4. Stock-Based Compensation

We have several stock-based compensation plans under which employees and non-employee directors receive stock options, nonvested retention shares, and nonvested stock units. We refer to the nonvested shares and stock units collectively as “retention awards”. We have elected to issue treasury shares to cover option exercises and stock unit vestings, while new shares are issued when retention shares are granted. Information regarding stock-based compensation appears in the table below:

Stock Options – We estimate the fair value of our stock option awards using the Black-Scholes option pricing model. The table below shows the year-to-date weighted-average assumptions used for valuation purposes:

The risk-free rate is based on the U.S. Treasury yield curve in effect at the time of grant; the dividend yield is calculated as the ratio of dividends paid per share of common stock to the stock price on the date of grant; the expected life is based on historical and expected exercise behavior; and volatility is based on the historical volatility of our stock price over the expected life of the option.

A summary of stock option activity during the six months ended June 30, 2011 is presented below:

Stock options are granted at the closing price on the date of grant, have ten-year contractual terms, and vest no later than three years from the date of grant. None of the stock options outstanding at June 30, 2011 are subject to performance or market-based vesting conditions.

At June 30, 2011, there was $25 million of unrecognized compensation expense related to nonvested stock options, which is expected to be recognized over a weighted-average period of 1.2 years. Additional information regarding stock option exercises appears in the table below:

Retention Awards – The fair value of retention awards is based on the closing price of the stock on the grant date. Dividends and dividend equivalents are paid to participants during the vesting periods.

Changes in our retention awards during the six months ended June 30, 2011 were as follows:

Retention awards are granted at no cost to the employee or non-employee director and vest over periods lasting up to four years. At June 30, 2011, there was $90 million of total unrecognized compensation expense related to nonvested retention awards, which is expected to be recognized over a weighted-average period of 2 years.

Performance Retention Awards – In February 2011, our Board of Directors approved performance stock unit grants. Other than different performance targets, the basic terms of these performance stock units are identical to those granted in February 2009 and February 2010, including using annual return on invested capital (ROIC) as the performance measure. We define ROIC as net operating profit adjusted for interest expense (including interest on the present value of operating leases) and taxes on interest divided by average invested capital adjusted for the present value of operating leases.

Stock units awarded to selected employees under these grants are subject to continued employment for 37 months and the attainment of certain levels of ROIC. We expense the fair value of the units that are probable of being earned based on our forecasted ROIC over the 3-year performance period. We measure the fair value of these performance stock units based upon the closing price of the underlying common stock as of the date of grant, reduced by the present value of estimated future dividends. Dividend equivalents are paid to participants only after the units are earned.

The assumptions used to calculate the present value of estimated future dividends related to the February 2011 grant were as follows:

Changes in our performance retention awards during the six months ended June 30, 2011 were as follows:

At June 30, 2011, there was $45 million of total unrecognized compensation expense related to nonvested performance retention awards, which is expected to be recognized over a weighted-average period of 1.6 years. A portion of this expense is subject to achievement of the ROIC levels established for the performance stock unit grants.