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Earnings per Share (EPS)


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Financial Statements Overview

Earnings per Share


SFAS No. 128
Statement of Financial Accounting Standards (SFAS) No. 128
        a.  Earnings per Share
        b.  Issued in February 1997
        c.  SFAS No. 128 supersedes APB Opinion No. 15, Earnings per Share, May 1969

 Basic Earnings per Share (EPS)
           --> Basic EPS = BE / BS

           --> BE = income available to common stockholders
           --> BS = weighted-average number of common shares outstanding

 Income available to common stockholders
           --> Net income
                 - dividends on preferred stock (declared in the period)
                 - dividends on cumulative preferred stock (accumulated for the period)

 Diluted Earnings per Share (EPS)
           --> Diluted EPS = DE / DS

           --> DS = BS + Dilutive potential common shares
          
           --> DE = BE + Dilutive effect of assumed conversions         
           --> DE = BE + convertible preferred dividends
                              + interest (after-tax) on convertible debt
                              + effect of assumed conversion of potential common shares

 Antidilution is not allowed   
           If assumed conversion has an antidilutive effect on EPS
           --> such conversion is not assumed.

           a.  Antidilutive effect on EPS
           --> Diluted EPS > Basic EPS

           b.  If income from continuing operations < 0,
                     (loss from continuing operations)
           --> Potential common shares are not added.
                     (Diluted EPS = Basic EPS)
           --> even if net income > 0.

 Treasury Stock Method   
           --> Dilutive effect of call options and warrants

           a.  Exercise of options and warrants
           --> assumed
                 at the beginning of the period or
                 at the time of issuance, whichever is later.
                
           b.  Proceeds from exercise
           --> assumed to be used
                 to purchase common stock
                 at the average market price during the period.

           c.  Incremental shares
           --> included
                 in the denominator of diluted EPS

 Stock-based compensation to employees  
           Fixed awards and nonvested stock to be issued
           --> considered outstanding
                 as of grant date.

 If-Converted Method   
           --> Convertible securities

           a.  Preferred dividends to convertible preferred stock
           --> added to income available to common stockholders.

           b.  Interest charges (after-tax) to convertible debt
           --> added to income available to common stockholders.

           c.  Convertible preferred stock or convertible debt
           --> assumed to be converted
                 at the beginning of period or
                 at the time of issuance, whichever is later.

           d.  Conversion is not assumed
           --> if the effect is antidilutive. (Diluted EPS > Basic EPS)

 Stock Dividends or Stock Splits
           Basic and diluted EPS
           --> adjusted retroactively
                 for all periods presented.








Basic EPS


 Basic Earnings per Share (EPS)
           --> Basic EPS = BE / BS

           --> BE = income available to common stockholders
           --> BS = weighted-average number of common shares outstanding

 Example 1 (Issuance of stock)
 
Company A had
   3,000,000 shares of common stock outstanding on January 1, 2011.
   Net income for 2011 is $4,500,000.

   Additional stock transactions:
         April 1, 2011              Issuance of common stock      600,000 shares
         November 1, 2011     Purchase of treasury stock      120,000 shares

     Weighted average number of common shares:
 
Dates outstanding Shares outstanding Fraction of period Weighted average shares
1/1 - 3/31 3,000,000 3/12 750,000
Issuance on 4/1 600,000    
4/1 - 10/31 3,600,000 7/12 2,100,000
Purchase on 11/1 120,000    
11/1 - 12/31 3,480,000 2/12 580,000
Weighted average number of common shares outstanding     3,430,000

      Basic EPS = $4,500,000 / 3,430,000 shares = $1.31

     Weighted average number of common shares:

     3,000,000 shares x 3/12 =    750,000 shares
     3,600,000 shares x 7/12 = 2,100,000 shares
     3,480,000 shares x 2/12 =    580,000 shares
                            Total               3,430,000 shares


 Example 2 (Stock dividend and split)
 
Company B had
   3,000,000 shares of common stock outstanding on January 1, 2011.
   Net income for 2011 is $8,000,000.

