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Stock-Based Compensation (Tables) | 12 Months Ended
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Sep. 30, 2023
Disclosure of Compensation Related Costs, Share-based Payments [Abstract] |
Summary of stock-based compensation expense | The following table reflects stock-based compensation expense recorded during the fiscal years ended September 30, 2023, 2022 and 2021 (in thousands):
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Year Ended September 30,
​ |  | 2023 |  | 2022 |  | 2021
Restricted stock units | ​ | $ | 8,027 | ​ | $ | 10,597 | ​ | $ | 18,923
Employee stock purchase plan | ​ |  | 1,349 | ​ |  | 1,846 | ​ |  | 1,128
Total stock-based compensation expense for continuing and discontinued operations | ​ | $ | 9,376 | ​ | $ | 12,443 | ​ | $ | 20,051
Income tax benefit | ​ | ​ | (1,406) | ​ | ​ | (1,929) | ​ | ​ | (3,208)
Total compensation expense included in the statement of operations | ​ | ​ | 7,970 | ​ | ​ | 10,514 | ​ | ​ | 16,843
Summary of restricted stock unit activity | The following table summarizes restricted stock unit activity for the fiscal year ended September 30, 2023 (in thousands, except for weighted average grant-date fair value):
​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted
​ | ​ | ​ | ​ | Average
​ | ​ | ​ | ​ | Grant-Date
​ | ​ | Shares | ​ | Fair Value
Outstanding as of September 30, 2022 |  | 538,238 | ​ | $ | 71.99
Granted |  | 590,066 | ​ | $ | 57.22
Vested |  | (267,834) | ​ | $ | 55.86
Forfeited |  | (141,516) | ​ | $ | 72.04
Outstanding as of September 30, 2023 |  | 718,954 | ​ | $ | 67.40
Restricted stock units granted with performance goals may also have a required service period following the achievement of all or a portion of the performance goals. The following table reflects restricted stock units and stock awards granted during fiscal years ended September 30, 2023, 2022 and 2021 (in thousands):
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Year Ended September 30,
​ |  | 2023 |  | 2022 |  | 2021
Time-based restricted stock units | ​ | 311,609 | ​ | 120,066 | ​ | 166,570
Common stock awards |  | — |  | 18,471 |  | 14,713
Performance-based restricted stock units |  | 278,457 |  | 111,148 |  | 168,647
Total units |  | 590,066 |  | 249,685 |  | 349,930
Summary of valuation assumptions for an employee stock purchase plan | The fair value of shares issued under the employee stock purchase plan is estimated on the commencement date of each offering period using the Black-Scholes option-pricing model with the following weighted average assumptions for the fiscal years ended September 30, 2023, 2022 and 2021:
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Year Ended September 30, |
​ |  | 2023 |  | 2022 |  | 2021 |
Risk-free interest rate |  | 5.2 | % | 1.7 | % | 0.3 | %
Volatility |  | 57 | % | 49 | % | 53 | %
Expected life |  | 6 months |  | 6 months |  | 6 months |
Dividend yield |  | — | % | — | % | 0.6 | %

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- Definition Tabular disclosure of cost recognized for award under share-based payment arrangement by plan. Includes, but is not limited to, related tax benefit. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + Details
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- Definition Tabular disclosure of the number and weighted-average grant date fair value for restricted stock units that were outstanding at the beginning and end of the year, and the number of restricted stock units that were granted, vested, or forfeited during the year. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(1) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + Details
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- Definition Tabular disclosure of the significant assumptions used during the year to estimate the fair value of employee stock purchase plans, including, but not limited to: (a) expected term, (b) expected volatility of the entity's shares, (c) expected dividends, (d) risk-free rate(s), and (e) discount for post-vesting restrictions. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 718 -SubTopic 10 -Subparagraph (f)(2) -Name Accounting Standards Codification -Paragraph 2 -Section 50 -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + Details
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