The 2016 Long-Term Incentive Plan (“2016 LTIP”) authorizes us to issue stock options, stock appreciation rights, restricted stock awards, stock units, performance-based awards and cash awards to officers and key employees and expires on July 8, 2026, after which time no further awards may be made. The 2016 LTIP authorizes us to issue up to 2,803,242 shares of common stock, which includes all shares that have been issued under the 2016 LTIP. As of December 31, 2021, 1,040,066 shares were available for future grants under the 2016 LTIP, which includes anticipated future adjustments to shares for performance-based awards that have been previously granted.

The 2016 Directors Stock Unit Plan (“2016 Director’s Plan”) authorizes us to issue stock units to non-employee directors until July 2026. The 2016 Director’s Plan authorizes us to issue up to 250,000 shares of common stock, which includes all shares that have been issued under the 2016 Director’s Plan. As of December 31, 2021, 158,904 shares were available for future grants under the 2016 Director’s Plan.

The 2020 Inducement Award Plan (“2020 Inducement Plan”) authorizes us to issue stock options, stock appreciation rights, restricted stock awards and stock units to key employees and expires on December 14, 2030, after which time no further awards may be made. The 2020 Inducement Plan authorizes us to issue up to 19,000 shares of common stock. As of December 31, 2021, 3,452 shares were available for future grants under the 2020 Inducement Plan.

The following table presents stock option activity for the year ended December 31, 2021:


	Number of shares (thousands)			Weighted-average exercise price		Weighted-average remaining contractual term (years)		Aggregate intrinsic value (millions)
Option shares outstanding, December 31, 2020		139.6		$	42.41
Option shares exercised		(66.1	)	$	38.37
Option shares outstanding, December 31, 2021		73.5		$	46.05		1.4	$	5.2
Option shares exercisable, vested and expected to vest, December 31, 2021		73.5		$	46.05		1.4	$	5.2

We have reserved sufficient authorized shares to allow us to issue new shares upon exercise of all outstanding options. Options generally become exercisable in three years and expire 10 years from the date of grant. When options are exercised, we may issue new shares, use treasury shares (if available), acquire shares held by investors, or a combination of these alternatives in order to satisfy the option exercises.

The following table presents information related to stock option exercises:


	2021		2020		2019
Total intrinsic value of stock options exercised	$	4.1	$	5.6	$	15.9
Cash proceeds received from stock options exercised		2.5		4.7		14.5
Tax deduction realized from stock options exercised		0.4		1.2		3.3

The fair value of option grants was estimated on the date of grant using the Black-Scholes option pricing model. There have been no option grants since 2014.

We also grant non-vested stock awards in the form of Restricted Stock Units (“RSUs”), Performance Stock Units (“PSUs”) and Restricted Stock Awards ("RSAs"). A summary of the 2021 activity related to the RSUs, PSUs and RSAs is as follows:


	Non-Vested Stock Awards
	RSUs						PSUs						RSAs
	Number of shares (thousands)			Weighted- average fair value at grant date			Number of shares (thousands)			Weighted- average fair value at grant date			Number of shares (thousands)			Weighted- average fair value at grant date
December 31, 2020		66.8		$	83.14			330.3		$	75.49			94.2		$	77.96
Granted		23.6			92.30			113.8			102.46			-			-
Performance adjustments		-			-			23.1			52.56			-			-
Vested		(22.1	)		(78.32	)		(148.4	)		(55.63	)		(21.1	)		(77.88	)
Forfeited		(3.3	)		(86.23	)		(17.0	)		(93.03	)		(0.5	)		(77.22	)
December 31, 2021		65.0		$	87.94			301.8		$	92.74			72.6		$	77.99

RSUs entitle the recipient to a specified number of shares of AWI’s common stock provided the prescribed service period is fulfilled. PSUs entitle the recipient to a specified number of shares of AWI’s common stock provided the defined financial targets are achieved at the end of the performance period. Upon vesting, final adjustments based upon financial achievements are reflected as performance adjustments in the table above. RSUs and PSUs generally have vesting periods of three years at the grant date. RSUs and PSUs earn dividends during the vesting period that are subject to forfeiture if the awards do not vest.

In connection with the acquisition of Arktura in 2020, we issued RSAs to the sellers as of the acquisition date. These awards to sellers were not issued under the 2020 Inducement Plan and have a vesting period of five years from the grant date and earn dividends during the vesting period, which are subject to forfeiture if the awards do not vest. We also issued RSAs under the 2020 Inducement Plan to key employees as of the acquisition date, which have a vesting period of three years from the grant date and earn dividends during the vesting period, which are subject to forfeiture if the awards do not vest. Upon forfeiture, the key employee awards transfer to the Arktura sellers.

RSUs, PSUs and RSAs with non-market based performance conditions are measured at fair value based on the closing price of our stock on the date of grant. In 2021 and 2020, we granted 54,231 and 42,698 PSUs, respectively, with market-based performance conditions that are valued through the use of a Monte Carlo simulation. The weighted average assumptions for PSUs measured at fair value through the use of a Monte Carlo simulation are presented in the table below.


	2021			2020
Weighted-average grant date fair value of market-based PSUs granted (dollars per award)	$	117.85		$	97.75
Assumptions
Risk-free rate of return		0.3	%		1.2	%
Expected volatility		37.0	%		23.8	%
Expected term (in years)		3.1			3.1
Expected dividend yield		0.0	%		0.0	%

The risk-free rate of return was determined based on the implied yield available on zero coupon U.S. Treasury bills at the time of grant with a remaining term equal to the expected term of the PSUs. The expected volatility was based on historical volatility of our stock price commensurate with the expected term of the PSUs. The expected term represented the performance period on the underlying award. The expected dividend yield was assumed to be zero under the assumption that dividends distributed during the performance period are reinvested in AWI’s common stock.

In addition to the equity awards described above, we distributed 11,773 fully-vested phantom shares issued under the 2006 Phantom Stock Unit Plan. These awards are settled in cash and had vesting periods of one to three years. The total liability recorded for these shares as of December 31, 2020 was $1.2 million, which included non-forfeitable dividends. This liability was settled on January 5, 2021 and there are no shares outstanding under the plan as of December 31, 2021. The 2006 Phantom Stock Unit Plan is still in place, however, no additional shares will be granted under the plan.

As of December 31, 2021 and 2020, there were 130,393 and 126,474 RSUs, respectively, outstanding under the 2016 Directors Stock Unit Plan not reflected in the non-vested stock awards table above. In 2021 and 2020, we granted 8,314 and 12,278 restricted stock units, respectively, to non-employee directors. These awards generally have a vesting period of one year, and as of December 31, 2021 and 2020, 122,079 and 114,196 shares, respectively, were vested but not yet delivered. The awards are generally payable upon vesting or the director’s deferral election. These awards earn dividends during the vesting period that are subject to forfeiture if the underlying award does not vest.

We recognize share-based compensation expense on a straight-line basis over the vesting period. Share-based compensation cost was $11.3 million ($8.5 million net of tax benefit) in 2021, $6.9 million ($5.1 million net of tax benefit) in 2020, and $8.4 million ($6.3 million net of tax benefit) in 2019.

As of December 31, 2021, there was $19.3 million of total unrecognized compensation cost related to non-vested share-based compensation arrangements which is expected to be recognized over a weighted-average period of 2.4 years.