In this video, we walk through 6 FAR practice questions teaching about calculating basic and diluted earnings per share. These questions are from FAR content area 1 on the AICPA CPA exam blueprints: Financial Reporting.

The best way to use this video is to pause each time we get to a new question in the video, and then make your own attempt at the question before watching us go through it.

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**Calculating Basic and Diluted Earnings Per Share (EPS)**

Earnings Per Share (EPS) is one of the most important metrics for assessing a company’s profitability on a **per-share basis**. It’s a common measure used by investors to evaluate a company’s financial health, and it helps determine how much profit a company generates for each outstanding share of common stock.

**Basic EPS** is the simplest form of this calculation, focusing only on shares currently outstanding. **Diluted EPS**, on the other hand, takes into account any potential dilution that could result from securities like stock options or convertible bonds.

**Calculating Basic EPS**

The formula for **Basic EPS** is straightforward:

Basic EPS = (Net Income – Preferred Dividends) / Weighted Average Common Shares Outstanding

**Net Income**: The company’s total profit after all expenses and taxes have been deducted.**Preferred Dividends**: These must be subtracted because preferred shareholders are paid before common shareholders.**Weighted Average Common Shares Outstanding**: This accounts for shares issued or repurchased throughout the year. Shares are weighted by the portion of the year they were outstanding.

**Example**: If a company has **$2,000,000 in net income**, **1,000,000 shares of common stock outstanding**, and paid **$50,000 in preferred dividends**, the basic EPS would be:

Basic EPS = ($2,000,000 – $50,000) / 1,000,000 = $1.95

**Diluted EPS: Accounting for Potential Dilution**

**Diluted EPS** provides a more comprehensive picture by including all securities that could potentially dilute (reduce) earnings per share. This includes stock options, convertible preferred stock, and convertible bonds.

The formula for **Diluted EPS** is:

Diluted EPS = (Net Income + Adjustments) / (Weighted Average Shares + Additional Shares from Dilution)

Adjustments include:

- Adding back interest (net of tax) for convertible bonds.
- Adding back preferred dividends for convertible preferred stock.

**How to Calculate the Weighted Average of Common Shares**

The **weighted average number of common shares** outstanding is an important factor in both **Basic EPS** and **Diluted EPS** calculations. It accounts for any changes in the number of shares during the year due to issuances, repurchases, or other events like stock splits or stock dividends. Instead of using the total shares at the end of the year, this method considers how long each set of shares was outstanding.

**Steps to Calculate the Weighted Average of Shares:**

**Identify the shares outstanding at the beginning of the year.**This is your starting point for the calculation.**Adjust for stock transactions throughout the year.**If the company issues additional shares or repurchases shares during the year, calculate how long each set of shares was outstanding.**Weight each transaction by the portion of the year the shares were outstanding.**Divide the number of months the shares were outstanding by 12 to get the proportion of the year.**Apply adjustments for stock splits and stock dividends.**If a stock split or dividend occurs during the year, adjust the number of shares outstanding as if the split or dividend occurred at the beginning of the year.**Sum the weighted shares to get the total weighted average.**

**Example:**

**Scenario**:

At the beginning of the year, a company has 1,000,000 shares of common stock outstanding. On April 1st, the company issues 200,000 additional shares, and on October 1st, it repurchases 50,000 shares.

**Shares at the beginning of the year**:

1,000,000 shares × (12/12 months) =**1,000,000 shares**.**Shares issued on April 1st**:

200,000 shares × (9/12 months) =**150,000 shares**(since the new shares were outstanding for 9 months).**Shares repurchased on October 1st**:

(50,000 shares) × (3/12 months) =**(12,500) shares**(since the repurchased shares were no longer outstanding for 3 months).

Now, sum the weighted shares:

1,000,000 + 150,000 – 12,500 = **1,137,500 shares**.

The **weighted average number of common shares** outstanding for the year is **1,137,500** shares.

**Factors That Impact Basic and Diluted EPS**

**1. Stock Dividends and Stock Splits**

Both **stock dividends** and **stock splits** increase the number of shares outstanding, but they don’t impact the company’s value. In EPS calculations, these events are treated as if they occurred at the beginning of the year to maintain consistency.

**Stock Dividends**: For example, a 10% stock dividend on 1,000,000 shares would add 100,000 new shares, bringing the total to 1,100,000 shares.**Stock Splits**: In a 2-for-1 stock split, every outstanding share is doubled. So, 1,000,000 shares would become 2,000,000 shares.

These adjustments impact the **denominator** in the EPS formula. If a company’s net income is $1,500,000 and it undergoes a 2-for-1 stock split with 1,000,000 shares, the basic EPS calculation changes from:

$1,500,000 / 1,000,000 = $1.50to$1,500,000 / 2,000,000 = $0.75after the split.

**2. Preferred Stock Dividends**

Preferred dividends are always subtracted from net income before calculating **Basic EPS** because preferred shareholders have a right to dividends before common shareholders.

**Example**: If a company has $2,000,000 in net income and pays $100,000 in preferred dividends, the net income available to common shareholders is**$1,900,000**.

However, in **Diluted EPS**, if the preferred stock is **convertible**, the preferred dividends are added back to net income because after conversion, those dividends would no longer be paid.

**3. Convertible Preferred Stock**

Convertible preferred stock can be exchanged for common stock, which impacts **Diluted EPS**. When calculating diluted EPS, we assume the conversion has happened, meaning:

- Preferred dividends are added back to net income.
- The number of common shares increases by the amount of shares convertible from the preferred stock.

**Example**:

Suppose a company has $2,000,000 in net income, 100,000 shares of convertible preferred stock, and each preferred share is convertible into 5 shares of common stock. For **diluted EPS**, add back preferred dividends to net income and increase the number of shares by 500,000 (100,000 × 5).

**4. Convertible Bonds**

Convertible bonds can also dilute EPS. The conversion process assumes that bondholders exchange their bonds for common stock. In this case:

- The company no longer pays
**interest**on the bonds, so the**after-tax interest expense**is added back to net income. - The number of common shares increases by the number of shares the bonds would convert into.

**Example**:

If a company issued $1,000,000 of 5% convertible bonds, the interest is $50,000. If the company’s tax rate is 30%, the after-tax interest would be $50,000 × (1 – 30%) = $35,000. This amount is added back to net income in the **Diluted EPS** calculation.

**5. Stock Options and Antidilutive Securities**

Stock options can dilute EPS, but only if the **exercise price** is lower than the **market price**. When stock options are exercised, the company issues new shares, which increases the number of shares outstanding.

However, if the **exercise price** is higher than the market price, the stock options are considered **antidilutive**—meaning they would **increase** EPS, not decrease it. In this case, they are excluded from the diluted EPS calculation.

**Example**:

If a company has stock options with an exercise price of $50, but the market price is $45, the options are **antidilutive** and will not be considered in the diluted EPS calculation.

**Conclusion**

Understanding the impact of stock splits, stock dividends, convertible preferred stock, convertible bonds, and antidilutive securities is crucial for calculating **basic** and **diluted EPS** accurately. By taking into account potential dilution from convertible securities and excluding antidilutive securities, **diluted EPS** provides a more comprehensive view of the company’s earnings potential per share.