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Supplemental Guarantor Condensed Consolidating Financial Statements (Cash Flows) (Details) - USD ($)
$ in Millions
9 Months Ended
May 31, 2019
May 31, 2018
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by operating activities $ 312.0 $ 299.7
Cash flows from investing activities:    
Purchases of property, plant, and equipment (39.8) (32.2)
Investments in subsidiaries   0.0
Acquisitions of business, net of cash acquired 0.0 (163.5)
Other investing activities 2.9 1.0
Net cash used for investing activities (36.9) (194.7)
Cash flows from financing activities:    
Borrowings on credit facility 86.5 237.3
Repayments of borrowings on credit facility (86.5) (236.1)
Repayments of long-term debt (0.3) (0.3)
Proceeds from stock option exercises and other 0.5 1.6
Repurchases of common stock (48.7) (298.4)
Withholding taxes on net settlement of equity awards (4.9) (7.2)
Intercompany Capital   0.0
Dividends paid (15.6) (16.2)
Net cash used for financing activities (69.0) (319.3)
Effect of exchange rates changes on cash (1.5) (2.5)
Net change in cash and cash equivalents 204.6 (216.8)
Cash and cash equivalents at beginning of period 129.1 311.1
Cash and cash equivalents at end of period 333.7 94.3
Parent    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by operating activities 245.0 252.6
Cash flows from investing activities:    
Purchases of property, plant, and equipment 0.0 0.0
Investments in subsidiaries   (163.5)
Acquisitions of business, net of cash acquired   0.0
Other investing activities 0.8 1.0
Net cash used for investing activities 0.8 (162.5)
Cash flows from financing activities:    
Borrowings on credit facility 0.0 0.0
Repayments of borrowings on credit facility 0.0 0.0
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.5 1.6
Repurchases of common stock (48.7) (298.4)
Withholding taxes on net settlement of equity awards (4.9) (7.2)
Intercompany Capital   0.0
Dividends paid (15.6) (16.2)
Net cash used for financing activities (68.7) (320.2)
Effect of exchange rates changes on cash 0.2 0.0
Net change in cash and cash equivalents 177.3 (230.1)
Cash and cash equivalents at beginning of period 80.5 237.7
Cash and cash equivalents at end of period 257.8 7.6
Subsidiary Issuer    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by operating activities 48.4 19.1
Cash flows from investing activities:    
Purchases of property, plant, and equipment (33.0) (21.9)
Investments in subsidiaries   0.0
Acquisitions of business, net of cash acquired   (136.6)
Other investing activities 2.1 0.0
Net cash used for investing activities (30.9) (158.5)
Cash flows from financing activities:    
Borrowings on credit facility 86.5 237.3
Repayments of borrowings on credit facility (86.5) (236.1)
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0
Intercompany Capital   136.6
Dividends paid 0.0 0.0
Net cash used for financing activities 0.0 137.8
Effect of exchange rates changes on cash (0.3) 1.6
Net change in cash and cash equivalents 17.2 0.0
Cash and cash equivalents at beginning of period 0.0 0.0
Cash and cash equivalents at end of period 17.2 0.0
Subsidiary Guarantor    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by operating activities 0.0 0.0
Cash flows from investing activities:    
Purchases of property, plant, and equipment 0.0 0.0
Investments in subsidiaries   0.0
Acquisitions of business, net of cash acquired   0.0
Other investing activities 0.0 0.0
Net cash used for investing activities 0.0 0.0
Cash flows from financing activities:    
Borrowings on credit facility 0.0 0.0
Repayments of borrowings on credit facility 0.0 0.0
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0
Intercompany Capital   0.0
Dividends paid 0.0 0.0
Net cash used for financing activities 0.0 0.0
Effect of exchange rates changes on cash 0.0 0.0
Net change in cash and cash equivalents 0.0 0.0
Cash and cash equivalents at beginning of period 0.0 0.0
Cash and cash equivalents at end of period 0.0 0.0
Non- Guarantors    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by operating activities 18.6 28.0
Cash flows from investing activities:    
Purchases of property, plant, and equipment (6.8) (10.3)
Investments in subsidiaries   0.0
Acquisitions of business, net of cash acquired   (26.9)
Other investing activities 0.0 0.0
Net cash used for investing activities (6.8) (37.2)
Cash flows from financing activities:    
Borrowings on credit facility 0.0 0.0
Repayments of borrowings on credit facility 0.0 0.0
Repayments of long-term debt (0.3) (0.3)
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0
Intercompany Capital   26.9
Dividends paid 0.0 0.0
Net cash used for financing activities (0.3) 26.6
Effect of exchange rates changes on cash (1.4) (4.1)
Net change in cash and cash equivalents 10.1 13.3
Cash and cash equivalents at beginning of period 48.6 73.4
Cash and cash equivalents at end of period 58.7 86.7
Consolidating Adjustments    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by operating activities 0.0 0.0
Cash flows from investing activities:    
Purchases of property, plant, and equipment 0.0 0.0
Investments in subsidiaries   163.5
Acquisitions of business, net of cash acquired   0.0
Other investing activities 0.0 0.0
Net cash used for investing activities 0.0 163.5
Cash flows from financing activities:    
Borrowings on credit facility 0.0 0.0
Repayments of borrowings on credit facility 0.0 0.0
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0
Intercompany Capital   (163.5)
Dividends paid 0.0 0.0
Net cash used for financing activities 0.0 (163.5)
Effect of exchange rates changes on cash 0.0 0.0
Net change in cash and cash equivalents 0.0 0.0
Cash and cash equivalents at beginning of period 0.0 0.0
Cash and cash equivalents at end of period $ 0.0 $ 0.0