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Share-Based Compensation
9 Months Ended
Sep. 30, 2015
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Share-Based Compensation
SHARE-BASED COMPENSATION
Under our Stock and Cash Incentive Plan (the “Stock Plan”), we award: (1) stock options (our “Stock Option Program”) to purchase our Class A Common Stock (“common stock”); (2) stock appreciation rights (“SARs”) for our common stock (our “SAR Program”); (3) restricted stock units (“RSUs”) of our common stock; and (4) deferred stock units. We also issue performance-based RSUs (“PSUs”) to named executive officers and some of their direct reports under the Stock Plan. We grant awards at exercise prices or strike prices that equal the market price of our common stock on the date of grant.
We recorded share-based compensation expense for award grants of $29 million for the 2015 third quarter and $28 million for the 2014 third quarter, $84 million for the 2015 first three quarters, and $81 million for the 2014 first three quarters. Deferred compensation costs for unvested awards totaled $145 million at September 30, 2015 and $114 million at December 31, 2014.
RSUs and PSUs
We granted 1.3 million RSUs during the 2015 first three quarters to certain officers and key employees, and those units vest generally over four years in equal annual installments commencing one year after the grant date. We also granted 0.1 million PSUs during the 2015 first three quarters to certain executive officers, subject to the satisfaction of certain performance conditions based on achievement of pre-established targets for Adjusted EBITDA, RevPAR Index, room openings, and net administrative expense over, or at the end of, a three-year vesting period. RSUs, including PSUs, granted in the 2015 first three quarters had a weighted average grant-date fair value of $79.
SARs
We granted 0.3 million SARs to officers, key employees, and non-employee directors during the 2015 first three quarters. These SARs generally expire ten years after the grant date and both vest and may be exercised in cumulative installments of one quarter at the end of each of the first four years following the grant date. The weighted average grant-date fair value of SARs granted in the 2015 first three quarters was $26 and the weighted average exercise price was $83.
We used the following assumptions as part of a binomial lattice-based valuation to determine the fair value of the SARs we granted during the 2015 first three quarters:
Expected volatility
30%
Dividend yield
1.04%
Risk-free rate
1.9 - 2.3%
Expected term (in years)
6 - 10

In making these assumptions, we base expected volatility on the historical movement of the Company’s stock price. We base risk-free rates on the corresponding U.S. Treasury spot rates for the expected duration at the date of grant, which we convert to a continuously compounded rate. The dividend yield assumption takes into consideration both historical levels and expectations of future dividend payout. The weighted average expected terms for SARs are an output of our valuation model which utilizes historical data in estimating the period of time that the SARs are expected to remain unexercised. We calculate the expected terms for SARs for separate groups of retirement eligible and non-retirement eligible employees and non-employee directors. Our valuation model also uses historical data to estimate exercise behaviors, which includes determining the likelihood that employees will exercise their SARs before expiration at a certain multiple of stock price to exercise price. In recent years, non-employee directors have generally exercised grants in their last year of exercisability.
Other Information
As of the end of the 2015 third quarter, we had 24 million remaining shares authorized under the Stock Plan, including 6 million shares under the Stock Option Program and the SAR Program.