Certain warrants are recorded as liabilities at their estimated fair value at the date of issuance, with the subsequent changes in estimated fair value recorded in other income (expense) in the Company’s condensed consolidated statement of operations in each subsequent quarterly period. The change in the estimated fair value of our warrant liability for the three months ended September 30, 2016 and 2015 resulted in non-cash income of approximately $0.1 million and $1.1 million, respectively. The change in the estimated fair value of our warrant liability for the nine months ended September 30, 2016 and 2015 resulted in non-cash income of approximately $1.6 million and $2.7 million, respectively. The Company utilizes the Monte Carlo simulation valuation method to value the liability classified warrants.

On June 30, 2016 we came to agreement with the 2014 warrant holders that in return for reducing the strike price of the warrants from $11.55 per share to $6.25 per share, the warrant holders would amend certain provisions of the warrant agreement. The revised warrants are classified as equity in the condensed consolidated financial statements. The loss on the modification of these outstanding warrants was approximately $0.1 million and this loss was reported in other expenses. The value of the 2014 warrants at the time of the warrant modification was approximately $0.6 million. The valuation of the amended 2014 warrants was approximately the same under both the Black Scholes pricing model and Monte Carlo valuation method.

The estimated fair value of the liability classified warrants is determined using Level 3 inputs. Inherent in the Monte Carlo 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.

The following table summarizes the calculated aggregate fair values, along with the assumptions utilized in each calculation:

The nature of the warrant liability is such (i.e., the warrant holders receive more value when the Company’s stock price is higher) that increases in the Company’s stock price during the period result in losses on the Company’s statement of operations while decreases in the Company’s stock price result in the Company recording income. The warrant liability decreased on September 30, 2016 due to the decrease in stock price and the settlement of the 2014 warrants, resulting in the 2014 warrants being treated as equity instead of a derivative liability at June 30, 2016.