# Diluted EPS

Selected information from Gerrard, Inc.’s financial activities in the most recent year was as follows: Net income was \$330,000. The tax rate was 40%. 700,000 shares of common stock were outstanding on January 1. The average market price per share for the year was \$6. Dividends were paid during the year. 2,000 shares of 8% 500 par value preferred shares, convertible into common shares at a rate of 200 common shares for each preferred share, were outstanding for the entire year. 200,000 shares of common stock were issued on March 1. Gerrard, Inc.’s diluted earnings per share (diluted EPS) was closest to: A. .197 B. .261 C. .289 Answer is B To compute Gerrard’s basic earnings per share (EPS) ((net income – preferred dividends) / weighted average common shares outstanding), the weighted average common shares outstanding must be computed. 700,000 shares were outstanding from January 1, and 200,000 shares were issued on March 1, so the weighted average is (700,000 + (200,000 × 10 / 12) =) 866,667. Basic EPS was (\$330,000 − (2,000 × \$500 × 0.08)) / 866,667 =) \$0.289. If the convertible preferred shares were converted to common stock as of January 1 (2,000 × 200 =) 400,000 additional common shares would have been issued and dividends on the preferred stock would not have been paid. Diluted EPS was (\$330,000 / (866,667 + 400,000) =) \$0.261. ******************************************* My questions is should we add back dividends of \$80k to NI because converted preferred stock is dilutive compared to basic EPS? ******************************************* Here’s the rule below: If convertible preferred stock is dilutive (meaning EPS will fall if it is converted to common stock), the convertible preferred dividends must be added to earnings available to common shareholders.

It arrives at that answer by adding back .6*80, the after-tax preferred dividends.

the answer B is right. if there was no conversion so the net income available to common share holder (basic eps) is 330000 - preferred dividend. if there was bond convertible during the period, the net income available is 330000 + bond interest*(1-tax rate). the basic eps is greater than diluted eps so we take the value of diluted eps.

No, I agree with adding in bond interest *(1-tax rate) to NI, if basic eps is higher then diluted eps, but in this problem they didn’t?? Did Q Bank make a mistake? Should we add back 48k =(1-.40)(2,000 × \$500 × 0.08)) to net income in this problem? In this problem they get the answer by (\$330,000 / (866,667 + 400,000) =) \$0.261

Please take a look back at the CFA text book. The tax rate here was a trick since there was no bond outstanding. - Basic EPS = (net income - preferred dividends)/weight average number of shares outstanding. - Diluted EPS = (net income)/ (if converted weight average number of shares outstanding)

This was a case of preferred stocks being converted to common shares. in that case - the preferred dividend would no longer be payable - and needs to be added back to the numerator.