Stockholder's Equity and Stock-Based Compensation Expense

Stock-Based Compensation

The total number of shares issued or reserved for future issuance under outstanding stock options at March 31, 2020 and 2019 was 669,209 and 778,875, respectively, and the total number of shares of restricted stock and shares reserved for restricted stock units outstanding at March 31, 2020 and 2019 was 903,204 and 988,426, respectively. The total number of stock appreciation rights (“SARs”) awards outstanding at March 31, 2020 and 2019 was 937,597 and 1,305,013, respectively. The following table presents a summary of the activity related to stock options, restricted stock, restricted stock unit awards and SARs awards for the three months ended March 31, 2020:



	Stock Options		Restricted Stock and Unit Awards		Stock Appreciation Rights
	Number of Shares
Outstanding at December 31, 2019	689,209		908,754		954,679
Granted	—		67,500		—
Stock options and SARs exercised/restricted stock and unit awards vested	—		(16,089	)	—
Cancelled/forfeited	(20,000	)	(56,961	)	(17,082	)
Outstanding at March 31, 2020	669,209		903,204		937,597

Stock-based compensation expense recognized for the three months ended March 31, 2020 and 2019, totaled $0.6 million and $1.3 million, respectively. SARs (credit) expense recognized for the three months ended March 31, 2020 and 2019, totaled $(1.1) million and $4.5 million, respectively.

SARs awards are considered liability awards as they are ultimately settled in cash. As such, these amounts are incrementally accrued in the liability section of the condensed consolidated balance sheets over the service period. All of the Company’s currently outstanding SARs awards achieve vesting through both a market condition and a service condition. SARs awards that are fully vested under both conditions are measured at intrinsic value (i.e. the difference between the market price on the last day of the quarter and the strike price of the awards times the number of awards vested and outstanding) and marked to market each quarter until settled. SARs awards that are not fully vested are incrementally accrued over the service period and adjusted to their fair value each quarter until settled based on a valuation model. The Company calculated the fair value of each award at March 31, 2020 and December 31, 2019 using a Monte Carlo simulation model. The following assumptions were used:



Risk-free interest rates	1.9	%
Expected lives (in years)	5.31
Expected dividend yield	—	%
Expected volatility	79	%