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Stock-Based Compensation
6 Months Ended
May 31, 2019
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Stock-Based Compensation
Stock-Based Compensation
Stock Options. We estimate the grant-date fair value of stock options using the Black-Scholes option-pricing model. The following table summarizes stock option transactions for the six months ended May 31, 2019:
 
Options
 
Weighted
Average Exercise
Price
Options outstanding at beginning of period
7,237,544

 
$
16.02

Granted

 

Exercised
(1,097,927
)
 
14.95

Cancelled
(30,000
)
 
38.24

Options outstanding at end of period
6,109,617

 
$
16.11

Options exercisable at end of period
5,820,743

 
$
16.10


As of May 31, 2019, the weighted average remaining contractual life of stock options outstanding and stock options exercisable was 3.9 years and 3.7 years, respectively. Total unrecognized compensation expense related to unvested stock option awards was nominal as of May 31, 2019 and is expected to be recognized over a weighted average period of 0.4 years. For the three months ended May 31, 2019, stock-based compensation expense was nominal compared to $.2 million for the three months ended May 31, 2018. For the six months ended May 31, 2019 and 2018, stock-based compensation expense associated with stock options totaled $.1 million and $.4 million, respectively. The aggregate intrinsic values of stock options outstanding and stock options exercisable were $66.7 million and $64.1 million, respectively, at May 31, 2019. (The intrinsic value of a stock option is the amount by which the market value of a share of the underlying common stock exceeds the exercise price of the stock option.)
Other Stock-Based Awards. From time to time, we grant restricted stock and PSUs to various employees as a compensation benefit. We recognized total compensation expense of $5.8 million and $4.8 million for the three months ended May 31, 2019 and 2018, respectively, related to restricted stock and PSUs. We recognized total compensation expense of $9.9 million and $8.4 million for the six months ended May 31, 2019 and 2018, respectively, related to restricted stock and PSUs.