Note 9. 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 2008, we sold 1,379,310 units to institutional investors at a price of $14.50 per unit, for gross proceeds of $20,000,000. The units, each of which consisted of one share of common stock and a warrant to purchase 0.75 shares of common stock at an exercise price of $23.00 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 $18,637,000. We recorded the fair value of the warrants to purchase 1,034,483 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 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.

The assumptions used for the Black-Scholes option pricing model are as follows:


	To Calculate Fair Value of Warrant Liability at
	June 30, 2013			December 31, 2012
Expected life (years)		1.0			1.4
Risk-free interest rate		0.1	%		0.2	%
Expected volatility		58.1	%		108.2	%
Expected dividend yield		0	%		0	%


	At June 30, 2013		At December 31, 2012		Change in Fair Value of Warrant Liability
Fair value of liability for warrants issued in 2008	$	0	$	44,628	$	(44,628	)

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 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.

The assumptions used for the Black-Scholes option pricing model are as follows:


	To Calculate Fair Value of Warrant Liability at
	June 30, 2013			December 31, 2012
Expected life (years)		1.8			2.3
Risk-free interest rate		0.3	%		0.3	%
Expected volatility		96.7	%		94.5	%
Expected dividend yield		0	%		0	%


	At June 30, 2013		At December 31, 2012		Change in Fair Value of Warrant Liability
Fair value of liability for warrants issued in 2009	$	42,192	$	63,340	$	(21,148	)

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, an aggregate of 2,198,571 Series A Warrants were exercised. For the exercise of these warrants, we issued 2,198,571 shares of our common stock. In the first quarter of 2013, an aggregate of 334,534 Series A Warrants were exercised. For the exercise of these warrants, we issued 334,534 shares of our common stock and received gross proceeds of approximately $468,000. The shares were offered under our shelf registration statement previously filed with previously filed with, and declared effective by, the SEC.

The assumptions used for the Monte Carlo simulation model to value the Series A Warrants at June 30, 2013 are as follows:


Risk-free interest rate per year	0.8	%
Expected volatility per year	81.4	%
Expected dividend yield	0	%
Expected life in years	3.5

The use of a 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 for the three-month period ended June 30, 2013:


	Series A
	Number of Warrants		Fair value $
Balance at March 31, 2013		8,166,895	$	8,952,059
Less exercised		—		—
Changes in fair value		—		(716,808	)

Balance at June 30, 2013		8,166,895	$	8,235,251

The following table is a summary of our warrant liability as of June 30, 2013:


Warrants	Number Outstanding		Exercise Price ($) per share		Fair value
Warrants issued in 2008		1,034,483		23.00	$	—
Warrants issued in 2009		400,000		15.00		42,192
Series A Warrants		8,166,895		1.40		8,235,251

Total		9,601,378			$	8,277,443

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.