PACCAR has certain plans under which officers and key employees may be granted options to purchase shares of the Company’s authorized but unissued common stock under plans approved by stockholders. Non‑employee directors and certain officers may be granted restricted shares of the Company’s common stock under plans approved by stockholders. Options outstanding under these plans were granted with exercise prices equal to the fair market value of the Company’s common stock at the date of grant. Options expire no later than ten years from the grant date and generally vest after three years. Restricted stock awards generally vest over three years or earlier upon meeting certain age and service requirements.

The Company recognizes compensation cost on these options and restricted stock awards on a straight-line basis over the requisite period the employee is required to render service less estimated forfeitures based on historical experience. The maximum number of shares of the Company’s common stock authorized for issuance under these plans is 46.7 million shares, and as of December 31, 2019, the maximum number of shares available for future grants was 12.5 million.

The estimated fair value of each option award is determined on the date of grant using the Black-Scholes-Merton option pricing model that uses assumptions noted in the following table. The risk-free interest rate is based on the U.S. Treasury yield curve in effect at the time of grant. Expected volatility is based on historical volatility. The dividend yield is based on an estimated future dividend yield using projected net income for the next five years, implied dividends and Company stock price. The expected term is based on the period of time that options granted are expected to be outstanding based on historical experience.

		2019			2018			2017
Risk-free interest rate		2.55	%		2.64	%		1.97	%
Expected volatility		23	%		23	%		23	%
Expected dividend yield		4.9	%		3.8	%		3.1	%
Expected term	6 years			6 years			5 years
Weighted average grant date fair value of options per share	$	8.26		$	10.67		$	10.56

The fair value of options granted was $7.3, $6.3 and $6.4 for the years ended December 31, 2019, 2018 and 2017, respectively. The fair value of options vested during the years ended December 31, 2019, 2018 and 2017 was $5.8, $5.3 and $5.2, respectively.

		2019		2018		2017
Intrinsic value of options exercised	$	31.9	$	13.4	$	22.0
Cash received from stock option exercises		60.9		19.7		40.0
Tax benefit related to stock award exercises		3.8		2.4		4.9
Stock-based compensation		15.1		13.2		12.7
Tax benefit related to stock-based compensation		1.9		1.9		4.6

The summary of options as of December 31, 2019 and changes during the year then ended are presented below:

				PER SHARE		REMAINING		AGGREGATE
	NUMBER			EXERCISE		CONTRACTUAL		INTRINSIC
	OF SHARES			PRICE*		LIFE IN YEARS*		VALUE
Options outstanding at January 1		4,090,900		$	55.32
Granted		883,600			65.56
Exercised		(1,288,800	)		47.47
Cancelled		(197,400	)		66.60
Options outstanding at December 31		3,488,300		$	60.18		6.22	$	66.0
Vested and expected to vest		3,401,100		$	60.01		6.15	$	64.9
Exercisable		1,792,800		$	53.71		4.28	$	45.5

The fair value of restricted shares is determined based upon the stock price on the date of grant. The summary of nonvested restricted shares as of December 31, 2019 and changes during the year then ended is presented below:

	NUMBER			GRANT DATE
NONVESTED SHARES	OF SHARES			FAIR VALUE*
Nonvested awards outstanding at January 1		189,500		$	63.85
Granted		147,100			64.34
Vested		(186,100	)		62.56
Nonvested awards outstanding at December 31		150,500		$	65.92

As of December 31, 2019, there was $5.8 of total unrecognized compensation cost related to nonvested stock options, which is recognized over a remaining weighted average vesting period of 1.50 years. Unrecognized compensation cost related to nonvested restricted stock awards of $2.1 is expected to be recognized over a remaining weighted average vesting period of 1.37 years.

Year Ended December 31,	2019	2018	2017
Additional shares	621,300	785,100	1,038,400
Antidilutive options	1,489,400	1,176,600	696,400