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Dilutive Securities and Earnings per Share [EPS]



Dilutive Securities and Earnings Per Share [EPS]During the past 30 years, a wide variety of new financial instruments have been introduced into the marketplace. In addition to the traditional basic securities of common stock, preferred stock, and bonds, one can now also own convertible bonds, convertible preferred stock, bonds with detachable stock warrants, stock rights, and employee stock options. How are they accounted?

The first half of this post will discuss each one of these instruments; the second half will discuss earnings per share and demonstrate the role that these instruments play in the determination of earnings per share. Follow on…



Convertible Bonds

Many corporations issue convertible bonds. These bonds may be traded in by the investor before maturity for common stock. Thus the investor has the option of either holding the bonds until maturity and collecting principal and interest or trading them in at an earlier date for stock. Because of this attractive feature, convertible bonds will usually pay a lower rate of interest than non-convertibles.

The accounting for these bonds at the date of issuance is no different from non-convertibles.


The Large Corporation issues $100,000 par, 5-year, 8% bonds at 103. The bonds are convertible into 5,000 shares of $15 par common stock after 3 years. The entry at issuance is:

[Debit]. Cash = 103,000
[Credit]. Bonds Payable = 100,000
[Credit]. Bond Premium = 3,000

Notice that no indication was made regarding the conversion feature.


If a conversion eventually takes place, the entry is made based upon book values. Market values are ignored, and therefore, no gain or loss is recognized upon the conversion.

Thus the book value at this time is $101,200. Assuming the market value of these bonds at this point is 104, the entry would be:

[Debit]. Bonds Payable = 100,000
[Debit]. Bond Premium = 1,200
[Credit]. Common Stock (Par) = 75,000
[Credit]. Paid-in Capital in Excess of Par = 26,200 (plug)

The Bonds Payable and Premium accounts are closed and replaced by the Common Stock and Paid-in Capital in Excess of Par accounts. Notice that the market value of 104 is totally ignored. Sometimes a corporation may try to induce the bondholder to trade in the bond by giving a cash payment. This is called a “sweetener” and is debited to an expense account.


If in the previous example the bondholder refused to convert the bonds unless paid a sweetener of $5,000, an additional entry would be made as follows:

[Debit]. Debt Conversion Expense = 5,000
[Credit]. Cash 5,000

Convertible Preferred Stock

Once again, as was the case for convertible bonds, the book value method is used and market values are ignored. The Preferred Stock account and any related premium accounts are canceled (debited) and Common Stock is credited at par. If a credit is needed to balance the entry, it goes to Paid-in Capital in Excess of Par; if a debit is needed, it goes to retained earnings.


Preferred stock of $1,000 par with a related premium of $100 is converted into 100 shares of $9 par common stock. The entry is:

[Debit]. Preferred Stock = 1,000
[Debit]. Paid-in Capital in Excess of Par—Preferred = 100
[Credit]. Common Stock = 900
[Credit]. Paid-in Capital in Excess of Par—Common = 200

Assume the same information as in the previous example except that the par of the common is $13. The entry is:

[Debit]. Preferred Stock 1,000
[Debit]. Paid-in Capital in Excess of Par—Preferred = 100
[Debit]. Retained Earnings = 200
[Credit]. Common Stock = 1,300

Bonds With Detachable Stock Warrants

A stock warrant is a certificate that enables its holder to purchase shares of stock at a certain fixed price for a given time period. Many times corporations will attach these warrants to a bond in order to make the bond more attractive. A key difference between these bonds and convertible bonds is that in the latter case, the investor trades in the bond for stock, while in the former case, he or she keeps the bond and hands in the warrant plus cash.

Since these warrants are detachable and can be traded separately from the bonds, the profession has ruled that the sale of this entire package be considered an issuance of both debt and equity securities. Accordingly, the entry involves a credit to the Bonds Payable account and to a stockholders’ equity account as well. The allocation between the two is based upon their respective market values. This is called the proportional method.


