Scholes model is based on the implied US Treasury bill yield curve at the date of grant with a remaining term equal to the Company’s expected term assumption. The Company has never declared or paid a dividend on its shares of Common Stock.
Stock-based payments are subject to service based vesting requirements and expense is recognized on a straight-line basis over the vesting period. Forfeitures are accounted for as they occur. No stock options were forfeited during the three months ended March 31, 2024.
Stock Appreciation Right Awards
As approved by the Compensation Committee, 755,436 of the employee related exercised SARs shown in the table below were paid in cash in the amount of $10.0 million based on the difference between (a) the fair market value of a share of Common Stock on the date of exercise, over (b) the grant date price; during the first quarter of 2023.
During the three months ended March 31, 2024, as approved by the Compensation Committee, 163,043 of the employee related exercised SARs shown in the table below were paid in cash in the amount of $1.3 million based on the difference between (a) the fair market value of a share of Common Stock on the date of exercise, over (b) the grant date price.
The table below represents the changes in SARs:
| | | | | | | |
| | Number of Units | | | Weighted-Average Exercise Price | | Weighted-Average Remaining Contractual Term (Years) |
Outstanding SARs at December 31, 2023 | | 714,539 | | $ | 1.82 | | 7.17 |
Exercised | | (163,043) | | | 1.79 | | - |
Outstanding SARs at March 31, 2024 | | 551,496 | | $ | 1.83 | | 6.92 |
538,043 SARs were exercisable at a weighted average exercise price of $1.79 at March 31, 2024.
Under the authoritative guidance for stock-based compensation, these SARs are considered liability-based awards. The Company recognized a liability associated with its SARs of approximately $5.2 million as of March 31, 2024, all of which is included in accrued liabilities in the accompanying consolidated balance sheet as of March 31, 2024. The liability associated with these SAR awards recognized as of December 31, 2023, was approximately $5.4 million, all of which is included in accrued liabilities in the accompanying consolidated balance sheet as of December 31, 2023. These SARs were valued using the Black-Scholes option pricing model with the following assumptions on the grant date: the expected volatility was approximately 43.5%, the term was 6.25 years, the dividend rate was 0.0% and the risk-free interest rate was approximately 1.07%, which resulted in a calculated fair value of approximately $0.78 per SAR as of the grant date. The fair value of these liability awards will be remeasured at each reporting period until the date of settlement. At March 31, 2024, these SARs were valued using the Black-Scholes option pricing model with the following assumptions for awards granted on February 25, 2021 and August 5, 2021, respectively: the expected volatility was approximately 79.06% and 78.83%, the term was 3.46 years and 3.77 years, the dividend rate was 0.0% and 0.0%, the risk-free interest rate was approximately 4.31% and 4.28%, and the exercise price was $1.79 and $3.54, which resulted in a calculated fair value of approximately $9.54 and $8.68 per SAR, respectively, as of March 31, 2024. At December 31, 2023, these SARs were valued using the Black-Scholes option pricing model with the following assumptions for awards granted on February 25, 2021 and August 5, 2021, respectively: the expected volatility was approximately 35.78% and 53.39%, the term was 0.08 years and 0.30 years, the dividend yield was 0.0% and 0.0%, the risk-free rate was approximately 5.52% and 5.33%, and the exercise price was $1.79 and $3.54, which resulted in a calculated fair value of approximately $7.95 and $6.25 per SAR, respectively, as of December 31, 2023.
The estimated weighted-average fair value of each SAR as of March 31, 2024 and December 31, 2023 was $9.52 and $7.96, respectively. Increases and decreases in stock-based compensation expense are recognized over the vesting period, or immediately for vested awards. For three months ended March 31, 2024 and 2023, the Company recognized compensation expense related to these awards of approximately $1.2 million and $3.5 million, respectively, in selling, general and administrative expense in the consolidated statements of comprehensive income. At March 31, 2024,