Notes to Consolidated Financial Statements – (continued)
(Amounts in Millions, Except Per Share Amounts)
Stock options are granted with the exercise price equal to the fair market value of our common stock on the grant date. They are generally exercisable between two and four years from the grant date and expire ten years from the grant date (or earlier in the case of certain terminations of employment).
The following tables are a summary of stock option activity during 2014.
Stock options outstanding as of January 1, 2014
Stock options outstanding as of December 31, 2014
Stock options vested and expected to vest as of December 31, 2014
Stock options exercisable as of December 31, 2014
Date Fair Value
Non-vested as of January 1, 2014
Non-vested as of December 31, 2014
There were 1.7, 5.2 and 1.2 stock options exercised in 2014, 2013 and 2012, respectively. The total intrinsic value of stock options exercised during 2014, 2013 and 2012 was $10.7, $26.2 and $2.0, respectively. The cash received from the stock options exercised in 2014, 2013 and 2012 was $25.2, $59.5 and $11.7, respectively. As of December 31, 2014, there was $1.2 of total unrecognized compensation expense related to non-vested stock options granted, which is expected to be recognized over a weighted-average period of 0.9 years.
We use the Black-Scholes option-pricing model to estimate the fair value of options granted, which requires the input of subjective assumptions including the option’s expected term and the price volatility of the underlying stock. Changes in the assumptions can materially affect the estimate of fair value and our results of operations could be materially impacted. There were no stock options granted during the year ended December 31, 2014. The weighted-average grant-date fair value per option during the years ended December 31, 2013 and 2012 was $4.14 and $4.24, respectively.
The fair value of each option grant has been estimated with the following weighted-average assumptions.
Years ended December 31,
Expected volatility 1
Expected term (years) 2
Risk free interest rate 3
Expected dividend yield 4
The expected volatility used to estimate the fair value of stock options awarded is based on a blend of: (i) historical volatility of our common stock for periods equal to the expected term of our stock options and (ii) implied volatility of tradable forward put and call options to purchase and sell shares of our common stock.
The estimate of our expected term is based on the average of (i) an assumption that all outstanding options are exercised upon achieving their full vesting date and (ii) an assumption that all outstanding options will be exercised at the midpoint between the current date (i.e., the date awards have ratably vested through) and their full contractual term. In determining the estimate, we considered several factors, including the historical option exercise behavior of our employees and the terms and vesting periods of the options.
The risk free rate is determined using the implied yield currently available for zero-coupon U.S. government issuers with a remaining term equal to the expected term of the options.
The expected dividend yield is calculated based on an annualized dividend of $0.38 per share in 2014, $0.30 per share in 2013 and $0.24 per share in 2012.