# diluted EPS on options

Hi,

I was trying to solve a question on Diluted EPS, on Schweser Note. Correct answer is C, but my answer is different from the official one. I know I might wrong, but I don’t know how. Why the correct answer calculate (\$55-\$50) at numerator ? Could you please explain to me? Thank you

Best regards,

Q.

------------------------------------------------.

Following is the question.

Given the following information, how many shares should be used in computing diluted EPS?

• 300,000 shares outstanding.
• 100,000 warrants exercisable at \$50 per share.
• Average share price is \$55.
• Year-end share price is \$60.

A. 9,091. B. 90,909. C. 309,091.

C is correct. Since the exercise price of the warrants is less than the average share price, the warrants are dilutive. Using the treasury stock method to determine the denominator impact:

（\$55 - \$50） / \$55 * 100k shares = 9091 shares.

------------------------------------------------.

My opinion: ( \$50 / \$55) * 100k shares = 90910 shares. Why the correct answer calculate (\$55-\$50) at numerator ?

You issue 100,000 shares and receive \$5,000,000 (= 100,000 × \$50/share) in cash.

You repurchase 90,909 shares (= \$5,000,000 ÷ \$55/share).

The net is 9,091 (= 100,000 − 90,909) shares issued.

Because you are buying back some of the shares with your warrant proceeds.

100 000 warrants exercised at \$50 = \$5 000 000

\$ 5 000 000/\$55 (average stock price) = \$90 909.09

100 000 share created and you buy back 90 909.09 = 9091

Total shares to calculate diluted EPS = 309091

To answer your question directly, you are using 55-50 because you need to deduct the shares repurchased from total number of shares created via warrants. If you only use 50 in the numerator, it does not take into account that are are repurchasing 90 909.09 of them with the cash generated by the exercised warrants.

Thank you so much. @S2000magician, @cfageist, I’m humbled and grateful.

My pleasure.