Financial Ratios - Calculating Basic and Fully Diluted EPS in a Complex Capital Structure

There are some basic rules for calculating basic and fully diluted ESP in a complex capital structure. The basic ESP is calculated in the same fashion as it is in a simple capital structure.

Basic and fully diluted EPS are calculated for each component of income: income from continuing operations, income before extraordinary items or changes in accounting principle, and net income.

To calculate fully diluted EPS:

Diluted EPS = [(net income - preferred dividend) / weighted average number of shares outstanding - impact of convertible securities - impact of options, warrants and other dilutive securities]

Other form:
(net income - preferred dividends) + convertible preferred dividend + (convertible debt interest * (1-t))

Divided by

weighted average shares + shares from conversion of convertible preferred shares + shares from conversion of convertible debt + shares issuable from stock options.

To understand this complex calculation we will look at each possibility:

If the company has convertible bonds, use the if-converted method:

1.Treat conversion as occurring at the beginning of the year or at issuance date, if it occurred during the year (additive to denominator).
2.Eliminate related interest expense, net of tax (additive to numerator).

If the company has convertible preferred stock, use the if-converted method:

1. Eliminate preferred dividend from numerator (decrease numerator).
2. Treat conversion as occurring at the beginning of the year or at issuance date, if it occurred during the year (additive to denominator). Furthermore, use the most advantageous conversion rate available to the holder of the security.

Options and warrants use the treasury-stock method:

1.Assume that exercise occurred at the beginning of the year or issue date, if it occurs during the year.
2.Assume that proceeds are used to purchase common stock for treasury stock.
3.If exercise price < market price of stock, dilution occurs.
4.If exercise price > market price, securities are anti-dilative and can be ignored in the diluted EPS calculation.

Example:

Company ABC has:

- Net income of $2m and 2m weighted average number of shares outstanding for the accounting period.
- Bonds convertible to common stock worth $50,000: 50 at $1,000, with an interest of 12%. They are convertible to 1,000 shares of common stock.
- A total of 1,000 convertible preferred stock paying a dividend of 10% and convertible to 2,000 shares of common stock, with a par of $100 per preferred stock.
- A total of 2,000 stock options outstanding, 1,000 of which were issued with an exercise price of $10 and the other 1,000 of which have an exercise price of $50. Each stock option is convertible to
10 common stocks.
- A tax rate of 40%.
- Stock whose average trading price is $20 per share.

Calculate the fully diluted EPS

1.Convertible debt

Assume conversion:

If the debt is converted, the company would have to issue an additional 50,000 (50*1,000) common stock. As a result the WASO would increase to 2,050,000.

Since the debt would be converted, no interest would have to be paid. Interest was $6,000 per annum. The interest expense would flow through to common stockholders but not before the IRS get a portion of it. So net of taxes the company would have generated an additional $3,600 [(6,000*(1-40%)] in net income.

Adjusted WASO: 2,050,000
Adjusted net income: $2,003,600

2. Convertible preferred stock

Assume conversion:

If the stock is converted the company would have to issue an additional 2,000 shares of common stock. As a result the WASO would increase to 2,052,000.

Since the preferred dividend would no longer be issued the company would not have to pay $10,000 dividends (100*1,000*10%). Since dividends are not tax deductible, there are no tax implications. So the company would have generated an additional $10,000 in net income attributable to common stockholders.

Adjusted WASO: 2,052,000
Adjusted net income: $2,003,600
Preferred dividend is reduced to zero, because Preferred Dividends will cancel each other out following the Diluted EPS Formula above (assuming all preferred stock is convertible preferred stock).

3.Stock options

If-converted method:

Say there are 1,000 stock options in the money (exercise price < market price of stock). The holders of the stock option can convert their options into stock for a profit at any point and time.

Say 1,000 stock options are out of the money (exercise price > market price of stock). The holders of the stock option would not convert their options, because it would be cheaper to purchase the stock on the open market.

The out-of-the-money option can be ignored. The in-the-money options need to be accounted for.

Here is how in-the-money options are accounted for:

1) Calculate the amount raised through the exercise of options:

1000 * 10 *$10 = $100,000

2) Calculate the number of the common shares that can be repurchased using the amount raised through the exercise of options (found in step #1):

$100,000 / 20 = 5,000

3) Calculate number of common shares created by the exercise of the stock options:

1000 * 10 = 10,000

4) Find the net number by which the number of new common shares, created as result of the stock options exercised (found in step #3), exceed the number of common shares repurchased at the market price with proceeds received from the exercise of the options (found in step #2):

10,000 - 5,000 = 5,000

5) Find the total number of shares if the stock options are exercised: add weighted average number of shares to what you found in step #4:

2,052,000 + 5,000 = 2,057,000

Fully diluted EPS= 2,000,000 + 3,600 - 10,000 + 10,000 = 2,003,600 = 0.974
2,000,000 +50,000 + 2,000 +5,000 2,057,000

Presentation and disclosure

Simple capital structure
a. Basic EPS is presented for income from continuing operations, income before extraordinary items or change in accounting principle, and net income.
b. Reported for all accounting periods presented
c. Prior-period EPS is restated for any prior-period adjustments.
d. Footnotes are required for stock splits and stock dividends.

Complex capital structure
a. Basic and fully diluted EPS are presented for income from continuing operations, income before extraordinary items or change in accounting principle, and net income.
b. Reported for all accounting periods presented
c. Prior-period EPS is restated for any prior-period adjustments.
d. Footnotes are required for diluted EPS.

Introduction
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