(4)   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. Stock-based compensation expense, included in selling, general and administrative expense in the accompanying condensed consolidated statements of operations, was $8 million and $7 million for the three months ended June 30, 2025 and 2024, respectively, and $10 million and $20 million for the six months ended June 30, 2025 and 2024, respectively.

Grants of Awards

Options granted during the six months ended June 30, 2025 are summarized as follows:

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The Company did not grant any options to purchase shares of Series A or Series B Liberty Formula One or Liberty Live common stock during the six months ended June 30, 2025.

Also during the six months ended June 30, 2025, the Company granted 178 thousand and 62 thousand time-based RSUs of Series C common stock of Liberty Formula One and Liberty Live, respectively, to our CEO.  The RSUs had a weighted average GDFV of $94.11 per share and $76.45 per share, respectively, and cliff vest on December 15, 2029.

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, when available, 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.

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 Formula One

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Liberty Live

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As of June 30, 2025, there were no outstanding options to purchase shares of Series A or Series B Liberty Formula One or Liberty Live common stock.

As of June 30, 2025, the total unrecognized compensation cost related to unvested Awards was approximately $40 million. Such amount will be recognized in the Company's condensed consolidated statements of operations over a weighted average period of approximately 0.8 years.

As of June 30, 2025, Liberty reserved 3.6 million shares and 1.2 million shares of Series C common stock of Liberty Formula One and Liberty Live, respectively, for issuance under exercise privileges of outstanding stock options.