Question

On December 31, 2017, Berclair Inc. had 460 million shares of common stock and 4 million shares of 9%, $100 par value cumulative preferred stock issued and outstanding. On March 1, 2018, Berclair purchased 128 million shares of its common stock as treasury stock. Berclair issued a 5% common stock dividend on July 1, 2018. Four million treasury shares were sold on October 1. Net income for the year ended December 31, 2018, was $800 million. Also outstanding at December 31 were 30 million incentive stock options granted to key executives on September 13, 2013. The options were exercisable as of September 13, 2017, for 30 million common shares at an exercise price of $56 per share. During 2018, the market price of the common shares averaged $70 per share.

Compute diluted earnings per share for the year ended December 31, 2018.

Answer 1

Diluted earning per share = ( net income - preferred dividend ) /( weighted average outstanding shares + Diluted shares )
Diluted earning per share = ( $ 800 million - $ 36 million ) /( 372 million shares + 6 million shares )
Diluted earning per share= $ 764 million / 378 million shares
Diluted earning per share= $ 2.02 per share ( rounded to 2 decimal )
ALL EXPLANATION IS GIVEN BELOW :
Net income :
Net income for year ended December 31, 2018 is $ 800 million
Preferred dividend :
Here , preferred stock is cumulative, the dividend is deducted whether paid or not
Preferred stock ( 4 million shares*$ 100 par value ) = $ 400 million
Dividend on preferred stock = $ 400 million *9% =$ 36 million
so, Preferred Dividend = $ 36 million
weighted average outstanding common shares:
Jan 1,2018 to Dec 31 2018	for common stock	$ 483 million
	( 460 million share * 12/12* $1.05 )
Mar 1,2018 to Dec 31,2018	for treasury stock purchased	(112 million)
	(128 million shares * 10/12 *$ 1.05)
Oct 1,2018 to Dec 31,2018	for treasury stock sold	1 million
	(4 million *3/12 )
	weighted average outstanding shares	372 million shares
Diluted shares:
shares are dilutive , because exercise price of $ 56 per share is less than market price of $ 70 per share
assume exercise date of issue is Jan 1,2018
in Treasury stock method, assume that the proceeds received upon exercise of $ 1,680
( 30 million shares *$ 56 per share ) are used to buy back stock at average market price is 24 million shares
($ 1680 / $ 70 per share)= 24 million shares
Hence, net increase in number of shares= 6 million shares
( 30 million shares are issued upon exercise - 24 million shares repurchased )