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Share-based Compensation Plans (Tables)
12 Months Ended
Dec. 31, 2020
Share-based Payment Arrangement [Abstract]  
Nonvested share activity
Compensation expenses for the last three years and the amount of unrecognized expense for awards outstanding at December 31, 2020, were as follows:
Compensation ExpenseUnrecognized Expense for Nonvested Awards atWeighted-average No. of Years Unrecognized Expense to be Recognized
Years Ended December 31,Dec 31, 2020
(in millions except years)202020192018
Performance Share Units$20.2 25.8 15.8 $17.7 1.5
Market Share Units — 0.1 — 0.0
Restricted Stock Units6.0 6.6 6.6 9.4 1.7
Deferred Stock Units and fees paid in stock 1.2 1.2 1.2 0.3 0.3
Performance-based Options2.3 8.1 4.5 0.3 0.1
Time-based Options1.6 1.0 — 1.8 1.6
Cash based awards1.4 — — 1.3 1.9
Share-based payment expense32.7 42.7 28.2   
Income tax benefit(7.4)(9.2)(6.5)  
Share-based payment expense, net of tax$25.3 33.5 21.7   
The following table summarizes RSU activity during 2020:
Shares
(in thousands)
Weighted-Average Grant Date Fair Value Per Share
Nonvested balance as of December 31, 2019172.7 $71.87 
Activity from January 1 to December 31, 2020:  
Granted178.6 70.85 
Forfeited(12.5)78.86 
Conversion to cash settled awards(a)
(1.3)72.80 
Vested(85.7)67.44 
Nonvested balance as of December 31, 2020251.8 $72.30 

(a)Certain RSUs were modified in the first quarter of 2020 to change the awards' classification from share-settled to cash-settled. The weighted-average grant date fair value per share shown above is the removal of the original fair value.
The following table summarizes all PSU activity during 2020:
Shares
(in thousands)
Weighted-Average Grant Date Fair Value Per Share
Nonvested balance as of December 31, 2019564.2 $70.10 
Activity from January 1 to December 31, 2020:  
Granted248.4 83.68 
Forfeited(27.0)76.32 
Conversion to cash settled awards(a)
(4.6)65.42 
Vested(b)
(204.3)56.72 
Nonvested balance as of December 31, 2020576.7 $80.43 

(a)Certain IM PSUs were modified in the first quarter of 2020 to change the awards' classification from share-settled to cash-settled. The weighted-average grant date fair value per share shown above is the removal of the original fair value.
(b)The vested PSUs presented are based on the target amount of the award. In accordance with the terms of the underlying award agreements, the actual shares earned and distributed for the performance period ended December 31, 2019 were 394.0 thousand, compared to target shares of 204.3 thousand,
The following table summarizes all DSU activity during 2020:
Shares
(in thousands)
Weighted-Average Grant-Date Fair Value
Nonvested balance as of December 31, 201912.1 $79.69 
Activity from January 1 to December 31, 2020:
Granted21.6 40.46 
Vested(12.1)79.69 
Nonvested balance as of December 31, 202021.6 $40.46 
Share-based Compensation, Fair Value of Shares Vested
The value of shares distributed or options exercised in the last three years is as follows:
Value of Shares Distributed or Exercised(a)
Years Ended December 31,
(in millions)202020192018
Performance Share Units$33.3 28.7 25.3 
Market Share Units — 8.2 
Restricted Stock Units6.9 11.8 8.0 
Deferred Stock Units and fees paid in stock0.6 0.9 0.7 
Performance-based Options(a)
0.5 5.4 — 
Time-based vesting Options(a)
 — 2.2 
Total$41.3 46.8 44.4 
Income tax benefit realized$9.0 10.2 9.9 
(a)Intrinsic value for options.
Fair value of options calculation assumptions
The following table provides the terms and weighted-average assumptions used in the Monte Carlo simulation model for the TSR PSUs granted in 2020, 2019 and 2018:
Terms and Assumptions Used to Estimate Grant Date Fair Value 2020 TSR PSUs2019 TSR PSUs2018 TSR PSUs
Terms of awards:
Performance periodJan. 1, 2020 toJan. 1, 2019 toJan. 1, 2018 to
 Dec. 31, 2022Dec. 31, 2021Dec. 31, 2020
Weighted-average assumptions used to estimate fair value: 
Expected dividend yield(a)
0.7 %0.8 %0.8 %
Expected stock price volatility(b)
29.6 %30.8 %29.9 %
Risk-free interest rate(c)
1.4 %2.5 %2.4 %
Contractual term in years2.92.82.9
Weighted-average fair value estimates at grant date:
In millions$3.6 $3.0 3.2 
Fair value per share$94.53 $105.16 79.05 
 
