Earnings per Share

9 Months Ended

Sep. 30, 2020

20. Earnings per Share:

Basic earnings per share is calculated as income (loss) available to common stockholders, divided by the weighted average number of common shares outstanding during the period. The weighted average number of common shares outstanding during the period for the computation of basic earnings per share excludes restricted stock awards that have legally been issued but are nonvested during the period, as the sale of these shares is prohibited pending satisfaction of certain vesting conditions by the award recipients in order to earn the rights to the shares.

Diluted earnings per share is calculated as income (loss) available to common stockholders, divided by the weighted average number of common and potential common shares outstanding during the period, if dilutive. Potential common shares reflect (1) unvested restricted stock awards and restricted stock units with service vesting conditions, (2) performance stock units with vesting conditions considered probable of achievement and (3) options to purchase common stock, all of which have been included in the diluted earnings per share calculation using the treasury stock method.

The reconciliation from basic to diluted weighted average shares outstanding is as follows:


	Three months ended September 30,		Nine months ended September 30,
	2020	2019	2020	2019
Weighted average shares outstanding – Basic	135,106,969	134,511,819	135,292,163	134,213,571
Dilutive effect of unvested common shares and restricted stock units with service conditions, performance stock units considered probable of vesting and assumed stock option exercises and conversions	872,149	1,137,891	895,870	1,091,799
Weighted average shares outstanding – Diluted	135,979,118	135,649,710	136,188,033	135,305,370

Basic and diluted earnings per share are calculated as follows:


	Three months ended September 30,				Nine months ended September 30,
	2020		2019		2020		2019
Numerator:
Net income attributable to PQ Group Holdings Inc.	$	7,512	$	26,713	$	23,662	$	60,438

Denominator:
Weighted average shares outstanding – Basic	135,106,969		134,511,819		135,292,163		134,213,571
Weighted average shares outstanding – Diluted	135,979,118		135,649,710		136,188,033		135,305,370
Net income per share:
Basic income per share	$	0.06	$	0.20	$	0.17	$	0.45
Diluted income per share	$	0.06	$	0.20	$	0.17	$	0.45

The table below presents the details of the Company’s weighted average equity-based awards outstanding during each respective period that were excluded from the calculation of diluted earnings per share:


	Three months ended September 30,		Nine months ended September 30,
	2020	2019	2020	2019
Restricted stock awards with performance only targets not yet achieved	950,174	1,537,572	1,323,270	1,601,474
Stock options with performance only targets not yet achieved	503,526	578,564	509,782	583,204
Anti-dilutive restricted stock awards, restricted stock units and performance stock units	1,539,506	—	1,432,906	—
Anti-dilutive stock options	844,475	863,063	846,578	863,063

Restricted stock awards and stock options with performance only vesting conditions were not included in the dilution calculation, as the performance targets have not been achieved nor were probable of achievement as of the end of the respective periods. On a weighted average basis, options to purchase 603,159 and 621,747 shares of common stock at $16.97 per share for the three months ended September 30, 2020 and 2019, respectively, and options to purchase 241,316 shares of common stock at $17.50 per share for the three months ended September 30, 2020 and 2019, were excluded from the computation of diluted earnings per share for the respective periods, because the combination of the options’ exercise price and remaining unamortized stock-based compensation expense was greater than the average market price of the common shares. On a weighted average basis, options to purchase 605,262 and 621,747 shares of common stock at $16.97 per share for the nine months ended September 30, 2020 and 2019, respectively, and options to purchase 241,316 shares of common stock at $17.50 per share for the nine months ended September 30, 2020 and 2019, were excluded from the computation of diluted earnings per share for the respective periods, because the combination of the options’ exercise price and remaining unamortized stock-based compensation expense was greater than the average market price of the common shares. The stock options with an exercise price of $16.97 per share expire on October 2, 2027, while the stock options with an exercise price of $17.50 per share expire on August 9, 2028. Anti-dilutive awards are not included in the dilution calculation, as their inclusion would have the effect of increasing diluted income per share.