Quarterly report pursuant to Section 13 or 15(d)

Note 4 - Warrants

Note 4 - Warrants
6 Months Ended
Jun. 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:



June 30, 2021


December 31, 2020


Risk-free interest rate

  0.1% to 0.7%     0.1% to 0.3%  


  87.6% to 129.1%     113.7% to 127.4%  

Expected life (years)

  0.6 to 4.1     1.1 to 4.6  

Dividend yield







A summary of the Company's liability classified warrant activity during the six months ended June 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 June 30, 2021

    2,723,645     $ 6.30     $ 16.80     $ 9.46       3.1  

Exercisable at June 30, 2021

    2,723,645     $ 6.30     $ 16.80     $ 9.46       3.1  


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


Equity Classified Warrants


During the six months ended June 30, 2021, the Company granted equity-classified warrants to purchase 71,500 shares of common stock vesting quarterly over five years while services are being rendered. 


At June 30, 2021, the Company had 146,502 equity classified warrants outstanding and 54,410 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 $11,000 and $5,000 for the three and six months ended June 30, 2021 and 2020, respectively and $328,000 of unrecognized stock compensation expense related to the Company's equity classified warrants.