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Equity-based Compensation (Tables) | 12 Months Ended
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Sep. 30, 2023
Share-Based Payment Arrangement [Abstract] |
Summary of Option Activity | The following tables summarize information about stock options to purchase the Company’s ordinary shares, restricted stock and restricted stock units, as well as changes during the fiscal year ended September 30, 2023: Stock Options:
|  | Number of Stock Options |  |  | Weighted Average Exercise Price |
Outstanding as of October 1, 2022 |  |  | 2,441 |  |  | $ | 62.66 |
Granted |  |  | — |  |  |  | — |
Exercised |  |  | (799 | ) |  |  | 60.91 |
Forfeited |  |  | (45 | ) |  |  | 67.05 |
Outstanding as of September 30, 2023 |  |  | 1,597 |  |  | $ | 63.41 |
Exercisable as of September 30, 2023 |  |  | 1,373 |  |  | $ | 62.55 |
As of September 30, 2023, the weighted average remaining contractual life of outstanding and exercisable stock options was 4.95 and 4.73 years, respectively. The total intrinsic value of stock options exercised during fiscal years 2023, 2022 and 2021 was $24,721, $33,096 and $27,023, respectively. The aggregate intrinsic value of outstanding and exercisable stock options as of September 30, 2023 was $33,662 and $30,120, respectively.
Summary of Restricted Stock and Restricted Stock Units Activity | Restricted Stock:
|  | Number of Restricted Stock |  |  | Weighted Average Grant Date Fair Value |
Outstanding as of October 1, 2022 |  |  | 1,774 |  |  | $ | 70.83 |
Granted |  |  | 1,082 |  |  |  | 83.05 |
Vested |  |  | (705 | ) |  |  | 69.96 |
Forfeited |  |  | (97 | ) |  |  | 76.86 |
Outstanding as of September 30, 2023 |  |  | 2,054 |  |  | $ | 77.28 |
The value of restricted stock vested during fiscal years 2023, 2022 and 2021 was $60,646, $40,615 and $25,400, respectively, based on the market value of the Company's common stock on the vest date. Restricted Stock Units:
|  | Number of Restricted Stock Units |  |  | Weighted Average Grant Date Fair Value |
Outstanding as of October 1, 2022 |  |  | 445 |  |  | $ | 71.50 |
Granted |  |  | 296 |  |  |  | 87.38 |
Vested |  |  | (146 | ) |  |  | 71.13 |
Forfeited |  |  | (35 | ) |  |  | 75.85 |
Outstanding as of September 30, 2023 |  |  | 560 |  |  | $ | 79.73 |
Employee Equity-Based Compensation Pre-Tax Expense | Employee equity-based compensation pre-tax expense, including grants of employee stock options, restricted stock, restricted stock units and ESPP for the years ended September 30, 2023, 2022 and 2021 was as follows:
|  | Year Ended September 30, |
|  | 2023 |  |  | 2022 |  |  | 2021 |
Cost of revenue |  | $ | 42,969 |  |  | $ | 32,096 |  |  | $ | 22,691 |
Research and development |  |  | 7,509 |  |  |  | 5,631 |  |  |  | 4,021 |
Selling, general and administrative |  |  | 39,220 |  |  |  | 34,080 |  |  |  | 27,537 |
Total |  | $ | 89,698 |  |  | $ | 71,807 |  |  | $ | 54,249 |
The income tax benefit related to equity-based compensation expense was $17,986, $15,066 and $8,479 for the years ended 2023, 2022 and 2021, respectively.
Assumptions Used in Calculating Fair Value of Options | The fair value of ESSP and fair value of stock options granted, estimated on the date of grant using the Black-Scholes pricing model, as described in Note 2, with the following weighted average assumptions: ESPP:
|  | Year Ended September 30*, |  |
|  | 2023 |  |
Risk-free interest rate(1) |  |  | 5.46 | % |
Expected life of ESPP (2) |  |  | 0.50 |  |
Expected volatility(3) |  |  | 18.4 | % |
Expected dividend yield(4) |  |  | 1.84 | % |
Fair value per ESPP |  | $ | 19.35 |  |
Stock Options:
|  | Year Ended September 30**, |  |
|  | 2021 |  |
Risk-free interest rate(1) |  |  | 0.30 | % |
Expected life of stock options(2) |  |  | 4.50 |  |
Expected volatility(3) |  |  | 21.3 | % |
Expected dividend yield(4) |  |  | 2.22 | % |
Fair value per option |  | $ | 7.82 |  |
* The ESPP was commenced in fiscal year 2023. ** There were no stock options grants during fiscal years 2023 and 2022, and the above stock option weighted average assumptions were applicable when calculating the fair value of options granted in fiscal year 2021. (1) Risk-free interest rate is based upon U.S. Treasury yield curve appropriate for the term of the Company’s employee stock options and ESPP. (2) Expected life of stock options is based upon historical experience. Expected life of ESPP is based upon the purchase period. (3) Expected volatility is based on blended volatility. (4) Expected dividend yield is based on the Company’s history and future expectation of dividend payouts.

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- Definition Tabular disclosure of the significant assumptions used during the year to estimate the fair value of stock options, including, but not limited to: (a) expected term of share options and similar instruments, (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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- Definition Disclosure of the number and weighted-average grant date fair value for restricted stock and restricted stock units that were outstanding at the beginning and end of the year, and the number of restricted stock and restricted stock units that were granted, vested, or forfeited during the year. + References No definition available. + Details
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