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Employee plans (Tables)
 12 Months Ended
Dec. 31, 2021
Defined Benefit Plan Disclosure [Line Items]  
Schedule of Restricted Stock Unit Activity
A summary of restricted stock and restricted stock unit (RSU) activity for the year ended December 31, 2021 follows (shares in thousands):
 
     Restricted
Stock and
RSU’s		      Weighted-
Average
Grant-Date

Fair Value		  
Outstanding at December 31, 2020
      1,726      $ 17.87  
Granted
      1,590        25.38  
Vested
      (923 )       16.60  
Forfeited and expired
      (269 )       19.02  
  
 
 
     
 
 
  
Outstanding at December 31, 2021
      2,124        22.73  
  
 
 
     
 
 
  
Schedule of Weighted-Average Assumptions The fair value of awards with market conditions is estimated using a Monte Carlo simulation with the following weighted-average assumptions.
 
Year ended December 31,
   
2021
     2020  
Weighted-average fair value of grant
   
$
40.02
 
   $ 28.33  
Risk-free interest rate
(i)
   
 
0.27
% 
     1.35 % 
Expected volatility
(ii)
   
 
57.08
% 
     51.81 % 
Expected life of restricted stock units in years
(iii)
   
 
2.84
 
     2.86  
Expected dividend yield
   
 
—  
% 
     —   % 
 
(i)
 
Represents the continuously compounded semi-annual
zero-coupon
U.S. treasury rate commensurate with the remaining performance period
(ii)
 
Based on historical volatility for the company that is commensurate with the length of the performance period
(iii)
 
Represents the remaining life of the longest performance period
 
Schedule of Accumulated Benefit Obligation in Excess of Plan Assets
Information for defined benefit retirement plans with an accumulated benefit obligation in excess of plan assets follows:
 
As of December 31,
   
2021
      2020  
Accumulated benefit obligation
   
$
4,498.8
 
    $ 6,060.7  
Fair value of plan assets
   
$
3,587.7
 
    $ 4,839.5  
Schedule of Projected Benefit Obligation in Excess of Plan Assets
Information for defined benefit retirement plans with a projected benefit obligation in excess of plan assets follows:
 
As of December 31,
   
2021
      2020  
Projected benefit obligation
   
$
4,500.5
 
    $ 6,063.0  
Fair value of plan assets
   
$
3,587.7
 
    $ 4,839.5  
Schedule of Assumed Health Care Cost Trend Rates
Assumed health care cost trend rates at December 31,
   
2021
     2020  
Health care cost trend rate assumed for next year
   
 
6.5
% 
     5.4 % 
Rate to which the cost trend rate is assumed to decline (the ultimate trend rate)
   
 
4.5
% 
     4.5 % 
Year that the rate reaches the ultimate trend rate
   
 
2033
 
     2025  
Schedule of Plan Assets (Liabilities) at Fair Value
The following table sets forth by level, within the fair value hierarchy, the plans’ assets (liabilities) at fair value at December 31, 2021.
 
     U.S. Plans      International Plans  
As of December 31, 2021
    Fair
Value		     Level 1     Level 2     Level 3      Fair
Value		      Level 1      Level 2      Level 3  
Pension plans
                     
Equity Securities
                     
Common Stocks
   
$
654.3
 
  
$
652.4
 
  
$
1.9
 
  
$
—  
 
   
$
—  
 
   
$
—  
 
   
$
—  
 
   
$
—  
 
Commingled Funds
   
 
398.9
 
    
 
398.9
 
     
 
34.1
 
      
 
34.1
 
   
Debt Securities
                     
U.S. Govt. Securities
   
 
413.2
 
  
 
413.2
 
                
Other Fixed Income
   
 
479.3
 
    
 
479.3
 
     
 
3.0
 
      
 
3.0
 
   
Insurance Contracts
            
 
110.2
 
         
 
110.2
 
Commingled Funds
   
 
525.2
 
    
 
525.2
 
     
 
383.8
 
      
 
383.8
 
   
Real Estate
                     
Real Estate Investment Trusts
   
 
154.1
 
  
 
154.1
 
                
Other
                     
Derivatives
(i)
   
 
(53.7
) 
  
 
5.8
 
  
 
(59.5
) 
              
Commingled Funds
            
 
390.0
 
      
 
390.0
 
   
Pooled Funds
   
 
108.4
 
    
 
108.4
 
              
Cumulative futures contracts variation margin paid to brokers
   
 
(5.8
) 
  
 
(5.8
) 
                
Cash
   
 
0.2
 
  
 
0.2
 
       
 
28.7
 
   
 
28.7
 
      
Receivables
   
 
15.7
 
  
 
15.7
 
                
Payables
   
 
(1.1
) 
  
 
(1.1
) 
                
  
 
 
    
 
 
    
 
 
    
 
 
     
 
 
     
 
 
     
 
 
     
 
 
  
Total plan assets in fair value hierarchy
   
$
2,688.7
 
  
$
1,234.5
 
  
$
1,454.2
 
  
$
—  
 
   
$
949.8
 
   
$
28.7
 
   
$
810.9
 
   
$
110.2
 
  
 
 
    
 
 
    
 
 
    
 
 
     
 
 
     
 
 
     
 
 
     
 
 
  
Plan assets measured using NAV as a practical expedient
(ii):
                     
Commingled Funds
                     
Equity
   
$
—  
 
         
$
404.5
 
         
Debt
   
 
78.6
 
         
 
1,077.3
 
         
Other
   
 
112.5
 
                  
Private Real Estate
   
 
234.2
 
                  
Private Equity
   
 
25.3
 
                  
  
 
 
           
 
 
           
Total pension plan assets
   
$
3,139.3
 
         
$
2,431.6
 
         
  
 
 
           
 
 
           
Other postretirement plans
                     
Insurance Contracts
   
$
5.6
 
      
$
5.6
 
            
 
(i)
 
Level 1 derivatives represent unrealized appreciation or depreciation on open futures contracts. The value of open futures contracts includes derivatives and the cumulative futures contracts variation margin paid to or received from brokers.
(ii)
 
Investments measured at fair value using NAV as a practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table for these investments are included to permit reconciliation of the fair value hierarchy to the total plan assets.
 
The following table sets forth by level, within the fair value hierarchy, the plans’ assets (liabilities) at fair value at December 31, 2020.
 
     U.S. Plans      International Plans  
As of December 31, 2020
    Fair
Value		     Level 1     Level 2     Level 3      Fair
Value		     Level 1     Level 2      Level 3  
Pension plans
                   
Equity Securities
                   
Common Stocks
    $ 774.1     $ 771.2     $ 2.9     $ —        $ —       $ —       $ —        $ —    
Commingled Funds
      640.6         640.6          153.4         153.4     
Debt Securities
                   
U.S. Govt. Securities
      388.5       388.5                
Other Fixed Income
      589.9         589.9          125.8         125.8     
Insurance Contracts
               127.5            127.5  
Commingled Funds
      689.9         689.9          471.2         471.2     
Real Estate
                   
Real Estate Investment Trusts
      112.1       112.1            2.0         2.0     
Other
                   
Derivatives
(i)
      (67.3 )      5.0       (72.3 )         20.5         20.5     
Commingled Funds
               381.4         381.4     
Pooled Funds
      233.4         233.4          178.0         178.0     
Cumulative futures contracts variation margin received from brokers
      (1.1 )      (1.1 )               
Cash
      21.8       21.8            111.7       111.7       
Receivables
      28.8       28.8            2.1       2.1       
Payables
      (7.3 )      (7.3 )           (20.7 )      (20.7 )      
  
 
 
    
 
 
    
 
 
    
 
 
     
 
 
    
 
 
    
 
 
     
 
 
  
Total plan assets in fair value hierarchy
    $ 3,403.4     $ 1,319.0     $ 2,084.4     $ —        $ 1,552.9     $ 93.1     $ 1,332.3      $ 127.5  
  
 
 
    
 
 
    
 
 
    
 
 
     
 
 
    
 
 
    
 
 
     
 
 
  
Plan assets measured using NAV as a practical expedient
(ii):
                   
