Shared-Based Compensation (Tables)

12 Months Ended

Aug. 31, 2024

Share-Based Payment Arrangement [Abstract]

Schedule of Share-Based Compensation Expense

The following table summarizes share-based compensation expense for fiscal 2024, 2023, and 2022:

	For the years ended August 31,
($ in thousands)	2024			2023			2022
Share-based compensation expense included in cost of    operating revenues	$	183		$	183		$	257
Engineering and research		190			232			210
Selling		650			632			577
General and administrative		5,473			5,651			4,637
Share-based compensation expense included in    operating expenses		6,313			6,515			5,424
Total share-based compensation expense		6,496			6,698			5,681
Tax benefit		(1,527	)		(1,574	)		(1,335	)
Share-based compensation expense, net of tax	$	4,969		$	5,124		$	4,346

Schedule of Assumptions Used

The table below shows the annual weighted average assumptions used for valuation purposes.

	Grant year
	Fiscal 2024			Fiscal 2023			Fiscal 2022
Risk-free interest rate		4.8	%		4.4	%		1.2	%
Dividend yield		1.2	%		0.9	%		0.9	%
Expected life (years)		5			5			5
Volatility		37.8	%		35.7	%		33.8	%
Weighted average grant-date fair value of options granted	$	44.22		$	55.53		$	41.80

Summary of Stock Option Activity

The following table summarizes stock option activity for fiscal 2024:

	Number of stock options			Average exercise price		Average remaining contractual term (years)		Aggregate intrinsic value (thousands)
Stock options outstanding at August 31, 2023		118,470		$	115.96		6.6	$	2,139
Granted		31,199			120.54
Exercised		(5,217	)		91.87				217
Forfeited/cancelled		(2,276	)		141.58				6
Stock options outstanding at August 31, 2024		142,176		$	117.44		6.4	$	2,075
Stock options exercisable at August 31, 2024		90,964		$	108.34		5.1	$	1,968

Summary of Share Based Compensation Additional Information

Additional information regarding stock option exercises is summarized in the table below.

	For the years ended August 31,
($ in thousands, except fair value amounts)	2024		2023		2022
Intrinsic value of stock options exercised	$	217	$	23	$	1,737
Cash received from stock option exercises	$	479	$	32	$	2,894
Tax benefit realized from stock option exercises	$	18	$	1	$	140
Weighted average grant-date fair value of stock options vested	$	27.14	$	40.66	$	34.19

Summary of Restricted Stock Unit Activity

The following table summarizes restricted stock unit activity for fiscal 2024:

	Number of  restricted stock units			Weighted average grant- date fair value
Restricted stock units outstanding at August 31, 2023		41,572		$	108.54
Granted		33,558			119.85
Vested		(20,072	)		137.91
Forfeited / Cancelled		(2,477	)		131.95
Restricted stock units outstanding at August 31, 2024		52,581		$	131.12

Schedule of Performance Stock Unit Activity

The table below summarizes performance stock unit activity for fiscal 2024:

	Number of performance stock units			Weighted average grant- date fair value
Performance stock units outstanding at August 31, 2023		37,510		$	151.67
Granted		21,248			141.63
Vested		(10,892	)		127.16
Forfeited / cancelled		(1,444	)		154.48
Performance stock units outstanding at August 31, 2024		46,422		$	152.67

Schedule of Assumptions Used to Estimate Fair Value of TSR Portion of Awards Granted

The fair value of the TSR portion of the awards granted in fiscal 2024, 2023, and 2022 was estimated at the grant date using a Monte Carlo simulation model which included the following assumptions:

	Grant year
	Fiscal 2024			Fiscal 2023			Fiscal 2022
Expected term (years)		3			3			3
Risk-free interest rate		4.9	%		4.5	%		0.7	%
Volatility		34.6	%		38.6	%		39.1	%
Dividend yield		1.2	%		0.9	%		0.9	%