the grant date fair value of options is estimated using the black-scholes option-pricing model . the weighted-average assumptions used in valuations for 2017 , 2016 and 2015 are , respectively : risk-free interest rate , based on u.s . treasury yields , 1.7 percent , 1.9 percent and 1.9 percent ; dividend yield , 3.6 percent , 3.8 percent and 3.1 percent ; and expected volatility , based on historical volatility , 24 percent , 27 percent and 28 percent