculation above, the final \$8.70 average price is lower than the simple average price of \$10 per outstanding stock option. This is because the option with the most shares also has the lowest price, and the application of that weighting to the calculation reduces the average price per share.

Though not a perfect formula, weighting does provide a more accurate view of how value is distributed across the various grants.

While the scenarios where weighted averages are used in equity compensation may vary, the process for performing a weighted calculation is the same.