   Additional stock transactions:
         April 1, 2011                 Issuance of common stock      600,000 shares
         May 1, 2011                10% stock dividend
         November 1, 2011        2-for-1 stock split

     Weighted average number of common shares:
 
Dates outstanding Shares outstanding Effect of Stock Dividend Effect of Stock Split Fraction of period Weighted average shares
1/1 - 3/31 3,000,000 1.10 2.00 3/12 1,650,000
Issuance on 4/1 600,000        
4/1 - 4/30 3,600,000 1.10 2.00 1/12 660,000
10% stock dividend, 5/1 360,000        
5/1 - 10/31 3,960,000   2.00 6/12 3,960,000
2-for-1 stock split, 11/1 3,960,000        
11/1 - 12/31 7,920,000     2/12 1,320,000
Weighted average number of common shares outstanding         7,590,000

      Basic EPS = $8,000,000 / 7,590,000 shares = $1.05


     Alternatively,
     Weighted average number of common shares:

     3,000,000 shares x 3/12 =    750,000 shares
     3,600,000 shares x 9/12 = 2,700,000 shares
                            Total               3,450,000 shares

     Effect of stock dividend               x 1.1
     Effect of stock split                      x 2.0

     Weighted average             = 7,590,000 shares
 


 Stock Dividends or Stock Splits
           --> adjust the number of shares outstanding retroactively
                 for all periods presented.

           Due to retroactive adjustments,
           --> dates (during the year) of stock dividends and splits
                 do not affect the number of shares outstanding.

 Example 3 (Preferred stock dividend)
 
Company C had
   3,000,000 shares of common stock outstanding on January 1, 2011.

   Preferred stock outstanding:
         200,000 shares of 5% cumulative preferred stock ($10 par)

   Net income:
         2011:    $4,600,000
         2012:  - $1,100,000 (loss)

   Preferred stock dividend declared:
         2011:  $100,000
         2012:  $0

     Weighted average number of common shares:
          2011:  3,000,000 shares
          2012:  3,000,000 shares

     Income available to common stockholders:
          2011:    $4,600,000 - $100,000 (*1) = $4,500,000
          2012:  - $1,100,000 - $100,000 (*2) = - $1,200,000 (loss)

     (*1)  $100,000 dividend on preferred stock (declared in the period)
     (*2)  $100,000 dividend on cumulative preferred stock (accumulated for the period)

     Preferred stock dividend
              = ($10 par x 5%) x 200,000 shares
              = $.50 x 200,000 shares = $100,000

     Basic EPS:
          2011:    $4,500,000 / 3,000,000 shares =   $1.50 per share
          2012:  - $1,200,000 / 3,000,000 shares = - $.40 per share (loss)

 Income available to common stockholders
           --> Net income
                 - dividends on preferred stock (declared in the period)
                 - dividends on cumulative preferred stock (accumulated for the period)

 If there is a loss,
           --> amount of loss is increased by preferred dividends.


Diluted EPS, Treasury Stock Method


 Basic Earnings per Share (EPS)
           --> Basic EPS = BE / BS
           --> BE = income available to common stockholders
           --> BS = weighted-average number of common shares outstanding

 Diluted Earnings per Share (EPS)
           --> Diluted EPS = DE / DS
           --> DS = BS + Dilutive potential common shares

 Example 4 (Treasury stock method)
 
Company D had
   3,000,000 shares of common stock outstanding on January 1, 2011.
   Net income for 2011 is $4,650,000.

   Stock options and warrants issued:
         April 1, 2011:  Options for 200,000 shares, $20 per share exercise price
         October 1, 2011:  Warrants for 250,000 shares, $30 per share exercise price

   Average market price of Company A's common stock during 2011:  $50

     Weighted average number of common shares:  3,000,000
     Income available for common stockholders:  $4,650,000
     Basic EPS = $4,650,000 / 3,000,000 shares = $1.55

     Incremental shares from stock options:
           a.  Proceeds from assumed exercise:
           --> April 1, 2011:  200,000 shares x $20 = $4,000,000

           b.  Number of shares assumed to be repurchased:
           --> $4,000,000 / $50 = 80,000 shares

           c.  Incremental shares from assumed exercise:
           --> Incremental shares = 200,000 shares - 80,000 shares = 120,000 shares

           Alternatively,
           200,000 shares - [(200,000 shares x $20 ) / $50]
           = 200,000 shares x (1 - $20/$50)
           = 200,000 shares x ($50/$50 - $20/$50)
           = 200,000 shares x [($50 - $20) / $50]
           = 200,000 shares x .60 = 120,000 shares

           Option shares x [(Average market price - Exercise price) / Average market price]

     Incremental shares from stock warrants:
           a.  Proceeds from assumed exercise:
           --> October 1, 2011:  250,000 shares x $30 = $7,500,000

           b.  Number of shares assumed to be repurchased:
           --> $7,500,000 / $50 = 150,000 shares

           c.  Incremental shares from assumed exercise:
           --> Incremental shares = 250,000 shares - 150,000 shares = 100,000 shares

           Alternatively,
           250,000 shares - [(250,000 shares x $30 ) / $50]
           = 250,000 shares x (1 - $30/$50)
           = 250,000 shares x ($50/$50 - $30/$50)
           = 250,000 shares x [($50 - $30) / $50]
           = 250,000 shares x .40 = 100,000 shares

