republic services , inc . notes to consolidated financial statements 2014 ( continued ) in december 2008 , the board of directors amended and restated the republic services , inc . 2006 incentive stock plan ( formerly known as the allied waste industries , inc . 2006 incentive stock plan ( the 2006 plan ) ) . allied 2019s stockholders approved the 2006 plan in may 2006 . the 2006 plan was amended and restated in december 2008 to reflect that republic services , inc . is the new sponsor of the plan , that any references to shares of common stock is to shares of common stock of republic services , inc. , and to adjust outstanding awards and the number of shares available under the plan to reflect the acquisition . the 2006 plan , as amended and restated , provides for the grant of non-qualified stock options , incentive stock options , shares of restricted stock , shares of phantom stock , stock bonuses , restricted stock units , stock appreciation rights , performance awards , dividend equivalents , cash awards , or other stock-based awards . awards granted under the 2006 plan prior to december 5 , 2008 became fully vested and nonforfeitable upon the closing of the acquisition . awards may be granted under the 2006 plan , as amended and restated , after december 5 , 2008 only to employees and consultants of allied waste industries , inc . and its subsidiaries who were not employed by republic services , inc . prior to such date . at december 31 , 2012 , there were approximately 15.5 million shares of common stock reserved for future grants under the 2006 plan . stock options we use a binomial option-pricing model to value our stock option grants . we recognize compensation expense on a straight-line basis over the requisite service period for each separately vesting portion of the award , or to the employee 2019s retirement eligible date , if earlier . expected volatility is based on the weighted average of the most recent one year volatility and a historical rolling average volatility of our stock over the expected life of the option . the risk-free interest rate is based on federal reserve rates in effect for bonds with maturity dates equal to the expected term of the option . we use historical data to estimate future option exercises , forfeitures ( at 3.0% ( 3.0 % ) for each of the period presented ) and expected life of the options . when appropriate , separate groups of employees that have similar historical exercise behavior are considered separately for valuation purposes . the weighted-average estimated fair values of stock options granted during the years ended december 31 , 2012 , 2011 and 2010 were $ 4.77 , $ 5.35 and $ 5.28 per option , respectively , which were calculated using the following weighted-average assumptions: .

2012: expected volatility: -27.8
risk-free interest rate: -0.8
dividend yield: -3.2
expected life ( in years ): 4.5
contractual life ( in years ): 7
2011: expected volatility: -27.3
risk-free interest rate: -1.7
dividend yield: -2.7
expected life ( in years ): 4.4
contractual life ( in years ): 7
2010: expected volatility: -28.6
risk-free interest rate: -2.4
dividend yield: -2.9
expected life ( in years ): 4.3
contractual life ( in years ): 7

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Questions:
what was the net change in the dividend yield percent from 2011 to 2012?
what is that divided by the 2011 value?

Answers:
0.5
18.5%