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The Bancorp uses assumptions, which are evaluated and revised as necessary, in estimating the grant-date fair value of each SAR grant. The weighted-average assumptions were as follows for the years ended: 

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The expected option life is derived from historical exercise patterns and represents the amount of time that options granted are expected to be outstanding. The expected volatility is based on a combination of historical and implied volatilities of the Bancorp’s common stock. The expected dividend yield is based on annual dividends divided by the Bancorp’s stock price. Annual dividends are based on projected dividends, estimated using a historical long-term dividend payout ratio, over the estimated life of the awards. The risk-free interest rate for periods within the 

## NOTES TO CONSOLIDATED FINANCIAL STATEMENTS 

contractual life of the option is based on the U.S. Treasury yield curve in effect at the time of grant. 

Stock-based compensation expense was $64 million, $51 million and $56 million for the years ended December 31, 2010, 2009 and 2008, respectively, and is included as compensation expense in the Consolidated Statements of Income. The total related income tax benefit recognized was $18 million, $18 million and $20 million for the years ended December 31, 2010, 2009 and 2008, respectively. 

## Stock Appreciation Rights (SARs) 

The weighted-average grant-date fair value of SARs granted was $5.10, $2.41 and $2.09 per share for the years ended 2010, 2009 and 2008, respectively. The total grant-date fair value of SARs that vested during 2010, 2009 and 2008 was $25 million, $26 million and $61 million, respectively. 

At December 31, 2010, there was $37 million of stock-based compensation expense related to nonvested SARs not yet recognized. The expense is expected to be recognized over a remaining weighted-average period of approximately 2.7 years. 

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The following table summarizes outstanding and exercisable SARs by grant price at December 31, 2010: 

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## Restricted Stock Awards (RSAs) 

The total grant-date fair value of RSAs that vested during 2010, 2009 and 2008 was $30 million, $36 million and $24 million, respectively. At December 31, 2010, there was $50 million of stock-based compensation expense related to nonvested restricted 

stock not yet recognized. The expense is expected to be recognized over a remaining weighted-average period of approximately 2.4 years. 

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