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Stock-based Compensation (Tables)
12 Months Ended
Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Assumptions Used in Black-Scholes Option Valuation Model
 Year Ended September 30,
 202120202019
Expected life of option (years)6.56.56.4
Risk-free interest rate0.60%1.67%2.77%
Expected volatility of the Company’s stock27.60%22.40%21.80%
Expected dividend yield on the Company’s stock2.28%2.49%3.29%
Summary of Stock Option Activity
A summary of stock option activity at September 30, 2021, and changes for the year then ended, is presented below:
Weighted
Average
Option Price
Shares
Subject to
Option
Weighted
Average
Remaining
Contractual
Life (years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding, September 30, 2020$37.14 10,114,905 
Granted45.69 932,678 
Exercised36.70 (4,840,511)
Forfeited or expired37.16 (256,061)
Outstanding, September 30, 2021$38.84 5,951,011 5.9$174 
Exercisable, September 30, 2021$37.01 3,536,889 4.3$110 
Assumptions Used in Black-Scholes Stock Appreciation Rights Valuation Model
The assumptions used to determine the fair value of the SAR awards at September 30, 2021 were as follows:
Expected life of SAR (years)
0.01 - 4.29
Risk-free interest rate
0.07% - 0.88%
Expected volatility of the Company’s stock27.60%
Expected dividend yield on the Company’s stock2.28%
Summary of Stock Appreciation Rights Activity
A summary of SAR activity at September 30, 2021, and changes for the year then ended, is presented below:
Weighted
Average
SAR Price
Shares
Subject to
SAR
Weighted
Average
Remaining
Contractual
Life (years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding, September 30, 2020$30.14 212,637 
Granted45.69 35,254 
Exercised28.16 (88,600)
Forfeited or expired32.45 (18,708)
Outstanding, September 30, 2021$34.99 140,583 3.1$
Exercisable, September 30, 2021$31.40 105,329 1.0$
Summary of Nonvested Restricted Stock Awards
A summary of non-vested restricted stock awards at September 30, 2021, and changes for the fiscal year then ended, is presented below:
Weighted
Average
Price
Shares/Units
Subject to
Restriction
Non-vested, September 30, 2020$38.58 3,229,879 
Granted48.29 1,865,566 
Vested37.80 (1,439,284)
Forfeited41.32 (321,724)
Non-vested, September 30, 2021$44.06 3,334,437 
Schedule of share-based payment award, performance share, valuation assumptions
 Year Ended September 30,
 202120202019
Risk-free interest rate0.20%1.60%2.76%
Expected volatility of the Company’s stock30.90%21.80%22.90%
Summary of Nonvested PSUs
A summary of the status of the Company’s non-vested PSUs at September 30, 2021, and changes for the fiscal year then ended, is presented below:
Weighted
Average
Price
Shares/Units
Subject to
PSU
Non-vested, September 30, 2020$39.06 1,617,944 
Granted50.53 410,934 
Vested38.75 (789,129)
Forfeited41.86 (43,431)
Non-vested, September 30, 2021$43.11 1,196,318