In the first quarter of fiscal year 2017, the Board terminated the Company’s prior stock repurchase program and replaced it with a new program for the repurchase of up to $500,000 of Woodward’s outstanding shares of common stock on the open market or in privately negotiated transactions over a three year period that ended in November 2019 (the “2017 Authorization”). Effective upon the expiration of the 2017 Authorization in November 2019, the Board approved a new program for the repurchase of up to $500,000 of Woodward’s outstanding shares of common stock on the open market or in privately negotiated transactions over a three year period that will end in 2022 (the “2019 Authorization”). In the first half of fiscal year 2021, Woodward purchased no shares of its common stock under the 2019 Authorization. Woodward repurchased 124 shares of common stock for $13,346 under the 2019 Authorization in the first half of fiscal year 2020.

Provisions governing outstanding stock option awards are included in the 2017 Omnibus Incentive Plan, as amended from time to time (the “2017 Plan”) and the 2006 Omnibus Incentive Plan (the “2006 Plan”), as applicable.

The 2017 Plan was approved by Woodward’s stockholders in January 2017 and is a successor plan to the 2006 Plan. As of September 14, 2016, the effective date of the 2017 Plan, the Board delegated authority to administer the 2017 Plan to the compensation committee of the Board (the “Committee”), including, but not limited to, the power to determine the recipients of awards and the terms of those awards. On January 29, 2020 and January 27, 2021, Woodward’s stockholders approved an additional 1,000 and 1,500 shares, respectively, of Woodward’s common stock to be made available for future grants. Under the 2017 Plan, there were approximately 2,692 shares of Woodward’s common stock available for future grants as of March 31, 2021 and 1,972 shares as of September 30, 2020.

Woodward believes that stock options align the interests of its employees and directors with the interests of its stockholders. Stock option awards are granted with an exercise price equal to the market price of Woodward’s stock at the date the grants are awarded, a ten year term, and generally have a four year vesting schedule at a rate of 25% per year.

The fair value of options granted is estimated as of the grant date using the Black-Scholes-Merton option-valuation model using the assumptions in the following table. Woodward calculates the expected term, which represents the average period of time that stock options granted are expected to be outstanding, based upon historical experience of plan participants. Expected volatility is based on historical volatility using daily stock price observations. The estimated dividend yield is based upon Woodward’s historical dividend practice and the market value of its common stock. The risk-free rate is based on the U.S. treasury yield curve, for periods within the contractual life of the stock option, at the time of grant.

		Three-Months Ended								Six-Months Ended
		March 31,								March 31,
		2021					2020		2021				2020
Weighted-average exercise price per share	$	122.88					$	127.84	$	82.46			$	104.91
Weighted-average grant date market value of Woodward stock	$	122.88					$	127.84	$	82.46			$	104.91
Expected term (years)			6.5	-		8.7		6.5		6.5	-	8.7		6.4	-	8.7
Estimated volatility		33.9%		-	36.2%			25.7%		33.3%	-	36.2%		25.7%	-	30.1%
Estimated dividend yield		0.5%		-	0.6%		0.9%			0.3%	-	0.6%		0.6%	-	0.9%
Risk-free interest rate		0.6%		-	1.1%			1.7%		0.4%	-	1.1%		1.6%	-	1.7%

The following is a summary of the activity for stock option awards during the three and six-months ended March 31, 2021:

	Three-Months Ended					Six-Months Ended
	March 31, 2021					March 31, 2021
	Number of options			Weighted-Average Exercise Price per Share		Number of options			Weighted-Average Exercise Price per Share
Options, beginning balance		5,901		$	65.47		5,443		$	62.00
Options granted		26			122.88		773			82.46
Options exercised		(410	)		41.71		(696	)		40.93
Options forfeited		—			—		(3	)		87.38
Options, ending balance		5,517			67.50		5,517			67.50

Changes in non-vested stock options during the three and six-months ended March 31, 2021 were as follows:

	Three-Months Ended					Six-Months Ended
	March 31, 2021					March 31, 2021
	Number of options			Weighted-Average Grant Date Fair Value per Share		Number of options			Weighted-Average Grant Date Fair Value Per Share
Non-vested options outstanding, beginning balance		2,170		$	25.40		2,078		$	24.69
Options granted		26			42.45		773			28.22
Options vested		(90	)		20.66		(742	)		25.19
Options forfeited		—			—		(3	)		25.18
Non-vested options outstanding, ending balance		2,106			25.81		2,106			25.81

Information about stock options that have vested, or are expected to vest, and are exercisable at March 31, 2021 was as follows:

	Number of options		Weighted-Average Exercise Price		Weighted-Average Remaining Life in Years		Aggregate Intrinsic Value
Options outstanding		5,517	$	67.50		6.4	$	293,200
Options vested and exercisable		3,423		58.05		5.1		214,223
Options vested and expected to vest		5,425		67.25		6.4		289,632

Woodward recognizes stock-based compensation expense on a straight-line basis over the requisite service period. Pursuant to form stock option agreements used by the Company, with terms approved by the administrator of the applicable plan, the requisite service period can be less than the four year vesting period based on grantee’s retirement eligibility. As such, the recognition of stock-based compensation expense associated with some stock option grants can be accelerated to a period of less than four years, including immediate recognition of stock-based compensation expense on the date of grant.

At March 31, 2021, there was approximately $15,693 of total unrecognized compensation expense related to non-vested stock-based compensation arrangements, including both stock options and restricted stock awards. The pre-vesting forfeiture rates for purposes of determining stock-based compensation expense recognized were estimated to be 0% for members of the Board and 7.3% for all others. The remaining unrecognized compensation cost is expected to be recognized over a weighted-average period of approximately 2.1 years.