Warrants

9 Months Ended

12 Months Ended

Sep. 30, 2024

Dec. 31, 2023

(6)Warrants

The Company’s grants of warrants to purchase common stock are primarily in connection with equity financing. See Note 5 for additional information about equity financings and the related issuance of warrants. Warrant activity for the nine months ended September 30, 2024 is as follows:


		Shares
Balance December 31, 2023		268,937
Issued		—
Exercised		(187,415)
Cancelled		(90)
Balance September 30, 2024		81,432

On February 8, 2023, the Company completed a public offering in which three classes of warrants were issued. There were 37,921 common stock purchase warrants issued with an alternative cashless exercise provision. The alternative cashless exercise allows the holder to exercise one warrant share for 0.5 shares of common stock or exercise via the cash exercise price of $464.00 per share of common stock per warrant. The Company classifies these warrants as a liability, and the Company utilized a bifurcated Black-Scholes option pricing model to consider the cash exercise option and cashless exercise option. The bifurcated Black-Scholes option pricing model used an exercise price where the two exercise methods would be indifferent with market inputs of the stock price on the issuance, risk free interest rate, expected share price volatility and dividend yield. The Company calculates the fair value of the warrants at each reporting period and when a warrant is exercised, with the changes in fair value recognized in the statement of operations.

Below is a summary of the initial inputs used in the bifurcated Black-Scholes option pricing model.


	Cash Exercise			Cashless Exercise
Stock Price	$	5.905		$	5.905
Exercise Price	$	16.00		$	0.00
Term (years)		5.00			5.00
Volatility		96.50	%		96.50	%
Risk Free Rate		3.784	%		3.784	%
Dividend Yield		0	%		0	%

The following table presents the changes in the fair value of warrant liabilities:


	Common Stock
	Purchase Warrants
Fair value as of December 31, 2023	$	72
Gain on changes in fair value of liability warrants		(46)
Fair value as of September 30, 2024	$	26

In addition, one of the investors purchased 1,552 pre-funded warrants at a price of $463.94 per warrant. These warrants have an exercise price of $0.01 per share and do not expire. The pre-funded warrants were valued at $0.5 million using the fair value approach

at the time of issuance. The fair value of the pre-funded warrants was determined using a Black Scholes option pricing model using a risk-free rate of 3.784%, an expected term of 5.0 years, expected dividends of zero and expected volatility of 96.5%.

As part of the terms of the offering, the Company issued 1,265 representative’s warrants with an exercise price of $510.40 per share and expiration date on February 3, 2028. The representative’s warrants were valued at $0.3 million using the fair value approach at the time of issuance. The fair value of the representative’s warrants was determined using a Black Scholes option pricing model using a risk-free rate of 3.786%, an expected term of 4.99 years, expected dividends of zero and expected volatility of 96.5%.

(10)

Warrants

The Company’s grants of warrants to purchase common stock are primarily in connection with equity and debt financings. See Note 9 for additional information about equity financings and the related issuance of warrants. Warrant activity was as follows:

	Shares
Balance December 31, 2021	2,398
Issued	2,504	⁽¹⁾
Exercised	(1,459)	⁽²⁾
Cancelled	(107)
Balance December 31, 2022	3,336
Issued	619,185	⁽³⁾
Exercised	(353,581)	⁽⁴⁾
Cancelled	(3)
Balance December 31, 2023	268,937

(1)	Warrants issued in 2022 includes: 1,289 reload warrants, 995 common stock purchase warrants, 50 representative’s warrants, and 170 pre-funded warrants.

(2)	Warrants exercised in 2022 includes: 1,289 reload warrants at an exercise price of $1,933.14 per share, and 170 pre-funded warrants at an exercise price of $2.90 per share.

(3)	Warrants issued in 2023 includes: 472,672 common stock purchase warrants, of which 37,921 are classifies as liability warrants, 136,713 pre-funded warrants, and 9,800 representative’s warrants.

(4)

Warrants exercised in 2023 includes: 188,000 common stock purchase warrants at an exercise price range of $19.14 per share and $13.34 per share, 28,869 common stock purchase warrants (liability warrants) exercised with the alternative cash less option, 136,712 pre-funded warrants at an exercise price range of $0.06 and $0.01 per share.

Warrant Assumptions – 2023 Warrants Issued

The following table provides the assumptions used to calculate the fair value of the new warrants issued during 2023, using a Black-Scholes model:


	Warrants		Strike Price	Volatility		Expected Term	Risk Free Rate
Pre-funded warrants - February 2023	1,552	$	0.01	96.5	%	5.0	3.78	%
Representative’s warrants - February 2023	1,265	$	510.40	96.5	%	5.0	3.79	%
Common stock warrants - April 2023	13,806	$	178.06	88.4	%	5.5	3.56	%
Pre-funded warrants - April 2023	8,782	$	0.01	88.4	%	5.5	3.56	%
Representative’s warrants - April 2023	691	$	196.04	96.3	%	5.0	3.57	%
Common stock warrants - October 2023	235,345	$	19.14	89.1	%	5.0	4.74	%
Pre-funded warrants - October 2023	126,380	$	0.06	89.1	%	5.0	4.74	%
Representative’s warrants - October 2023	7,845	$	21.05	89.2	%	5.0	4.74	%

The following table provides the assumptions used to calculate the fair value of the new warrants issued during 2023, using a Monte Carlo model:


	Warrants		Strike Price	Volatility		Expected Term	Risk Free Rate
Common stock warrants - November 2023	185,604	$	13.34	86.9	%	5.5	4.40	%

The following table provides the assumptions used in the bifurcated Black-Scholes option pricing model for the common stock purchase warrants classified as a liability:


	Cash Exercise			Cashless Exercise
Stock Price	$	342.49		$	342.49
Exercise Price	$	928.00		$	0.00
Term (years)		5.00			5.00
Volatility		96.50	%		96.50	%
Risk Free Rate		3.784	%		3.784	%
Dividend Yield		0	%		0	%

The following table presents the changes in the fair value of the liability warrants:


	Common Stock
	Purchase Warrants
Fair value as of February 8, 2023 (issuance date)	$	10,363
Fair value of liability warrants in excess of proceeds, at issuance		(164)
Exercises of liability warrants		(6,249)
Gain on changes in fair value of liability warrants		(3,878)
Fair value as of December 31, 2023	$	72

Warrant Assumptions – 2022 Warrants Issued

The following table provides the assumptions used to calculate the fair value of the Series G warrants issued during 2022, using a Black-Scholes model:


	Warrants		Strike Price	Volatility		Expected Term	Risk Free Rate
Reload warrants - June 2022	1,290	$	1,933.14	64.8	%	7.5	3.32	%
Reload warrants - November 2022	995	$	870.00	84.3	%	5.5	4.21	%
Representative’s warrants	50	$	870.00	84.3	%	5.0	4.23	%
Pre-funded warrants	170	$	2.90	84.3	%	5.5	4.21	%