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Shared-Based Compensation (Tables)

12 Months Ended

Aug. 31, 2023

Share-Based Payment Arrangement [Abstract]

Schedule of Share-Based Compensation Expense

The following table summarizes share-based compensation expense for fiscal 2023, 2022, and 2021:

		For the years ended August 31,
($ in thousands)		2023				2022				2021
Share-based compensation expense included in cost of    operating revenues		$	183			$	257			$	258
Engineering and research			232				210				202
Selling			632				577				544
General and administrative			5,651				4,637				5,524
Share-based compensation expense included in    operating expenses			6,515				5,424				6,270
Total share-based compensation expense			6,698				5,681				6,528
Tax benefit			(1,574	)			(1,335	)			(1,534	)
Share-based compensation expense, net of tax		$	5,124			$	4,346			$	4,994

Schedule of Assumptions Used

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

		Grant year
		Fiscal 2023				Fiscal 2022				Fiscal 2021
Risk-free interest rate			4.4	%			1.2	%			0.5	%
Dividend yield			0.9	%			0.9	%			1.1	%
Expected life (years)			5				5				6
Volatility			35.7	%			33.8	%			32.8	%
Weighted average grant-date fair value of options granted		$	55.53			$	41.80			$	31.38

Summary of Stock Option Activity

The following table summarizes stock option activity for fiscal 2023:

		Number of stock options				Average exercise price				Average remaining contractual term (years)				Aggregate intrinsic value (thousands)
Stock options outstanding at August 31, 2022			97,140			$	106.80				7.0			$	5,203
Granted			21,743				156.16
Exercised			(413	)			76.37								23
Forfeited/cancelled			—				—								—
Stock options outstanding at August 31, 2023			118,470			$	115.96				6.6			$	2,139
Stock options exercisable at August 31, 2023			76,143			$	99.05				5.5			$	2,072

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)		2023				2022				2021
Intrinsic value of stock options exercised		$	23			$	1,737			$	2,125
Cash received from stock option exercises		$	32			$	2,894			$	3,965
Tax benefit realized from stock option exercises		$	1			$	140			$	499
Weighted average grant-date fair value of stock options vested		$	40.66			$	34.19			$	25.95

Summary of Restricted Stock Unit Activity

The following table summarizes restricted stock unit activity for fiscal 2023:

		Number of  restricted stock units				Weighted average grant- date fair value
Restricted stock units outstanding at August 31, 2022			44,251			$	126.50
Granted			24,123				151.38
Vested			(24,342	)			122.06
Forfeited / Cancelled			(2,460	)			140.26
Restricted stock units outstanding at August 31, 2023			41,572			$	108.54

Schedule of Performance Stock Unit Activity

The table below summarizes performance stock unit activity for fiscal 2023:

		Number of performance stock units				Weighted average grant- date fair value
Performance stock units outstanding at August 31, 2022			32,358			$	127.78
Granted			14,496				173.17
Vested			(9,344	)			102.28
Forfeited / cancelled			—				—
Performance stock units outstanding at August 31, 2023			37,510			$	151.67

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 2023, 2022, and 2021 was estimated at the grant date using a Monte Carlo simulation model which included the following assumptions:

		Grant year
		Fiscal 2023				Fiscal 2022				Fiscal 2021
Expected term (years)			3				3				3
Risk-free interest rate			4.5	%			0.7	%			0.2	%
Volatility			38.6	%			39.1	%			38.6	%
Dividend yield			0.9	%			0.9	%			1.2	%

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