Stock Purchase Warrants

The Company has historically issued warrants to purchase shares of the Company’s common stock in connection with certain of its common stock offerings and in September 2016 and December 2017 the Company issued warrants in connection with the amended debt agreement discussed in note 7 (collectively the Debt Warrants). The warrants issued in August 2013 (August 2013 Warrants) expired in August 2018, and included anti-dilution price protection provisions that required cash settlement of the warrants and accordingly required the warrants to be recorded as liabilities of the Company at the estimated fair value at the balance sheet date, with changes in estimated fair value recorded as income or expense (non-cash) in the Company’s statement of operations in each subsequent period. The following table describes the outstanding warrants as of September 30, 2018:



	September 2016 Warrants	December 2017 Warrants
Exercise price	$2.25	$4.27
Expiration date	September 9, 2022	December 6, 2023
Total shares issuable on exercise	58,537	53,902

During the nine months ended September 30, 2018, the Company issued 565,895 and 45,625 shares of common stock upon the exercise of August 2013 and September 2016 Warrants with an exercise price of $4.80 and $2.25 per share, respectively for proceeds of $2.7 million. As of September 30, 2018, the unexercised August 2013 warrants expired and no August 2013 warrants are outstanding.

The fair value of the warrants described in the table above were initially measured using the Black-Scholes valuation model. Inherent in the Black-Scholes valuation model are assumptions related to expected stock-price volatility, expected life, risk-free interest rate and dividend yield. The Company estimates the volatility of its common stock based on historical volatility that matches the expected remaining life of the warrants. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield curve on the grant date for a maturity similar to the expected remaining life of the warrants. The expected life of the warrants is assumed to be equivalent to their remaining contractual term. The dividend rate is based on the historical rate, which the Company anticipates to remain at zero.