Diluted EPS – Mock Exam Question – Why is my answer wrong?

Question

This is my first time posting. Below is a sample mock exam question:

A company has outstanding the entire year 100,000 shares of common stock and 50,000 shares of convertible preferred stock. Each share of preferred stock is convertible into three shares of common stock. It also has 100,000 stock options outstanding the entire year, each of which allows the holder to acquire one share of common stock for $10. During the year, the company paid dividends of $0.50 per share on the common stock and $5.00 per share on the preferred stock. Net income for the year was $450,000 and the income tax rate was 30%. Average market price of the common stock for the year was $25.

Diluted EPS is closest to:

A. $1.00
B. $1.25
C. $1.45

The answer is B, $1.25. The rationale provided is that factoring in the convertible preferred shares EPS ($1.67) is anti-dilutive when compared to the stock options EPS ($1.25). So you use the lower of the two, or so the answer key says. My question is, why don't you combine both dilutive securities in the final EPS calculations? Both convertible preferred shares and options in this case are dilutive when compared to basic EPS, which is $2.00 per share. I did this to get choice C, $1.45. Thanks for any assistance!

Sarah · Answer

I also agree with the solution and arrived at the answer b.  The convertible preferred shares are anti-dilutive because (450,000+250,000)/(100,000+250,000)=2 which is the same as the EPS of (450,000-250,000)/100,000=2.

Therefore to calculate the dilutive EPS=(450,000-250,000)/(100,000+60,000)=1.25

(100,000x10)/25=40,000 so that means the net dilutive impact of the stock option  is 100,000-40,000 (that the company was able to reduce by buying back share in the open market due the the funds received.)

Hope that helps.

lulu123 · Answer

@ajost14

Agree with @diya

Except that the preferred convertible shares are anti-dilutive because:
save dividend/issue common shares = 250,000$ / 150,000 = 1.67 (not 2$, the pref are 3-1 with common)

And remember that options are ALWAYS dilutive so always do them first anyway (because nothing is added to numerator!)