4. STOCK-BASED COMPENSATION

Accounting for Stock-Based Compensation

During the six-month periods ended June 30, 2019 and 2018 options granted were 321,930 and 8,000, respectfully. The following table summarizes amounts charged to expense for stock-based compensation related to employee and director stock option grants and recorded in connection with stock options granted to non-employee consultants:

 

On October 12, 2018, we granted 167,430, net of forfeitures, contingent non-statutory stock option awards at an exercise price of $2.61 per share to our current non-employee directors and our employees, and on January 17, 2019, we granted 118,750, net of forfeitures, contingent non-statutory stock option awards at an exercise price of $1.99 per share to our current employees. Each of these grants was contingent on approval by the Company’s stockholders of the amendment to the 2015 Stock Incentive Plan at the 2019 Annual Meeting of Stockholders, and stockholders approved the amendment on June 13, 2019. In accordance with the timing of the stockholder approval, all related expenses were recognized by the Company in June 2019, including the catch-up for compensation expenses for recognition of contingent non-statutory stock option awards from October 2018.

Assumptions Used in Determining Fair Value

Valuation and amortization method. The fair value of each stock award is estimated on the grant date using the Black-Scholes option-pricing model. The estimated fair value of employee stock options is amortized to expense using the straight-line method over the required service period which is generally the vesting period. The estimated fair value of the non-employee options is amortized to expense over the period during which a non-employee is required to provide services for the award (usually the vesting period).

Volatility. The Company estimates volatility based on an average of (1) the Company’s historical volatility since its common stock has been publicly traded and (2) review of volatility estimates of publicly held drug development companies with similar market capitalizations.

Risk-free interest rate. The risk-free interest rate is based on the U.S. Treasury yield curve in effect at the time of grant commensurate with the expected term assumption.

Expected term. The expected term of stock options granted is based on an estimate of when options will be exercised in the future. The Company applied the simplified method of estimating the expected term of the options, as described in the SEC’s Staff Accounting Bulletins 107 and 110, as the historical experience is not indicative of the expected behavior in the future. The expected term, calculated under the simplified method, is applied to groups of stock options that have similar contractual terms. Using this method, the expected term is determined using the average of the vesting period and the contractual life of the stock options granted. The Company applied the simplified method to non-employees who have a truncation of term based on termination of service and utilizes the contractual life of the stock options granted for those non-employee grants which do not have a truncation of service.

Forfeitures. The Company records stock-based compensation expense only for those awards that are expected to vest. A forfeiture rate is estimated at the time of grant and revised, if necessary, in subsequent periods if actual forfeitures differ from initial estimates. An annual forfeiture rate of 2% was applied to all unvested options for employees and no forfeiture rate to directors for the six months ended June 30, 2019 and for the year ended December 31, 2018. Ultimately, the actual expense recognized over the vesting period will be for only those shares that vest.

Dividends. The Company has not historically recorded dividends related to stock options.

Exercise prices for all grants made during the six months ended June 30, 2019 and 2018 were equal to the market value of the Company’s common stock on the date of grant. There were 154,500 stock option grants during the six months ended June 30, 2019. Additionally, in June 2019, 167,430, net of forfeitures, stock option grants from October 12, 2018 were recognized upon approval by the Company's stockholders of the amendment to the 2015 Stock Incentive Plan at the 2019 Annual Meeting of Stockholders.

Stock Option Activity

A summary of stock option activity is as follows:

 

The aggregate intrinsic value of options outstanding is calculated based on the positive difference between the estimated per-share fair value of common stock at the end of the respective period and the exercise price of the underlying options. There have been no option exercises to date. Shares of common stock issued upon the exercise of options are from authorized but unissued shares.

As of June 30, 2019, there was approximately $685,093 of total unrecognized compensation cost related to unvested stock-based compensation arrangements. Of this total amount, the Company expects to recognize approximately $272,106,  $262,553,  147,749 and $2,685 during 2019, 2020, 2021 and 2022, respectively. The Company’s expense estimates are based upon the expectation that all unvested options will vest in the future, less the forfeiture rate discussed above. The weighted-average grant-date fair value of vested and unvested options outstanding at June 30, 2019 was $20.18 and $1.91, respectively.

Restricted Stock Grants. During 2017, the Company issued 46,000 shares under the 2015 Plan of restricted common stock with a weighted average grant date fair value of $20.96. The shares vest annually over a three-year period. The following table summarizes the restricted stock grants: