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Warrants | 12 Months Ended
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Dec. 31, 2021
Warrants |
Warrants | Note 11 — Warrants Early Warrant Exercise Transaction In July 2020, the Company entered into letter agreements with certain of the Company’s Series A warrant holders (the “Series A Warrant Holders”), who were previously issued warrants (the “Original Warrants”) to purchase shares of common stock of the Company in a private placement. The Series A Warrant Holders agreed to the early exercise of Series A warrants pursuant to the letter agreements (the “Early Warrant Exercise Transaction”). The transaction closed in August 2020. The Company raised net proceeds of $2.5 million in the Early Warrant Exercise Transaction. Pursuant to the letter agreements and in consideration of the Series A Warrant Holders exercising Series A warrants to purchase an aggregate of 1,176,137 shares of common stock, the Company issued to the Series A Warrant Holders new Series C warrants to purchase up to an aggregate of 705,688 shares of common stock with an exercise price of $8.90 per share and an expiration date of August 4, 2025. The estimated fair value of the Series C warrants, calculated using the Black-Scholes model, was $3.7 million on the date of issuance and was recognized as a non-cash warrant inducement expense within other income (expenses) in the statement of operations. The assumptions used in the Black-Scholes model for these warrants are as follows: ​
​ | ​ | ​ | ​
Average risk-free interest rate |  | 0.22 | %
Expected dividend yield |  | — | %
Expected life |  | 5 years | ​
Expected volatility |  | 90 | %
​ To the extent that a Series A Warrant Holder’s exercise of Original Warrants would result in such holder exceeding beneficial ownership of 9.99% of the outstanding common stock of the Company, such excess warrant shares would be held in abeyance for the benefit of such Series A Warrant Holder until such time as its right thereto would not result in the holder exceeding this limitation. All excess warrant shares held in abeyance were issued in the year ended December 31, 2021 and, as a result there were no excess warrant shares held in abeyance at December 31, 2021. At December 31, 2020, 803,300 excess warrant shares were held in abeyance. A summary of the Company’s warrant activity and related information is as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Warrants | ​ | Pre-Funded Warrants
​ |  | ​ |  | Weighted |  | ​ |  | Weighted
​ | ​ | ​ | ​ | Average | ​ | ​ | ​ | Average
​ | ​ | ​ | ​ | Exercise | ​ | ​ | ​ | Exercise
​ | ​ | Warrants | ​ | Price | ​ | Warrants | ​ | Price
Outstanding at December 31, 2019 |  | 2,463,063 | ​ | $ | 7.96 |  | 868,443 | ​ | $ | 0.001
Issued |  | 705,688 | ​ | $ | 8.90 |  | — | ​ | $ | —
Exercised |  | (589,941) | ​ | $ | 2.39 |  | (548,242) | ​ | $ | 0.001
Held in abeyance | ​ | (803,300) | ​ | $ | 2.32 | ​ | — | ​ | $ | —
Expired | ​ | (625,642) | ​ | $ | 24.44 | ​ | — | ​ | $ | —
Outstanding at December 31, 2020 | ​ | 1,149,868 | ​ | $ | 6.36 | ​ | 320,201 | ​ | $ | 0.001
Exercised | ​ | (363,448) | ​ | $ | 8.90 | ​ | (66,373) | ​ | $ | 0.001
Outstanding at December 31, 2021 | ​ | 786,420 | ​ | $ | 5.19 | ​ | 253,828 | ​ | $ | 0.001
​ All warrants were exercisable at December 31, 2021 although warrants may generally be exercised only to the extent that the total number of shares of common stock then beneficially owned by these shareholders does not exceed 4.99% (or, at the investor’s election, 9.99%) of the outstanding shares of the Company’s stock. The weighted average remaining life, excluding the 253,828 pre-funded warrants with no expiration date, of the outstanding warrants is 3.2 years. The estimated aggregate pre-tax intrinsic value (the difference between the Company’s stock price on the last day of the year ended December 31, 2021 and the exercise prices, multiplied by the number of in-the-money warrants) is $8.5 million.

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