Commingled Funds
                   
Equity
    $ —              $ 429.9         
Debt
      121.7              1,067.4         
Other
      104.2              27.4         
Private Real Estate
      208.0              51.8         
Private Equity
      10.5                  
  
 
 
           
 
 
         
Total pension plan assets
    $ 3,847.8            $ 3,129.4         
  
 
 
           
 
 
         
Other postretirement plans
                   
Insurance Contracts
    $ 6.0         $ 6.0            
 
(i)
 
Level 1 derivatives represent unrealized appreciation or depreciation on open futures contracts. The value of open futures contracts includes derivatives and the cumulative futures contracts variation margin received from brokers.
(ii)
 
Investments measured at fair value using NAV as a practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table for these investments are included to permit reconciliation of the fair value hierarchy to the total plan assets.
 
Schedule of Changes in Fair Value of Plans Assets
The following table sets forth a summary of changes in the fair value of the plans’ Level 3 assets for the year ended December 31, 2021.
 
     January 1,
2021		      Realized
gains
(losses)		     Purchases
or
acquisitions		      Sales
or
dispositions		     Currency and
unrealized
gains (losses)
relating to
instruments
still held at
December 31,
2021		     December 31,
2021		  
U.S. plans
               
Other postretirement plans
               
Insurance Contracts
   
$
6.0
 
   
$
(0.1
) 
  
$
—  
 
   
$
(0.3
) 
  
$
—  
 
  
$
5.6
 
International pension plans
               
Insurance Contracts
   
$
127.5
 
   
$
—  
 
  
$
36.1
 
   
$
(48.7
) 
  
$
(4.7
) 
  
$
110.2
 
The following table sets forth a summary of changes in the fair value of the plans’ Level 3 assets for the year ended December 31, 2020.
 
     January 1,
2020		      Realized
gains
(losses)		     Purchases
or
acquisitions		      Sales
or
dispositions		     Currency and
unrealized
gains (losses)
relating to
instruments
still held at
December 31,
2020		      December 31,
2020		  
U.S. plans
                
Other postretirement plans
                
Insurance Contracts
    $ 6.9      $ (0.4 )    $ —        $ (0.5 )    $ —        $ 6.0  
International pension plans
                
Insurance Contracts
    $ 123.1      $ —       $ 4.1      $ (11.5 )    $ 11.8      $ 127.5  
Schedule of Additional Information about Plan Assets Valued Using Net Asset Value
The following table presents additional information about plan assets valued using the net asset value as a practical expedient within the fair value hierarchy table.
 
     2021      2020  
     Fair Value      Unfunded
Commit-
ments		      Redemption
Frequency		      Redemption
Notice
Period
Range		      Fair Value      Unfunded
Commit-
ments		      Redemption
Frequency		      Redemption
Notice
Period
Range		  
U.S. plans
                        
Commingled Funds
                        
Debt
   
$
78.6
 
   
$
—  
 
      Monthly        45 days      $ 121.7      $ —          Monthly        45 days  
Other
   
 
112.5
 
   
 
—  
 
      Monthly        5 days        104.2        —          Monthly        5 days  
Private Real Estate
(i)
   
 
234.2
 
   
 
—  
 
      Quarterly        60-90 days        208.0        15.7        Quarterly        60-90 days  
Private Equity
(ii)
   
 
25.3
 
   
 
28.6
 
            10.5        20.9        
  
 
 
     
 
 
           
 
 
     
 
 
        
Total
   
$
450.6
 
   
$
28.6
 
          $ 444.4      $ 36.6        
  
 
 
     
 
 
           
 
 
     
 
 
        
International pension plans
                        
Commingled Funds
                        
Equity
   
$
404.5
 
   
$
—  
 
      Weekly       
 Up to 2
days		  
 		    $ 429.9      $ —          Weekly       
 Up to 2
days		  
 
Debt
   
 
1,077.3
 
   
 
138.9
 
     

 Weekly,
Monthly,
Quarterly		  
 
 		     
 Up to 120
days		  
 		      1,067.4        86.2       


 Weekly,
Bimonthly,
Monthly,
Quarterly		  
 
 
 		     
 Up to 120
days		  
 
Other
   
 
—  
 
   
 
