
	Three months ended June 30,				Six months ended June 30,
	2024		2023		2024		2023
Operations and support	$	771	$	2,140	$	1,629	$	4,975
General and administrative	705		4,980		2,550		11,283
Research and development	264		938		527		2,349
Sales and marketing	39		200		82		451
Total stock-based compensation expense	$	1,779	$	8,258	$	4,788	$	19,058

Stock Options: The Company measures stock-based compensation expense for stock options at the grant date fair value of the award and recognizes the expense on a straight-line basis over the requisite service period, which is generally the vesting period. The fair value of stock options is estimated using the Black-Scholes option-pricing model. During the three and six months ended June 30, 2024, the Company recorded stock-based compensation expense from stock options of approximately $0.4 million and $1.5 million, respectively. During the three and six months ended June 30, 2023 the Company recorded stock-based compensation expense from stock options of approximately $5.9 million and $14.4 million, respectively.

The Company recognizes only the portion of the option award granted that is ultimately expected to vest as compensation expense and elects to recognize gross share-based compensation expense with actual forfeitures as they occur.

Fair Value of Stock Options: The fair value of each stock option award is estimated using the Black-Scholes option-pricing model, which uses the fair value of the Company’s common stock and requires the input of the following subjective assumptions:

Expected term. The expected term for options granted to employees, officers, and directors is based on the historical pattern of option exercise behavior and the period of time they are expected to be outstanding.

Expected volatility. The expected volatility is based on the average volatility of similar public entities within the Company’s peer group as the Company’s stock has not been publicly trading for a long enough period to rely on its own expected volatility.

Expected Dividends. The dividend assumption is based on the Company’s historical experience. To date, Company has not paid any dividends on its common stock.

Risk-Free Interest Rate. The risk-free interest rate used in the valuation is the implied yield currently available on the United States Treasury zero-coupon issues, with a remaining term equal to the expected life term of the Company’s options.

The following table summarizes the key assumptions used to determine the fair value of the Company’s stock options granted to employees, non-employees, officers, and directors:


	Three months ended June 30,				Six months ended June 30,
	2024		2023		2024		2023
Expected term (in years)	6.09 - 6.22		6.21 - 6.22		6.09 - 6.22		6.21 - 6.22
Expected volatility	50.4% - 51.2%		50.5% - 50.6%		50.4% - 51.2%		50.4% - 50.6%
Dividend yield	—	%	—	%	—	%	—	%
Risk-free interest rate	3.50% - 4.40%		3.50% - 3.58%		3.50% - 4.40%		3.50% - 3.99%
Weighted-average grant-date fair value per share	$1.35 - $13.69		$5.80 - $6.40		$1.35 - $13.69		$5.80 - $13.60

The Company maintains certain performance and market-based equity awards. Refer to Note 11, Equity Incentive Plans and Stock-Based Compensation, of the Annual Report for details of the awards. From the awards, the Company recognized $0.2 million and $0.6 million for the three and six months ended June 30, 2024, respectively, and $0.5 million and $1.0 million for the three and six months ended June 30, 2023, respectively.

The fair value of the Company’s RSUs is expensed ratably over the vesting period. The Company’s RSUs generally vest over four years, with a cliff equal to one-fourth of the award after the first year, and then quarterly thereafter over the remaining service period. For the three and six months ended June 30, 2024, the Company recorded stock-based compensation expense from RSUs of approximately $1.0 million and $2.3 million, respectively. For the three and six months ended June 30, 2023, the Company recorded stock-based compensation expense from RSUs of approximately $1.6 million and $3.3 million, respectively.

In May 2022, the Company issued MSUs to certain key executives in accordance with the Company’s 2021 Management Equity Incentive Plan. One-sixth of the MSUs vest upon (including prior to but contingent on) the occurrence of each of six distinct triggering events, including if certain share price targets are met, within the five-year period ending July 17, 2027.

The Company determined the grant-date fair value of the MSUs using a Monte Carlo simulation. The Company recognizes stock-based compensation for the MSUs over the requisite service period, which is approximately four years, using the accelerated attribution method. During the three and six months ended June 30, 2024, the Company did not grant any MSUs. During the three and six months ended June 30, 2024, the Company recognized approximately $0.2 million and $0.4 million, respectively, in stock-based compensation expense from MSUs. For the three and six months ended June 30,