AKAO 2017 Annual Report

130 The following table summarizes information about stock options outstanding as of December 31, 2017: Options Outstanding Vested and Exercisable Exercise Price Number of Options Weighted- Average Remaining Contractual Life (in Years) Number of Options Weighted- Average Exercise Price $3.41 - $3.68 502,764 7.84 213,306 $ 3.65 $3.75 - $4.44 594,704 8.61 211,184 $ 4.28 $4.62 - $5.86 608,616 7.24 404,603 $ 5.18 $6.60 - $7.26 722,468 4.89 534,692 $ 7.03 $8.04 - $10.44 508,994 6.19 379,275 $ 9.17 $10.98 - $16.18 528,793 8.44 148,841 $ 12.41 $17.55 - $22.93 416,950 9.32 38,527 $ 22.08 $23.62 - $23.62 792,084 9.12 143,692 $ 23.62 $23.68 - $23.68 130,000 9.16 0 $ — $24.71 - $24.71 33,225 9.39 0 $ — 4,838,598 7.69 2,074,120 $ 8.25 Stock Options Granted to Employees and Non-Employee Directors During the years ended December 31, 2017, 2016 and 2015, the Company granted stock options to employees and directors to purchase 1,806,157, 1,477,600 and 929,100 shares, respectively, of common stock under the stock plans with a weighted-average estimated grant-date fair value of $21.12, $4.10 and $5.02 per share, respectively. As of December 31, 2017, there were unrecognized compensation costs of $22.2 million related to outstanding employee and non-employee director stock options, which are expected to be recognized over a weighted-average period of 2.95 years. The Company estimated the fair value of stock options using the Black-Scholes option valuation model for options with time-based vesting terms. The Black-Scholes model requires the input of subjective assumptions, including (a) the expected term of the award, (b) the expected stock price volatility, (c) the risk-free interest rate and (d) expected dividends. The estimated fair value of these employee stock options is being amortized on a straight- line basis over the requisite service period of the awards. The estimated grant date fair value of employee stock options with time-based vesting terms was calculated using the Black-Scholes valuation model, based on the following assumptions: Year Ended December 31, 2017 2016 2015 Expected term .............................................................. 5.0 – 6.0 years 5.3 – 6.0 years 5.4 – 6.0 years Expected volatility ....................................................... 78 - 81% 67 – 74% 65 – 75% Risk-free interest rate................................................... 1.7 – 2.3% 1.1 – 1.9% 1.5 – 1.9% Expected dividend yield............................................... —% —% —% The Company has opted to use the “simplified method” for estimating the expected term of options, whereby the expected term equals the arithmetic average of the vesting term and the original contractual term of the option. Prior to the Company's IPO in March 2014, due to the Company’s limited operating history and company specific stock price volatility data, the Company based its estimate of expected volatility on the historical price volatility of a group of similar companies that are publicly traded. Beginning in 2014, the Company began to include the historical price volatility of its own stock, along with data for the group of similar companies, to estimate expected volatility. When selecting these public companies to use in estimating its expected stock price volatility, the Company selected companies with comparable characteristics to it, including enterprise value, stages of clinical development, risk profiles, position within the industry and with historical share price information sufficient to meet the expected life of the stock-based awards. The risk-free rate assumption is based on the U.S. Treasury instruments with maturities similar to the expected term of the Company’s stock options. The expected dividend assumption is based on the