—  
 
            27.4        —          Monthly       
 Up to 30
days		  
 
Private Real Estate
   
 
—  
 
   
 
—  
 
            51.8        —          Monthly       
 Up to 90
days		  
 
  
 
 
     
 
 
           
 
 
     
 
 
        
Total
   
$
1,481.8
 
   
$
138.9
 
          $ 1,576.5      $ 86.2        
  
 
 
     
 
 
           
 
 
     
 
 
        
 
(i)
 
Includes investments in private real estate funds. The funds invest in U.S. real estate and allow redemptions quarterly, though queues, restrictions and gates may extend the period. A redemption has been requested from one fund, which has a redemption queue with estimates of full receipt of three to four years.
(ii)
 
Includes investments in limited partnerships, which invest primarily in secondary markets and private credit. The investments can never be redeemed.
 
Pension Plans  
Defined Benefit Plan Disclosure [Line Items]  
Schedule of Weighted-Average Assumptions Weighted-average assumptions used to determine net periodic pension cost were as follows:
 
     U.S. Plans     International Plans  
Year ended December 31,
   
2021
     2020     2019    
2021
     2020     2019  
Discount rate
   
 
2.85
% 
     3.53 %      4.50 %   
 
1.23
% 
     1.82 %      2.55 % 
Expected long-term rate of return on assets
   
 
6.07
% 
     6.50 %      6.80 %   
 
3.30
% 
     3.50 %      4.18 % 
Weighted-average assumptions used to determine benefit obligations at December 31 were as follows:
 
Discount rate
   
 
3.18
% 
     2.85 %      3.53 %   
 
1.73
% 
     1.23 %      1.82 % 
Schedule of Funded Status of Plan and Amounts Recognized in Consolidated Balance Sheet
Retirement plans’ funded status and amounts recognized in the company’s consolidated balance sheets follows:
 
     U.S. Plans      International Plans  
As of December 31,
   
2021
      2020     
2021
      2020  
Change in projected benefit obligation
            
Benefit obligation at beginning of year
   
$
4,545.3
 
    $ 4,755.6     
$
3,468.0
 
    $ 3,143.8  
Service cost
   
 
—  
 
      —       
 
3.0
 
      2.8  
Interest cost
   
 
117.6
 
      162.5     
 
36.7
 
      53.4  
Plan participants’ contributions
   
 
—  
 
      —       
 
1.0
 
      1.1  
Plan curtailment
   
 
—  
 
      —       
 
—  
 
      (1.6 ) 
Plan settlement
   
 
(513.8
) 
      (277.3 )    
 
(726.8
) 
      —    
Actuarial loss
   
 
(108.4
) 
      253.9     
 
2.0
 
      226.5  
Benefits paid
   
 
(331.1
) 
      (349.4 )    
 
(106.5
) 
      (119.0 ) 
Foreign currency translation adjustments
   
 
—  
 
      —       
 
(63.0
) 
      161.0  
  
 
 
     
 
 
     
 
 
     
 
 
  
Benefit obligation at end of year
   
$
3,709.6
 
    $ 4,545.3     
$
2,614.4
 
    $ 3,468.0  
  
 
 
     
 
 
     
 
 
     
 
 
  
Change in plan assets
            
Fair value of plan assets at beginning of year
   
$
3,847.8
 
    $ 3,334.2     
$
3,129.4
 
    $ 2,816.4  
Actual return on plan assets
   
 
130.4
 
      347.2     
 
134.0
 
      254.7  
Employer contribution
   
 
6.0
 
      793.1     
 
46.4
 
      33.1  
Plan participants’ contributions
   
 
—  
 
      —       
 
1.0
 
      1.1  
Plan settlement
   
 
(513.8
) 
      (277.3 )    
 
(726.8
) 
      —    
Benefits paid
   
 
(331.1
) 
      (349.4 )    
 
(106.5
) 
      (119.0 ) 
Foreign currency translation adjustments
   
 
—  
 
      —       
 
(45.9
) 
      143.1  
  
 
 
     
 
 
     
 
 
     
 
 
  
