Weighted Averages and Equity Compensation

Reporting on stock plans often involves weighted averages. For example, here are some common areas where weighted averages are used in equity compensation:

• Reporting multiple-lot sales for Section 16 insiders on an aggregate basis
• Calculating the denominator for basic and diluted earnings per share
• Reporting equity compensation plan information in the proxy statement
• Financial statement disclosures, e.g., stockholders’ equity

But what exactly is a weighted average and how does it differ from a simple or straight average? This article explains the math.

Weighted vs. Simple or Straight Averages

When computing a simple or straight average, you add up all the values you are averaging and then divide the result by the number of values. Let’s say that you want to compute the average of the following prices:

• $10
• $15
• $18
• $26

The average is $17.25. This is the sum of all four prices ($69) divided by the number of prices (4).

Calculating a weighted average is a little more complicated because some of the values will have a greater impact on the result. Unlike in our simple/straight average calculation, in a weighted average, the values aren’t all treated equally; each value carries a different amount of weight or importance in the calculation.

Let’s say that the prices in our example above are the amounts at which stock trades executed and that each trade involved a different number of shares, as follows:

• 500 shares at $10
• 300 shares at $15
• 100 shares at $18
• 200 shares at $26

In this scenario, computing a straight average for the four prices no longer makes sense. Instead, we want to know the average price for all the shares that were sold. This requires a weighted average calculation: each sale price must be weighted by the number of shares sold at that price.

This will involve a multi-step calculation:

1. Multiply each price by the number of shares sold at that price.
2. Sum the aggregate prices for the four trades.
3. Divide the result by the total number of shares sold.

Here’s the math for each trade:

• 500 shares x $10 = $5,000
• 300 shares x $15 = $4,500
• 100 shares x $18 = $1,800
• 200 shares x $26 = $5,200

An aggregate of 1,100 shares were sold at an aggregate price of $16,500. This results in a weighted average price of $15 ($16,500 divided by 1,100 shares).

What Are Examples of Averages That Are Weighted by the Number of Shares?

This is a calculation you will use quite frequently. Here are just a few examples.

Section 16 Reporting

When Section 16 insiders sell stock, their sales are often executed in multiple lots. The SEC allows the lots to be reported in aggregate, provided that the sale prices for each lot are all within a $1 range and the sales occur on the same day.

For example, say an insider sold 100,000 shares in ten lots of varying sizes ranging from 8,000 to 15,000 shares and at prices ranging from $50 to $50.99. The SEC allows the ten lots to be reported as a single transaction. The sale price reported for the aggregated transaction should be the weighted average price for the ten lots (and the range of sale prices should be disclosed in a footnote).

RSU Sell-to-Cover Prices

When multiple RSUs vest on the same day and shares are sold to cover the taxes due, the shares are often sold in multiple lots. Rather than tying each lot back to each individual award, some brokers compute a weighted average sale price for all the lots and report this as the sale price for all the shares that were sold. Because employees have no control over the order in which the shares are sold, this can be a fairer way of determining individual sale prices.

ASC 718 Disclosures

When disclosing plan activity for ASC 718 purposes (e.g., awards granted, exercised, vested, cancelled), an average price, FMV, or fair value is also typically disclosed for each type of transaction. This average should be weighted by the number of shares per price point.

For example, let’s say that, during its current fiscal period, a company issued grants for 20,000 shares at a fair value of $10 per share and 80,000 shares at a fair value of $12 per share. The company would disclose an aggregate of 100,000 shares granted at a weighted average fair value of $11.60 per share.

Equity Compensation Plan Information Table

If you are a public company, the Equity Compensation Plan Information Table that is included in your proxy statement reports the average exercise price for all options outstanding under your equity plans. This average should be weighted by the number of shares outstanding at each price.

Is the Weighting Always by the Number of Shares?

Given all the examples I describe above, it might seem this way, but this isn’t always the case. The weighting factor depends on what values you are averaging and the purpose for which you are calculating the average. When averaging prices, however, frequently the prices are weighted by the number of shares tied to each price.

How Do You Calculate a Company’s Weighted Average Common Stock Outstanding?

In this calculation, the average number of shares outstanding is weighted by the length of time each share is outstanding during the fiscal period. It is used to calculate a company’s earnings per share.

Companies report their earnings over a fiscal period. Shares that are outstanding for longer during the period are more dilutive to earnings than shares that are outstanding for less time during the period. Thus, when computing earnings per share, companies must weight all the shares included in the calculation for the length of time they are outstanding during the period.

Shares that are outstanding for the entire period are weighted at 100%. Shares that are outstanding for only a portion of the fiscal period are weighted at a commensurately lower percentage. For example, let’s assume the following for a company’s fiscal period:

• 100,000 shares are outstanding for the entire period. These shares will be weighted at 100%.
• 40,000 shares are issued after three-quarters of the period has elapsed. These shares are outstanding for only one-quarter of the period, so they are weighted at 25%.
• 30,000 shares are repurchased half-way through the period. These shares are outstanding for only half the period, so they are weighted at 50%.

Here’s the math:

• 100,000 shares x 100% = 100,000 shares
• 40,000 shares x 25% = 10,000 shares
• 30,000 shares x 50% = 15,000 shares

The weighted average common stock outstanding for the period is 125,000 shares. At the start of the period, 130,000 shares were outstanding and at the end of the period, only 110,000 shares are outstanding. The straight average for the period would be 120,000 shares outstanding, but this doesn’t truly reflect the economic effect of the mid-period transactions; for that, you need the weighted average.

This same weighting is applied to options and awards that are outstanding when companies calculate the common equivalents that are included in their diluted earnings per share. Options and awards that are outstanding for the entire period are weighted at 100%. Options and awards that are granted, settled, or cancelled during the period are weighted at a lower percentage commensurate with the period they are outstanding.

See the article “Treatment of Stock Compensation in Diluted Earnings Per Share” for more information on how equity awards are included in earnings per share.

When Does a Straight Average Make Sense?

It makes sense to use a simple or straight average when all the values being averaged are of equal importance to the result. For example, when averaging the closing stock price of each day into, say, a trailing 30-day average price (e.g., for purposes of sizing equity grants—see “ 2 Reasons Multiday Averages Make Sense for Grant Sizing”). In this calculation, no single day’s price is any more important than any other day’s price, so a straight average is the right answer.