{"pre_text": ["vertex pharmaceuticals incorporated notes to consolidated financial statements ( continued ) d .", "stock-based compensation ( continued ) the company uses the black-scholes valuation model to estimate the fair value of stock options at the grant date .", "the black-scholes valuation model uses the option exercise price as well as estimates and assumptions related to the expected price volatility of the company 2019s stock , the period during which the options will be outstanding , the rate of return on risk-free investments , and the expected dividend yield for the company 2019s stock to estimate the fair value of a stock option on the grant date .", "the company validates its estimates and assumptions through consultations with independent third parties having relevant expertise .", "the fair value of each option granted under the stock and option plans during 2006 was estimated on the date of grant using the black- scholes option pricing model with the following weighted average assumptions : the weighted-average valuation assumptions were determined as follows : 2022 expected stock price volatility : in 2006 , the company changed its method of estimating expected volatility from relying exclusively on historical volatility to relying exclusively on implied volatility .", "options to purchase the company 2019s stock with remaining terms of greater than one year are regularly traded in the market .", "expected stock price volatility is calculated using the trailing one month average of daily implied volatilities prior to grant date .", "2022 risk-free interest rate : the company bases the risk-free interest rate on the interest rate payable on u.s .", "treasury securities in effect at the time of grant for a period that is commensurate with the assumed expected option term .", "2022 expected term of options : the expected term of options represents the period of time options are expected to be outstanding .", "the company uses historical data to estimate employee exercise and post-vest termination behavior .", "the company believes that all groups of employees exhibit similar exercise and post-vest termination behavior and therefore does not stratify employees into multiple groups in determining the expected term of options .", "2022 expected annual dividends : the estimate for annual dividends is $ 0.00 , because the company has not historically paid , and does not intend for the foreseeable future to pay , a dividend .", "expected stock price volatility 57.10 % (  % ) risk-free interest rate 4.74 % (  % ) expected term 5.64 years ."], "post_text": ["."], "table": [["", "2006"], ["expected stock price volatility", "57.10% ( 57.10 % )"], ["risk-free interest rate", "4.74% ( 4.74 % )"], ["expected term", "5.64 years"], ["expected annual dividends", "2014"]], "table_ori": [["", "2006"], ["Expected stock price volatility", "57.10%"], ["Risk-free interest rate", "4.74%"], ["Expected term", "5.64 years"], ["Expected annual dividends", "—"]]}

Question: in 2006 what was the ratio expected stock price volatility to risk-free interest rate
Evidence:
table_1: the expected stock price volatility of 2006 is 57.10% ( 57.10 % ) ;
table_2: the risk-free interest rate of 2006 is 4.74% ( 4.74 % ) ;
Program: divide(57.10, 4.74)
Answer:
str_answer: 12.1%
exe_answer: 12.04641