SHARE-BASED AWARDS AND OPTIONS

We have granted nonqualified stock options and restricted stock awards to key employees, officers and directors under a long-term incentive plan, which permits grants of equity to employees, officers, directors and consultants. A total of 14.0 million shares of our common stock was reserved and made available for issuance pursuant to awards granted under the plan. The awards are held in escrow and released upon the grantee's satisfaction of conditions of the award certificate.

The following table summarizes share-based compensation expense and the related income tax benefit recognized for our share-based awards and stock options:



	Year Ended December 31,				Seven Months Ended December 31,		Year Ended May 31,
	2018		2017		2016		2016

	(in thousands)
Share-based compensation expense	$	57,826	$	39,095	$	18,707	$	30,809
Income tax benefit	$	13,038	$	13,849	$	6,582	$	9,879

Restricted Stock

Restricted stock awards vest in equal annual installments over a three-year period and in some cases vest at the end of a three-year service period. Restricted shares cannot be sold or transferred until they have vested. The grant date fair value of restricted stock awards, which is based on the quoted market value of our common stock on the grant date, is recognized as share-based compensation expense on a straight-line basis over the vesting period.

Performance Units

Certain of our executives have been granted performance units under our long-term incentive plan. Performance units are performance-based restricted stock units that, after a performance period, may convert into common shares, which may be restricted. The number of shares is dependent upon the achievement of certain performance measures during the performance period. The target number of performance units and any market-based performance measures ("at threshold," "target," and "maximum") are set by the compensation committee of our board of directors ("Compensation Committee"). Performance units are converted only after the compensation committee certifies performance based on pre-established goals.

The Compensation Committee may set a range of possible performance-based outcomes for performance units. For awards with only performance conditions, we recognize compensation expense on a straight-line basis over the performance period using the grant date fair value of the award, which is based on the number of shares expected to be earned according to the level of achievement of performance goals. If the number of shares expected to be earned were to change at any time during the performance period, we would make a cumulative adjustment to share-based compensation expense based on the revised number of shares expected to be earned. The performance periods for awards granted generally range from 28 months to three years.

During the year ended December 31, 2018, certain of our executives were granted performance units that may be earned based on achievement of an annual adjusted EPS growth target, as modified up or down by our total shareholder return performance rank relative to the Standard & Poors 500 Index over a three-year performance period. The maximum payout is four times the target number of performance units and the minimum payout is zero. To the extent earned, these performance units convert into unrestricted shares after performance results for the three-year performance period are certified by the Compensation Committee. We recognize share-based compensation expense based on the grant-date fair value of the performance-based restricted stock units, as determined by use of a Monte Carlo model, on a straight-line basis over the performance period.

Leveraged Performance Units

During the year ended May 31, 2015, certain executives were granted performance units that we refer to as "leveraged performance units," or "LPUs." LPUs contain a market condition based on our relative stock price growth over a three-year performance period. The LPUs contain a minimum threshold performance which, if not met, would result in no payout. The LPUs also contain a maximum award opportunity set as a fixed dollar and fixed number of shares. After the three-year performance period, which concluded in October 2017, one-third of the earned units converted to unrestricted common stock. The remaining two-thirds converted to restricted stock that will vest in equal installments on each of the first two anniversaries of the conversion date. We recognize share-based compensation expense based on the grant date fair value of the LPUs, as determined by use of a Monte Carlo model, on a straight-line basis over the requisite service period for each separately vesting portion of the LPU award.

The following table summarizes the changes in unvested restricted stock and performance awards for the years ended December 31, 2018 and 2017, the 2016 fiscal transition period and the year ended May 31, 2016:



	Shares		Weighted-Average Grant-Date Fair Value
	(in thousands)
Unvested at May 31, 2015	1,848			$28.97
Granted	461		57.04
Vested	(633	)	27.55
Forfeited	(70	)	34.69
Unvested at May 31, 2016	1,606		37.25
Granted	348		74.26
Vested	(639	)	31.38
Forfeited	(52	)	45.27
Unvested at December 31, 2016	1,263		49.55
Granted	899		79.79
Vested	(858	)	39.26
Forfeited	(78	)	59.56
Unvested at December 31, 2017	1,226		78.29
Granted	650		109.85
Vested	(722	)	60.08
Forfeited	(70	)	91.47
Unvested at December 31, 2018	1,084			$108.51

The total fair value of restricted stock and performance awards vested was $43.4 million and $33.7 million for the years ended December 31, 2018 and 2017, respectively, $20.0 million for the 2016 fiscal transition period and $17.4 million for the year ended May 31, 2016.

