Question

At December 31, 2010, Sager Co. had 1,200,000 shares of common stock outstanding. In addition, Sager had 450,000 shares of preferred stock which were convertible into 750,000 shares of common stock. During 2011, Sager paid $600,000 cash dividends on the common stock and $400,000 cash dividends on the preferred stock. Net income for 2011 was $3,400,000 and the income tax rate was 40%. The diluted earnings per share for 2011 is (rounded to the nearest penny)

a. $1.24.
b. $1.74.
c. $2.51.
d. $2.84.

Answer 1

To find the diluted EPS for Sager Co. for 2011, we consider the conversion of preferred stock and the net income after preferred dividends. The calculation leads to a diluted EPS of $1.53 when rounded to the nearest penny.

Step-by-step explanation:

To calculate the diluted earnings per share (EPS) for Sager Co. for 2011, we must consider both the common stock and the potential conversion of preferred stock into common stock.

The formula for diluted EPS is: Net Income minus Preferred Dividends, divided by the Weighted Average Shares Outstanding after considering any dilutive securities. In this case, the net income is $3,400,000 and the dividends on preferred stock are $400,000. Without converting the preferred shares, Sager Co. has 1,200,000 common shares outstanding. However, we need to treat the 450,000 preferred shares as if they were converted into 750,000 common shares because they are dilutive. The diluted share count would then be 1,200,000 (original common shares) + 750,000 (converted preferred shares) = 1,950,000 shares.

The formula hence becomes ($3,400,000 - $400,000) ÷ 1,950,000 = $1.53 which would be the diluted EPS for 2011, rounded to the nearest penny.