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) include anti-dilution price protection provisions that require cash settlement of the warrants and accordingly require 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 March 31, 2018:



	August 2013 Warrants	September 2016 Warrants	December 2017 Warrants
Exercise price	$4.80	$2.25	$4.27
Expiration date	August 16, 2018	September 9, 2022	December 6, 2023
Total shares issuable on exercise	365,150	117,074	53,902

During the three months ended March 31, 2018, the Company issued 359,800 shares of common stock upon the exercise of August 2013 Warrants with an exercise price of $4.80 per share for proceeds of $1.7 million.

On December 7, 2017, the Company issued 53,902 warrants to two holders in conjunction with the amended debt agreement described in note 7 (December 2017 Warrants). The initial valuation of the December 2017 Warrants was partially recorded as debt issuance costs and is being amortized over the remaining life of the loan agreement to interest expense and a portion was expensed as a loss on extinguishment of debt. The December 2017 Warrants are treated as equity instruments recorded at fair value with no subsequent remeasurement. Pursuant to the December 2017 Warrants, the holders may exercise their warrants for an aggregate of 53,902 shares of the Company’s common stock.

The fair value of the warrants described in the table above is 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. See further detail in note 8 of the condensed consolidated financial statements.

The assumptions used by the Company are summarized in the following tables:



August 2013 Warrants	March 31, 2018			December 31, 2017
Closing stock price	$	9.95		$	5.45
Expected dividend rate	—		%	—		%
Expected stock price volatility	75.4		%	63.7		%
Risk-free interest rate	1.95		%	1.65		%
Expected life (years)	0.38			0.62



September 2016 Warrants	September 9, 2016
Closing stock price	$	2.20
Expected dividend rate	—		%
Expected stock price volatility	89.8		%
Risk-free interest rate	1.4		%
Expected life (years)	6.00



December 2017 Warrants	December 6, 2017
Closing stock price	5.10
Expected dividend rate	—	%
Expected stock price volatility	86.4	%
Risk-free interest rate	2.2	%
Expected life (years)	6.00