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Chapter19: Share-Based Compensation and Earnings Per Share

Diluted Earnings Per Share

p. 1087

Potential Common Shares

Imagine a situation in which convertible bonds are outstanding that will significantly increase the number of common shares if bondholders exercise their options to exchange their bonds for shares of common stock. Should these potential shares be ignored when earnings per share is calculated? After all, they haven't been converted as yet, so to assume an increase in shares for a conversion that may never occur might mislead investors and creditors. On the other hand, if conversion is imminent, not taking into account the dilutive effect of the share increase might mislead investors and creditors. The profession's solution to the dilemma is to calculate earnings per share twice.

   Securities such as these convertible bonds, while not being common stock, may become common stock through their exercise or conversion. Therefore, they may dilute (reduce) earnings per share and are called potential common shares Securities that, while not being common stock may become common stock through their exercise, conversion, or issuance and therefore dilute (reduce) earnings per share.. A firm is said to have a complex capital structure potential common shares are outstanding. if potential common shares are outstanding. Besides convertible bonds, other potential common shares are convertible preferred stock, stock options, and contingently issuable securities. (We'll discuss each of these shortly.) A firm with a complex capital structure reports two EPS calculations. Basic EPS computed by dividing income available to common stockholders (net income less any preferred stock dividends) by the weighted-average number of common shares outstanding for the period. ignores the dilutive effect of such securities, diluted EPS incorporates the dilutive effect of all potential common shares. incorporates the dilutive effect of all potential common shares.

In a complex capital structure, a second EPS computation takes into account the assumed effect of potential common shares, essentially a “worstcase scenario.”

Options, Rights, and Warrants

Stock options, stock rights, and stock warrants are similar. Each gives its holders the right to exercise their option to purchase common stock, usually at a specified exercise price. The dilution that would result from their exercise should be reflected in the calculation of diluted EPS, but not basic EPS.

 

 LO8

   To include the dilutive effect of a security means to calculate EPS as if the potential increase in shares already has occurred (even though it hasn't yet). So, for stock options (or rights, or warrants), we pretend the options have been exercised. In fact, we assume the options were exercised at the beginning of the reporting period, or when the options were issued if that's later. We then assume the cash proceeds from selling the new shares at the exercise price are used to buy back as many shares as possible at the shares' average market price during the year. This is demonstrated in Illustration 19-9 on the next page.

Stock options are assumed to have been exercised when calculating diluted EPS.

   When we simulate the exercise of the stock options, we calculate EPS as if 15 million shares were sold at the beginning of the year. This obviously increases the number of shares in the denominator by 15 million shares. But it is insufficient to simply add the additional shares without considering the accompanying consequences. Remember, if this hypothetical scenario had occurred, the company would have had $300 million cash proceeds from the exercise of the options (15 million shares × $20 exercise price per share). What would have been the effect on earnings per share? This depends on what the company would have done with the $300 million cash proceeds. Would the proceeds have been used to buy more equipment? Increase the sales force? Expand facilities? Pay dividends?

 

FINANCIAL
Reporting Case

Q4,  p.1069

Obviously, there are literally hundreds of choices, and it's unlikely that any two firms would spend the $300 million exactly the same way. But remember, our objective is to create some degree of uniformity in the way firms determine earnings per share so the resulting numbers are comparable. So, standard-setters decided on a single assumption for all firms to provide some degree of comparability.

   For diluted EPS, we assume the proceeds from exercise of the options were used to reacquire shares as treasury stock at the average market price of the common stock during the reporting period. Consequently, the weighted-average number of shares is increased by the difference between the shares assumed issued and those assumed reacquired—in our illustration: 15 million shares issued minus 12 million shares reacquired ($300 million ÷ $25 per share) equals 3 million net increase in shares.

   The way we take into account the dilutive effect of stock options is called the treasury stock method because of our assumption that treasury shares are purchased with the cash proceeds of the exercise of the options. Besides providing comparability, this assumption actually is plausible because, if the options were exercised, more shares would be needed to issue to option-holders. And, as discussed in the previous chapter, many firms routinely buy back shares either to issue to option-holders or, equivalently, to offset the issuance of new shares.

p. 1088

ILLUSTRATION 19-9

Stock Options

Stock options give their holders (company executives in this case) the right to purchase common stock at a specified exercise price ($20 in this case).

The stock options do not affect the calculation of basic EPS.