(a)TSR is determined assuming that dividends are reinvested. The stock price projection in the Monte Carlo simulation model assumed a 0% dividend yield, which is mathematically equivalent to reinvesting dividends over the performance period. For the valuation of the TSR PSU, because the holders of the awards have no rights to any dividend paid during the vesting period, we applied a dividend yield in the Monte Carlo simulation model to reduce the projected stock price as of the grant date.
(b)The expected stock price volatility was calculated on the grant date for the most recent term equivalent to the contractual term in years.
(c)The risk-free interest rate on each date of grant is the rate for a zero-coupon U.S. Treasury bill that was commensurate with the grant date contractual term.
s.
The following table provides the term of the performance period and the weighted-average assumptions used in the Monte Carlo simulation model for the performance-based options granted in 2018:
Terms and Assumptions Used to Estimate Grant Date Fair Value of Performance-Based Options Granted2018
Terms of awards:
Performance period for achieving stock price hurdlesThree years from
 grant date
Assumptions used to estimate fair value:
Expected dividend yield(a)
0.8 %
Expected stock price volatility(b)
29.3 %
Risk-free interest rate(c)
2.6 %
Expected term in years(d)
4.5
Weighted-average fair value estimates at grant date:
In millions$7.0 
Fair value per share$16.73 
 
(a)Since the holders of the awards have no rights to any dividend paid during the vesting period, we applied a dividend yield in the Monte Carlo simulation model. At each grant date, the dividend yield was calculated based on the most recent annualized dividend payment and Brink's stock price at the date of grant.
(b)The expected stock price volatility was calculated on each grant date for the most recent 4.5 year term.
(c)The risk-free interest rate on each grant date is the rate for a zero-coupon U.S. Treasury bill that was commensurate with the expected life of 4.5 years.
(d)Because we did not have historical exercise behavior for instruments with premiums, we assumed that the exercise of vested options occurred at the mid-point between the three-year vesting date and the six-year contractual term. In the Monte Carlo simulation, at each iteration of forecasted Brink's stock prices, the option was assumed to be exercised at the mid-point of 4.5 years if the stock price hurdle had been achieved. When the hurdle is achieved, the exercise price was then subtracted from the projected stock price, and discounted back to the grant date. In situations where the projected price had not met the hurdle, no value was attributed.
The following table provides the weighted-average assumptions used in the Black-Scholes-Merton option pricing model for the time-based vesting options granted in 2020 and 2019:
Assumptions Used to Estimate Grant Date Fair Value of Time-Based Options20202019
Assumptions used to estimate fair value:
Expected dividend yield(a)
0.7 %0.8 %
Expected stock price volatility(b)
29.7 %30.3 %
Risk-free interest rate(c)
1.3 %2.5 %
Expected term in years(d)
4.54.5
Weighted-average fair value estimates at grant date:
In millions$1.7 $3.0 
Fair value per share$21.10 $21.58 

(a)The expected dividend yield is the calculated annual yield on Brink's stock at the time of the grant.
(b)The expected stock price volatility was calculated at time of the grant after reviewing the historic volatility of our stock using daily close prices.
(c)The risk-free interest rate at each grant date was the rate for a zero-coupon U.S. Treasury bill that was commensurate with the expected life of 4.5 years.
(d)The expected term of the options was based on historical exercise, expiration and post-cancellation behavior.
Option Activity
The table below summarizes the activity associated with grants of performance-based options:
Shares
(in thousands)
Weighted- Average
Exercise Price Per Share
Weighted-Average Grant Date Fair Value Per ShareWeighted- Average
Remaining Contractual
Term (in years)
Aggregate Intrinsic Value(a)
(in millions)
Outstanding at December 31, 2019(b)
1,191.1 $50.51 $11.52   
Granted— — — 
Forfeited or expired— — —   
Exercised(b)
(26.1)52.75 27.14   
Outstanding at December 31, 2020(b)(c)
1,165.0 $50.46 $11.17 2.2$25.7 
Of the above, as of December 31, 2020:    
Exercisable757.8 $38.11 1.7$25.7 
Expected to vest in future periods(d)
407.2 $73.45 3.0$— 

(a)The intrinsic value of a stock option is the difference between the market price of the shares underlying the option and the exercise price of the option.  The market price at December 31, 2020 was $72.00.
(b)Certain performance-based stock options were modified in the second quarter of 2019. The weighted-average grant date fair value per share for the outstanding options at December 31, 2019, the options exercised in 2020 and for the outstanding options at December 31, 2020 reflects the inclusion of the modified fair value per share.
(c)There were 485.0 thousand exercisable performance-based options with a weighted average exercise price of $29.87 at December 31, 2019 and no exercisable performance-based options at December 31, 2018.
(d)The number of options expected to vest takes into account an estimate of expected forfeitures. We currently have applied a 0% expected forfeiture rate to the performance-based options.
The table below summarizes the activity associated with grants of time-based vesting options:
Shares
(in thousands)
Weighted- Average
Exercise Price Per Share
Weighted-Average Grant Date Fair Value Per ShareWeighted- Average
Remaining Contractual
Term (in years)
Aggregate Intrinsic Value(a)
(in millions)
Outstanding at December 31, 2019127.0 $79.32 $21.56   
Granted80.8 84.42 21.10 
Forfeited or expired— — —   
Outstanding at December 31, 2020(b)
207.8 $81.30 $21.38 4.5$— 
Of the above, as of December 31, 2020:    
Exercisable2.7 $84.65 2.8$— 
Expected to vest in future periods(c)
205.1 $81.26 4.5$— 

(a)The intrinsic value of a stock option is the difference between the market price of the shares underlying the option and the exercise price of the option.  The market price at December 31, 2020 was $72.00.
(b)There were no exercisable options at December 31, 2019 and at December 31, 2018.
(c)The number of options expected to vest takes into account an estimate of expected forfeitures. We currently have applied a 0% expected forfeiture rate to the time-based vesting options.