11.Warrants

Warrants outstanding and exercisable are summarized as follows:

		Weighted
		Average
		Exercise		Range of
	Shares(1)	Price		Exercise Prices
Outstanding at December 31, 2015	913,441	$	7.45	$0.05 - $22.50
Exercised	(337,228)	$	0.05	$.05
Expired	(12,215)	$	22.50	$22.50

Outstanding at June 30, 2016	563,998	$	11.61	$6.10-$21.00

Exercisable at June 30, 2016	563,998	$	11.61	$6.10-$21.00

(1)

Outstanding and exercisable information includes 21,920 equity-classified warrants.

Warrant Liability

The Company’s warrant liability is carried at fair value and is classified as Level 3 in the fair value hierarchy because the warrants are valued based on unobservable inputs.

The Company determines the fair value of its warrant liability using the Black-Scholes option-pricing model unless the warrants are subject to market conditions, in which case it uses a Monte Carlo simulation model, which utilizes multiple input variables to estimate the probability that market conditions will be achieved. These models are dependent on several variables, such as the warrant’s expected term, expected strike price, expected risk-free interest rate over the expected term of the instrument, expected dividend yield rate over the expected term and the expected volatility. The expected strike price for warrants with full-ratchet down-round price protection is based on a weighted average probability analysis of the strike price changes expected during the term as a result of the full-ratchet down-round price protection.

The assumptions used in the Black-Scholes option-pricing model to estimate the fair value of the warrant liability for these warrants outstanding are as follows:

	June 30, 2016					December 31, 2015
Issued April 2014
Number of warrants	29,600		(1)	132,800		29,600		(1)	132,800
CDTi stock price	$	1.65		$	1.65	$	4.70		$	4.70
Strike price	$	8.50		$	21.00	$	8.50		$	21.00
Expected volatility	91.2%			103.8%		96.7%			94.4%
Risk-free interest rate	0.8%			0.8%		1.6%			1.5%
Dividend yield	—			—		—			—
Expected life in years	3.9			3.3		4.4			3.8

(1)

Concurrent with the November 2015 offering, these warrants were exchanged for warrants with a different strike price and term.

	June 30,		December 31,
	2016		2015
Issued November 2014
Number of warrants	77,677		77,677
CDTi stock price	$	1.65	$	4.70
Strike price	$	8.50	$	8.50
Expected volatility (1)	95.0%		96.6%
Risk-free interest rate	0.9%		1.6%
Dividend yield	—		—
Expected life in years	3.9		4.4

	June 30, 2016					December 31, 2015
Issued June 2015
Number of warrants	63,999		(1)	35,999		63,999		(1)	35,999
CDTi stock price	$	1.65		$	1.65	$	4.70		$	4.70
Strike price	$	8.50		$	13.25	$	8.50		$	13.25
Expected volatility	96.7%			93.5%		110.3%			102.3%
Risk-free interest rate	1.0%			0.9%		1.8%			1.7%
Dividend yield	—			—		—			—
Expected life in years	5.0			4.4		5.5			4.9

(1)

Concurrent with the November 2015 offering, these warrants were exchanged for warrants with a different strike price and term.

	June 30,		December 31,
	2016		2015
Issued November 2015
Number of warrants	154,199		154,199
CDTi stock price	$	1.65	$	4.70
Strike price	$	8.50	$	8.50
Expected volatility	96.5%		96.6%
Risk-free interest rate	1.0%		1.8%
Dividend yield	—		—
Expected life in years	5.0		5.5

The assumptions used in the Monte Carlo simulation model to estimate the fair value of the warrant liability for warrants outstanding with full-ratchet down-round protection are as follows:

	June 30, 2016					December 31, 2015
Issued July 2013
Number of warrants	18,800		(1)	13,000		18,800		(1)	13,000
CDTi stock price	$	1.73		$	1.73	$	4.70		$	4.70
Strike price	$	6.10		$	6.10	$	6.10		$	6.10
Expected volatility	95.2%			85.0%		95.5%			99.1%
Risk-free interest rate	0.8%			0.6%		1.5%			1.2%
Dividend yield	—			—		—			—
Expected life in years	3.4			2.0		3.9			2.5

(1)

In connection with a letter agreement, dated October 7, 2015, the Company agreed to amend the term of these warrants in order to extend the expiration date until November 11, 2019.

	June 30,		December 31,
	2016		2015
Issued November 2014
Number of warrants	16,000		16,000
CDTi stock price	$	1.73	$	4.70
Strike price	$	6.10	$	6.10
Expected volatility (1)	95.2%		95.5%
Risk-free interest rate	0.8%		1.5%
Dividend yield	—		—
Expected life in years	3.4		3.9

The warrant liability, included in accrued expenses and other current liabilities in the accompanying unaudited condensed consolidated balance sheets, is re-measured at the end of each reporting period with changes in fair value recognized in other expense, net in the accompanying unaudited condensed consolidated statements of comprehensive loss. Upon the exercise of a warrant that is classified as a liability, the fair value of the warrant exercised is re-measured on the exercise date and reclassified from warrant liability to additional paid-in capital.