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Share-based Compensation Plans (Tables)
 12 Months Ended
Dec. 31, 2018
Dec. 31, 2017
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]    
Nonvested share activity
The following table summarizes RSU activity during 2018:
 
Shares
(in thousands)
 
Weighted-Average Grant Date Fair Value Per Share
 
 
 
 
Nonvested balance as of December 31, 2017
265.8

 
$
39.80

Activity from January 1 to December 31, 2018:
 

 
 
Granted
86.3

 
72.31

Forfeited
(7.6
)
 
58.27

Vested
(108.7
)
 
37.64

Nonvested balance as of December 31, 2018(a)
235.8

 
$
52.63


(a)
Certain RSUs were modified in the fourth quarter of 2018 and the resulting impact was not material.  The weighted-average grant date fair value per share at December 31, 2018 reflects the inclusion of the modified fair value per share for the modified awards.

Compensation expenses for the last three years and the amount of unrecognized expense for awards outstanding at December 31, 2018, were as follows:
 
 
Compensation Expense
 
Unrecognized Expense for Nonvested Awards at
 
Weighted-average No. of Years Unrecognized Expense to be Recognized
 
Years Ended December 31,
 
Dec 31, 2018
 
 
(in millions except years)
2018
 
2017
 
2016
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Performance Share Units
$
15.8

 
9.5

 
4.1

 
$
16.6

 
1.7

Market Share Units
0.1

 
0.3

 
0.1

 
—

 
—

Restricted Stock Units
6.6

 
4.7

 
3.8

 
3.8

 
1.3

Deferred Stock Units and fees paid in stock
1.2

 
1.0

 
0.9

 
0.3

 
0.3

Performance-based Options
4.5

 
2.2

 
0.6

 
6.6

 
1.8

Time-based Vesting Options
—

 
—

 
—

 
—

 
1.8

Share-based payment expense
28.2

 
17.7

 
9.5

 
 
 
 
Income tax benefit
(6.5
)
 
(3.4
)
 
(3.0
)
 
 
 
 
Share-based payment expense, net of tax
$
21.7

 
14.3

 
6.5

 
 
 
 
The following table summarizes all PSU activity during 2018:
 
Shares
(in thousands)
 
Weighted-Average Grant Date Fair Value Per Share
 
 
 
 
Nonvested balance as of December 31, 2017
671.2

 
$
37.26

Activity from January 1 to December 31, 2018:
 

 
 
Granted
177.0

 
73.49

Forfeited
(13.2
)
 
60.31

Vested(a)
(137.7
)
 
29.17

Nonvested balance as of December 31, 2018(b)
697.3

 
$
47.74

(a)
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, 2017 were 344.3.
(b)
Certain PSUs were modified in the fourth quarter of 2018 and the resulting impact was not material.  The weighted-average grant date fair value per share at December 31, 2018 reflects the inclusion of the modified fair value per share for the modified awards.

The following table summarizes all MSU activity during 2018:
 
Shares
(in thousands)
 
Weighted-Average Grant Date Fair Value Per Share
 
 
 
 
Nonvested balance as of December 31, 2017
74.2

 
$
30.37

Activity from January 1 to December 31, 2018:
 

 
 
Vested(a)
(74.2
)
 
30.37

Nonvested balance as of December 31, 2018
—

 
$
—

(a)
The vested MSUs 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, 2017 were 111.3. No additional compensation expense was required to be recognized for the additional shares distributed, as the market condition was included in the $30.37 grant date fair value.
The following table summarizes all DSU activity during 2018:
 
Shares
(in thousands)
 
Weighted-Average Grant-Date Fair Value
 
 
 
 
Nonvested balance as of December 31, 2017
10.9

 
$
60.80

Activity from January 1 to December 31, 2018:
 
 
 
Granted
12.5

 
74.43

Vested
(10.9
)
 
60.80

Nonvested balance as of December 31, 2018
12.5

 
$
74.43

  
Share-based Compensation, Fair Value of Shares Vested  
The fair value of shares distributed or options exercised in the last three years is as follows:
 
Fair Value of Shares Distributed or Exercised(a)
 
Years Ended December 31,
(in millions)
2018
 
2017
 
2016
 
 
 
 
 
 
Performance Share Units
$
25.3

 
13.3

 
8.2

Market Share Units
8.2

 
4.3

 
2.7

Restricted Stock Units
8.0

 
7.3

 
4.1

Deferred Stock Units and fees paid in stock
0.7

 
2.7

 
1.9

Time-based Vesting Options(a)
2.2

 
2.0

 
5.3

Total
$
44.4

 
29.6

 
22.2

 
 
 
 
 
 
Income tax benefit realized
$
9.9

 
9.2

 
7.1


(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 2018, 2017 and 2016:
Terms and Assumptions Used to Estimate Fair Value
2018 TSR PSUs
 
2017 TSR PSUs
 
2016 TSR PSUs
 
 
 
 
 
 
Terms of awards:
 
