Stock Option Plans (Tables)

12 Months Ended

Dec. 31, 2017

Black-Scholes Option Pricing Model with Weighted Average

For purposes of expense recognition in 2017, 2016 and 2015, the estimated fair values of the stock option grants are amortized to expense over the options’ vesting period. We estimated the fair value of stock options at the date of grant using the Black-Scholes option pricing model with the following weighted average assumptions:


	Year Ended December 31,
	2017			2016			2015
Expected dividend yield		2.8	%		3.0	%		3.0	%
Expected risk-free interest rate		2.3	%		1.6	%		1.8	%
Volatility		27.2	%		27.7	%		28.2	%
Expected life (in years)		5.0			5.5			5.5

Stock Option Activity and Related Information

The following is a summary of our stock option activity and related information for 2017, 2016 and 2015 (in millions, except exercise price and year data):


	Shares Under Option			Weighted Average Exercise Price		Weighted Average Remaining Contractual Term (in years)		Aggregate Intrinsic Value
Year Ended December 31, 2017
Beginning balance		10.3		$	41.40
Granted		1.7			56.87
Exercised		(1.3	)		33.11
Forfeited or canceled		(0.1	)		34.33

Ending balance		10.6		$	44.95		3.94	$	193.4

Exercisable at end of year		2.5		$	37.81		1.74	$	64.0

Ending vested and expected to vest		10.4		$	44.88		3.92	$	191.1

Year Ended December 31, 2016
Beginning balance		8.8		$	39.25
Granted		2.6			43.72
Exercised		(1.1	)		29.50
Forfeited or canceled		—			—

Ending balance		10.3		$	41.40		4.15	$	108.8

Exercisable at end of year		2.2		$	32.37		1.73	$	43.7

Ending vested and expected to vest		10.1		$	41.34		4.12	$	107.5

Year Ended December 31, 2015
Beginning balance		8.4		$	35.49
Granted		1.9			46.19
Exercised		(1.4	)		27.59
Forfeited or canceled		(0.1	)		27.59

Ending balance		8.8		$	39.25		4.16	$	36.7

Exercisable at end of year		2.1		$	28.54		1.92	$	25.9

Ending vested and expected to vest		8.7		$	39.15		4.13	$	36.6

Other Information Regarding Stock Options Outstanding and Exercisable

Other information regarding stock options outstanding and exercisable at December 31, 2017 is summarized as follows (in millions, except exercise price and year data):


		Options Outstanding						Options Exercisable
Range of Exercise Prices		Number Outstanding		Weighted Average Remaining Contractual Term (in years)		Weighted Average Exercise Price		Number Exercisable		Weighted Average Exercise Price
	$ 23.76 - $ 39.17		2.6		1.53	$	36.18		2.0	$	35.47
	43.71 - 43.71		2.6		5.21		43.71		—		—
	46.17 - 46.87		3.7		3.71		46.51		0.5		46.87
	47.92 - 63.60		1.7		6.20		56.78		—		—

	$ 23.76 - $ 63.60		10.6		3.94	$	44.95		2.5	$	37.81