Note 8. Warrant Liability

We use various option pricing models, such as the Black-Scholes option pricing model and a Monte Carlo simulation model, to estimate fair value of warrants issued. In using these models, we make certain assumptions about risk-free interest rates, dividend yields, volatility, expected term of the warrants and other assumptions. Risk-free interest rates are derived from the yield on U.S. Treasury debt securities. Dividend yields are based on our historical dividend payments, which have been zero to date. Volatility is estimated from the historical volatility of our common stock as traded on NASDAQ. The expected term of the warrants is based on the time to expiration of the warrants from the date of measurement.

In November 2009, we sold 1,000,000 units to institutional investors at a price of $12.50 per unit, for gross proceeds of $12,500,000. The units, each of which consisted of one share of common stock and a warrant to purchase 0.40 shares of common stock at an exercise price of $15.00 per share, were offered as a registered direct offering under a shelf registration statement previously filed with, and declared effective by, the SEC. We received total proceeds, net of offering expenses and placement agency fees, of approximately $11,985,000. We recorded the fair value of the warrants to purchase 400,000 shares of our common stock as a liability. The fair value of the warrant liability is revalued at the end of each reporting period, with the change in fair value of the warrant liability recorded as a gain or loss in our condensed consolidated statements of operations. The November 2009 warrants expired unexercised by their own terms in April 2015.

In December 2011, we raised gross proceeds of $10,000,000 through a public offering of 8,000,000 units and 8,000,000 Series B Warrants. The combination of units and Series B Warrants were sold at a public offering price of $1.25 per unit. Each Series B Warrant gave the holder the right to purchase one unit at an exercise price of $1.25 per unit and was exercisable until May 2, 2012, the 90th trading day after the date of issuance. Each unit consists of one share of our common stock and one Series A Warrant. Each Series A Warrant gives the holder the right to purchase one share of our common stock at an initial exercise price of $1.40 per share. The Series A Warrants are immediately exercisable upon issuance and will expire in December 2016. In 2012, an aggregate of 2,700,000 Series B Warrants were exercised. For the exercise of these warrants, we issued 2,700,000 shares of our common stock and 2,700,000 Series A Warrants. The remaining 5,300,000 Series B Warrants expired unexercised by their terms on May 2, 2012. In 2012, 2013 and 2014, an aggregate of 2,198,571, 384,534 and 1,180,015 Series A Warrants were exercised, respectively. For the exercise of these warrants, in 2012, 2013 and 2014, we issued 2,198,571, 384,534 and 1,180,015 shares of our common stock and received gross proceeds of approximately $3,078,000, $538,000 and $1,652,000, respectively. The shares were offered under our shelf registration statement previously filed with previously filed with, and declared effective by, the SEC. The Series A Warrants contain full ratchet anti-dilution price protection so that, in most situations upon the issuance of any common stock or securities convertible into common stock at a price below the then-existing exercise price of the outstanding Series A Warrants, the Series A exercise price will be reset to the lower common stock sales price As a result of our April 2015 financing, the exercise price of the Series A warrants were reduced from $1.40 per share to $0.6999999 per share.

The assumptions used for the Monte Carlo simulation model to value the outstanding Series A Warrants at June 30, 2015 are as follows:


Risk-free interest rate per year	0.45	%
Expected volatility per year	67.7	%
Expected dividend yield	0	%
Expected life (years)	1.5

The use of the Monte Carlo simulation model requires the input of additional subjective assumptions including the progress of our R&D programs and its affect on potential future financings.

The following table is a summary of the changes in fair value of warrant liability for the Series A Warrants in 2015:


	Series A
	Number of Warrants		Fair value $
Balance at December 31, 2014		6,936,880	$	1,684,551
Changes in fair value		—		(641,037	)

Balance at June 30, 2015		6,936,880	$	1,043,514

The fair value of the warrant liability is revalued at the end of each reporting period, with the change in fair value of the warrant liability recorded as a gain or loss in our condensed consolidated statements of operations. The fair value of the warrants will continue to be classified as a liability until such time as the warrants are exercised, expire or an amendment of the warrant agreement renders these warrants to be no longer classified as a liability.