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Stock-Based Employee Benefit Plans - Assumptions Used to Estimate Fair Value of Stock Options (Details) | 12 Months Ended
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Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Weighted average volatility |  |  |
Equity Option [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Weighted average expected term (years) | 4 years 5 months 4 days | 4 years 5 months 19 days | 4 years 5 months 15 days
Expected volatility (range), minimum | 32.90% | 33.60% | 30.00%
Expected volatility (range), maximum | 34.10% | 34.40% | 35.90%
Weighted average volatility | 33.20% | 33.90% | 30.60%
Risk free interest rate, minimum | 1.18% | 0.29% | 0.36%
Risk free interest rate, maximum | 2.85% | 0.73% | 1.68%
Weighted average expected dividend yield | 0.00% | 0.00% | 0.00%

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- Definition The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(iii) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition The estimated measure of the maximum percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period. + References No definition available. + Details
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- Definition The estimated measure of the minimum percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period. + References No definition available. + Details
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- Definition The maximum risk-free interest rate assumption that is used in valuing an option on its own shares. + References No definition available. + Details
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- Definition The minimum risk-free interest rate assumption that is used in valuing an option on its own shares. + References No definition available. + Details
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- Definition Rate of weighted-average expected volatility for award under share-based payment arrangement. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(ii) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
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- Definition Expected term of award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(i) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 14.D.2) -URI http://asc.fasb.org/extlink&oid=122041274&loc=d3e301413-122809 + Details
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