Fair value of plan assets at end of year
   
$
3,139.3
 
    $ 3,847.8     
$
2,431.6
 
    $ 3,129.4  
  
 
 
     
 
 
     
 
 
     
 
 
  
Funded status at end of year
   
$
(570.3
) 
    $ (697.5 )    
$
(182.8
) 
    $ (338.6 ) 
  
 
 
     
 
 
     
 
 
     
 
 
  
Amounts recognized in the consolidated balance sheets consist of:
            
Prepaid postretirement assets
   
$
33.9
 
    $ 27.2     
$
125.8
 
    $ 160.3  
Other accrued liabilities
   
 
(5.9
) 
      (6.1 )    
 
(0.1
) 
      (0.2 ) 
Long-term postretirement liabilities
   
 
(598.3
) 
      (718.6 )    
 
(308.5
) 
      (498.7 ) 
  
 
 
     
 
 
     
 
 
     
 
 
  
Total funded status
   
$
(570.3
) 
    $ (697.5 )    
$
(182.8
) 
    $ (338.6 ) 
  
 
 
     
 
 
     
 
 
     
 
 
  
Accumulated other comprehensive loss, net of tax
            
Net loss
   
$
2,047.6
 
    $ 2,510.4     
$
797.6
 
    $ 1,116.9  
Prior service credit
   
$
(29.7
) 
    $ (32.3 )    
$
(40.2
) 
    $ (45.9 ) 
Accumulated benefit obligation
   
$
3,709.6
 
    $ 4,545.3     
$
2,612.7
 
    $ 3,360.4  
Schedule of Components of Net Periodic Cost (Income)
Net periodic pension cost (income) includes the following components:
 
     U.S. Plans     International Plans  
Year ended December 31,
   
2021
     2020     2019    
2021
     2020     2019  
Service cost
(i)
   
$
—  
 
   $ —       $ —      
$
3.0
 
   $ 2.8     $ 2.8  
Interest cost
   
 
117.6
 
     162.5       197.5    
 
36.7
 
     53.4       68.3  
Expected return on plan assets
   
 
(199.8
) 
     (208.6 )      (218.2 )   
 
(81.6
) 
     (90.6 )      (104.6 ) 
Amortization of prior service credit
   
 
(2.5
) 
     (2.5 )      (2.5 )   
 
(2.8
) 
     (2.5 )      (2.5 ) 
Recognized net actuarial loss
   
 
135.6
 
     135.5       116.6    
 
48.3
 
     43.2       34.2  
Curtailment gain
   
 
—  
 
     —         —      
 
—  
 
     —         (0.1 ) 
Settlement loss
   
 
288.1
 
     142.1       —      
 
211.3
 
     —         1.2  
  
 
 
    
 
 
    
 
 
    
 
 
    
 
 
    
 
 
  
Net periodic pension cost (income)
   
$
339.0
     $ 229.0     $ 93.4    
$
214.9
 
   $ 6.3     $ (0.7 ) 
  
 
 
    
 
 
    
 
 
    
 
 
    
 
 
    
 
 
  
 
(i)
 
Service cost is reported in cost of revenue and selling, general and administrative expenses. All other components of net periodic pension cost are reported in other (expense), net in the consolidated statements of income (loss).
Schedule of Investment Policy Targets and Ranges for Each Asset Category
The company’s investment policy targets and ranges for each asset category are as follows:
 
     U.S.     International  
Asset Category
    Target     Range     Target     Range  
Equity securities
      52 %     
47-57
 %      18 %     
15-20
 % 
Debt securities
      34 %     
29-39
 %      62 %     
57-66
 % 
Cash
      0 %      0-5 %      0 %      0-5 % 
Other
      14 %     
9-19
 %      20 %     
17-24
 % 
Schedule of Expected Future Benefit Payments
As of December 31, 2021, the following benefit payments are expected to be paid from the defined benefit pension plans:
 
Year
    U.S.      International  
2022
    $ 308.6      $ 87.9  
2023
      302.4        90.9  
2024
      295.5        94.4  
2025
      287.6        96.1  
2026
      279.1        99.6  
2027 - 2030
      1,240.5        538.2  
Other Postretirement Benefit Plans  
Defined Benefit Plan Disclosure [Line Items]  
Schedule of Weighted-Average Assumptions
Weighted-average assumptions used to determine net periodic postretirement benefit cost were as follows:
 
