Options

Option valuation models require the input of highly subjective assumptions. The fair value of stock-based payment awards was estimated using the Black-Scholes option model with a volatility figure derived from using the Company's historical stock prices. The Company accounts for the expected life of options based on the contractual life of options for non-employees. For employees, the Company accounts for the expected life of options in accordance with the "simplified" method, which is used for "plain-vanilla" options, as defined in the accounting standards codification.

The risk-free interest rate was determined from the implied yields of U.S. Treasury zero-coupon bonds with a remaining life consistent with the expected term of the options.

The following table summarizes the stock option activity for the three months ended March 31, 2018:

The aggregate intrinsic value in the preceding tables represents the total pretax intrinsic value, based on options with an exercise price less than the Company's stock price of $0.1325 as of March 31, 2018, which would have been received by the option holders had those option holders exercised their options as of that date.

The following table presents information related to stock options at March 31, 2018:

The stock-based compensation expense related to option grants was $78,535 and $78,535 during the three months ended March 31, 2018 and 2017, respectively.

As of March 31, 2018, stock-based compensation related to options of $52,357 remains unamortized and is expected to be amortized over the weighted average remaining period of 2 months.

Warrants

The following table summarizes the changes in warrants outstanding and the related prices for the shares of the Company’s common stock:

The following table summarizes the warrant activity for the two years ended December 31, 2017: