notes to the audited consolidated financial statements director stock compensation subplan eastman's 2018 director stock compensation subplan ( "directors' subplan" ) , a component of the 2017 omnibus plan , remains in effect until terminated by the board of directors or the earlier termination of the 2017 omnibus plan . the directors' subplan provides for structured awards of restricted shares to non-employee members of the board of directors . restricted shares awarded under the directors' subplan are subject to the same terms and conditions of the 2017 omnibus plan . the directors' subplan does not constitute a separate source of shares for grant of equity awards and all shares awarded are part of the 10 million shares authorized under the 2017 omnibus plan . shares of restricted stock are granted on the first day of a non- employee director's initial term of service and shares of restricted stock are granted each year to each non-employee director on the date of the annual meeting of stockholders . it has been the company's practice to issue new shares rather than treasury shares for equity awards for compensation plans , including the 2017 omnibus plan and the directors' subplan , that require settlement by the issuance of common stock and to withhold or accept back shares awarded to cover the related income tax obligations of employee participants . shares of unrestricted common stock owned by non-employee directors are not eligible to be withheld or acquired to satisfy the withholding obligation related to their income taxes . shares of unrestricted common stock owned by specified senior management level employees are accepted by the company to pay the exercise price of stock options in accordance with the terms and conditions of their awards . compensation expense for 2018 , 2017 , and 2016 , total share-based compensation expense ( before tax ) of approximately $ 64 million , $ 52 million , and $ 36 million , respectively , was recognized in "selling , general and administrative expense" in the consolidated statements of earnings , comprehensive income and retained earnings for all share-based awards of which approximately $ 9 million , $ 8 million , and $ 7 million , respectively , related to stock options . the compensation expense is recognized over the substantive vesting period , which may be a shorter time period than the stated vesting period for qualifying termination eligible employees as defined in the forms of award notice . approximately $ 3 million for 2018 , and $ 2 million for both 2017 and 2016 , of stock option compensation expense was recognized each year due to qualifying termination eligibility preceding the requisite vesting period . stock option awards options have been granted on an annual basis to non-employee directors under the directors' subplan and predecessor plans and by the compensation and management development committee of the board of directors under the 2017 omnibus plan and predecessor plans to employees . option awards have an exercise price equal to the closing price of the company's stock on the date of grant . the term of options is 10 years with vesting periods that vary up to three years . vesting usually occurs ratably over the vesting period or at the end of the vesting period . the company utilizes the black scholes merton option valuation model which relies on certain assumptions to estimate an option's fair value . the weighted average assumptions used in the determination of fair value for stock options awarded in 2018 , 2017 , and 2016 are provided in the table below: .
what was the sum of the approximate compensation expense recognized in millions
the volatility rate of grants is derived from historical company common stock price volatility over the same time period as the expected term of each stock option award . the volatility rate is derived by mathematical formula utilizing the weekly high closing stock price data over the expected term . the expected dividend yield is calculated using the company's average of the last four quarterly dividend yields . the average risk-free interest rate is derived from united states department of treasury published interest rates of daily yield curves for the same time period as the expected term. .