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101 Concepts for the Level I Exam

Concept 45: Earnings Per Share (EPS)


Earnings per share is a very important profitability measure. It depicts the earnings per ordinary share. Some basic terminology related to EPS are:

Potentially dilutive securities: Securities that can be converted into ordinary share are called potentially dilutive securities. This includes convertible bonds, convertible preferred stock, and employee stock options.
Simple capital structure: If a company has no potentially dilutive securities, it is said to have a simple capital structure.
Complex capital structure: If a company has potentially dilutive securities, it is said to have a complex capital structure.
Dilutive securities: A potentially dilutive security that decreases EPS when exercised is called a dilutive security.
Anti-dilutive security: A potentially dilutive security that increases EPS when exercised is called an anti-dilutive security.
Basic EPS: In this calculation, we do not consider the effect of any potentially dilutive securities. Basic EPS is calculated as:

     $$Basic\ EPS={{net\ income\ -\ preferred\ dividends}\over {weighted\ average\ number\ of\ shares\ outstanding}}$$

Weighted average number of shares outstanding is the number of shares outstanding during the year, weighted by the portion of the year they were outstanding. Stock splits and stock dividends are applied retroactively to the beginning of the year, so the old shares are converted to new shares for consistency.

During 2001, Company ABC had a net income of $100,000. It paid $22,000 dividends to its preference shareholders and $12,000 dividends to its common shareholders. The number of common shares outstanding during 2001 were as follows:

Shares as of January 1,2001: 10,000

Additional shares issue on July 1, 2001: 2,000

Calculate the basic EPS of the company for 2001.

Solution:

We had 10,000 shares outstanding for the first 6 months and 12,000 shares outstanding for the last 6 months.

Therefore weighted average number of shares outstanding = 10,000 x 6/12 + 12,000 x 6/12 = 11,000 shares.

     $$Basic\ EPS={{\$100,000-\$22,000}\over {11,000}}=\$7.09$$

Note: We ignore dividend paid to common shareholders.

Diluted EPS: In this calculation, we consider the effect of potentially dilutive securities. If a firm has a complex capital structure it has to report both basic and diluted EPS. Diluted EPS is calculated as:

     $$Diluted\ EPS=\ {{NI+conv\ debt\ int\ (1-t)-pref\ div+conv\ pref\ div}\over {wt\ avg\ shares+new\ shares\ issued}}$$

For preference shares, we need to subtract preference share dividends from the numerator and add new shares issued from conversion to the denominator.
During 2001, Company ABC had a net income of $100,000. It paid $22,000 dividends to its preference shareholders and $12,000 dividends to its common shareholders. It had 2,200 preference share and 11,000 common shares outstanding during 2001. Each preference share is convertible into 2 shares of common stock. Calculate the diluted EPS for the company.

Solution:

Number of common shares issued upon conversion = 2,200 x 2 = 4,400

     $$Diluted\ EPS=\ {{NI+conv\ debt\ int\ (1-t)-pref\ div+conv\ pref\ div}\over {Wt\ avg\ shares+New\ shares\ issued}}$$

     $$Diluted\ EPS=\ {{\$100,000+0-\$22,000+\$22,000}\over {11,000+4,400}}=\$6.5$$

For convertible bonds, we need to add the after tax interest cost savings to the numerator and new shares issued from conversion to the denominator.
During 2001, Company ABC had a net income of $100,000. The capital structure of the company for 2001 was as follows:

11,000 common shares

1,000 convertible bonds with par value of $100 and 10% coupon; convertible to 5,000 shares.

The tax rate of the company is 30%.

Calculate diluted EPS.

Solution:

Number of common shares issued upon conversion = 5,000

Interest payable on the bonds = 100 x $1,000 x 10% = $10,000

     $$Diluted\ EPS=\ {{NI+conv\ debt\ int\ (1-t)-pref\ div+conv\ pref\ div}\over {Wt\ avg\ shares+New\ shares\ issued}}$$

     $$Diluted\ EPS=\ {{\$100,000+\$10,000\ x\ 0.7-\$0+\$0}\over {11,000+5,000}}=\$6.69$$

For stock options we use the ‘Treasury Stock Method’, which assumes that the hypothetical funds received by the company from the exercise of options are used to purchase shares of the company’s common stock at the average market price over the reporting period. Thus, the numerator is unchanged and the number of shares to be added to the denominator = the number of shares created by exercising the options – number of shares hypothetically repurchased with the proceeds of the exercise.
During 2001, Company ABC had a net income of $100,000. It paid $22,000 dividends to its preference shareholders and $12,000 dividends to its common shareholders. The capital structure of the company for 2001 was as follows:

11,000 common shares

1,000 stock options outstanding, that have an exercise price of $20.

During 2001, the average market price for the company’s share was $25.

Calculate the diluted EPS.

Solution:

Number of common shares issued upon conversion = 1,000

Cash proceeds from the exercise of options = 1,000 x 20 = $20,000

Number of shares that can be purchased at the average market price with these funds = $20,000/25 = 800

Net increase in common shares outstanding = 1,000 – 800 = 200

     $$Diluted\ EPS=\ {{NI+conv\ debt\ int\ (1-t)-pref\ div+conv\ pref\ div}\over {Wt\ avg\ shares+New\ shares\ issued}}$$

     $$Diluted\ EPS=\ {{\$100,000+\$0-\$22,000+\$0}\over {11,000+200}}=\$6.96$$