CATERPILLAR INC | 2013 | FY | 3

The following table provides the assumptions used in determining the fair value of the stock-based awards for the years ended December 31, 2013, 2012 and 2011, respectively.
 
 
 
 
 
 
 
Grant Year
 
2013
 
2012
 
2011
Weighted-average dividend yield
2.1
%
 
2.2
%
 
2.2
%
Weighted-average volatility
30.6
%
 
35.0
%
 
32.7
%
Range of volatilities
23.4-40.6%

 
33.3-40.4%

 
20.9-45.4%

Range of risk-free interest rates
0.16-1.88%

 
0.17-2.00%

 
0.25-3.51%

Weighted-average expected lives
8 years

 
7 years

 
8 years

 
 
 
 
 
 

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