Alcoa 2010 Annual Report Download - page 132

The fair value of new options is estimated on the date of grant using a lattice-pricing model with the following
assumptions:
2010 2009 2008
Weighted average fair value per option $ 4.67 $ 3.34 $ 6.41
Average risk-free interest rate 0.14-3.62% 0.3-2.65% 3.01-3.66%
Dividend yield 1.1% 1.2% 2.1%
Volatility 47-51% 38-76% 31-34%
Annual forfeiture rate 4% 3% 3%
Exercise behavior 35% 43% 39%
Life (years) 5.6 4.2 4.0
The fair value of each reload option grant is estimated on the reload date using the lattice-pricing model. In 2010 and
2009, there were no reload option grants. In 2008, the fair value and related assumptions for reload option grants were
the same as the new option grants reflected in the table above.
The following assumption descriptions are applicable to both new option grants and reload option grants. 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. In 2008, 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 previously mentioned reduction in Alcoa’s quarterly common stock dividend. In 2010, the
dividend yield was based on a one-year average due to the stabilization of the global economy. Volatility is based on
historical and implied volatilities over the term of the option. Alcoa utilizes historical option exercise and 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):
2010 2009 2008
Outstanding, beginning of year:
Number of options 65.5 46.2 52.3
Weighted average exercise price $24.44 $35.61 $35.63
Granted:
Number of options 9.0 27.1 2.9
Weighted average exercise price $13.52 $ 8.34 $31.20
Exercised:
Number of options (1.6) - (6.0)
Weighted average exercise price $ 8.34 $ - $32.68
Expired or forfeited:
Number of options (16.8) (7.8) (3.0)
Weighted average exercise price $37.21 $34.60 $37.64
Outstanding, end of year:
Number of options 56.1 65.5 46.2
Weighted average exercise price $19.29 $24.44 $35.61
Exercisable, end of year:
Number of options 30.2 37.7 42.3
Weighted average exercise price $26.91 $35.51 $36.19
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