# Diluted EPS

The Fischer Company had net income of \$1,500,000. Fischer paid preferred dividends of \$5 on each of the 100,000 preferred shares. There are 1 million Fischer common shares outstanding. In addition to the common and preferred stock, Fischer has \$25 million of 4% bonds outstanding. The face value of each bond is \$1,000. Each bond is convertible into 40 common shares. If Fischer’s tax rate is 40%, determine its basic and diluted earnings per share (EPS)?

I need help calculating diluted EPS.  Thanks in advance.

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If the bonds had been converted:

• How many additional shares would be outstanding?
• How much interest would the company have saved?
• Using the new net income and the new number of shares, what’s the EPS?

Simplify the complicated side; don't complify the simplicated side.

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Firstly, you need to calculate the basic EPS to comparing whether the convertible bond is anti-diluted or diluted

Basic EPS = (NI- dividend for preferred shared)/(Average Common Share) =(  \$1,500,000-\$5*100,000 )/1,000,000 = \$1/ CS

Secondly, using “If-covered” method for convertible bond, ( I assumed that the company doesn’t have the complex capital structure like the option, warranty…):

If the bond was converted => interest expense*(1- Tax rate)/ (amount of common share can be converted from bond) = (4%*  \$25 million)*(1-40%)/(25,000*40) = 0.6 < basic EPS =1 => so we can conclude that the convertible bond will make EPS be diluted

Lastly calculate the Diluted EPS:

Diluted EPS = ( NI - Dividend for EPS + Interest * (1-Tax rate)/ ( Average Common Share + amount of common share can be converted from bond) = (\$1,500,000-\$5*100,000 + 4%*  \$25 million)*(1-40%) ) / ( 25,000*40 + 1,000,000) = \$0.8 / share

So when the convertible bonds are converted to Common share, the EPS will decline from \$1 / share to \$0.8/ share