Note 9. Stock-Based Compensation Plans

The Company has outstanding stock-based compensation awards granted under the 2013 Stock Incentive Plan (“2013 Plan”) and the 2017 Omnibus Incentive Plan (“2017 Plan”) as described in Note 16, “Stock-Based Compensation Plans” to the consolidated financial statements in its annual report on Form 10-K for the year ended December 31, 2018.

In the three month periods ended March 31, 2019 and 2018, the Company recognized stock-based compensation expense of approximately $7.5 million and $3.4 million, respectively. These costs are included in “Other operating expense, net” of the Condensed Consolidated Statements of Operations.

The $7.5 million of stock-based compensation expense for the three month period ended March 31, 2019 included expense of $0.7 million for the modification of a former employee’s equity awards, expense for equity awards granted under the 2013 Plan and 2017 Plan of $2.1 million and an increase in the liability for stock appreciation rights (“SAR”) of $4.7 million. The $0.7 million stock-based compensation expense for the modification incurred in the three month period ended March 31, 2019 provided continued vesting through scheduled vesting dates for certain awards of a former employee.

As of March 31, 2019, there was $38.4 million of total unrecognized compensation expense related to outstanding stock options and restricted stock awards.

SARs, granted under the 2013 Plan are expected to be settled in cash and are accounted for as liability awards. As of March 31, 2019, a liability of approximately $9.6 million for SARs was included in “Accrued liabilities” of the Condensed Consolidated Balance Sheets.

Stock Option Awards

A summary of the Company’s stock option (including SARs) activity for the three month period ended March 31, 2019 is presented in the following table (underlying shares in thousands).

	Shares			Weighted-Average Exercise Price (per share)
Outstanding at December 31, 2018		12,352		$	10.93
Granted		1,067		$	27.05
Exercised or settled		(2,271	)	$	8.55
Forfeited		(57	)	$	32.06
Outstanding at March 31, 2019		11,091		$	12.86
Vested at March 31, 2019		8,879		$	9.48

The following assumptions were used to estimate the fair value of options granted (excluding previously disclosed modified awards) during the three month periods ended March 31, 2019 and 2018 using the Black-Scholes option-pricing model.

	Three Month Period Ended March 31, 2019		Three Month Period Ended March 31, 2018
Assumptions
Expected life of options (in years)		6.3		7.0 - 7.5
Risk-free interest rate		2.6%		2.9%
Assumed volatility		31.8%		35.1 - 35.4%
Expected dividend rate		0.0%		0.0%

Restricted Stock Unit Awards

A summary of the Company’s restricted stock unit activity for the three month period ended March 31, 2019 is presented in the following table (underlying shares in thousands).

	Shares			Weighted-Average Grant-Date Fair Value
Non-vested as of December 31, 2018		362		$	31.78
Granted		417		$	27.05
Vested		(28	)	$	32.06
Forfeited		(25	)	$	32.06
Non-vested as of March 31, 2019		726		$	29.01