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Changes in Stockholders' Equity (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
3 Months Ended 6 Months Ended
Feb. 28, 2019
Nov. 30, 2018
Feb. 28, 2018
Nov. 30, 2017
Feb. 28, 2019
Feb. 28, 2018
Sep. 01, 2018
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Beginning balance $ 1,750.9 $ 1,716.8 $ 1,726.1 $ 1,665.6 $ 1,716.8 $ 1,665.6  
Net income 66.3 79.6 96.9 71.5 145.9 168.4  
Other comprehensive loss 6.3 (6.2) 4.3 (8.9)      
Amortization, issuance, and cancellations of restricted stock grants 7.1 3.8 7.6 2.6      
Employee stock purchase plan issuances 0.2 0.1 0.1 0.2      
Cash dividends of $0.13 per share paid on common stock (5.3) (5.2) (5.4) (5.5)      
Stock options exercised     0.5 0.6      
Repurchases of common stock (23.7) (25.0) (194.3)        
Ending balance $ 1,801.8 $ 1,750.9 $ 1,635.8 $ 1,726.1 1,801.8 1,635.8  
Cash dividends paid (usd per share) $ 0.13 $ 0.13 $ 0.13 $ 0.13      
Common Stock Outstanding              
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Beginning balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5  
Beginning balance (shares) 39.9 40.0 41.9 41.8 40.0 41.8  
Amortization, issuance, and cancellations of restricted stock grants (shares) 0.0 0.1 0.1 0.1      
Repurchases of common stock (shares) (0.2) (0.2) (1.2)        
Ending balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5  
Ending balance (shares) 39.7 39.9 40.8 41.9 39.7 40.8  
Paid-in Capital              
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Beginning balance $ 910.2 $ 906.3 $ 884.3 $ 881.0 $ 906.3 $ 881.0  
Amortization, issuance, and cancellations of restricted stock grants 7.1 3.8 7.6 2.5      
Employee stock purchase plan issuances 0.2 0.1 0.1 0.2      
Stock options exercised     0.5 0.6      
Ending balance 917.5 910.2 892.5 884.3 917.5 892.5  
Retained Earnings              
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Beginning balance 2,060.6 1,999.2 1,725.9 1,659.9 1,999.2 1,659.9  
Net income 66.3 79.6 96.9 71.5      
Cash dividends of $0.13 per share paid on common stock (5.3) (5.2) (5.4) (5.5)      
Ending balance 2,121.6 2,060.6 1,828.5 1,725.9 2,121.6 1,828.5  
Accumulated Other Comprehensive Loss              
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Beginning balance (121.0) (114.8) (108.6) (99.7) (114.8) (99.7)  
Other comprehensive loss 6.3 (6.2) 4.3 (8.9) 0.1 (4.6)  
Reclassification of stranded tax effects of the TCJA     (11.1)     (11.1)  
Ending balance (114.7) (121.0) (115.4) (108.6) (114.7) (115.4)  
Treasury Stock, at cost              
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Beginning balance (1,099.4) (1,074.4) (776.0) (776.1) (1,074.4) (776.1)  
Amortization, issuance, and cancellations of restricted stock grants       0.1      
Repurchases of common stock (23.7) (25.0) (194.3)        
Ending balance $ (1,123.1) $ (1,099.4) (970.3) $ (776.0) $ (1,123.1) $ (970.3)  
ASC 606              
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Reclassification of stranded tax effects of the TCJA     0.0        
ASC 606 adjustments and Reclassification of stranded tax effects of the TCJA             $ (13.0)
ASC 606 | Retained Earnings              
Increase (Decrease) in Stockholders' Equity [Roll Forward]              
Reclassification of stranded tax effects of the TCJA     $ 11.1        
ASC 606 adjustments and Reclassification of stranded tax effects of the TCJA             $ (13.0)