(3)   Stock-Based Compensation

Liberty grants, to certain of its directors, employees and employees of its subsidiaries, restricted stock, 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.

Included in the accompanying condensed consolidated statements of operations are the following amounts of stock-based compensation, as discussed below:

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Liberty—Grants of Awards

Options granted during the six months ended June 30, 2023 are summarized as follows:

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The Company did not grant any options to purchase Series A or Series B Liberty SiriusXM, Liberty Braves or Liberty Formula One common stock during the six months ended June 30, 2023.

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Also during the six months ended June 30, 2023, the Company granted 31 thousand and 81 thousand performance-based RSUs of Series C common stock of Liberty Braves and Liberty Formula One, respectively, to our CEO.  The RSUs had a GDFV of $34.44 per share and $75.12 per share, respectively, and cliff vest one year from the month of grant, subject to the satisfaction of certain performance objectives. Performance objectives, which are subjective, are considered in determining the timing and amount of compensation expense recognized. When the satisfaction of the performance objectives becomes probable, the Company records compensation expense. The probability of satisfying the performance objectives is assessed at the end of each reporting period.

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Liberty calculates the GDFV for all of its equity classified options and the subsequent remeasurement of its liability classified options using the Black-Scholes Model. Liberty estimates the expected term of the options based on historical exercise and forfeiture data. The volatility used in the calculation for options is based on the historical volatility of Liberty common stock and the implied volatility of publicly traded Liberty options. Liberty uses a zero dividend rate and the risk-free rate for Treasury Bonds with a term similar to that of the subject options.

Liberty—Outstanding Awards

The following tables present the number and weighted average exercise price ("WAEP") of options 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 options.  

Liberty SiriusXM

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Liberty Braves

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Liberty Formula One

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As of June 30, 2023, there were no outstanding Series A or Series B options to purchase shares of Series A or Series B Liberty SiriusXM common stock, Liberty Formula One common stock or Liberty Braves common stock.

As of June 30, 2023, the total unrecognized compensation cost related to unvested Awards was approximately $22 million. Such amount will be recognized in the Company's condensed consolidated statements of operations over a weighted average period of approximately 1.4 years.

As of June 30, 2023, Liberty reserved 5.8 million, 3.0 million and 6.3 million shares of Series C common stock of Liberty SiriusXM, Liberty Braves and Liberty Formula One, respectively, for issuance under exercise privileges of outstanding stock options.

On July 18, 2023, in connection with the Split-Off, as described in note 2, Liberty Braves Awards were exchanged into Atlanta Braves Holdings Awards. In addition, adjustments are expected to be made to the other outstanding Awards remaining after the Split-Off as a result of the Formula One Distribution and the Reclassification, as described in note 2.

Sirius XM Holdings — Stock-based Compensation

Sirius XM Holdings granted various types of stock awards to its employees during the six months ended June 30, 2023. As of June 30, 2023, Sirius XM Holdings has approximately 134 million options outstanding of which approximately 90 million are exercisable, each with a WAEP per share of $5.53 and $5.39, respectively. The aggregate intrinsic value of Sirius XM Holdings options outstanding and exercisable as of June 30, 2023 is $23 million and $22 million, respectively. During the six months ended June 30, 2023, Sirius XM Holdings granted approximately 12 million nonvested RSUs with a GDFV per share of $4.49. Stock-based compensation expense related to Sirius XM Holdings was $42 million and $47 million for the three months ended June 30, 2023 and 2022, respectively, and $87 million and $92 million for the six months ended June 30, 2023 and 2022, respectively. As of June 30, 2023, the total unrecognized compensation cost related to unvested Sirius XM Holdings stock options and RSUs was $381 million. The Sirius XM Holdings unrecognized compensation cost will be recognized in the Company's condensed consolidated statements of operations over a weighted average period of approximately 2.3 years.