(15)  Stock-Based Compensation

Liberty—Incentive Plans

Liberty grants, to certain of its directors, employees and employees of its subsidiaries, restricted stock (“RSAs”), restricted stock units (“RSUs”) and stock options to purchase shares of its common stock (collectively, "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). The Company measures the cost of employee services received in exchange for a liability classified Award based on the current fair value of the Award, and remeasures the fair value of the Award at each reporting date.

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.

Liberty—Grants of Stock Options

Awards granted in 2021, 2020 and 2019 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, the Company granted time-based and performance-based RSUs. During the year ended December 31, 2020, the Company granted 9 thousand, 7 thousand and 3 thousand time-based RSUs of Series C common stock of Liberty SiriusXM, Liberty Formula One and Liberty Braves, respectively, to our CEO.  The RSUs had a GDFV of $33.11, $24.68 and $18.17 per share, respectively, and cliff vested on December 10, 2020. These RSU grants were issued in lieu of our CEO receiving 50% of his remaining base salary for the last three quarters of calendar year 2020, and he waived his right to receive the other 50%, in each case, in light of the ongoing financial impact of COVID-19. During the year ended December 31, 2019, the Company 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, to our CEO. 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, 2021 and 2019, the Company granted 65 thousand and 60 thousand performance-based RSUs, respectively, of Series C Liberty Formula One common stock to our CEO. Such RSUs had a GDFV of $45.88 per share and $33.94 per share, respectively. During the years ended December 31, 2021 and 2019, the Company granted 31 thousand and 38 thousand performance-based RSUs, respectively, of Series C Liberty Braves common stock to our CEO. Such RSUs had a GDFV of $31.24 per share and $27.73 per share, respectively. The 2021 and 2019 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 re-measured at each reporting period.

The Company did not grant any options to purchase shares of Series A or Series B Liberty SiriusXM, Liberty Formula One or Liberty Braves common stock during the year ended December 31, 2021.

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 2021, 2020 and 2019, the range of expected terms was 5.3 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 2021, 2020 and 2019 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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As of December 31, 2021, Liberty Formula One and Liberty Braves each had 1 thousand Series A options outstanding and exercisable at a WAEP of $12.63 and $12.35, respectively, and each had a weighted average remaining contractual life of 1.0 year.

There were no outstanding Series A options to purchase shares of Series A Liberty SiriusXM common stock and 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 2021.

As of December 31, 2021, the total unrecognized compensation cost related to unvested Liberty Awards was approximately $49 million. Such amount will be recognized in the Company’s consolidated statements of operations over a weighted average period of approximately 1.6 years.

As of December 31, 2021, 7.4 million, 9.1 million and 3.1 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, 2021, 2020 and 2019 was $144 million, $8 million and $163 million, respectively.

Liberty—Restricted Stock and Restricted Stock Units

The Company had approximately 73 thousand, 138 thousand and 219 thousand unvested RSAs and RSUs 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, 2021. These Series A and Series C unvested RSAs and RSUs of Liberty SiriusXM common stock, Liberty Formula One common stock and Liberty Braves common stock had a weighted average GDFV of $41.81, $46.42 and $28.62 per share, respectively.

The aggregate fair value of all RSAs and RSUs of Liberty common stock that vested during the years ended December 31, 2021, 2020 and 2019 was $13 million, $45 million and $17 million, respectively.

Sirius XM Holdings—Stock-based Compensation

During the years ended December 31, 2021, 2020 and 2019, 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 2021, 2020 and 2019 was 33%, 28% and 26%, respectively. During the year ended December 31, 2021, Sirius XM Holdings granted approximately 54 million stock options with a weighted-average exercise price of $6.14 per share and a grant date fair value of $1.77 per share. As of December 31, 2021, Sirius XM Holdings has approximately 161 million options outstanding of which approximately 101 million are exercisable, each with a weighted-average exercise price per share of $5.47 and $5.01, respectively. The aggregate intrinsic value of these outstanding and exercisable options was $156 million and $144 million, respectively. During the year ended December 31, 2021, Sirius XM Holdings granted approximately 40 million RSUs and PRSUs with a grant date fair value of $6.35 per share. The stock-based compensation related to Sirius XM Holdings stock options and restricted stock awards was $202 million, $223 million and $229 million for the years ended December 31, 2021, 2020 and 2019, respectively. In addition, the acquisition costs recognized by Sirius XM Holdings during the year ended December 31, 2019 includes $21 million of stock-based compensation. As of December 31, 2021, the total unrecognized compensation cost related to unvested Sirius XM Holdings stock options was $455 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 2.5 years.