Equity Plans

As of February 28, 2019, 113 million shares of our common stock were available for future awards under our equity plans.

Stock Options

Stock options granted and assumptions used in the Black-Scholes option valuation model were as follows:



	Quarter ended				Six months ended
	February 28, 2019	March 1, 2018			February 28, 2019			March 1, 2018
Stock options granted	—	1			—			2
Weighted-average grant-date fair value per share	—	$	18.61		$	19.50		$	18.13
Average expected life in years	—	5.5			5.4			5.5
Weighted-average expected volatility	—	44		%	44		%	44		%
Weighted-average risk-free interest rate	—	2.2		%	2.9		%	2.2		%
Expected dividend yield	—	0.0		%	0.0		%	0.0		%

Restricted Stock and Restricted Stock Units ("Restricted Stock Awards")

Restricted Stock Awards activity is summarized as follows:



	Quarter ended				Six months ended
	February 28, 2019		March 1, 2018		February 28, 2019		March 1, 2018
Restricted stock award shares granted	—		2		6		4
Weighted-average grant-date fair value per share	$	37.01	$	43.21	$	39.83	$	41.51

Employee Stock Purchase Plan

Our first ESPP offering period ended in January 2019 and we issued 1 million shares to employees at a purchase price per share of $32.50 under the ESPP. Assumptions used in the Black-Scholes option valuation model for the offering period beginning February 2019 were as follows:



Weighted-average grant-date fair value per share	$	10.92
Average expected life in years	0.5
Weighted-average expected volatility	47		%
Weighted-average risk-free interest rate	2.5		%
Expected dividend yield	0.0		%

Stock-based Compensation Expense



	Quarter ended				Six months ended
	February 28, 2019		March 1, 2018		February 28, 2019		March 1, 2018
Stock-based compensation expense by caption
Cost of goods sold	$	23	$	22	$	49	$	42
Selling, general, and administrative	18		16		37		34
Research and development	16		14		32		27
	$	57	$	52	$	118	$	103

Stock-based compensation expense by type of award
Restricted stock awards	$	42	$	38	$	83	$	72
Stock options	7		14		19		31
Employee Stock Purchase Plan	8		—		16		—
	$	57	$	52	$	118	$	103

Income tax benefits related to share-based payment arrangements were $30 million and $53 million for the second quarter and first six months of 2019, respectively, and $58 million and $116 million for the second quarter and first six months of 2018, respectively. Income tax benefits related to share-based compensation for the first quarter of 2018 were offset by an increase in the U.S. valuation allowance. As of February 28, 2019, $450 million of total unrecognized compensation costs for unvested awards, before the effect of any future forfeitures, was expected to be recognized through the second quarter of 2023, resulting in a weighted-average period of 1.4 years.