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 plans, 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 83% 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 plans, 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 remaining service or vesting period.

VALUATION AND ASSUMPTIONS. We use the Black-Scholes option pricing model to calculate the fair value of stock options. The value of restricted stock awards is based on the stock price of the award on the grant date. We record stock-based compensation expense in the “Salaries and employee benefits” caption in the accompanying consolidated statements of income.

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. Many of these assumptions are judgmental and highly sensitive. Following is a table of 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 the options granted during the years ended May 31, and then a discussion of our methodology for developing each of the assumptions used in the valuation model:

		2011			2010			2009
Weighted-average Black-Scholes value		$	28.12		$	20.47		$	23.66
Intrinsic value of options exercised		$	80		$	77		$	7
Black-Scholes Assumptions:
	Expected lives		5.9 years			5.7 years			5.5 years
	Expected volatility		34	%		32	%		23	%
	Risk-free interest rate		2.36	%		3.24	%		3.28	%
	Dividend yield		0.558	%		0.742	%		0.492	%

Expected Lives. This is the period of time over which the options granted are expected to remain outstanding. Options granted have a maximum term of 10 years. We examine actual stock option exercises to determine the expected life of the options. An increase in the expected term will increase compensation expense.

Expected Volatility. Actual changes in the market value of our stock are used to calculate the volatility assumption. We calculate daily market value changes from the date of grant over a past period equal to the expected life of the options to determine volatility. An increase in the expected volatility will increase compensation expense.

Risk-Free Interest Rate. This is the U.S. Treasury Strip rate posted at the date of grant having a term equal to the expected life of the option. An increase in the risk-free interest rate will increase compensation expense.

Dividend Yield. This is the annual rate of dividends per share over the exercise price of the option. An increase in the dividend yield will decrease compensation expense.

The following table summarizes information about stock option activity for the year ended May 31, 2011:

		Stock Options
		Shares		Weighted-Average Exercise Price	Weighted-Average Remaining Contractual Term	Aggregate Intrinsic Value (in millions)⁽¹⁾
Outstanding at June 1, 2010		20,238,056	$	78.32
	Granted	2,474,603		81.86
	Exercised	(2,043,050)		53.13
	Forfeited	(506,446)		104.38
Outstanding at May 31, 2011		20,163,163	$	81.20	5.7 years	$	327
Exercisable		12,968,690	$	84.74	4.3 years	$	181
Expected to vest		6,618,915	$	74.83	8.2 years	$	135
Available for future grants		11,928,567

⁽¹⁾	Only presented for options with market value at May 31, 2011 in excess of the exercise price of the option.

The options granted during the year ended May 31, 2011 are primarily related to our principal annual stock option grant in June 2010.

The following table summarizes information about vested and unvested restricted stock for the year ended May 31, 2011:

		Restricted Stock
		Shares	Weighted-Average Grant Date Fair Value
Unvested at June 1, 2010		637,296	$	74.02
	Granted	235,998		78.74
	Vested	(234,716)		81.11
	Forfeited	(12,198)		70.91
Unvested at May 31, 2011		626,380	$	73.20

During the year ended May 31, 2010, there were 391,786 shares of restricted stock granted with a weighted-average fair value of $57.07. During the year ended May 31, 2009, there were 197,180 shares of restricted stock granted with a weighted-average fair value of $90.57.

The following table summarizes information about stock option vesting during the years ended May 31:

	Stock Options
	Vested during the year	Fair value (in millions)
2009	2,414,815	$	64
2010	2,296,211		63
2011	2,721,602		67

As of May 31, 2011, there was $132 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, 2011 represented 10% of the total outstanding common and equity compensation shares and equity compensation shares available for grant.