Stock compensation

12 Months Ended

Dec. 31, 2015

Note 9. Stock Compensation

We recorded $69.9 million, $62.2 million and $38.4 million, respectively, of stock compensation expense for the years ended December 31, 2015, 2014 and 2013. We utilized the Black-Scholes valuation model for estimating the fair value of the stock options granted, with the following weighted‑average assumptions:


							Employee Stock
	Employee Stock Options						Purchase Plan
	For the Year Ended						For the Year Ended
	December 31,						December 31,
	2015		2014		2013		2015		2014		2013
Average risk-free interest rates	1.35	%	1.21	%	0.62	%	0.81	%	0.55	%	0.27	%
Average expected life (in years)	5.03		4.54		4.27		0.50		0.50		0.50
Volatility	49	%	51	%	48	%	55	%	48	%	49	%
Weighted-average fair value (in dollars)	34.55		25.65		8.18		16.26		9.56		4.22

The risk‑free interest rate is derived from the U.S. Federal Reserve rate in effect at the time of grant. The expected life calculation is based on the observed and expected time to the exercise of options by our employees based on historical exercise patterns for similar type options. Expected volatility is based on the historical volatility of our common stock over the period commensurate with the expected life of the options. A dividend yield of zero is assumed based on the fact that we have never paid cash dividends and have no present intention to pay cash dividends.

Total compensation cost of options granted but not yet vested, as of December 31, 2015, was $31.8 million, which is expected to be recognized over the weighted average period of 3.0 years. Total compensation cost of RSUs granted but not yet vested, as of December 31, 2015, was $23.6 million, which is expected to be recognized over the weighted average period of 3.0 years. Total compensation cost of PSUs granted but not yet vested, as of December 31, 2015, was $0.9 million, which is expected to be recognized over the weighted average period of 3.0 years, should the underlying performance conditions be deemed probable of achievement.