Fair Value Measurements

The Company measures and records warrant liabilities at fair value in the accompanying financial statements. Fair value is defined as the exchange price that would be received for an asset or paid to transfer a liability, an exit price, in the principal or most advantageous market for the asset or liability in an orderly transaction between market participants on the measurement date. Valuation techniques used to measure fair value must maximize the use of observable inputs and minimize the use of unobservable inputs. The three-tier fair value hierarchy, which prioritizes the inputs used in measuring fair value, includes:


•	Level 1 – Observable inputs for identical assets or liabilities such as quoted prices in active markets;


•	Level 2 – Inputs other than quoted prices in active markets that are either directly or indirectly observable; and


•	Level 3 – Unobservable inputs in which little or no market data exists, which are therefore developed by the Company using estimates and assumptions that reflect those that a market participant would use.

The following tables represent the Company’s fair value hierarchy for its financial assets and liabilities measured at fair value on a recurring basis as of December 31, 2018 and 2017:



	As of December 31, 2018
	Level 1		Level 2		Level 3		Total
Assets:
Cash and cash equivalents	$	1,130	$	—	$	—	$	1,130
Short-term investments	—		503,810		—		503,810
Total assets	$	1,130	$	503,810	$	—	$	504,940
Liabilities:
Accrued warrant liability	$	—	$	—	$	78,637	$	78,637
	As of December 31, 2017
	Level 1		Level 2		Level 3		Total
Assets:
Cash and cash equivalents	$	551,088	$	—	$	—	$	551,088
Short-term investments	3,606,499		954,858		—		4,561,357
Total assets	$	4,157,587	$	954,858	$	—	$	5,112,445
Liabilities:
Accrued warrant liability	$	—	$	—	$	1,041,455	$	1,041,455

The Company has certain warrants that could require settlement in cash if a fundamental transaction occurs, as defined in the respective agreements. These agreements specify the amount due to warrant holders is based on the Black-Scholes pricing model.

The following are the assumptions used to measure the accrued warrant liability at December 31, 2018 and 2017:

"Risk-free interest rate" means the range of U.S. Treasury rates with a term that most closely resembles the expected life of the option as of the date the option is granted.

"Expected dividend yield" means the anticipated dividend return for an investor over the expected life. For the Company, this amount is zero as it is not anticipated that dividends will be paid for the foreseeable future.

"Expected life" means the period of time that options granted are expected to remain outstanding, based wholly on the use of the simplified (safe harbor) method. The simplified method is used because the Company does not yet have adequate historical exercise information to estimate the expected life the options granted.

"Expected volatility" means a measure of the amount by which a financial variable, such as share price, has fluctuated (historical volatility) or is expected to fluctuate (implied volatility) during a period. Expected volatility is based on the Company’s historical volatility and incorporates the volatility of the common stock of comparable companies when the expected life of the option exceeds the Company’s trading history.



	December 31,
	2018			2017
Stock Price	$	1.01		$	4.01
Exercise Price	$ 3.64 - 24.40			$ 3.00 - 24.40
Term in years	0.04 - 2.60			0.25 - 3.60
Volatility	88.07 - 108.18%			71.48 - 139.58%
Annual rate of quarterly dividends	0		%	0		%
Discount rate- bond equivalent yield	0.12 - 2.48%			0.44 - 2.05%

The following table sets forth a summary of changes in the fair value of the Company’s Level 3 fair value measurement of the accrued warrant liability for the years ended December 31, 2018 and 2017:



	Year Ended December 31, 2018
Beginning Balance	$	1,041,455
Total (gains) or losses, realized and unrealized, included in earnings (1)	(962,818		)
Balance at December 31, 2018	$	78,637
	Year Ended December 31, 2017
Beginning Balance	$	949,419
Total (gains) or losses, realized and unrealized, included in earnings (1)	4,426,146
Settlements	(4,334,110		)
Balance at December 31, 2017	$	1,041,455


(1)	Unrealized gains or losses related to the accrued warrant liability were included as change in value of accrued warrant liability.

Separate disclosure is required for assets and liabilities measured at fair value on a recurring basis, as documented above, from those measured at fair value on a nonrecurring basis. As of December 31, 2018 and 2017, the Company had no assets or liabilities that were measured at fair value on a nonrecurring basis.

The Company considers the accrued warrant liability measurement to be Level 3 because some of the inputs into the measurements are neither directly or indirectly observable. The following table summarizes the unobservable inputs into the fair value measurements:



	December 31, 2018
Description	Fair Value		Valuation Technique	Unobservable Input	Range in years
Accrued warrant liability	$	78,637	Black-scholes pricing model	Expected term	0.04 - 2.60

Management believes the value of the accrued warrant liability is more sensitive to changes in the Company’s stock price at the end of the respective reporting period as opposed to changes in the expected term. At December 31, 2018, a 10% increase in the expected term of the Company’s warrants measured using the Black-Scholes pricing model would increase the warrant liability by approximately 6%, while a 10% decrease in the expected term would decrease the warrant liability by approximately 6%. A 10% increase in the Company’s stock price would result in an increase in the accrued warrant liability of approximately 17%, while a 10% decrease in the stock price would decrease the warrant liability by approximately 16%.

The carrying amounts of the Company’s remaining financial instruments, which include cash, short-term investments, accounts receivable and accounts payable, approximate their fair values due to their short maturities.