## Weighted Average of Shares Outstanding

The Weighted Average of Shares Outstanding is a calculation that provides the average number of company shares that have been outstanding over a specific time period, adjusted for changes like stock splits, issuance of new shares, or buybacks. This weighted average is used in the computation of key financial metrics, such as earnings per share (EPS).

The purpose of using a weighted average rather than a simple average is to account for the varying amounts of time that different quantities of shares have been outstanding. This provides a more accurate picture of the company’s financial performance over a given period.

### Formula:

The formula to calculate the weighted average of shares outstanding is:

\(\text{Weighted Average Shares Outstanding} = \sum \left( \text{Number of Shares} \times \frac{\text{Time Outstanding}}{\text{Total Time Period}} \right) \)Where:

**Number of Shares**: The quantity of shares outstanding during a specific time interval within the total time period.**Time Outstanding**: The length of time during which those specific shares were outstanding.**Total Time Period**: The total length of the period for which you are calculating the weighted average.

## Example of Weighted Average of Shares Outstanding

Let’s go through a concrete example to illustrate how the weighted average of shares outstanding is calculated.

**Scenario:**

Imagine a small tech company, TechX, started the year 2023 with 500,000 shares outstanding. On July 1, 2023, TechX issued an additional 100,000 shares, bringing the total to 600,000 shares. The year ends on December 31, 2023.

We will calculate the weighted average of shares outstanding for the year 2023.

**Steps:**

**1. Identify the time periods and the number of shares for each period**

**January 1 – June 30**: 500,000 shares were outstanding for 181 days (since 2023 is not a leap year)**July 1 – December 31**: 600,000 shares were outstanding for 184 days

**2. Calculate the weighted shares for each period**

**For the first period (January 1 – June 30):**

500,000 shares × 181 days / 365 days = 248,767 weighted shares

**For the second period (July 1 – December 31):**

600,000 shares × 184 days / 365 days = 302,192 weighted shares

**3. Sum up the weighted shares**

248,767 weighted shares (first period) + 302,192 weighted shares (second period) = 550,959 weighted average shares for the year 2023

**Result:**

The weighted average of shares outstanding for TechX for the year 2023 would be 550,959 shares. This figure would be used in calculating financial metrics like Earnings Per Share (EPS) to give a more accurate picture of the company’s performance over the entire year.