Summary of compensation expense and related income tax benefit related to the stock-based compensation expense recognized

The following table summarizes the compensation expense and related income tax benefit related to the Company’s stock-based compensation arrangements recognized in the accompanying consolidated statements of operations during the periods presented (in thousands):


	Year Ended December 31,
	2019		2020		2021
Stock-based compensation expense, net of $0 tax in 2019, 2020, and 2021	$	3,880	$	2,957	$	14,994

Schedule of fair value measurement of warrants

The Company estimated the fair value of its outstanding commodity swap contracts based on the following inputs as of December 31, 2020 and 2021:


	December 31, 2020			December 31, 2021
Significant Unobservable Inputs	Input Range	Weighted Average		Input Range	Weighted Average
ULSD Gulf Coast Forward Curve	$1.47 - $1.54	$	1.50	$ 2.03 - $ 2.15	$	$2.11
Historical Differential to PADD 3 Diesel	$0.81 - $1.58	$	0.99	$ .87 - $ 1.58	$	$1.03
Historical Differential to PADD 5 Diesel	$1.66 - $2.58	$	2.01	$ 1.82 - $ 2.69	$	$2.13

The Company estimated the fair value of embedded derivatives in its fueling agreements under the Zero Now truck financing program based on the following inputs as of December 31, 2020 and 2021:


	December 31, 2020			December 31, 2021
Significant Unobservable Inputs	Input Range	Weighted Average		Input Range	Weighted Average
ULSD Gulf Coast Forward Curve	$1.47 - $1.54	$	1.50	$ 2.03 - $ 2.15	$	$2.11
Historical Differential to PADD 3 Diesel	$0.81 - $1.58	$	0.99	$ .87 - $ 1.58	$	$1.03
Historical Differential to PADD 5 Diesel	$1.66 - $2.58	$	2.01	$ 1.82 - $ 2.69	$	$2.13

Schedule of fair value measurement of warrants

Non-cash stock-based sales incentive contra-revenue charges (“Amazon Warrant Charges”) associated with the Amazon Warrant are recognized as the customer purchases fuel and vesting conditions become probable of being achieved, based on the grant date fair value of the Amazon Warrant. The fair values of the Amazon Warrant were determined as of the grant date in accordance with ASC 718, Compensation – Stock Compensation, using the Black-Scholes option pricing model and the following assumptions:


	April 16, 2021	June 14, 2021
Dividend yield	0.0%	0.0%
Expected volatility	66.46%	67.97
Risk-free interest rate	1.59%	1.49%
Expected term in years	10.0	9.8

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]

Schedule of assumptions used to estimate the fair value of each award using the Black-Scholes option pricing model

The fair value of each service-based stock option granted was estimated as of the date of grant using the Black-Scholes option pricing model and using the following assumptions:


	Year Ended December 31,
	2019	2020	2021
Dividend yield	0.0%	0.0%	0.0%
Expected volatility	57.3% to 61.5%	65.8% to 83.9%	76.8% to 96.8%
Risk-free interest rate	2.11% to 2.53%	0.37% to 1.21%	0.58% to 1.31%
Expected life in years	6.0	6.0	5.6 to 5.8

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]

Schedule of assumptions used to estimate the fair value of each award using the Black-Scholes option pricing model

The fair value of each performance-based stock option granted was estimated as of the date of grant using the Black-Scholes option pricing model and using the following assumptions:


		Year Ended
		December 31,
		2021
Dividend yield		0.0%
Expected volatility		77.1%
Risk-free interest rate		1.36%
Expected life in years		6.2

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]

Schedule of assumptions used to estimate the fair value of each award using the Black-Scholes option pricing model

The fair value of each market-based stock option granted was estimated on the date of grant using the Monte Carlo simulation model. The Monte Carlo simulation method is subject to variability as certain assumptions must be made, including the derived service period, which is estimated based on likely future stock price performance and volatility of the Company’s common stock price. The fair value of each market-based stock option granted was estimated using the following assumptions: