Note 10 — Warrants

During the year ended December 31, 2019 and in connection with the Offering, the Company issued pre-funded warrants to purchase 868,443 shares of common stock that are immediately exercisable and have no expiration date. The pre-funded warrants were recorded as a component of stockholders' equity within additional paid-in capital. Also in connection with the Offering, investors received warrants to purchase 1,766,751 shares of common stock at an exercise price of $2.32 per share that will expire five year from the date of issuance. The placement agreement received 70,670 warrants to purchase shares of common stock as part of its placement agent fee. The placement agent warrant has an exercise price of $2.9716 per share and expires five year from the date of issuance.

The warrants were sold with shares of common stock or pre-funded warrants for $2.4763 per unit. The unit price was allocated to the warrants and common stock or pre-funded warrants based upon the relative fair value of the securities, with the warrants valued using the Black-Scholes model. The allocated fair value of the warrants was estimated to be $1.6 million on the date of issuance. In addition, the placement agent warrant was valued at $98,592 on the date of issuance.

The assumptions used in the Black-Scholes model for these warrants are as follows:

A summary of the Company’s warrant activity and related information is as follows:

All warrants were exercisable at December 31, 2019. The weighted average remaining life, excluding the 868,443 pre-funded warrants with no expiration date, is 3.7 years. The estimated aggregate pre-tax intrinsic value (the difference between the Company’s stock price on the last day of the year ended December 31, 2019 and the exercise prices, multiplied by the number of in-the-money warrants) is $0.

For certain investors in the Offering, including the Company's four largest beneficial owners, the warrants they received in connection with the Offering as well as certain other warrants may be exercised only to the extent that the total number of shares of common stock then beneficially owned by these shareholders does not exceed 4.99% (or, at the investor's election, 9.99)% of the outstanding shares of the Company's stock.