Share-based compensation is designed to reward employees for their long-term contributions to the Company and provide incentives for them to remain with the Company. The number and frequency of share grants are based on competitive practices, operating results of the Company, and individual performance. As of August 31, 2023, the Company’s share-based compensation plan was the 2015 Long-Term Incentive Plan (the “2015 Plan”). The 2015 Plan was approved by the shareholders of the Company, and became effective on January 26, 2015, and replaced the Company’s 2010 Long Term Incentive Plan. At August 31, 2023, the Company had share-based awards outstanding under the 2015 Plan.

The 2015 Plan provides for awards of stock options, restricted shares, restricted stock units, stock appreciation rights, performance shares and performance stock units to employees and non-employee directors of the Company. The maximum number of shares as to which stock awards may be granted under the 2015 Plan is 626,968 shares, exclusive of any forfeitures from the 2010 Long-Term Incentive Plan. At August 31, 2023, 217,146 shares of common stock (including forfeitures from prior plans) remained available for issuance under the 2015 Plan. All stock awards will be counted against the 2015 Plan in a 1 to 1 ratio. The 2015 Plan also limits the total awards that may be made to any individual.

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

As of August 31, 2023, there was $8.2 million pre-tax of total unrecognized compensation cost related to non-vested share-based compensation arrangements which is expected to be recognized over a weighted average period of 1.8 years.

Stock Options – Stock option awards have an exercise price equal to the closing price on the date of grant, expire no later than ten years from the date of grant and vest evenly over a three or four year period. The fair value of stock option awards is estimated using the Black-Scholes option pricing model. 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

The risk-free rate is based on the U.S. Treasury yield curve in effect at the time of grant; the dividend yield is calculated as the ratio of dividends paid per share of common stock to the stock price on the date of grant; the expected life is based on historical and expected exercise behavior; and volatility is based on the historical volatility of the Company’s stock price over the expected life of the option.

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

There were 19,617, 47,222, and 38,954 outstanding stock options that vested during fiscal 2023, 2022, and 2021, respectively. 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

Restricted stock units – The restricted stock units have a grant-date fair value equal to the fair market value of the underlying stock on the grant date less present value of expected dividends. The restricted stock units granted to employees vest over a three year period at approximately 33 percent per year. The restricted stock units granted to non-employee directors generally vest over a nine month period.

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

Restricted stock units are generally settled with the issuance of shares with the exception of certain restricted stock units awarded to internationally-based employees that are settled in cash. At August 31, 2023, 2022, and 2021, outstanding restricted stock units included 4,039, 4,412, and 4,656 units, respectively, that will be settled in cash. The fair value of restricted stock units that vested during the period was $3.7 million and $4.1 million for each of the years ended August 31, 2023 and 2022, respectively. Share issuances are presented net of share repurchases to cover payroll taxes of $2.5 million, $1.2 million, and $1.3 million for each of the years ended August 31, 2023, 2022, and 2021, respectively.

Performance stock units – The performance stock units have a grant-date fair value equal to the fair market value of the underlying stock on the grant date less present value of expected dividends. The performance stock units granted to employees cliff vest after a three year period and a specified number of shares of common stock will be awarded under the terms of the performance stock units, if performance measures relating to revenue growth and a return on net assets are achieved.

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

Performance stock units outstanding as of August 31, 2023 and issued during fiscal 2023, 2022, and 2021 include performance goals based on a return on invested capital and total shareholder return ("TSR") relative to the Company’s peers during the performance period. The awards actually earned will range from zero to two hundred percent of the targeted number of performance stock units and will be paid in shares of common stock. Shares earned will be distributed upon vesting on the first day of November following the end of the three-year performance period. For the return on invested capital portion of the award, the Company is accruing compensation expense based on the estimated number of shares expected to be issued utilizing the most current information available to the Company at the date of the financial statements. For the TSR portion of the award, compensation expense is recorded ratably over the three-year term of the award based on the estimated grant date fair value. In fiscal 2023 and 2022 performance stock units that vested represented 18,688 and 18,998, respectively, actual shares of common stock issued. In fiscal 2021, no shares were issued related to performance stock units.

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	%