Stock-Based Compensation (Tables)

6 Months Ended

Apr. 30, 2023

Share-Based Payment Arrangement [Abstract]

The compensation cost recognized in the condensed consolidated statements of income for our stock compensation arrangements was as follows:


	Three Months Ended April 30,				Six Months Ended April 30,
	2023		2022		2023		2022
	(in thousands)
Cost of products	$	16,895	$	13,078	$	32,924	$	24,285
Cost of maintenance and service	7,531		5,893		14,686		10,476
Research and development expense	75,355		58,109		144,586		107,649
Sales and marketing expense	26,937		19,291		51,844		37,092
General and administrative expense	16,540		13,690		33,445		26,330
Stock-based compensation expense before taxes	143,258		110,061		277,485		205,832
Income tax benefit	(23,193)		(17,852)		(44,925)		(33,386)
Stock-based compensation expense after taxes	$	120,065	$	92,209	$	232,560	$	172,446

Schedule of Share-Based Payment Award, Restricted Stock Units, Valuation Assumptions

The grant date fair value of the market-based RSUs and the assumptions used in the Monte Carlo simulation model to determine the grant date fair value during the periods were as follows:


	Three Months Ended April 30,						Six Months Ended April 30,
	2023			2022			2023	2022
Expected life (in years)	2.70 years			1.69 years			0.90 years - 2.70 years	1.69 years
Risk-free interest rate	4.36		%	1.33		%	4.36% - 4.63%	1.33		%
Volatility	35.84		%	33.01		%	35.84% - 42.86%	33.01		%
Grant date fair value	$	357.29		$	280.82		$357.29 - $408.55	$	280.82

Schedule of Intrinsic Value of Equity Awards Exercised

The intrinsic values of equity awards exercised during the periods were as follows:


	Three Months Ended April 30,				Six Months Ended April 30,
	2023		2022		2023		2022
	(in thousands)
Intrinsic value of awards exercised	$	63,447	$	46,464	$	118,223	$	159,389