 
 
 
 
Performance period
Jan. 1, 2018 to
 
Jan. 1, 2017 to
 
Jan. 1, 2016 to
 
Dec. 31, 2020
 
Dec. 31, 2019
 
Dec. 31, 2018
 
 
 
 
 
 
Weighted-average assumptions used to estimate fair value:
 
 
 
 
 

Expected dividend yield(a)
0.8
%
 
0.8
%
 
1.4
%
Expected stock price volatility(b)
29.9
%
 
30.6
%
 
29.1
%
Risk-free interest rate(c)
2.4
%
 
1.4
%
 
0.8
%
Contractual term in years
2.9

 
2.9

 
2.7

 
 
 
 
 
 
Weighted-average fair value estimates at grant date:
 
 
 
 
 
In millions
$
3.2

 
$
2.0

 
2.3

Fair value per share
$
79.05

 
$
67.81

 
31.64

 
(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 weighted-average assumptions used in the Black-Scholes-Merton option pricing model for the time-based vesting options granted in 2017:
Assumptions Used to Estimate Fair Value of Time-Based Options
2017
 
 
Assumptions used to estimate fair value:
 
Expected dividend yield(a)
0.7
%
Expected stock price volatility(b)
28.9
%
Risk-free interest rate(c)
1.7
%
Expected term in years(d)
4.5

 
 
Weighted-average fair value estimates at grant date:
 
In millions
$
0.1

Fair value per share
$
21.09


(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 the 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.
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:
Terms and Assumptions Used to Estimate Fair Value of Performance-Based Options Granted
2018
 
2017
 
2016
 
 
 
 
 
 
Terms of awards:
 
 
 
 
 
Performance period for achieving stock price hurdles
Three years from
 
Three years from
 
Three years from
 
grant date
 
grant date
 
grant date
 
 
 
 
 
 
Assumptions used to estimate fair value:
 
 
 
 
 
Expected dividend yield(a)
0.8
%
 
0.8
%
 
1.3
%
Expected stock price volatility(b)
29.3
%
 
29.3
%
 
30.9
%
Risk-free interest rate(c)
2.6
%
 
1.8
%
 
1.1
%
Expected term in years(d)
4.5

 
4.5

 
4.5

 
 
 
 
 
 
Weighted-average fair value estimates at grant date:
 
 
 
 
 
In millions
$
7.0

 
$
3.6

 
$
3.5

Fair value per share
$
16.73

 
$
11.97

 
$
6.01

 
(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.
 
Option Activity
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 Share
 
Weighted- Average
Remaining Contractual
Term (in years)
 
Aggregate Intrinsic Value(a)
(in millions)
 
 
 
 
 
 
 
 
 
 
Outstanding at December 31, 2017
40.6

 
$
26.74

 
$
8.66

 
 

 
 

Exercised
(37.9
)
 
22.57

 
7.77

 
 

 
 

Outstanding at December 31, 2018(b)
2.7

 
$
84.65

 
$
21.09

 
4.8

 
$
—

 
 
 
 
 
 
 
 
 
 
Of the above, as of December 31, 2018:
 

 
 

 
 
 
 

 
 

Exercisable
—

 
$
—

 
 
 
—

 
$
—

Expected to vest in future periods(c)
2.4

 
$
84.65

 
 
 
4.8

 
$
—


(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, 2018 was $64.65 and, as a result, there was no intrinsic value associated with any of the options outstanding at December 31, 2018.
(b)
There were less than 0.1 million shares of exercisable options with a weighted-average exercise price of $22.57 per share at December 31, 2017 and 0.1 million shares of exercisable options with a weighted-average exercise price of $28.80 per share at December 31, 2016.
(c)
The number of options expected to vest takes into account an estimate of expected forfeitures.
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 Share
 
Weighted- Average
Remaining Contractual
Term (in years)
 
Aggregate Intrinsic Value(a)
(in millions)
 
 
 
 
 
 
 
 
 
 
Outstanding at December 31, 2017
879.8

 
$
37.95

 
$
8.04

 
 

 
 

Granted
417.6

 
73.45

 
16.73

 
 
 
 
Forfeited or expired
(10.4
)
 
73.45

 
17.92

 
 

 
 

Outstanding at December 31, 2018(b)
1,287.0

 
$
49.18

 
$
10.88

 
4.2

 
$
23.5

 
 
 
 
 
 
 
 
 
 
Of the above, as of December 31, 2018:
 

 
 

 
 
 
 

 
 

Exercisable
—

 
$
—

 
 
 
—

 
$
—

Expected to vest in future periods(c)
1,271.2

 
$
49.10

 
 
 
4.2

 
$
23.3



(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, 2018 was $64.65.
(b)
Certain performance options were modified in the fourth quarter of 2018 and the resulting impact was not material.  The weighted-average grant date fair value per share at December 31, 2018 reflects the inclusion of the modified fair value per share for the modified options.
(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 majority of the performance-based options.