Diluted EPS help

Lawson, Inc.’s net income for the year was \$1,060,000 with 420,000 shares outstanding. Lawson has 2,000 shares of 8%, \$1,000 par value convertible preferred stock that were outstanding the entire year. Each share of preferred is convertible into 50 shares of common stock. Lawson’s diluted earnings per share are closest to: A) \$2.04. B) \$1.94. C) \$2.14. Lawson’s basic EPS ((net income – preferred dividends) / weighted average common shares outstanding) is (\$1,060,000 – (2,000 × \$1,000 × 0.08)) / 420,000 = \$2.14. To calculate diluted EPS the convertible preferred shares are presumed to have been converted, the preferred dividends paid are added back to the numerator of the EPS equation, and the additional common shares are added to the denominator of the equation. Lawson’s diluted EPS is \$1,060,000 / (420,000 + 100,000) = \$2.04. Can anyone please explain why convertible shares are assumed to have been converted and thus not included in the diluted EPS calculation? On other similar questions I think they are sometimes?

The idea of (fully) diluted EPS is to present what would be the worst situation for common shareholders. Anything that could increase the number of common shares outstanding has the potential for diluting the EPS, so you check all the possible securities that could increase the number of common shares outstanding: convertible preferred, convertible bonds, stock options, and stock warrants.

The conventional treatment for these potentially dilutive securities is to assume that they are all converted/exercised at the earliest possible time during the fiscal year; on the Level I CFA exam that will always be at the beginning of the year. (In real life, you might have some convertible bonds issued, say, 5 months into the fiscal year, so you would treat them as if they were converted at issuance, and return only 7 months of interest (net of taxes) to net income. That won’t happen on this exam.)

If preferred stock is converted, then the preferred stock goes away, to be replaced by common stock. When the preferred stock goes away, so do the dividends owed to the preferred shareholders.

If bonds are converted, then the bonds go away, to be replaced by common stock. When the bonds go away, so does the interest (net of taxes) paid to the bondholders.

If options or warrants are exercised, common shares are issued, and the company receives cash for the strike price of the options/warrants. The conventional treatment for that cash is to repurchase common stock (at the average stock price for the year) to limit, somewhat, the dilutive effect of the stock issuance.

Thank you for taking the time to respond.

I think i’ve almost got it so will take what you have said and go over a few more questions and re-read the section in the textbook. Thanks.

A curveball that got me in the mock exam was diluted EPS for stock re-purchases and stock issuances at different timeframes in that fiscal year (I simply took the total converted and issued/repurchased and divided into EPS and chose the wrong answer)

After you get the dilution peice down, definitely look into weighting the diluted EPS to account for issuances at multiple dates within the fiscal year.

My pleasure.

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