# Basic and diluted EPS

Hey everyone, could you tell me that in the following question, if the preferred share is anti-dilutive or not?

A company has outstanding the entire year 100,000 shares of common stock and 50,000 shares of convertible preferred stock. Eash 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 dividend of \$0.5 per share on the comon 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 yar was \$25.00.

What are the basic and diluted earnings per share?

Basic: 2.00, 3.00, 4.50

Diluted: 1.00, 1.25, 1.45.

I got basic EPS=2.00 and diluted EPS=1.45. But the answer for diluted EPS is 1.25.

I don’t understand how the preferred stock is anti-dilutive. When I use the formula given in the book to check the effect on preferred stock: 5*50000/(3*50000)=1.67, which is smaller than the basic EPS 2.00. Therefore to me, this PS is dilutive and therefore should be included in the calculation of the diluted EPS. But the answer says it is antidilutive because 1.67 is greated than 1.25, the basic EPS with just the options (200,000/(100000+60000)). But I mean, 1.67 should be compared to basic EPS of 2.00, no??

Also, the book presents us the method to check if a particular preferred share and convertible bond are antidilutive or not, but nothing for the options. Therefore, do we always assume the options are dilutive and should always include them in our dilutive EPS calculation?

NI – pref. div. = \$450,000 – (50,000 × \$5.00) = \$200,000.

Basic EPS = \$200,000 / 100,000sh = _ \$2.00/sh _.

If the preferred were converted:

NI = \$450,000, shares = 100,000 + (50,000 × 3) = 250,000; EPS = \$450,000 / 250,000sh = \$1.80/sh < \$2.00/sh, so the convertible preferred is dilutive.

If the options were exercised:

100,000 shared issued, 100,000 × \$10 = \$1,000,000 received.

\$1,000,000 ÷ \$25/sh = 40,000sh.

Net issuance: 100,000sh – 40,000sh = 60,000sh.

EPS = \$200,000 / (100,000sh + 60,000sh) = \$1.25/sh < \$2.00/sh, so the options are dilutive.

If the preferred is converted and the options exercised, EPS = \$450,000 / (100,000sh + 150,000sh + 60,000sh) = \$1.45/sh < \$2.00/sh, so together they’re dilutive.

The smallest of the bunch is _ \$1.25/sh _; that’s the fully diluted EPS.

Neither CFA Institute nor Schweser explains this particularly well. You have to try all of the combinations and pick the lowest EPS of all.

(By the way, be careful if the company shows a loss. Remember that -\$1.25/sh > -\$2.00/sh, so the options would be antidilutive if those were the numbers.)

If the preferred shares are converted then we also add the preferred dividend on the numerator which makes it 450,000 + 250,000 = 700,000. Therefore the EPS works out to be \$700,000/250,000sh = \$2.8/sh. Hence anti dilutive.

You’re mistaken; you don’t add the preferred dividend to net income; you simply don’t subtract it as you did for basic EPS. (Another way to look at it is that you add the preferred dividend to the basic EPS numerator; it’s the same either way.)

Basic EPS numerator = \$450,000 – \$250,000 = \$200,000.

Converting preferred numerator = (\$450,000 – \$250,000) + \$250,000 = \$450,000 ≠ \$700,000.

Hey! Thx for the detailed explaination! But…This process seems so long. It will take more than 3 minutes to try all the combinations! On Schweser, the example simply compares each single case (the one for PS, the one for convertible debt, the options) with basic EPS and if it is smaller than the basic EPS, it is dilutive, so should be included in the calculation.

Imagine if the question gives you all 3 of them, and you gotta try all possible combinations? It just dones’t make sense to me…something seems not right.

And BTW, I think if the earning is negative, EPS will be a useless measure. I doubt they will test us a question with negative EPS… I suspect that on the exam you’ll have only one potentially dilutive security in a fully-diluted EPS question, for exactly that reason.

I wouldn’t be so sanguine.