The calculation of diluted EPS assumes that the shares specified by stock options were issued at the exercise price and that the proceeds were used to buy back (as treasury stock) as many of those shares as can be purchased at the market price during the period.

Sovran Financial Corporation reported net income of $154 million in 2011 (tax rate 40%). Its capital structure included:

Common Stock

Jan. 1

60 million common shares were outstanding

Mar. 1

12 million new shares were sold

June 17

A 10% stock dividend was distributed

Oct. 1

8 million shares were reacquired as treasury stock

(The average market price of the common shares during 2011 was $25 per share.)

Preferred Stock, Nonconvertible

January 1–December 31

5 million 8%, $10 par, shares

Incentive Stock Options
Executive stock options granted in 2006, exercisable after 2010 for 15 million common shares* at an exercise price of $20 per share

(amounts in millions, except per share amounts)
Basic EPS (unchanged)

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Diluted EPS

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*Adjusted for the stock dividend. Prior to the stock dividend, the options were exercisable for 137/11 million of the “old” shares. Upon the stock dividend, the new equivalent of 137/11 became 15 million (137/11×1.10) of the “new” shares.

Shares Reacquired for Diluted EPS

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Convertible Securities

Sometimes corporations include a conversion feature as part of a bond offering, a note payable, or an issue of preferred stock. Convertible securities can be converted into (exchanged for) shares of stock at the option of the holder of the security. For that reason, convertible securities are potentially dilutive. EPS will be affected if and when such securities are converted and new shares of common stock are issued. In the previous section you learned that the potentially dilutive effect of stock options is reflected in diluted EPS calculations by assuming the options were exercised. Similarly, the potentially dilutive effect of convertible securities is reflected in diluted EPS calculations by assuming they were converted.

 

 LO9
p. 1089

  
ADDITIONAL CONSIDERATION

In our diluted EPS calculation, we “pretend” the options are exercised at the end of the period or at the time of actual exercise, if earlier, with shares repurchased at the average share price on that date. Let's say the options in our illustration were exercised on October 1 and that the per-share price of the stock then was $24. In that case, we assume the proceeds (15 million shares × $20 = $300 million) are used to purchase shares at $24, or 12.5 million shares:

15

million shares

× $20

(exercise price)

$300

million

÷ $24

(market price at exercise)

12.5

million shares

   The incremental number of shares to be included in the computation of diluted EPS, then, is weighted for the period the options were outstanding, the 9 months from January 1–October 1, or 9/12 of a year. Thus, we would add to the denominator:

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   By the if converted method as it's called, we assume the conversion into common stock occurred at the beginning of the period (or at the time the convertible security is issued, if that's later). We increase the denominator of the EPS fraction by the additional common shares that would have been issued upon conversion. We increase the numerator by the interest (after-tax) on bonds or other debt or the preferred dividends that would have been avoided if the convertible securities had not been outstanding due to having been converted.

When we assume conversion, the denominator of the EPS fraction is increased by the additional common shares that would have been issued upon conversion.

CONVERTIBLE BONDS.   Now, let's return to our continuing illustration and modify it to include the existence of convertible bonds (Illustration 19-10). We increase the denominator by the 12 million shares that would have been issued if the bonds had been converted. However, if that hypothetical conversion had occurred, the bonds would not have been outstanding during the year. What effect would the absence of the bonds have had on income? Obviously, the bond interest expense (10% × $300 million = $30 million) would have been saved, causing income to be higher. But saving the interest paid would also have meant losing a $30 million tax deduction on the income tax return. With a 40% tax rate that would mean paying $12 million more income taxes. So, to reflect in earnings the $18 million after-tax interest that would have been avoided in the event of conversion, we add back the $30 million of interest expense, but deduct 40% × $30 million for the higher tax expense.

The numerator is increased by the aftertax interest that would have been avoided.

ILLUSTRATION 19-10

Convertible Bonds

The convertible bonds do not affect the calculation of basic EPS.

If the bonds had been converted, 12 million more common shares would have been issued, and net income would have been higher by the interest saved (after tax) from not having the bonds outstanding.

Sovran Financial Corporation reported net income of $154 million in 2011 (tax rate 40%). Its capital structure included:

Common Stock

Jan. 1

60 million common shares were outstanding

Mar. 1

12 million new shares were sold

June 17

A 10% stock dividend was distributed

Oct. 1

8 million shares were reacquired as treasury stock

(The average market price of the common shares during 2011 was $25 per share.)

