Alcoa 2011 Annual Report Download - page 137
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The fair value of new options is estimated on the date of grant using a lattice-pricing model with the following
assumptions:
2011 2010 2009
Weighted average fair value per option $ 4.96 $ 4.67 $ 3.34
Average risk-free interest rate 0.19-3.44% 0.14-3.62% 0.3-2.65%
Dividend yield 0.9% 1.1% 1.2%
Volatility 36-43% 47-51% 38-76%
Annual forfeiture rate 5% 4% 3%
Exercise behavior 45% 35% 43%
Life (years) 5.8 5.6 4.2
The range of average risk-free interest rates is based on a yield curve of interest rates at the time of the grant based on
the contractual life of the option. Prior to 2009, the dividend yield was based on a five-year average. For 2009, the
dividend yield was based on a three-month average as a result of the significant decline in Alcoa’s stock price in 2008,
due to the then-global economic downturn, and the reduction in Alcoa’s quarterly common stock dividend from $0.17
per share to $0.03 per share. In 2010, the dividend yield was extended to a one-year average due to the stabilization of
the global economy. In 2011, Alcoa continued to use a one-year average for the dividend yield. Volatility is based on
historical and implied volatilities over the term of the option. Alcoa utilizes historical option forfeiture data to estimate
annual pre- and post-vesting forfeitures. The exercise behavior assumption represents a weighted average exercise ratio
(exercise patterns for grants issued over the number of years in the contractual option term) of an option’s intrinsic
value resulting from historical employee exercise behavior. The life of an option is an output of the lattice-pricing
model based upon the other assumptions used in the determination of the fair value.
The activity for stock options was as follows (options in millions):
2011 2010 2009
Outstanding, beginning of year:
Number of options 56.1 65.5 46.2
Weighted average exercise price $19.29 $24.44 $35.61
Granted:
Number of options 4.5 9.0 27.1
Weighted average exercise price $16.24 $13.52 $ 8.34
Exercised:
Number of options (4.3) (1.6) -
Weighted average exercise price $ 8.59 $ 8.34 $ -
Expired or forfeited:
Number of options (9.5) (16.8) (7.8)
Weighted average exercise price $31.90 $37.21 $34.60
Outstanding, end of year:
Number of options 46.8 56.1 65.5
Weighted average exercise price $17.41 $19.29 $24.44
Exercisable, end of year:
Number of options 28.8 30.2 37.7
Weighted average exercise price $20.90 $26.91 $35.51
The total intrinsic value of options exercised during 2011 and 2010 was $34 and $8, respectively. In 2011 and 2010,
the cash received from option exercises was $37 and $13 and the total tax benefit realized from these exercises was $11
and $2, respectively. There were no options exercised in 2009.
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