           Warrant shares x [(Average market price - Exercise price) / Average market price]

     Weighted average number of common shares:
Dates outstanding Shares outstanding Fraction of period Weighted average shares
1/1 - 3/31 3,000,000 3/12 750,000
Incremental shares from options on 4/1 120,000    
4/1 - 9/30 3,120,000 6/12 1,560,000
Incremental shares from warrants on 10/1 100,000    
10/1 - 12/31 3,220,000 3/12 805,000
Weighted average number of common shares outstanding     3,115,000

     3,000,000 shares x 3/12 =    750,000 shares
     3,120,000 shares x 6/12 = 1,560,000 shares
     3,220,000 shares x 3/12 =    805,000 shares
                            Total               3,115,000 shares


      Diluted EPS = $4,650,000 / 3,115,000 shares = $1.49


Diluted EPS, If-converted Method


 Basic Earnings per Share (EPS)
           --> Basic EPS = BE / BS
           --> BE = income available to common stockholders
           --> BS = weighted-average number of common shares outstanding

 Diluted Earnings per Share (EPS)
           --> Diluted EPS = DE / DS
           --> DS = BS + Dilutive potential common shares
           --> DE = BE + Dilutive effect of assumed conversions         
           --> DE = BE + convertible preferred dividends
                              + interest (after-tax) on convertible debt
                              + effect of assumed conversion of potential common shares

 Example 5 (If-converted method, Convertible bonds)
 
Company E had
   3,000,000 shares of common stock outstanding on January 1, 2011.
   Net income for 2011 is $4,500,000.

   Convertible Bonds:
         April 1, 2011:  $1,000,000 convertible bonds, 8% annual interest rate.
         $1,000 bonds can be converted to 100 shares of common stock.

   Income tax rate:  40%

     Weighted average number of common shares:  3,000,000
     Income available for common stockholders:  $4,500,000
     Basic EPS = $4,500,000 / 3,000,000 shares = $1.50

     If convertible bonds are converted:
           a.  Incremental shares:
           --> April 1, 2011:  ($1,000,000 / $1,000) x 100 shares = 100,000 shares

           b.  Weighted average number of common shares:
           --> 3,000,000 shares x 3/12 =    750,000 shares
                 3,100,000 shares x 9/12 = 2,325,000 shares
                                         Total        = 3,075,000 shares

           c.  Interest expense:
           --> $1,000,000 x 8% x 9/12 = $60,000
           --> After tax:  $60,000 x (1 - 40%) = $36,000

           d.  Income available to common stockholders:
           --> $4,500,000 + $36,000 = $4,536,000

     Diluted EPS = $4,536,000 / 3,075,000 shares = $1.48

           Convertible preferred stock or convertible debt
           --> assumed to be converted
                 at the beginning of period or
                 at the time of issuance, whichever is later.

 Example 6 (If-converted method, Convertible preferred stock)
 
Company F had
   2,000,000 shares of common stock outstanding on January 1, 2011.
   Net income for 2011 is $3,500,000.

   Cumulative preferred stock outstanding:
         200,000 shares of 5% cumulative preferred stock ($10 par)
         100,000 shares of 3% convertible cumulative preferred stock ($20 par)
         One share of convertible preferred stock ($20 par)
               is convertible into one share of common stock.

     Preferred stock dividends:
          5% ($10 par) preferred stock: 
              = ($10 par x 5%) x 200,000 shares
              = $.50 x 200,000 shares = $100,000

          3% ($20 par) preferred stock: 
              = ($20 par x 3%) x 100,000 shares
              = $.60 x 100,000 shares = $60,000

     Income available for common stockholders
              = $3,500,000 - $100,000 - $60,000 = $3,340,000
         
     For  Basic EPS,
           --> Income available for common stockholders
                 = Net income
- all preferred stock dividends

     Weighted average number of common shares:  2,000,000

     Basic EPS = $3,340,000 / 2,000,000 shares = $1.67

     If convertible preferred stocks are converted:
           a.  Incremental shares:
           --> 100,000 shares

           b.  Weighted average number of common shares:
           --> 3,000,000 shares + 100,000 shares = 3,100,000 shares

           c.  Dividends on convertible preferred stock:
           --> 3% ($20 par) preferred stock: 
              = ($20 par x 3%) x 100,000 shares
              = $.60 x 100,000 shares = $60,000

           d.  Income available to common stockholders:
           --> $3,340,000 + $60,000 = $3,400,000

     For  Diluted EPS (If-method method)
           --> Income available for common stockholders for Diluted EPS
                 = Income available for common stockholders for Basic EPS
                
+ Dividends on convertible preferred stock

     Diluted EPS = $3,400,000 / 3,100,000 shares = $1.10



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