For restricted stock and performance awards, we recognized compensation expense of $53.2 million and $35.2 million for the years ended December 31, 2018 and 2017, respectively, $17.2 million for the 2016 fiscal transition period and $28.8 million for the year ended May 31, 2016. As of December 31, 2018, there was $62.7 million of unrecognized compensation expense related to unvested restricted stock and performance awards that we expect to recognize over a weighted-average period of 2.0 years. Our restricted stock and performance award plans provide for accelerated vesting under certain conditions.

Stock Options

Stock options are granted with an exercise price equal to 100% of fair market value of our common stock on the date of grant and have a term of ten years. Stock options vest in equal installments on each of the first three anniversaries of the grant date. Our stock option plans provide for accelerated vesting under certain conditions.

The following table summarizes changes in stock option activity for the years ended December 31, 2018 and 2017, the 2016 fiscal transition period and the year ended May 31, 2016:



	Options		Weighted-Average Exercise Price		Weighted-Average Remaining Contractual Term	Aggregate Intrinsic Value
	(in thousands)				(years)	(in millions)
Outstanding at May 31, 2015	894			$25.47	5.2		$23.9
Granted	145		55.92
Forfeited	(8	)	16.10
Exercised	(220	)	22.46			9.4
Outstanding at May 31, 2016	811		31.81		5.8	36.8
Granted	73		74.66
Forfeited	(1	)	22.93
Exercised	(124	)	22.26			6.5
Outstanding at December 31, 2016	759		37.51		6.0	24.5
Granted	124		79.45
Forfeited	—		—
Exercised	(160	)	23.50			10.1
Outstanding at December 31, 2017	723		47.79		6.4	37.9
Granted	103		114.70
Forfeited	(22	)	100.38
Exercised	(206	)	42.65			16.5
Outstanding at December 31, 2018	598			$59.16	6.2		$27.3

Options vested and exercisable at December 31, 2018	427			$44.34	5.2		$25.1

We recognized compensation expense for stock options of $2.7 million and $2.6 million during the years ended December 31, 2018 and 2017, respectively, $1.1 million during the 2016 fiscal transition period and $1.4 million during the fiscal year ended May 31, 2016. As of December 31, 2018, we had $3.3 million of unrecognized compensation expense related to unvested stock options that we expect to recognize over a weighted-average period of 1.8 years.

The weighted-average grant-date fair value of stock options granted during the years ended December 31, 2018 and 2017, the 2016 fiscal transition period and during the year ended May 31, 2016 was $35.09, $23.68, $21.87 and $15.60, respectively. Fair value was estimated on the date of grant using the Black-Scholes valuation model with the following weighted-average assumptions:



	Year Ended December 31,				Seven Months Ended December 31,		Year Ended May 31,
	2018		2017		2016		2016
Risk-free interest rate	2.60	%	1.99	%	1.05	%	1.62	%
Expected volatility	29	%	30	%	32	%	29	%
Dividend yield	0.04	%	0.06	%	0.06	%	0.10	%
Expected term (years)	5		5		5		5

The risk-free interest rate is based on the yield of a zero coupon U.S. Treasury security with a maturity equal to the expected life of the option from the date of the grant. Our assumption on expected volatility is based on our historical volatility. The dividend yield assumption is calculated using our average stock price over the preceding year and the annualized amount of our most current quarterly dividend per share. We based our assumptions on the expected term of the options on our analysis of the historical exercise patterns of the options and our assumption on the future exercise pattern of options.