Our total stock-based compensation expense for the years ended May 31 was as follows (in millions):

We have two types of equity-based compensation: stock options and restricted stock.

STOCK OPTIONS. Under the provisions of our incentive stock plan, key employees and non-employee directors may be granted options to purchase shares of our common stock at a price not less than its fair market value on the date of grant. Vesting requirements are determined at the discretion of the Compensation Committee of our Board of Directors. Option-vesting periods range from one to four years, with 82% of our options vesting ratably over four years. Compensation expense associated with these awards is recognized on a straight-line basis over the requisite service period of the award.

RESTRICTED STOCK. Under the terms of our incentive stock plan, restricted shares of our common stock are awarded to key employees. All restrictions on the shares expire ratably over a four-year period. Shares are valued at the market price on the date of award. The terms of our restricted stock provide for continued vesting subsequent to the employee’s retirement. Compensation expense associated with these awards is recognized on a straight-line basis over the shorter of the requisite service period or the stated vesting period.

ASSUMPTIONS. The key assumptions for the Black-Scholes valuation method include the expected life of the option, stock price volatility, a risk-free interest rate and dividend yield. The following table includes the weighted-average Black-Scholes value of our stock option grants, the intrinsic value of options exercised (in millions) and the key weighted-average assumptions used in the valuation calculations for options granted during the years ended May 31, followed by a discussion of our methodology for developing each of the assumptions used in the valuation model:

	2019			2018			2017
Weighted-average Black-Scholes value	$	61.42		$	55.72		$	43.99
Intrinsic value of options exercised	$	122		$	359		$	274
Black-Scholes Assumptions:
Expected lives	6.4 years			6.5 years			6.5 years
Expected volatility		21	%		23	%		25	%
Risk-free interest rate		2.94	%		2.07	%		1.64	%
Dividend yield		0.935	%		0.796	%		0.719	%

The expected life represents an estimate of the period of time options are expected to remain outstanding, and we examine actual stock option exercises to determine the expected life of the options. Options granted have a maximum term of 10 years. Expected volatilities are based on the actual changes in the market value of our stock and are calculated using daily market value changes from the date of grant over a past period equal to the expected life of the options. The risk-free interest rate is the U.S. Treasury Strip rate posted at the date of grant having a term equal to the expected life of the option. The expected dividend yield is the annual rate of dividends per share over the exercise price of the option.

The following table summarizes information regarding stock option activity for the year ended May 31, 2019:

	Stock Options
	Shares			Weighted- Average Exercise Price		Weighted- Average Remaining Contractual Term		Aggregate Intrinsic Value (in millions)⁽¹⁾
Outstanding at June 1, 2018		12,984,917		$	147.98
Granted		2,383,158			244.16
Exercised		(1,112,160	)		91.01
Forfeited		(633,400	)		212.85
Outstanding at May 31, 2019		13,622,515		$	166.89		6.1	$	260
Exercisable		8,344,344		$	134.70		4.8	$	260
Expected to vest		4,950,924		$	217.78		8.3	$	—
Available for future grants		13,894,509

The options granted during 2019 are primarily related to our principal annual stock option grant in June 2018.

The following table summarizes information regarding vested and unvested restricted stock for the year ended May 31, 2019:

	Restricted Stock
	Shares			Weighted- Average Grant Date Fair Value
Unvested at June 1, 2018		337,590		$	185.16
Granted		149,579			253.28
Vested		(153,734	)		180.65
Forfeited		(8,957	)		218.08
Unvested at May 31, 2019		324,478		$	217.76

During the year ended May 31, 2018, there were 155,624 shares of restricted stock granted with a weighted-average fair value of $212.60 per share. During the year ended May 31, 2017, there were 153,984 shares of restricted stock granted with a weighted-average fair value of $166.12 per share.

	Stock Options
	Vested during the year		Fair value (in millions)
2019		2,249,301	$	115
2018		2,465,493		112
2017		2,427,837		104

As of May 31, 2019, there was $221 million of total unrecognized compensation cost, net of estimated forfeitures, related to unvested share-based compensation arrangements. This compensation expense is expected to be recognized on a straight-line basis over the remaining weighted-average vesting period of approximately two years.

Total shares outstanding or available for grant related to equity compensation at May 31, 2019 represented 10% of the total outstanding common and equity compensation shares and equity compensation shares available for grant.