Quarterly report pursuant to Section 13 or 15(d)

Note 4 - Warrants

Note 4 - Warrants
9 Months Ended
Sep. 30, 2021
Notes to Financial Statements  
Warrants Disclosure [Text Block]

4. Warrants


Liability Classified Warrants


The Company uses the Black-Scholes option pricing model to determine the fair value of its warrants at the date of issue and outstanding at each reporting date. The risk-free interest rate assumption is based upon observed interest rates on zero coupon U.S. Treasury bonds linearly interpolated to obtain a maturity period commensurate with the term of the warrants. Estimated volatility is a measure of the amount by which the Company's stock price is expected to fluctuate each year during the expected life of the warrants. Beginning in 2020, only the volatility of the Company's own stock is used in the Black-Scholes option pricing model as it now has sufficient historic data in its stock price. 


The assumptions used in determining the fair value of the liability classified warrants are as follows:



September 30, 2021


December 31, 2020


Risk-free interest rate

  0.0% to 0.7%     0.1% to 0.3%  


  41.2% to 123.1%     113.7% to 127.4%  

Expected life (years)

  0.4 to 3.9     1.1 to 4.6  

Dividend yield







A summary of the Company's liability classified warrant activity during the nine months ended September 30, 2021 and related information follows: 



Number of Shares


Range of Warrant Exercise


Weighted Average


Weighted Average Remaining Contractual


Under Warrant


Price per Share


Exercise Price


Life (Years)


Balance at January 1, 2021

    2,733,645     $ 6.30     $ 16.80     $ 9.45       3.6  




    (10,000 )     6.30       6.30       6.30        



Balance at September 30, 2021

    2,723,645     $ 6.30     $ 16.80     $ 9.46       2.9  

Exercisable at September 30, 2021

    2,723,645     $ 6.30     $ 16.80     $ 9.46       2.9  


For a summary of the changes in fair value associated with the Company's warrant liability for the nine months ended September 30, 2021, see Note 2 - Basis of presentation, principles of consolidation and significant accounting policies - Fair Value of Financial Instruments.


Equity Classified Warrants


In April 2021, the Company granted equity-classified warrants to purchase 71,500 shares of common stock with a five-year term and an exercise price of $3.63 vesting quarterly over five years while services are being performed. In August 2021, the Company entered into a portfolio development advisory agreement with a related party entity and in connection with the agreement, the Company granted equity-classified warrants to purchase 250,000 shares of common stock with a ten-year term and an exercise price of $3.08. The August 2021 warrants vest as follows: (a) 50% vests upon execution of the agreement, provided the advisor does not terminate the agreement prior to the end of the one-year term; and (b) 50% vests 60 days after the end of the one-year term, subject to the Company's Board of Directors determining that the services provided have been adequately performed. Also, both the April 2021 and August 2021 warrants vest in full if there is a change of control event, as defined in the agreement.


At September 30, 2021, the Company had 396,502 equity classified warrants outstanding and 182,985 warrants were exercisable. At  December 31, 2020, the Company had 109,639 equity classified warrants outstanding and 85,472 warrants were exercisable.


The Company recorded stock compensation expense for equity classified warrants of $422,000 and zero for the three months ended  September 30, 2021 and 2020, respectively, and $432,000 and $5,000 during the nine months ended September 30, 2021 and 2020, respectively. At  September 30, 2021, there was $632,000 of unrecognized stock compensation expense related to the Company's equity classified warrants.