The Company issues stock options, restricted stock units, and restricted shares as part of its stock incentive plans for employees and non-employee directors. Stock-based compensation expense for fiscal years 2021, 2020, and 2019, was $24.7 million, $22.5 million, and $19.7 million, respectively. The Company recognizes stock-based compensation expense ratably over the vesting period or the individual's retirement eligibility date.

At October 31, 2021, there was $19.3 million of total unrecognized compensation expense from stock-based compensation arrangements granted under the plans. This compensation is expected to be recognized over a weighted-average period of approximately 1.4 years. During fiscal years 2021, 2020, and 2019, cash received from stock option exercises was $45.9 million, $81.8 million, and $59.9 million, respectively.

Shares issued for option exercises, restricted stock units, and restricted shares may be either authorized but unissued shares or shares of treasury stock. The number of shares available for future grants was 12.5 million at October 31, 2021, 13.7 million at October 25, 2020, and 14.9 million at October 27, 2019.

Stock Options: The Company’s policy is to grant options with the exercise price equal to the market price of the common stock on the date of grant. Options typically vest over four years and expire ten years after the date of the grant.

Effective with fiscal 2020 grants, the Company has determined the equity award value for eligible employees will be delivered 50 percent in stock options as described above and 50 percent in restricted stock units with a three-year cliff vesting period.


	Shares (in thousands)	Weighted-Average Exercise Price		Weighted-Average Remaining Contractual Term (Years)	Aggregate Intrinsic Value (in thousands)
Stock Options Outstanding at October 25, 2020	21,073	$	30.39
Granted	1,277	47.45
Exercised	(3,050)	17.61
Forfeited	(277)	37.23
Expired	(1)	36.25
Stock Options Outstanding at October 31, 2021	19,022	$	33.49	4.9	$	182,432
Stock Options Exercisable at October 31, 2021	13,047	$	29.91	3.8	$	164,766

The weighted-average grant date fair value of stock options granted and the total intrinsic value of options exercised during each of the past three fiscal years, are:


	Fiscal Year Ended
	October 31,		October 25,		October 27,
(in thousands, except per share amounts)	2021		2020		2019
Weighted-average Grant Date Fair Value	$	7.52	$	7.71	$	9.24
Intrinsic Value of Exercised Options	94,108		182,821		138,282

The fair value of each option award is calculated on the date of grant using the Black-Scholes valuation model utilizing the following weighted-average assumptions:


	Fiscal Year Ended
	October 31,		October 25,		October 27,
	2021		2020		2019
Risk-free Interest Rate	1.0	%	1.7	%	2.8	%
Dividend Yield	2.1	%	2.0	%	1.9	%
Stock Price Volatility	20.0	%	19.0	%	19.0	%
Expected Option Life	7.4 years		7.5 years		8.0 years

As part of the annual valuation process, the Company reassesses the appropriateness of the inputs used in the valuation models. The Company establishes the risk-free interest rate using U.S. Treasury yields as of the grant date. The dividend yield is based on the dividend rate approved by the Company’s Board of Directors and the stock price on the grant date. The expected volatility assumption is based primarily on historical volatility. The expected life assumption is based on an analysis of past exercise behavior by option holders. In performing the valuations for option grants, the Company has not stratified option holders as exercise behavior has historically been consistent across all employees.

Restricted Stock Units: Restricted stock units are valued equal to the market price of the common stock on the date of the grant and generally vest after three years. These awards accumulate dividend equivalents, which are provided as additional units and are subject to the same vesting requirements as the underlying grant. A reconciliation of the restricted stock units as of October 31, 2021, is:


	Shares (in thousands)	Weighted- Average Grant Date Fair Value		Weighted-Average Remaining Contractual Term (Years)	Aggregate Intrinsic Value (in thousands)
Restricted Stock Units Outstanding at October 25, 2020	188	$	45.91
Granted	225	47.52
Dividend Equivalents	6	46.62
Vested	(31)	46.56
Forfeited	(3)	46.52
Restricted Stock Units Outstanding at October 31, 2021	385	$	46.81	1.7	$	16,277

The weighted-average grant date fair value of restricted stock units granted and the total fair value of restricted stock units granted during each of the past three fiscal years, are:


	Fiscal Year Ended
	October 31,		October 25,		October 27,
(in thousands, except per share amounts)	2021		2020		2019
Weighted-average Grant Date Fair Value	$	47.52	$	45.88	$	—
Fair Value of Restricted Stock Units Granted	10,699		9,383		—
Fair Value of Restricted Stock Units Vested	$	1,460	$	839	$	—

Restricted Shares: Restricted shares awarded to non-employee directors annually on February 1 are subject to a restricted period which expires the date of the Company’s next annual stockholders meeting. Newly elected directors receive a prorated award of restricted shares of the Company's common stock, which expires on the date of the Company's second succeeding annual stockholders meeting. A reconciliation of the restricted shares as of October 31, 2021, is:


(in thousands, except per share amounts)	Shares	Weighted- Average Grant Date Fair Value
Restricted Shares Outstanding at October 25, 2020	45	$	47.03
Granted	38	46.92
Vested	(45)	47.03

Restricted Shares Outstanding at October 31, 2021	38	$	46.92

The weighted-average grant date fair value of restricted shares granted, the total fair value of restricted shares granted, and the fair value of shares that have vested during each of the past three fiscal years are:


	Fiscal Year Ended
	October 31,		October 25,		October 27,
(in thousands, except per share amounts)	2021		2020		2019
Weighted-average Grant Date Fair Value	$	46.92	$	47.29	$	42.23
Fair Value of Restricted Shares Granted	1,760		1,973		2,134
Fair Value of Restricted Shares Vested	$	2,133	$	1,974	$	1,760