(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).

In connection with the Recapitalization during 2016, all outstanding Awards with respect to Liberty Media Corporation common stock (“Liberty Awards”) were adjusted pursuant to the anti-dilution provisions of the incentive plans under which the equity awards were granted, such that a holder of a Liberty Award received new corresponding equity awards relating to shares of one or more series of Liberty SiriusXM common stock, Liberty Braves common stock and Liberty Formula One common stock (collectively, the “Adjusted Liberty Awards”).

All of the pre-Recapitalization value of the Liberty Awards was allocated among the Adjusted Liberty Awards.

Liberty—Grants of stock options

Awards granted in 2018,  2017 and 2016 are summarized as follows:

In addition to the stock option grants to the Liberty CEO, and in connection with his employment agreement, Liberty granted performance-based restricted stock units (“RSUs”). During the years ended December 31, 2018 and 2017, Liberty granted 86 thousand and 50 thousand RSUs, respectively, of Series C Liberty Formula One common stock. Such RSUs had a GDFV of $31.99 per share and $33.92 per share, respectively. During the year ended December 31, 2018, Liberty granted 12 thousand RSUs of Series C Liberty Braves common stock with a GDFV of $23.34 per share. During the year ended December 31, 2016, Liberty granted 39 thousand RSUs of Series C Liberty Media Corporation common stock. Such RSUs had a GDFV of $37.76 per share. The 2018, 2017 and 2016 performance-based RSUs cliff vested in one year, 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 Company did not grant any options to purchase Series A or Series B of Liberty SiriusXM, Liberty Braves or Liberty Formula One common stock during the year ended December 31, 2018.

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 2018,  2017 and 2016, 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 2018,  2017 and 2016 grants.

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

 

Liberty Formula One

 

Liberty Braves

 

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 2018.

As of December 31, 2018, the total unrecognized compensation cost related to unvested Liberty Awards was approximately $22 million. Such amount will be recognized in the Company’s consolidated statements of operations over a weighted average period of approximately 1.3 years.

As of December 31, 2018, 12.9 million, 7.0 million and 1.5 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, 2018,  2017 and 2016 was $22 million, $31 million and $24 million, respectively.

Liberty—Restricted Stock

The Company had approximately 218 thousand, 211 thousand and 46 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, 2018. 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 $26.74, $28.79, and $20.16 per share, respectively.

The aggregate fair value of all restricted shares of Liberty common stock that vested during the years ended December 31, 2018,  2017 and 2016 was $9 million, $85 million and $7 million, respectively.

SIRIUS XM—Stock-based Compensation

During the years ended December 31, 2018, 2017 and 2016, SIRIUS XM 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 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’s option grants during 2018,  2017 and 2016 was 23%,  24% and 22%, respectively. During the year ended December 31, 2018, SIRIUS XM granted approximately 31.7 million stock options with a weighted-average exercise price of $6.59 per share and a grant date fair value of $1.45 per share. As of December 31, 2018, SIRIUS XM has approximately 243.4 million options outstanding of which approximately 143.8 million are exercisable, each with a weighted-average exercise price per share of $4.22 and $3.60, respectively. The aggregate intrinsic value of these outstanding and exercisable options was $392 million and $303 million, respectively. During the year ended December 31, 2018, SIRIUS XM granted approximately 17.5 million RSUs and PRSUs with a grant date fair value of $6.40 per share. The stock-based compensation related to SIRIUS XM stock options and restricted stock awards was $133 million, $124 million and $109 million for the years ended December 31, 2018,  2017, and 2016, respectively. As of December 31, 2018, the total unrecognized compensation cost related to unvested SIRIUS XM stock options was $254 million. The SIRIUS XM unrecognized compensation cost will be recognized in the Company’s consolidated statements of operations over a weighted average period of approximately 1.8 years.