Bell Labs issued 100 bonds, $100 par, each with a detachable stock warrant. Each warrant may be exercised to purchase 1 share of $100 par common stock at $110. The total selling price is the par of $10,000 ($100×100). At the time of the sale, the market value of the bonds (without the warrants) is 102, while the market value of the warrants is $30. The allocation of the $10,000 selling price is as follows:

Market Value
Bonds: 100 × 102     =           $10,200
Warrants: 100 × $30 =               3,000
Total market value    =           $13,200

Bond allocation: 10,200/13,200 × $10,000 = $7,727 (rounded)
Warrant allocation: 3,000/13,200 × $10,000 = $2,273

Thus the bonds have been issued at a discount of $2,273 ($10,000 par – $7,727). The entries are:

[Debit]. Cash = $7,727
[Debit]. Bond Discount = 2,273
[Credit]. Bonds Payable = 10,000

[Debit]. Cash = 2,273
[Credit]. Paid-in Capital—Stock Warrants*) = 2,273

Note: *)A stockholders’ equity account



If in the previous example the warrants are exercised by the investors to purchase 100 shares at $110, the entry would be:

[Debit]. Cash (100 × $110) = 11,000
[Debit]. Paid-in Capital—Stock Warrants = 2,273
[Credit]. Common Stock = 10,000*)
[Credit]. Paid-in Capital in Excess of Par = 3,273

Note: *)At par: 100 × $100


If the warrants were instead allowed by the investors to expire, the following entry would be made:

[Debit]. Paid-in Capital—Stock Warrants = 2,273
[Credit]. Paid-in Capital—Expired Stock Warrants = 2,273

In the above situation, the market values of both the warrants and the bonds were known. If, however, only one market value is known, then that security would be allocated market value for its share of the total selling price, while the remainder would go to the other security. This is referred to as the incremental method.


If in Example 6 only the market value of the warrants was known ($3,000), the original entries would be:

[Debit]. Cash = 7,000
[Debit]. Bond Discount = 3,000
[Credit]. Bonds Payable = 10,000

[Debit]. Cash = 3,000
[Credit]. Paid-in Capital—Stock Warrants = 3,000

Of the $10,000 selling price, the warrants received their market value of $3,000 and the remaining $7,000 was allocated to the bonds.


The previous discussion centered around bonds with detachable warrants. If the warrants are nondetachable, no recognition would be made in the entries for the warrants. Thus the entire selling price would go to the bonds.


A corporation issues 100 bonds, $100 par per bond, with nondetachable stock warrants for $10,000. The market values of the bonds and the warrants are 102 and $30, respectively. The entry is:

[Debit]. Cash = 10,000
[Credit]. Bonds Payable = 10,000

Notice that the warrants are ignored in the entry.


Stock Warrants Issued Alone

In the previous section we discussed a situation where the stock warrants were attached to a bond. Sometimes corporations issue stock warrants unattached to any bond. These warrants, as before, give the holder the right to buy shares of stock at a certain fixed price for a given time. They are usually given to common stockholders to enable them to be first on line when new shares are issued.

No journal entry is required for the issuance of these stock warrants. The corporation merely makes a memorandum entry indicating how many warrants are outstanding.

Employee Stock Options

Corporations often establish stock option plans where employees may purchase shares of stock, for a limited time, at a discount. The purpose of these plans is to help recruit high-quality employees and as additional compensation for superior performance.

These plans require an annual entry to recognize an expense called “compensation expense.” The total expense is calculated at the “measurement date” and is evenly spread over the “service period.” The measurement date is the date when both the number of shares the employees are entitled to receive and the option price are known; the service period begins from the date of the grant and ends when the employee may begin to exercise the options.


If options are granted to purchase 1,000 shares at $20 and the market price on the grant date is $50, total compensation cost would be ($50 – $20) × 1,000 = $30,000. If the service period is 5 years, then $6,000 of this cost ($30,000 [:] 5) would be recognized each year.

