The 2013 Equity Plan authorizes the issuance of various types of share-based awards to the Company’s employees, officers, directors, and other eligible participants. As of December 31, 2018, the total number of shares of the Company’s class A common stock authorized for issuance under the 2013 Equity Plan was 2,300,000 shares. As of December 31, 2018, there were 566,250 shares of class A common stock reserved and available for future issuance under the 2013 Equity Plan.

During 2018, stock options to purchase an aggregate of 710,000 shares of class A common stock were granted pursuant to the 2013 Equity Plan. As of December 31, 2018, there were options to purchase 1,479,983 shares of class A common stock outstanding under the 2013 Equity Plan.

Shares issued under the 2013 Equity Plan may consist in whole or in part of authorized but unissued shares or treasury shares. No awards may be issued more than 10 years after the 2013 Equity Plan’s effective date. Stock options that are granted under the 2013 Equity Plan must have an exercise price equal to at least the fair market value of the Company’s class A common stock on the date of grant, become exercisable as established by the Board of Directors or the Compensation Committee, and expire no later than 10 years following the date of grant. The Company recognizes share-based compensation expense associated with such stock option awards on a straight-line basis over the award’s requisite service period (generally, the vesting period). The stock option awards granted to date vest in equal annual installments over an approximately four-year vesting period (unless accelerated in connection with a change in control event under specified conditions as set forth in the applicable option agreement or otherwise in accordance with provisions of the 2013 Equity Plan or applicable option agreement).

Share-based compensation expense is based on the fair value of the stock option awards on the date of grant, as estimated using the Black-Scholes option pricing model. The Black-Scholes option pricing model requires the input of certain management assumptions, including the expected term, expected stock price volatility, risk-free interest rate, and expected dividend yield. The Company estimates the term over which option holders are expected to hold their stock options by using the simplified method for “plain-vanilla” stock option awards because the Company’s stock option exercise history does not provide a reasonable basis to compute the expected term for stock options granted under the 2013 Equity Plan. The Company relies exclusively on its historical stock price volatility to estimate the expected stock price volatility over the expected term because the Company believes future volatility is unlikely to differ from the past. In estimating the expected stock price volatility, the Company uses a simple average calculation method. The risk-free interest rate is based on U.S. Treasury securities with terms that approximate the expected term of the stock options. The expected dividend yield is based on the Company’s past cash dividend history and anticipated future cash dividend payments. The expected dividend yield is zero, as the Company has not previously declared cash dividends and does not currently intend to declare cash dividends in the foreseeable future. These assumptions are based on management’s best judgment, and changes to these assumptions could materially affect the fair value estimates and amount of share-based compensation expense recognized.

The following table summarizes the Company’s stock option activity (in thousands, except per share data and years) for the periods indicated:

	Stock Options Outstanding
				Weighted Average		Aggregate		Weighted Average
				Exercise Price		Intrinsic		Remaining Contractual
	Shares			Per Share		Value		Term (Years)
Balance as of January 1, 2016		1,323		$	129.04
Granted		45		189.62
Exercised		(112	)	97.82		$	8,102
Forfeited/Expired		(370	)	110.28
Balance as of December 31, 2016		886			143.89
Granted	175				169.04
Exercised		(12	)		143.35	$	541
Forfeited/Expired		(57	)		196.52
Balance as of December 31, 2017		992			145.28
Granted	710				130.27
Exercised		(21	)		121.13	$	196
Forfeited/Expired		(201	)		154.49
Balance as of December 31, 2018		1,480		$	137.16
Exercisable as of December 31, 2018		701		$	136.01	$	3,317	5.5
Expected to vest as of December 31, 2018		779		$	138.20		174	9.0
Total		1,480		$	137.16	$	3,491	7.3

Stock options outstanding as of December 31, 2018 are comprised of the following range of exercise prices per share (in thousands, except per share data and years):

