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Note 6 - Stock-based Compensation Expense
 6 Months Ended 12 Months Ended
Jun. 30, 2024
Dec. 31, 2023
Notes to Financial Statements    
Share-Based Payment Arrangement [Text Block]

7.

Stock-Based Compensation Expense

 

Stock-based compensation expense related to stock options is recognized on a straight-line basis over the requisite service period for the award and is allocated to research and development expense or general and administrative expense based upon the classification of the individual to whom the award is granted. Stock-based compensation expense related to stock option grants was $101,640 and $205,209 during the three-month and six-month periods ended June 30, 2024, respectively, as compared to $226,013 and $454,052, respectively, during the same periods of 2023. As of June 30, 2024, there is $342,156 of unrecognized compensation expense that we expect to recognize over a weighted-average period of 1.1 years.

 

We have also issued shares of our restricted common stock to consultants and recognize the related expense over the terms of the related agreements. During the three-month and six-month periods ended June 30, 2024 we recorded stock-based compensation expense of $-0- and $54,167, respectively, associated with common stock issued for consulting services, as compared to $43,500 and $61,500, respectively, for the same periods of 2023.

6.

Stock-Based Compensation Expense

 

Stock-based compensation expense related to stock options is recognized on a straight-line basis over the requisite service period for the award and is allocated to research and development expense or general and administrative expense based upon the classification of the individual to whom the award is granted.

 

We use the Black-Scholes model for determining the grant date fair value of our stock option grants. This model utilizes certain information, such as the interest rate on a risk-free security with a term generally equivalent to the expected life of the option being valued and requires certain other assumptions, such as the expected amount of time an option will be outstanding until it is exercised or expired, to calculate the fair value of stock options granted. We granted no stock options during 2023. The significant assumptions we used in our fair value calculations for stock options granted during 2022 were as follows:

 

Weighted average risk-free interest rates

     3.54 %

Expected dividend yield

     0.0 %

Expected life of option (in years)

     7.0  

Expected volatility

     160.0 %

 

The weighted-average grant date fair values of stock options granted during 2023 and 2022 were $-0- and $10.98, respectively.  As of December 31, 2023, there is $554,592 of unrecognized compensation expense that will be recognized over a weighted-average period of 1.5 years.

 

We also have issued shares of restricted common stock to consultants and recognize the related expense over the terms of the related agreements. As of December 31, 2023, there is $16,667 recorded as a prepaid expense for these arrangements, which will be recognized as expense over the terms of the related agreements.

 

The following table summarizes our total stock-based compensation expense for employees, directors and consultants for the years ended December 31, 2023 and 2022:

 

   

2023

    

2022

  

Stock options:

                

Research and development

   $ 291,094     $ 225,031  

General and administrative

     564,030       548,346  

Total stock option expense

     855,124       773,377  

Stock awards (consultants):

                

General and administrative

     219,833       128,697  

Total stock-based compensation expense

   $ 1,074,957     $ 902,074