The journal entry to recognize compensation expense each year, is:

[Debit]. Compensation Expense = 6,000
[Credit]. Paid-in Capital—Employee Stock Options = 6,000


When the stock is later issued, the Paid-in Capital account and Cash would be debited, and Common Stock would be credited.


On January 1, 2009, Lie Dharma Putra Corporation grants options to its five employees to purchase 1,000 shares of $40 par common stock at $50 per share, beginning on January 1, 2012, and ending on January 1, 2013. The service period is from the grant date (1/1/2009) until the earliest exercise date (1/1/2012)—a total of 3 years.

On Dec 31 of 2009, 2010 and 2011, the following entry is made:

[Debit]. Compensation Expense = 2,000*)
[Credit]. Paid-in Capital—Employee Stock Options = 2,000

Note: *) (56 – 50)1,000 = 6,000 [:] 3 years = 2,000


The income statement for 2009 compensation expense of $2,000 and the December 31, 2009, balance sheet would contain the following in its stockholders’ equity section:

Paid-in Capital—Employee Stock Options = 2,000



If in the previous example the employee exercises the options during 2012 to purchase 1,000 shares at $50, the entry is:

[Debit]. Cash = 50,000
[Debit]. Paid-in Capital—Employee Stock Options = 6,000
[Credit]. Common Stock (Par) = 40,000
[Credit]. Paid-in Capital in Excess of Par = 16,000 (to balance the entry)


If the employees do not exercise the options and allow them to lapse, an entry would be made debiting Paid-in Capital—Employee Stock Options, and crediting Paid-in Capital—Lapsed Stock Options.

On the next page, I am going to talk about accounting for “Stock Appreciation Rights (SARs)” a plan that involves the issuance of certain rights (SARs) to employees, “Earnings Per Share [Basic]” a very popular ratio used by financial analysts to evaluate a company’s performance, “Diluted EPS—Convertible Preferred Stock” a complex capital structure, and “Diluted EPS—Convertible Bonds“. Read them all on the next page. Use the page navigation below:


Stock Appreciation Rights (SARs)

This is a plan that involves the issuance of certain rights (SARs) to employees, which upon exercise require the company to pay cash for the difference between the grant price and the market price of the company stock on the exercise date. For example, if the grant price is $10 per share and the market price is $15, the company will give the employee a bonus of $5 per share.

The total compensation cost must be allocated, as discussed previously, to the service period involved. Since neither the market price nor the exercise date is known in advance, estimates must be made to record annual compensation expense.

The annual expense calculation would be done as follows:

Total expense (as currently estimated)
X cumulative fraction
– cumulative expense recognized so far

The entry each year, based upon an estimate using that year’s ending market price, is:

[Debit] Compensation Expension  = XXX
[Credit]. Stock Appreciation Plan Liability = XXX

At the date of exercise, the liability would be debited and cash would be credited.


On January 1, 2010, General Motors grants one employee 4,000 SARs. For each SAR the employee is entitled to receive the difference between the grant price of $10 and the market price of the company’s stock on the measurement date, which is 4 years later on December 31, 2013. The employee may not exercise these rights before that date. The service period is thus 4 years.

The year-end market prices were as follows:

2010: $12          2012: $14
2011: $13          2013: $15

For each year (2010–2013) an entry must be made to recognize compensation cost. Since the market price on the measurement date is presently unknown, we use each year’s ending market price as a best estimate.

For December 31, 2010:

[Debit]. Compensation Expense = 2,000
[Credit]. Stock Appreciation Plan Liability = 2,000

The $2,000 is based upon (12 – 10) $4,000 = $8,000 × 1/4 = $2,000.
For December 31, 2011:

[Debit]. Compensation Expense = 4,000*)
[Credit]. Stock Appreciation Plan Liability = 4,000

Note: *) ($13 – $10)4,000 = ($12,000 × 2/4) – 2,000

For December 31, 2012:

[Debit]. Compensation Expense = 6,000 *)
[Credit]. Stock Appreciation Plan Liability = 6,000

