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 8,949,000 shares of common stock, which includes all shares that have been issued under the 2016 LTIP. As of December 31, 2018, 3,616,626 shares were available for future grants under the 2016 LTIP.

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 550,000 shares of common stock, which includes all shares that have been issued under the 2016 Director’s Plans. As of December 31, 2018, 189,477 shares were available for future grants under the 2016 Director’s Plan.

The following table presents stock option activity for the year ended December 31, 2018:

	Number of shares (thousands)			Weighted-average exercise price			Weighted-average remaining contractual term (years)		Aggregate intrinsic value (millions)
Option shares outstanding, December 31, 2017		1,272.4		$	34.23
Option shares exercised		(669.9	)		(27.51	)
Option shares outstanding, December 31, 2018		602.5		$	41.71			2.9	$	9.9
Option shares exercisable, vested and expected to vest, December 31, 2018		602.5		$	41.71			2.9	$	9.9

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.

	2018		2017			2016
Total intrinsic value of stock options exercised	$	23.7	$	0.9		$	0.4
Cash proceeds received from stock options exercised	$	18.4	$	3.3		$	0.7
Tax deduction (expense) realized from stock options exercised	$	6.1	$	(0.2	)	$	(0.1	)

The fair value of option grants was estimated on the date of grant using the Black-Scholes option pricing model. There were no option grants in 2018, 2017 or 2016.

Historically, we have also granted non-vested stock awards in the form of restricted stock, Restricted Stock Units (“RSUs”), performance restricted stock and Performance Stock Units (“PSUs”). As of December 31, 2017 and 2016, we have no outstanding restricted stock or performance restricted stock. A summary of the 2018 activity related to these awards follows:

	Non-Vested Stock Awards
	RSUs						PSUs
	Number of shares (thousands)			Weighted- average fair value at grant date			Number of shares (thousands)			Weighted- average fair value at grant date
December 31, 2017		171.6		$	45.27			379.7		$	41.08
Granted		33.8			59.33			148.2			56.16
Vested		(97.7	)		(45.72	)		-			-
Forfeited		(7.4	)		(50.00	)		(24.7	)		(50.82	)
December 31, 2018		100.3		$	48.69			503.2		$	45.14

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. RSUs and PSUs generally had vesting periods of three years at the grant date. RSUs and PSUs earn dividends during the vesting period that are forfeitable if the awards do not vest.

The table above contains 5,680 and 8,354 RSUs as of December 31, 2018 and 2017, respectively, which are accounted for as liability awards as they are able to be settled in cash. There are no outstanding PSUs accounted for as liability awards as of December 31, 2018 and 2017, as none of the awards are able to be settled in cash. Employee liability awards outstanding for all periods represent awards to certain employees of our EMEA and Pacific Rim businesses. The underlying liability is reflected as a component of current liabilities from discontinued operations on our consolidated balance sheets.

RSUs and PSUs 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 2018 and 2017, we granted 69,669 and 69,769 PSUs 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.

	2018			2017
Weighted-average grant date fair value of market based PSUs granted (dollars per award)	$	53.01		$	43.29
Assumptions
Risk free rate of return		2.4	%		1.5	%
Expected volatility		26.3	%		28.0	%
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 an average of the actual historical volatilities of the stock prices of AWI and a peer group of companies. We elected to not rely solely on AWI’s actual historical stock price volatility due to the separation of AFI. The expected life represented the performance period on the underlying award. The expected dividend yield was assumed to be zero because, at the time of each grant, we had no plans to declare a dividend.

In addition to the equity awards described above, as of December 31, 2018 we had 11,773 fully-vested phantom shares outstanding for non-employee directors under the 2006 Phantom Stock Unit Plan not reflected in the non-vested stock awards table above. These awards are settled in cash and had vesting periods of one to three years. The awards are generally payable six months following the director’s separation from service on the Board of Directors. The total liability recorded for these shares as of December 31, 2018 was $1.3 million which includes associated non-forfeitable dividends. The 2006 Phantom Stock Unit Plan is still in place; however, no additional shares will be granted under the plan.

As of December 31, 2018 and 2017, there were 163,564 and 191,725 RSUs, respectively, outstanding under the 2016 Directors Stock Unit Plan not reflected in the Non-Vested Stock Awards table above. In 2018 and 2017, we granted 13,058 and 22,433 restricted stock units, respectively, to non-employee directors. These awards generally have a vesting period of one year, and as of December 31, 2018 and 2017, 150,506 and 169,292 shares, respectively, were vested but not yet delivered. The awards are generally payable six months following the director’s separation from service on the Board of Directors and earn dividends during the vesting period that are non-forfeitable.

We recognize share-based compensation expense on a straight-line basis over the vesting period. Share-based compensation cost was $12.9 million ($9.6 million net of tax benefit) in 2018, $9.8 million ($5.9 million net of tax benefit) in 2017, and $11.0 million ($6.6 million net of tax benefit) in 2016.

As of December 31, 2018, there was $13.0 million of total unrecognized compensation cost related to non-vested share-based compensation arrangements. That cost is expected to be recognized over a weighted-average period of 1.4 years.