# Dilutive EPS question - Schweser

The following data pertains to the Sapphire Company: Net income equals \$15,000 5,000 shares of common stock issued on January 1st 10% stock dividend issued on June 1st 1,000 shares of common stock were repurchased on July 1st 1,000 shares of 10%, \$100 par preferred stock each convertible into 8 shares of common were outstanding the whole year What is the company’s diluted earnings per share (EPS)? A) \$1.00. B) \$2.50. C) \$1.15. D) \$1.20. Your answer: A was correct ******************************************* I’m fine with the answer; I just disagree with a portion of the explanation. I don’t understand why the anti-dilutive (“Dilutive calculation”) value is \$1.15 a share. I believe it should be \$1.92 a share. (\$15,000 + \$10,000) / (5,000 +500-500+8,000) = \$1.92 This still leads to the same conclusion, so I would have by chance got this question correct, although I’m unclear as to the Schweser explanation below. ******************************************** Number of average common shares: 1/1 5,500 shares issued (includes 10% stock dividend on 6/1) × 12 = 66,000 7/1 1,000 shares repurchased × 6 months = -6,000 = 60,000 60,000 shares / 12 months = 5,000 average shares Preferred dividends = (\$10)(1,000) = \$10,000 Number of shares from the conversion of the preferred shares = (1,000 preferred shares)(8 shares of common/share of preferred) = 8,000 common Diluted EPS = [\$15,000(NI) − \$10,000(pfd) + \$10,000(pfd)] / 5000(common shares) + 8000(shares from the conv. pfd. shares) = \$15,000 / 13,000 shares = \$1.15/share This number needs to be compared to basic EPS to see if the preferred shares are antidilutive. Basic EPS = [\$15,000(NI) − \$10,000(preferred dividends)] / 5,000 shares = \$5,000 / 5,000 shares = \$1/share Since the EPS after the conversion of the preferred shares is greater than before the conversion the preferred shares are antidilutive and they should not be treated as common in computing diluted EPS. Therefore diluted EPS is the same as basic EPS or \$1/share.

Char-Lee, Can you explain why you are adding 15,000 + 10,000 to find the net income for your dilutive calculation? I thought the original net income was 15,000 and 10,000 in prefered dividends was subtracted for basic EPS. net income 15,000 - 10,000 = 5,000 for basic EPS If I am following the problem correctly, we should add back the 10,000 to the 5,000 when the prefered shares are converted. net income: 5,000 + 10,000 = 15,000 for dilutive EPS Am I missing a step?

The following data pertains to the Sapphire Company: Net income equals \$15,000 5,000 shares of common stock issued on January 1st 10% stock dividend issued on June 1st 1,000 shares of common stock were repurchased on July 1st 1,000 shares of 10%, \$100 par preferred stock each convertible into 8 shares of common were outstanding the whole year What is the company’s diluted earnings per share (EPS)? A) \$1.00. B) \$2.50. C) \$1.15. D) 1.20. Basic EPS: WASO calculation 1/1 \*\*\*\*\* 5000 x 1.1 x 12/12 = 5500 6/1 10% Stock div 7/1 (1000) \* 6/12 = (500) ============================ WASO = 5000 Basic EPS: 15000 - (1000 \* 100 \* .1) / 5000 = 1.00 / share. Diluted EPS: 15000 / (5000 + 8000 ) = 1.15\$ / share ============================================ CP

the truth is I was missing the step… thanks for pointing that out… lesson here is to slow down when working a problem and THINK thnx

and another thing while on the same point – note the time line on the calculation of the WASO. Not that the conversion of Preferred stock could happen in the middle of the year – if the preferred stock was issued in the middle of the year – so then the conversion would have to account for that on the denominator. So E.g. if the problem had stated that the Preferred stock of 1000 was outstanding for 1/2 the year – both the Preferred dividend and the Converted # of shares would have to take into account the time factor. So Basic EPS: (15000 - 1000 * 1/2 * 100 * .1) / 5000 = 2.00 / share Diluted EPS = 15000 / (5000 + 8000 \* .5) = 15000 / 9000 = 1.67 / share. Just another spin that they could throw you in the problem. CP

cpk I got the same thing you did except for the denominator used for the average common shares outstanding. Why wouldn’t the answer for diluted earnings p/share be: 15000 / (4,500 + 8000) = \$1.20? Where 4,500 is the weighted average shares outstanding after taking into consideration that the company repurchased 1,000 shares on July 1st. Is it always assumed that dividends are used to repurchase stock? Thanks TheChad

The WASO from the common stock was 5000, as shown with the calculations above. WASO calculation 1/1 ***** 5000 x 1.1 x 12/12 = 5500 6/1 10% Stock div 7/1 (1000) * 6/12 = (500) ============================ WASO = 5000 The 6/1 Stock Div of 10% is across the whole year. So the 5000 * 1.1 gets accounted for, for 12 months of the year. July 1st Repurchase of 1000 applies for 1/2 a year, leading to 500 shares reduction. So net – 5000 Shares. CP

Thanks for the clarification, I wasn’t careful enough when I read through the problem and didn’t realize it was a STOCK dividend as opposed to a regular dividend. Hence, my question. Thanks again cpk, this is the second question of mine you answered, great job! TheChad

cpk123 Wrote: ------------------------------------------------------- > and another thing while on the same point – note > the time line on the calculation of the WASO. > > Not that the conversion of Preferred stock could > happen in the middle of the year – if the > preferred stock was issued in the middle of the > year – so then the conversion would have to > account for that on the denominator. > > So E.g. if the problem had stated that the > Preferred stock of 1000 was outstanding for 1/2 > the year – both the Preferred dividend and the > Converted # of shares would have to take into > account the time factor. > > So Basic EPS: (15000 - 1000 * 1/2 * 100 * .1) / > 5000 = 2.00 / share \> Diluted EPS = 15000 / (5000 + 8000 \* .5) = 15000 / \> 9000 = 1.67 / share. > > Just another spin that they could throw you in the > problem. > > CP According to Schweser, time of issuing convertible securities is a factor for calculating if-converted shares as CPK123 illustrated. However, in the curriculum page 174, it says " diluted EPS is calculated using the if-converted method (i.e. what EPS would have been if the convertible preferred securities had been converted AT THE BEGINNING OF THE PERIOD." It sounds like if-converted method ignores timing factor. Unfortunately, the example in the book doesn’t illustrate this point. Anyone? Thanks

Why is stock split not applied to the preferred shares in the calculation of denominator ? According to the definition stock split is adjusted for all the shares outstanding prior to the date of stock split. so, using if method total outstanding shares from conversion of preferred stocks will be 8000*1.1*12/12 = 8,800 am I missing something basic here ?

i believe stock div and stock splits apply to only the common pool unless stated explicitly. cp

What is the stock dividends effect on the number of convertible preferred stock ?

None. Preferred stock has cash dividends, cummulative, with seniority over common stock. Never heard of preferred stock dividends in the form of stock.

what if a preferred stock is converted to common stock on Jan 1. June company declares stock divided on common stock. Then why wouldn’t that stock dividend adjustment apply on common stocks that were created through conversion from preffered stocks ?

Than you no longer have a complex capital structure (that is if you don’t have some convertible debt, or outstanding options or warrants). Preferred stock dividends are in fix amount (percentage of par).