	Stock Options Outstanding at December 31, 2018
			Weighted Average		Weighted Average
			Exercise Price		Remaining Contractual
Range of Exercise Prices per Share	Shares		Per Share		Term (Years)
$117.85 - $120.00		23	$	118.50		3.1
$120.01 - $150.00		1,174	$	126.66		7.6
$150.01 - $180.00		121	$	168.44		5.8
$180.01 - $201.25		162	$	192.40		7.3
Total		1,480	$	137.16		7.3

An aggregate of 251,250, 215,000, and 222,500 stock options with an aggregate fair value of $15.5 million, $13.0 million, and $13.7 million vested during the years ended December 31, 2018, 2017, and 2016, respectively. Beginning January 1, 2017, the Company made an accounting policy election to prospectively account for forfeitures as they occur. Therefore, share-based compensation expense has not been adjusted for any estimated forfeitures.

The weighted average grant date fair value of stock option awards using the Black-Scholes option pricing model was $51.68, $68.67, and $75.54 for each share subject to a stock option granted during the years ended December 31, 2018, 2017, and 2016, respectively, based on the following assumptions:

The Company recognized approximately $14.6 million, $14.3 million, and $11.8 million in share-based compensation expense for the years ended December 31, 2018, 2017, and 2016, respectively, from stock options granted under the 2013 Equity Plan. As of December 31, 2018, there was approximately $33.8 million of total unrecognized share-based compensation expense related to unvested stock options. As of December 31, 2018, the Company expected to recognize this remaining share-based compensation expense over a weighted-average vesting period of approximately 3.0 years.

During the year ended December 31, 2016, the Company was able to recognize and utilize tax deductions related to equity compensation in excess of compensation recognized for financial reporting that was generated under the 2013 Equity Plan. Accordingly, additional paid-in capital increased by $1.2 million during the year ended December 31, 2016. Beginning January 1, 2017, excess tax benefits are no longer recognized as additional paid-in capital; instead they are prospectively included within the provision for income taxes.

During the year ended December 31, 2016, the Company wrote off $1.7 million of deferred tax assets related to certain vested stock options that were no longer exercisable. Accordingly, additional paid-in capital decreased by $1.7 million during the year ended December 31, 2016. No such adjustment was made during the years ended December 31, 2018 and 2017.

During the year ended December 31, 2016, the Company paid $3.7 million to tax authorities related to the net exercise of a stock option under the 2013 Equity Plan. This payment resulted in a $3.7 million reduction to additional paid-in capital during the year ended December 31, 2016. No net exercises of stock options were made during the years ended December 31, 2018 and 2017.

During 2018, the Company granted certain awards characterized as “other stock-based awards” under the 2013 Equity Plan. These other stock-based awards are similar to stock options, but these awards are settled in cash only and not in shares of the Company’s class A common stock. Upon exercise of one of these awards, the participant would be entitled to receive an amount in cash equal to the fair market value of the Company’s class A common stock in excess of a stated exercise price. These awards vest in equal annual installments over a four-year period (unless accelerated in connection with a change in control event under specified conditions as set forth in the applicable award agreement or otherwise in accordance with provisions of the 2013 Equity Plan or applicable award agreement). During 2018, the Company granted such other stock-based awards with respect to an aggregate of 10,000 underlying shares of class A common stock with a weighted average exercise price per share of $129.90 pursuant to the 2013 Equity Plan.

Similar to stock option awards, the Company recognizes share-based compensation expense associated with these awards on a straight-line basis over the award’s requisite service period (generally, the vesting period), with share-based compensation expense based on the fair value of the award estimated using the Black-Scholes option pricing model. However, due to the required cash settlement feature, these awards are classified as liabilities in the Company’s Consolidated Balance Sheets and the fair value of the awards is remeasured each quarterly reporting period with resulting adjustments to share-based compensation expense recorded until the earlier of settlement or expiration.

For the year ended December 31, 2018, the Company did not recognize a material amount in share-based compensation expense from these awards. As of December 31, 2018, there was approximately $0.4 million of total unrecognized share-based compensation expense related to these awards. The Company expects to recognize this remaining share-based compensation expense over a weighted average vesting period of approximately 3.4 years, subject to additional fair value adjustments through the earlier of settlement or expiration.