# Earnings Per Share: Part 2

What is diluted earnings per share and how do you calculate it?

If you have not read Earnings Per Share: Part 1, be sure to do so before reading this article as it describes what EPS is, and the components used to calculate basic earnings per share.

Basic EPS is calculated when a company has a simple capital structure, which means that the company has not issued any securities that can increase the company’s number of outstanding shares: the company only issues common stock, and non-convertible preferred stock or debt securities. Because many companies issue instruments that can increase the number of outstanding shares, such as convertible preferred stock, convertible debt, or options and warrants, you will need to take these into consideration, which is where diluted EPS is introduced, as this method calculates EPS assuming all convertible securities have been exercised.

Diluted EPS is an important calculation as it will give an analyst a more realistic number for a company’s earnings per share.  Note, however, that if you calculate diluted EPS and it turns out to be higher than basic EPS, then some of the securities used in the diluted calculation are anti-dilutive (and according to IFRS and GAAP these are not to be included). In any case where your diluted earnings per share is higher than the basic EPS, just use basic earnings per share.

There are three different methods of calculating diluted earnings per share, the method used will depend on what type of convertible securities the company has outstanding.

## If-Converted Method (Preferred Stock)

When trying to calculate the diluted EPS of a company that has convertible preferred shares outstanding, you will need to use this method.  If these preferred shares were converted into common stock, two changes will need to be considered: first, the company would have a higher number of outstanding common shares, which will affect the number of weighted average shares.  Second, the company would not have paid preferred dividends if the preferred shares were converted which means the net income available to common shareholders will be higher than the net income used in the basic EPS calculation.

The formula for calculating diluted EPS using the if-converted method for a company with convertible preferred stock is:

Diluted EPS = Net Income / (Weighted Average Number of Shares Outstanding + New Common Shares After Conversion)

Example: Peter’s Pizzeria had net income of \$750,000 and had 425,000 shares of common stock outstanding, as well as 35,000 shares of convertible preferred stock that pay a 6\$ per share dividend, and that are convertible into 5 shares of the company’s common stock.  Calculate the company’s basic and diluted EPS. ## If-Converted Method (Convertible Bonds)

When a company has convertible debt outstanding, the if-converted method will be used.  Similar to convertible preferred stock, the conversion of convertible debt will increase the total number of outstanding shares. Also, the net income will be higher than the basic EPS calculation because if the company converts debt into common shares, they will not have to pay interest on the principal outstanding.  Therefore, the net income increase equals the interest expense on the security multiplied by one minus the interest rate.

The formula for calculating diluted EPS using the if-converted method for a company with convertible debt is:

Diluted EPS = Net Income + ((Security’s Principal x Interest Rate)(1 – Tax Rate)) – Preferred Dividends / (Weighted Average Number of Shares Outstanding + New Common Shares After Conversion)

Example: Peter’s Pizzeria had net income of \$750,000 and had a weighted average of 425,000 common shares outstanding.  Additionally, the company had 35,000 shares of preferred stock outstanding with a \$5 dividend, and a \$75,000 convertible bond that pays 7% and is convertible into 15,000 common shares.  Assuming the company has a tax rate of 30%, calculate the basic and diluted EPS. ## Treasury Method

This last method of calculating diluted earnings per share is used when a company has stock options or warrants outstanding.  The treasury method assumes that upon exercise of these dilutive securities, the company receives cash and then uses these proceeds to purchase treasury shares at an averaged market price (hence the treasury method name).  The number of shares the company has outstanding will increase by the number of shares what would be issued when these securities are exercised minus the number of shares the company would purchase as treasure stock.

To determine the amount of shares that you need to increase the company’s outstanding number of shares by, simply find the difference between the average market price the company will purchase shares at and the option/warrant exercise price, and multiple that by the number of options/warrants outstanding.  Next, divide this number by the average market price the company will purchase shares at.  This number will then be added to the number of outstanding shares.

The formula for calculating diluted EPS using the treasury stock method for a company with outstanding options/warrants is broken down into two parts:

Additional Shares = ((Average Stock Price – Exercise Price) x Number Outstanding Options/Warrants) / Average Stock Price

Diluted EPS = (Net Income – Preferred dividends) / Weighted Average Number of Shares Outstanding + Additional Shares

Example: Peter’s Pizzeria had net income of \$780,000 and had a weighted average of 445,000 common shares outstanding.  At the beginning of the fiscal year, the only potentially dilutive securities the company had outstanding were 25,000 options with an exercise price of \$15.  Over the course of the last fiscal year, the company’s market price per share has averaged \$32.  Calculate Peter’s Pizzeria’s basic and diluted EPS. Additional Shares: ((32 – 15) x 25,000) / 32 = 13,281

Earnings per share is a very important metric when analyzing a company’s profitability  (although it is not the only metric that should be looked at when deciding to invest).  Understanding how to calculate EPS, as well as diluted EPS, will be useful or those studying for the CPA or CFA exams, or for those who just want to learn more about financial analysis techniques.  Have any questions?  Leave a comment.