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Warrant Liabilities | 12 Months Ended
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Dec. 31, 2023
Warrants and Rights Note Disclosure [Abstract] |
Warrant Liabilities | Warrant Liabilities As part of dMY’s initial public offering, dMY issued to third-party investors 23.0 million units, each consisting of one share of dMY Class A common stock and one-half of one Public Warrant, at a price of $10.00 per unit. Each whole Public Warrant entitled the holder to purchase one share of Class A Common Stock at an exercise price of $11.50 per share. Simultaneously with the dMY initial public offering, dMY sold 6,600,000 Private Placement Warrants to the Sponsor and issued an additional 75,000 Working Capital Warrants to the Sponsor upon the Closing in connection with converting certain working capital loans into warrants. Each Private Warrant allows the Sponsor to purchase one share of Class A Common Stock at $11.50 per share. The Company classified the Warrants pursuant to ASC 815-40 as derivative liabilities on its consolidated balance sheets at fair value as of each reporting date, with subsequent changes in their respective fair values recognized in its consolidated statements of operations. Public Warrants On February 22, 2021, the Company announced the redemption of all the Public Warrants, which were exercisable for an aggregate of approximately 11.5 million shares of Class A Common Stock at a price of $11.50 per share. During the year ended December 31, 2021, 11,442,389 Public Warrants were exercised, resulting in cash proceeds of approximately $131.6 million and the issuance of 11,442,389 shares of Class A Common Stock. None of the Public Warrants remained outstanding as of December 31, 2023 and 2022. The Company determined the fair value of its Public Warrants based on the publicly listed trading price of such warrants as of the valuation date. Accordingly, the Public Warrants were classified as Level 1 financial instruments. The aggregate fair value of the Public Warrants on the dates of exercise throughout March 2021 was $77.5 million. Private Warrants On March 26, 2021, the Private Warrants were exercised in full on a cashless basis, resulting in the issuance of 2,571,808 shares of Class A Common Stock. None of the Private Warrants remained outstanding as of December 31, 2023 and 2022. The estimated fair value of the Private Warrants was determined with Level 3 inputs using the Black-Scholes model. The significant inputs and assumptions in this method are the stock price, exercise price, volatility, risk-free rate, and term or maturity. The underlying stock price input is the closing stock price as of each valuation date and the exercise price is the price as stated in the warrant agreement. The volatility input was determined using the historical volatility of comparable publicly traded companies that operate in a similar industry or compete directly against the Company. Volatility for each comparable publicly traded company is calculated as the annualized standard deviation of daily continuously compounded returns. The Black-Scholes analysis is performed in a risk-neutral framework, which requires a risk-free rate assumption based upon constant-maturity treasury yields, which are interpolated based on the remaining term of the Private Warrants as of each valuation date. The term/maturity is the duration between each valuation date and the maturity date, which is five years following the Closing, or December 29, 2025. The Private Warrants were valued as of December 31, 2020 and March 26, 2021 (the exercise date). The following table provides quantitative information regarding Level 3 fair value measurement inputs at their measurement dates:
| March 26, 2021 |  | December 31, 2020
Exercise price | $ | 11.50 |  | $ | 11.50
Stock price | $ | 15.96 |  | $ | 22.76
Volatility | 42.6% |  | 41.4%
Term (years) | 4.77 |  | 5.00
Risk-free interest rate | 0.76% |  | 0.37%
The fair value of the Private Warrants was $50.8 million as of March 26, 2021. The Company recorded $41.8 million to change in fair value of warrant liabilities on the Company’s consolidated statement of operations, representing the change in fair value of the Public Warrants and Private Warrants from December 31, 2020 through the dates of exercise. The following table summarizes the fair values of warrant liabilities and change in fair value at each measurement date:
($ in thousands) | Public Warrants (Level 1) |  | Private Warrants (Level 3) |  | Total
Fair value of warrants at December 31, 2020 | $ | 88,079 |  |  | $ | 82,030 |  |  | $ | 170,109 |
Change in fair value of warrant liability | (10,570) |  |  | (31,232) |  |  | (41,802) |
Fair value of warrants at redemption | (77,509) |  |  | (50,798) |  |  | (128,307) |
Fair value of warrants at December 31, 2021 | $ | — |  |  | $ | — |  |  | $ | — |

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