Stockholders' equity | Stockholders’ equity Recent issuances On March 21, 2019, the Company completed a public offering of 3,345,282 Common Shares. Net proceeds to the Company were $6.6 million after deducting discounts, fees, and expenses. On April 5, 2019, the Company completed a public offering of 2,554,590 Common Shares. Net proceeds to the Company were $5.2 million after deducting discounts, fees, and expenses. On April 17, 2019, the Company issued 346,488 Common Shares in conjunction with the overallotment exercise by the Company’s investment banker. Net proceeds to the Company were $696 thousand after deducting discounts, fees, and expenses. Warrants The following table summarizes information about outstanding warrants at September 30, 2019 : Number of warrant shares Weighted average exercise price Outstanding at December 31, 2018 1,745,868 $3.25 Exercised (83,564 ) 3.25 Outstanding at September 30, 2019 1,662,304 $3.25 Exercisable at September 30, 2019 1,662,304 $3.25 During the nine months ended September 30, 2019 , the Company issued 83,564 Common Shares at $3.25 per share in conjunction with the exercise of warrants, with total proceeds of $272 thousand . Share-based compensation Restricted stock A summary of the Company’s shares of restricted stock as of September 30, 2019 , is as follows: Shares Weighted average grant date fair value Balance at December 31, 2018 8,867 $3.51 Granted 176,561 2.13 Vested (127,133 ) 2.19 Balance at September 30, 2019 58,295 $2.21 During the nine months ended September 30, 2019 and 2018 , the Company expensed $279,026 and $20,421 , respectively, related to the restricted stock awards. At September 30, 2019 , the balance of unearned share-based compensation to be expensed in future periods related to the restricted stock awards is $128,307 . The period over which the unearned share-based compensation is expected to be earned is approximately 2.5 years. Stock options The Company’s option activity is summarized as follows: Number of options Weighted average exercise price Outstanding at December 31, 2018 339,964 $7.09 Issued 278,500 2.21 Expired (79,539 ) 3.41 Outstanding at September 30, 2019 538,925 $5.11 Exercisable at September 30, 2019 401,847 $5.99 Unless otherwise indicated, options issued to employees, members of the Board of Directors, and non-employees are vested over one to three years and are exercisable for a term of ten years from the date of issuance. The fair values of stock option grants to employees and members of the Board of Directors during 2019 were measured on the date of grant using Black-Scholes, with the following weighted average assumptions: March 2019 April 2019 June 2019 Expected volatility 89% 94% 96% Risk free interest rate 2.53% 2.28% 1.85% Expected dividend yield 0% 0% 0% Expected life (in years) 5 5 5 The weighted average fair value of stock options granted during the nine months ended September 30, 2019 , was $ 2.21 . The total intrinsic value of all options outstanding was $80,305 and $0 at September 30, 2019 , and December 31, 2018 , respectively. The total intrinsic value of exercisable options was $41,492 and $0 at September 30, 2019 , and December 31, 2018 , respectively. The following table summarizes information about options outstanding and exercisable at September 30, 2019 : Weighted average exercise price of outstanding options Number of options outstanding Weighted average remaining estimated life (in years) Number of options exercisable Weighted average exercise price of outstanding and exercisable options $2.50 - $5.70 403,663 9.1 270,120 $6.90 - $9.60 52,841 3.0 52,841 $10.50 - $10.80 4,000 4.4 4,000 $14.20 - $23.40 78,421 6.5 74,886 538,925 401,847 $5.99 Total share-based compensation on stock options amounted to $374,426 and $171,261 for the nine months ended September 30, 2019 and 2018 , respectively. At September 30, 2019 , the balance of unearned share-based compensation to be expensed in future periods related to unvested share-based awards was $229,807 . The period over which the unearned share-based compensation is expected to be earned is approximately 0.8 years. During the period ended June 30, 2019, the Company recognized share based compensation of $134,258 related to the accelerated vesting and exercisable term change for options to purchase an aggregate of 153,940 shares for the Company’s former CEO, who retired June 30, 2019. Each option granted was revalued as of June 30, 2019, using the following Black-Scholes values to determine the incremental charges for the option modification: expected volatility of 97% , risk free interest rate of 1.71% to 1.92% , expected dividend yield of 0.0% , and expected life of 1.5 to 5 years. The following table summarizes the expense related to the options revalued at June 30, 2019: Expense Grant date Number of options Previous Accelerated Incremental Total 1/11/2011 16,667 $ 109,769 $ — $ 11,782 $ 121,551 1/20/2014 6,667 120,712 — 7,621 128,333 2/27/2018 60,606 99,738 — 12,313 112,051 4/21/2017 20,000 70,346 20,736 13,485 104,567 4/30/2019 50,000 13,453 67,047 1,274 81,774 153,940 $ 414,018 $ 87,783 $ 46,475 $ 548,276 |