Note: *) (14 – 10)4,000 = (16,000 × 3/4) – (2,000 + 4,000) = $6,000.
For December 31, 2013:

[Debit]. Compensation Expense = 8,000 *)
[Credit]. Stock Appreciation Plan Liability = 8,000

Note: *)
($15 – $10)4,000  = $20,000
Less 2010 amount = (2,000)
Less 2011 amount = (4,000)
Less 2012 amount = (6,000)
When the rights are exercised, the entry is:

[Debit]. Stock Appreciation Plan Liability = 20,000
[Credit]. Cash = 20,000


Earnings Per Share—Basic

A very popular ratio used by financial analysts to evaluate a company’s performance is earnings per share (EPS). Broadly speaking, this ratio determines how much of the net income “pie” has been “earned” for each share of common stock.

There are two types of EPS: basic and diluted. Basic EPS is used for a “simple capital structure” —a corporation that has no convertible securities (convertible bonds, convertible preferred stock, or stock warrants) outstanding. Diluted EPS is used for complex capital structures.

The formula for basic EPS is:

EPS = (net income                        –                        preferred dividend)
weighted average of common shares outstanding during year


If the preferred stock is cumulative, then the preferred dividend must be subtracted regardless of whether or not it was declared. However, if it is noncumulative, it is subtracted only if declared.

The calculation of a weighted average will be discussed later on near the end of this post.


Corporation C had net income of $110,000 in 2009 and 20,000 shares of common stock were outstanding during the year. There were also 1,000 shares of $100 par, 10%, preferred stock outstanding as well. Thus the preferred dividend is 10% × $100 × 1,000 = $10,000. Basic EPS is:

= [$110,000 – $10,000] / 20,000
= $5.00

Diluted EPS—Convertible Preferred Stock

In a complex capital structure containing either convertible preferred stock, convertible bonds, or stock warrants, the accounting profession requires the presentation of diluted EPS in addition to basic EPS. Let’s discuss convertible preferred stock first.

If there is preferred stock outstanding that can be converted into common stock, we “make-believe” as if the conversion has actually taken place. Accordingly, in the numerator we will not subtract the preferred dividend—because the preferred stock has “magically” been converted into common—and thus there is no preferred dividend. In the denominator we will add the additional common shares created by this “conversion.”


A company had net income of $110,000 in 19X5 with 20,000 shares of common stock outstanding. There were also 1,000 shares of $100 par, 7% cumulative, convertible preferred stock outstanding as well. There shares can be converted into 2,000 shares of common stock.

Basic EPS would be:

[$110,000 – $7,000] / 20,000 = $5.15

Diluted EPS assumes conversion of the preferred stock. Thus diluted EPS would be:

$110,000 / [20,000 + 2,000] = $5.00

Notice that because we assume conversion into common stock has taken place, we do not subtract the preferred dividend in the numerator, and in the denominator we add the new 2,000 common shares.


If the convertible preferred stock has been outstanding for only part of the year, then the denominator should be increased by a prorated amount representing that fraction.


If in the previous example the preferred stock was issued April 1 and thus was outstanding for only three-fourths of the year, the denominator would only be increased by 3/4 × 2,000 = 1,500 shares. Thus EPS would be $5.12.



Diluted EPS—Convertible Bonds

If a corporation has bonds outstanding that are convertible into common stock, then for diluted EPS we consider them “as if” converted. When conversion is assumed, the denominator must be increased by the number of common shares the bonds are convertible into.

The numerator containing the net income must also be increased because net income consists of revenue minus expense. Bonds generate interest expense. Since we are “assuming” the bonds have been converted into stock, there is no interest expense and therefore this interest must be added back into the net income.


A company had 10,000 shares of common stock outstanding, net income of $90,000 and a $100,000 par, 10% bond convertible into 20,000 shares of common stock within 3 years. Let’s simplify matters temporarily by assuming there are no taxes. Thus for diluted EPS, the denominator would be increased by 20,000 and the numerator by $10,000 ($100,000×0.10).

The computation is:

[$90,000 + $10,000] / 30,000 = $3.33


In the above example we assumed no taxes. Since in the real world there are taxes, the interest saving is made smaller by the tax. To get the net saving, we must multiply the interest by 1 – the tax rate.


If in the above example the tax rate was 30%, the interest saving would be $10,000 (1 – 0.30) = $7,000.


If the bonds have been outstanding for less than a full period, the interest saving in the numerator and the increase of shares in the denominator would have to be reduced accordingly.


If a $100,000 par, 10% bond convertible into 20,000 shares was outstanding for only one half year, and the tax rate is 30%, the denominator would only be increased by 10,000 (20,000× 1/2). The numerator would be increased by the interest of 10,000 × (1 – 0.30) × 1/2 year = $3,500.


If the bond was sold at a premium or discount, the interest adjustment in the numerator must take this into account. Discounts increase interest expense while premiums reduce interest expense.


Assume a 10-year, $1,000 par, 10% convertible bond was sold at 102. The use of the straight-line method of premium amortization results in a reduction of the interest by the amount of $2 ($20 [:] 10 years). Thus the interest savings would be $98 (10% × $1,000 – $2).


If the bond in the previous example was sold at 95, the discount amortization per year would be $50 [:] 10 = $5, which increases the annual interest expense. Therefore the interest saving would be $105 ($100 + $5).


Three more topics left on the next page: (1) Fully Diluted EPS—Stock Warrants; (2) The Antidilutive and 3% Tests; and (3) Weighted Average Shares [Contingent Shares]. Use the page navigation below:


Fully Diluted EPS—Stock Warrants

If there are stock warrants (options) outstanding enabling the holder to purchase stock, we once again, for diluted EPS, “make-believe” these warrants were exercised.

The proceeds received by the corporation upon the exercise of these warrants are assumed to be used to purchase treasury shares in the marketplace. The purchase price of these shares is the average market price for the period.


A corporation has 10,000 stock warrants outstanding enabling the holders to purchase 1 common share per warrant at a price of $100, within 4 years.


At first glance it would seem that since we assume conversion, we must add 10,000 shares to the denominator. However, the corporation has now received $1 million (10,000 × $100). What does it do with this money? We assume it uses this money to go into the marketplace and buy back its own shares for the treasury.

Let’s assume the average market price for common stock is $110. For diluted EPS, $1 million can buy back 9,091 shares ($1,000,000 [:] $110 = 9,091 rounded). Thus, while on the one hand it has issued 10,000 shares, on the other hand it has bought back 9,091 shares! The net increase is, therefore, only 909 shares, which would be added into the denominator.

If the stock warrants were only outstanding for a partial period, then the effect of the conversion should be prorated, as discussed previously for convertible bonds and preferred stock.

There is a limitation on the number of shares that we assume can be repurchased for the treasury. The maximum is 20% of the presently outstanding common shares. If there are any funds still left over, we assume they are used to retire short-term and long-term debt, and then to buy U.S. government securities. Any interest savings or earnings on these items should be added to the numerator.


Assume a corporation has 70,000 shares of common stock outstanding and 20,000 stock warrants that can be used to purchase 20,000 shares at $50 per share, thus bringing in $1,000,000 (20,000 × $50). If the market value of the stock is $55, then 18,182 shares can then be repurchased for the treasury ($1,000,000 [:] $55). However, the maximum is limited to 14,000 shares (20% of 70,000 shares outstanding). Accordingly the denominator can only be increased by 14,000.

Thus 14,000 × $55 = $770,000 will be spent on treasury stock. The remainder of the $1,000,000 ($330,000) can be used to retire short- and long-term debt. If there is no debt and U.S. government securities yielding 10% interest are purchased instead, the interest of $33,000 minus taxes are added into the numerator.


The Antidilutive And 3% Tests

In general, diluted EPS will be less than or equal to basic EPS. The reason for this is that diluted EPS, having added additional shares to the denominator, results in a smaller final fraction.

