Stock-based Compensation (Tables)

The following table summarizes stock-based compensation costs for the years ended December 31, 2015, 2014, and 2013.



	Year Ended December 31
Millions of dollars	2015			2014			2013
Stock-based compensation cost	$	294		$	298		$	264
Tax benefit	(99		)	(90		)	(81		)
Stock-based compensation cost, net of tax	$	195		$	208		$	183

The assumptions and resulting fair values of options granted were as follows:



	Year Ended December 31
	2015	2014	2013
Expected term (in years)	5.16	5.23	5.27
Expected volatility	39%	37%	40%
Expected dividend yield	1.51 - 1.85%	0.94 - 1.77%	0.94 - 1.33%
Risk-free interest rate	1.43 - 1.72%	1.57 - 1.86%	0.77 - 1.73%
Weighted average grant-date fair value per share	$13.47	$19.26	$14.34

The following table represents our stock options activity during 2015.



	Number of Shares (in millions)		Weighted Average Exercise Price per Share		Weighted Average Remaining Contractual Term (years)	Aggregate Intrinsic Value (in millions)
Outstanding at January 1, 2015	17.4		$	43.73
Granted	4.3		43.49
Exercised	(0.8	)	30.81
Forfeited/expired	(0.9	)	49.88
Outstanding at December 31, 2015	20.0		$	43.90	7.1	$	20
Exercisable at December 31, 2015	11.2		$	39.95	5.8	$	20

The assumptions and resulting fair values were as follows:



	Year Ended December 31
	2015			2014			2013
Expected volatility	35		%	23		%	27		%
Expected dividend yield	1.82		%	1.07		%	1.12		%
Risk-free interest rate	0.01		%	0.04		%	0.06		%
Weighted average grant-date fair value per share	$	8.62		$	11.80		$	8.40

The following table represents our restricted stock awards and restricted stock units granted, vested, and forfeited during 2015.



	Number of Shares (in millions)		Weighted Average Grant-Date Fair Value per Share
Nonvested shares at January 1, 2015	16.1		$	45.88
Granted	6.5		43.24
Vested	(4.8	)	42.86
Forfeited	(1.3	)	47.57
Nonvested shares at December 31, 2015	16.5		$	45.59