PART II  NOTE 14 Share-Based Compensation Stock Compensation Stock Options BLACK SCHOLES VALUATION ASSUMPTIONS FOR 2010, 2009 AND 2008 STOCK OPTION GRANTS 60 FMC CORPORATION    2010 Form 10K not recognize any excess tax benefits in our consolidated balance sheets  from the exercise of stock options and the vesting of restricted awards,  due to our U.S. net operating loss carryforward position. At December 31, 2010 and 2009, there were restricted stock units  representing an aggregate of 41,374 shares and 35,828 shares of common  stock, respectively, credited to the directors’ accounts. We recognized a total of $14.7 million ($9.1 million after-tax),  $11.2 million ($6.9 million after-tax) and $10.6 million ($6.6 million  after-tax) in share-based compensation expense during the years ended  December 31, 2010, 2009 and 2008, respectively. This expense is  classified as selling, general and administrative in our consolidated  statements of income. During the second and third quarter of 2010 we utilized the remaining  U.S. financial net operating losses as we generated U.S. income during  2010 suffi cient to absorb the remaining unrecognized excess tax  benefi ts. As a result, we recognized all of the excess tax benefi ts from  the exercise of stock options and the vesting of restricted stock awards  from 2006 through 2009 as well as the excess tax benefi ts generated  during the period from January 1, 2010 through December 31, 2010.  As of December 31, 2010, we recognized $56.3 million of excess tax  benefits, of which $44 million related to years 2006 through 2009, on  our consolidated balance sheet as a component of equity. Th  is amount  is also included as a financing activity in our consolidated statements  of cash flows for the year ended December 31, 2010. We received $18.1 million, $10.2 million and $13.1 million in cash related  to stock option exercises for the years ended December 31, 2010, 2009  and 2008, respectively. The shares used for the exercise of stock options  occurring during the years ended December 31, 2010, 2009 and 2008  came from treasury shares. For tax purposes, share-based compensation expense is deductible in  the year of exercise or vesting based on the intrinsic value of the award  on the date of exercise or vesting. For fi nancial reporting purposes,  share-based compensation expense is based upon grant-date fair value  and amortized over the vesting period. Excess tax benefits represent the  difference between the share-based compensation expense for fi nancial  reporting purposes and the deduction taken for tax purposes. Th  ese  excess tax benefits cannot be reported in our fi nancial statements  while a net operating loss exists. From the adoption of share-based  compensation accounting in 2006 through March 31, 2010 we did  The grant-date fair values of the stock options we granted in the years  ended December 31, 2010, 2009 and 2008 were estimated using the  Black-Scholes option valuation model, the key assumptions for which  are listed in the table below. The expected volatility assumption is based  on the actual historical experience of our common stock. Th  e expected  life represents the period of time that options granted are expected to  be outstanding. The risk-free interest rate is based on U.S. Treasury  securities with terms equal to the expected timing of stock option  exercises as of the grant date. The dividend yield assumption refl ects our  announcement of the payment of a dividend on our common stock. 2010 2009 2008 Expected dividend yield 0.87% 1.13% 0.75% Expected volatility 42.17% 41.90% 31.30% Expected life (in years) 6.5 6.5 6.5 Risk-free interest rate 3.13% 2.82% 3.26% The weighted-average grant-date fair value of options granted during the years ended December 31, 2010, 2009 and 2008 was $24.50, $18.17  and $19.53 per share, respectively.