Occasionally, a convertible item may add so much more to the numerator than to the denominator that the result is a diluted EPS figure higher than basic EPS. Such items are called antidilutive and should be ignored in all EPS calculations.


A company’s basic EPS is $100,000/20,000 shares = $5.00. For diluted EPS there are convertible bonds, 15%, $100,000 par, convertible into 2,000 shares of stock. The tax rate is 10%. Thus the numerator will now be increased by the interest saving: $100,000 × 0.15 × (1 – 0.10) = $13,500, and the denominator by 2,000. The result will be: ($100,000 + $13,500)/22,000 = $5.16.

Since $5.16 is greater than basic EPS of $5.00, these convertible bonds must be ignored, and diluted EPS will be the same as basic EPS.


If the difference between basic EPS and diluted EPS is less than 3%, no presentation of diluted EPS is made since the difference is trivial. Only basic EPS would be presented.


Basic EPS is $5.00. If diluted EPS is $4.85 or less, it would be shown. Otherwise, only the basic EPS of $5.00 is shown.


Weighted Average Shares; Contingent Shares

If the number of common shares changes during the period, we must use a weighted average. This is done by multiplying the shares by the number of months they were outstanding, and then dividing the total by 12.


The Nice Corporation engaged in the following stock transactions during 2010:

Jan. 1 Issued 10,000 shares.
July 1 Issued another 5,000 shares.
Sept. 1 Bought back 2,000 treasury shares.
Oct. 1 Issued 7,000 shares.

The weighted average calculation is as follows:

Jan. 1–July 1 = 6 months × 10,000 shares      =  60,000
July 1–Sept. 1 = 2 months × 15,000*) shares =   30,000
Sept. 1–Oct. 1 = 1 month × 13,000**) shares =  13,000
Oct. 1–Dec. 31 = 3 months × 20,000 shares =   60,000
Total                                                              = 163,000
[:] 12
(rounded) = 13,583 shares

*)10,000 + 5,000
**)10,000 + 5,000 – 2,000


If a stock dividend or stock split occurred during the year, we treat it as if it took place at the beginning of the year. Accordingly, a retroactive adjustment must be made.


The following stock transactions took place for Corporation X during 2010:

Jan. 1 Issued 9,000 shares.
Apr. 1 Issued another 1,000 shares.
June 1 Issued a 100% stock dividend (10,000 shares).
Sept. 1 Issued 4,000 shares.

We treat the stock dividend of June 1 as if it were issued on January 1. Thus the stock transactions of January 1 and April 1 must be retroactively adjusted by multiplying them by a factor of 2. The computations are:

Jan. 1–Apr. 1 = 3 months × 9,000 shares × 2 =     54,000
Apr. 1–June 1 = 2 months × 10,000 shares × 2 =  40,000
June 1–Sept. 1 = 3 months × 20,000*) shares =     60,000
Sept. 1–Dec. 31 = 4 months × 24,000 shares  =    96,000
Total                                                                =   250,000
[:]       12
(rounded) = 20,883

*) (9,000 + 1,000) × 2


Companies occasionally contractually commit to issue additional common shares at some future point. The trigger may be simply the passage of time, or the fulfillment of a condition. For basic earnings per share, since these shares have not yet actually been issued, they are not included in the denominator.

What about for diluted earnings per share? Should we “make-believe” they have been issued?

The answer is that it depends on the nature of the trigger. If the trigger is merely the passage of time, then we make believe now that the shares were issued. If, however, the trigger is the fulfillment of a condition, then the rule is as follows: if the condition has already been fulfilled by today, then we include the shares; if not, we do not include the shares. This is demonstrated by the next example.


It is now December 31, 2009. Optimistic Corp. has contractually committed itself to issue 1,000 new shares on December 31, 2010 if its 2009 net income is at least $500,000.

Case A: Its 2009 income was $400,000
Case B: Its 2009 income was $550,000.


In Case A, since the condition has not yet been presently fulfilled we do not include the shares. But in Case B, since the condition has been fulfilled, we do.

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