(14)  Stock-Based Compensation

Liberty—Incentive Plans

Pursuant to the Liberty Media Corporation 2017 Omnibus Incentive Plan (the “2017 Plan”), the company may grant Awards to purchase shares of Series A, Series B and Series C Liberty Media Corporation common stock. The 2017 Plan provides for Awards to be made in respect of a maximum of 50.0 million shares of Liberty Media Corporation common stock. Awards generally vest over 1-5 years and have a term of 7-10 years. Liberty issues new shares upon exercise of equity awards. The Company measures the cost of employee services received in exchange for an equity classified Award (such as stock options and restricted stock) based on the grant-date fair value (“GDFV”) of the Award, and recognizes that cost over the period during which the employee is required to provide service (usually the vesting period of the Award).

Liberty—Grants of stock options

Awards granted in 2019, 2018 and 2017 are summarized as follows:

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In addition to the stock option grants to the Liberty CEO, and in connection with his employment agreement, Liberty granted time-based and performance-based restricted stock units (“RSUs”). During the year ended December 31, 2019, Liberty granted 12 thousand and 2 thousand time-based RSUs of Series C Liberty Formula One common stock and Series C Liberty Braves common stock, respectively. Such RSUs had a GDFV of $33.94 per share and $27.73 per share, respectively, at the time they were granted and cliff vested on March 11, 2019.  During the years ended December 31, 2019, 2018 and 2017, Liberty granted 60 thousand, 86 thousand and 50 thousand performance-based RSUs, respectively, of Series C Liberty Formula One common stock. Such RSUs had a GDFV of $33.94 per share, $31.99 per share and $33.92 per share, respectively. During the years ended December 31, 2019 and 2018, Liberty granted 38 thousand and 12 thousand performance-based RSUs, respectively, of Series C Liberty Braves common stock. Such RSUs had a GDFV of $27.73 per share and $23.34 per share, respectively. The 2019, 2018 and 2017 performance-based RSUs cliff vest one year from the month of grant, subject to the satisfaction of certain performance objectives and based on an amount determined by the compensation committee. Performance objectives, which are subjective, are considered in determining the timing and amount of the compensation expense recognized. As the satisfaction of the performance objectives becomes probable, the Company records compensation expense. The value of the grant is remeasured at each reporting period. The stock option grants include the first upfront award related to the CEO’s new employment agreement. See discussion in note 13 regarding the new compensation agreement with the Company’s CEO.

The Company did not grant any options to purchase Series A or Series B of Liberty SiriusXM, Liberty Formula One or Liberty Braves common stock during the year ended December 31, 2019.

The Company has calculated the GDFV for all of its equity classified awards using the Black-Scholes Model. The Company estimates the expected term of the Awards based on historical exercise and forfeiture data. For grants made in 2019, 2018 and 2017, the range of expected terms was 3.5 to 6.3 years. The volatility used in the calculation for Awards is based on the historical volatility of Liberty’s stocks and the implied volatility of publicly traded Liberty options. The Company uses a zero dividend rate and the risk-free rate for Treasury Bonds with a term similar to that of the subject options.

The following table presents the volatilities used by the Company in the Black-Scholes Model for the 2019, 2018 and 2017 grants.

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Liberty—Outstanding Awards

The following tables present the number and weighted average exercise price (“WAEP”) of Awards to purchase Liberty common stock granted to certain officers, employees and directors of the Company, as well as the weighted average remaining life and aggregate intrinsic value of the Awards.

Liberty SiriusXM

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Liberty Formula One

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Liberty Braves

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There were no outstanding Series B options to purchase shares of Series B Liberty SiriusXM common stock, Liberty Formula One common stock or Liberty Braves common stock during 2019.

As of December 31, 2019, the total unrecognized compensation cost related to unvested Liberty Awards was approximately $34 million. Such amount will be recognized in the Company’s consolidated statements of operations over a weighted average period of approximately 2.1 years.

As of December 31, 2019, 9.8 million, 8.3 million and 1.3 million shares of Series A and Series C Liberty SiriusXM, Liberty Formula One and Liberty Braves common stock, respectively, were reserved for issuance under exercise privileges of outstanding stock Awards.

Liberty—Exercises

The aggregate intrinsic value of all options exercised during the years ended December 31, 2019, 2018 and 2017 was $163 million, $22 million and $31 million, respectively.

Liberty—Restricted Stock

The Company had approximately 94 thousand, 149 thousand and 73 thousand unvested restricted shares of Liberty SiriusXM, Liberty Formula One and Liberty Braves common stock, respectively, held by certain directors, officers and employees of the Company as of December 31, 2019. These Series A and Series C unvested restricted shares of Liberty SiriusXM common stock, Liberty Formula One common stock and Liberty Braves common stock had a weighted average GDFV of $36.07, $34.03 and $27.31 per share, respectively.

The aggregate fair value of all restricted shares of Liberty common stock that vested during the years ended December 31, 2019, 2018 and 2017 was $17 million, $9 million and $85 million, respectively.

Sirius XM Holdings—Stock-based Compensation

During the years ended December 31, 2019, 2018 and 2017, Sirius XM Holdings granted various types of stock awards to its employees and members of its board of directors. Stock-based awards are generally subject to a graded vesting requirement, which is generally three to four years from the grant date.  Stock options generally expire ten years from the date of grant.  Restricted stock units include performance-based restricted stock units (“PRSUs”), the vesting of which are subject to the achievement of performance goals and the employee's continued employment and generally cliff vest on the third anniversary of the grant date. Sirius XM Holdings calculates the grant-date fair value for all of its equity classified awards and any subsequent remeasurement of its liability classified awards using the Black-Scholes Model. The weighted average volatility applied to the fair value determination of Sirius XM Holdings’ option grants during 2019, 2018 and 2017 was 26%, 23% and 24%, respectively. During the year ended December 31, 2019, Sirius XM Holdings granted approximately 15 million stock options with a weighted-average exercise price of $6.10 per share and a grant date fair value of $1.26 per share. As of December 31, 2019, Sirius XM Holdings has approximately 208 million options outstanding of which approximately 148 million are exercisable, each with a weighted-average exercise price per share of $4.46 and $3.96, respectively. The aggregate intrinsic value of these outstanding and exercisable options was $560 million and $472 million, respectively. During the year ended December 31, 2019, Sirius XM Holdings granted approximately 38 million RSUs and PRSUs with a grant date fair value of $6.01 per share. In addition, 48 million RSUs with a grant date fair value per share of $5.83 were granted during the year ended December 31, 2019 in connection with the Pandora acquisition. The stock-based compensation related to Sirius XM Holdings stock options and restricted stock awards was $229 million, $133 million and $124 million for the years ended December 31, 2019, 2018, and 2017, respectively. In addition, the acquisition and other costs recognized by Sirius XM Holdings during the year ended December 31, 2019 includes $21 million of stock-based compensation. As of December 31, 2019, the total unrecognized compensation cost related to unvested Sirius XM Holdings stock options was $415 million. The Sirius XM Holdings unrecognized compensation cost will be recognized in the Company’s consolidated statements of operations over a weighted average period of approximately 2.4 years.