Year ended December 31,
   
2021
     2020     2019  
Discount rate
   
 
2.21
% 
     5.13 %      5.67 % 
Expected return on plan assets
   
 
5.50
% 
     5.50 %      5.50 % 
Weighted-average assumptions used to determine benefit obligation at December 31 were as follows:
 
Year ended December 31,
   
2021
     2020     2019  
Discount rate
   
 
2.70
% 
     2.21 %      5.13 % 
Schedule of Funded Status of Plan and Amounts Recognized in Consolidated Balance Sheet A reconciliation of the benefit obligation, fair value of the plan assets and the funded status of the postretirement benefit plans follows:
 
As of December 31,
   
2021
      2020  
Change in accumulated benefit obligation
      
Benefit obligation at beginning of year
   
$
80.2
 
    $ 95.7  
Service cost
   
 
0.4
 
      0.5  
Interest cost
   
 
1.8
 
      4.4  
Plan participants’ contributions
   
 
1.7
 
      2.3  
Amendments
   
 
1.2
 
      —    
Actuarial loss (gain)
   
 
1.8
 
      (13.8 ) 
Benefits paid
   
 
(5.9
) 
      (8.8 ) 
Foreign currency translation and other adjustments
   
 
(0.1
) 
      (0.1 ) 
  
 
 
     
 
 
  
Benefit obligation at end of year
   
$
81.1
 
    $ 80.2  
  
 
 
     
 
 
  
Change in plan assets
      
Fair value of plan assets at beginning of year
   
$
6.0
 
    $ 6.9  
Actual return on plan assets
   
 
(0.2
) 
      (0.4 ) 
Employer contributions
   
 
4.0
 
      6.0  
Plan participants’ contributions
   
 
1.7
 
      2.3  
Benefits paid
   
 
(5.9
) 
      (8.8 ) 
  
 
 
     
 
 
  
Fair value of plan assets at end of year
   
$
5.6
 
    $ 6.0  
  
 
 
     
 
 
  
Funded status at end of year
   
$
(75.5
) 
    $ (74.2 ) 
  
 
 
     
 
 
  
Amounts recognized in the consolidated balance sheets consist of:
      
Other accrued liabilities
   
$
(6.1
) 
    $ (5.4 ) 
Long-term postretirement liabilities
   
 
(69.4
) 
      (68.8 ) 
  
 
 
     
 
 
  
Total funded status
   
$
(75.5
) 
    $ (74.2 ) 
  
 
 
     
 
 
  
Accumulated other comprehensive loss, net of tax
      
Net loss (income)
   
$
1.4
 
    $ (3.0 ) 
Prior service credit
   
 
(2.1
) 
      (4.9 ) 
Schedule of Components of Net Periodic Cost (Income)
Net periodic postretirement benefit cost follows:
 
Year ended December 31,
   
2021
      2020      2019  
Service cost
(i)
   
$
0.4
 
    $ 0.5      $ 0.5  
Interest cost
   
 
1.8
 
      4.4        4.8  
Expected return on assets
   
 
(0.3
) 
      (0.4 )       (0.4 ) 
Amortization of prior service cost
   
 
(1.7
) 
      (1.6 )       (1.7 ) 
Recognized net actuarial (gain) loss
   
 
(2.1
) 
      1.0        0.7  
  
 
 
     
 
 
     
 
 
  
Net periodic benefit cost
   
$
(1.9
) 
    $ 3.9      $ 3.9  
  
 
 
     
 
 
     
 
 
  
 
(i)
 
Service cost is reported in selling, general and administrative expenses. All other components of net periodic benefit cost are reported in other (expense), net in the consolidated statements of income (loss).
Schedule of Expected Future Benefit Payments
As of December 31, 2021, the following benefits are expected to be paid from the company’s postretirement plans:
 
Year
    Expected
Payments		  
2022
    $ 7.1  
2023
      6.7  
2024
      6.2  
2025
      5.7  
2026
      5.3  
2027 - 2031
      21.1