Preferred Stock, Nonconvertible

January 1–December 31

5 million 8%, $10 par, shares

Incentive Stock Options
Executive stock options granted in 2006, exercisable after 2010 for 15 million common shares* at an exercise price of $20 per share

p. 1090

Convertible Bonds
10%, $300 million face amount issued in 2010, convertible into 12 million common shares

(amounts in millions, except per share amounts)
Basic EPS (unchanged)

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0077328787/student/spi10831_un1906.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

Diluted EPS

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ADDITIONAL CONSIDERATION

The $300 million of convertible bonds in our illustration were issued at face value. Suppose the bonds had been issued for $282 million. In that case, the adjustment to earnings would be modified to include the amortization of the $18 million bond discount. Assuming straight-line amortization and a 10-year maturity, the adjustment to the diluted EPS calculation would have been:

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0077328787/student/spi10831_eq1909.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

to reflect the fact that the interest expense would include the $30 million stated interest plus one-tenth of the bond discount.

  

*This is an alternative way to represent the after-tax adjustment to interest since subtracting 40% of the interest expense is the same as multiplying interest expense by 60%.

   Our illustration describes the treatment of convertible bonds. The same treatment pertains to other debt that is convertible into common shares such as convertible notes payable. Remember from our discussion of debt in earlier chapters that all debt is similar whether in the form of bonds, notes, or other configurations.

CONVERTIBLE PREFERRED STOCK.    The potentially dilutive effect of convertible preferred stock is reflected in EPS calculations in much the same way as convertible debt. That is, we calculate EPS as if conversion already had occurred. Specifically, we add shares to the denominator of the EPS fraction. We do not subtract the preferred dividends in the numerator because those dividends would have been avoided if the preferred stock had been converted. In Illustration 19-11 we assume our preferred stock is convertible into 3 million shares of common stock.

p. 1091

  
ADDITIONAL CONSIDERATION

Notice that we assumed the bonds were converted at the beginning of the reporting period since they were outstanding all year. However, if the convertible bonds had been issued during the reporting period, we would assume their conversion occurred on the date of issue. It would be illogical to assume they were converted before they were issued. If the convertible bonds in our illustration had been sold on September 1, for instance, the adjustment to the EPS calculation would have been:

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0077328787/student/spi10831_eq1910.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

to reflect the fact that the net increase in shares would have been effective for only nine months of the year.

  

We assume convertible securities were converted (or options exercised) at the beginning of the reporting period or at the time the securities are issued, if later.

ILLUSTRATION 19-11

Convertible Preferred Stock

Since diluted EPS is calculated as if the preferred shares had been converted, there are no dividends.

Sovran Financial Corporation reported net income of $154 million in 2011 (tax rate 40%). Its capital structure included:

Common Stock

Jan. 1

60 million common shares were outstanding

Mar. 1

12 million new shares were sold

June 17

A 10% stock dividend was distributed

Oct. 1

8 million shares were reacquired as treasury stock

(The average market price of the common shares during 2011 was $25 per share.)

Preferred Stock, Convertible into 3 million common shares*

January 1–December 31

5 million 8%, $10 par, shares

Incentive Stock Options
Executive stock options granted in 2006, exercisable after 2010 for 15 million common shares* at an exercise price of $20 per share

Convertible Bonds
10%, $300 million face amount issued in 2010, convertible into 12 million common shares

(amounts in millions, except per share amounts)
Basic EPS (unchanged)

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0077328787/student/spi10831_un1908.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

Diluted EPS

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p. 1092

   The adjustment for the conversion of the preferred stock is applied only to diluted EPS computations. Basic EPS is unaffected.

   However, when diluted EPS is calculated, we hypothetically assume the convertible preferred stock was not outstanding. Accordingly, no preferred dividends on these shares would have been paid.




*Adjusted for the stock dividend. For example, prior to the stock dividend, the bonds were exercisable for 1010/11 million of the “old” shares which became 12 million <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0077328787/student/spi10831_im1912.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a> of the “new” shares after the stock dividend.

See Chapter 14 if you need to refresh your memory about bond discount amortization.

*Adjusted for the stock dividend. For example, prior to the stock dividend, the preferred shares were convertible into <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0077328787/student/spi10831_im1913.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a> of the “old” shares which became 3 million <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0077328787/student/spi10831_im1914.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a> of the “new” shares after the stock dividend.

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