We determine our product warranty liability by applying historical claim rate experience to the current field population and dealer inventory. Generally, we base historical claim rates on actual warranty experience for each product by machine model/engine size by customer or dealer location (inside or outside North America). We develop specific rates for each product shipment month and update them monthly based on actual warranty claim experience. 


                                                                             First Three Months 
(Millions of dollars)                                                        2021      2020 
Warranty liability, beginning of period....................................  USD 1,612   USD 1,541 
Reduction in liability (payments)........................................    (225)     (227) 
Increase in liability (new warranties)...................................... 244       219 
Warranty liability, end of period.........................................   USD 1,631   USD 1,533

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12. Profit per share 
Computations of profit per share:                                                                  Three Months Ended 
                                                                                                   March 31 
(Dollars in millions except per share data)                                                        2021    2020 
Profit for the period (A) 1 
                                                                                                           USD 1,092 
 ............................................................................USD 1,530 
Determination of shares (in millions): 
Weighted-average number of common shares outstanding (B).........................                  546.4   546.8 
Shares issuable on exercise of stock awards, net of shares assumed to be purchased out of proceeds 
                                                                                                   5.0     4.3 
at average market price................................................... 
Average common shares outstanding for fully diluted computation (C) 2                              551.4   551.1 
Profit per share of common stock: 
Assuming no dilution (A/B)...............................................                          USD 2.80  USD 2.00 
Assuming full dilution (A/C) 2 
                                                                                                           USD 1.98 
 ............................................................................USD 2.77 
Shares outstanding as of March 31 (in millions).....................................               547.8   542.0

1 Profit attributable to common shareholders.

2 Diluted by assumed exercise of stock-based compensation awards using the treasury stock method.

For the three months ended March 31, 2021 and 2020, we excluded 1.1 million and 4.9 million of outstanding stock options, respectively, from the computation of diluted earnings per share because the effect would have been antidilutive.

In July 2018, the Board approved a share repurchase authorization (the 2018 Authorization) of up to USD10.0 billion of Caterpillar common stock effective January 1, 2019, with no expiration. As of March 31, 2021, approximately USD4.8 billion remained available under the 2018 Authorization.

For the three months ended March 31, 2021, we did not repurchase any shares of Caterpillar common stock. For the three months ended March 31, 2020, we repurchased 9.3 million shares of Caterpillar common stock, at an aggregate cost of USD1.2 billion. We made these purchases through a combination of accelerated stock repurchase agreements with third-party financial institutions and open market transactions.

13. Accumulated other comprehensive income (loss)

We present comprehensive income and its components in the Consolidated Statement of Comprehensive Income. Changes in the balances for each component of Accumulated other comprehensive income (loss) were as follows: 


                                                                                  Three Months Ended 
                                                                                  March 31 
(Millions of dollars)                                                             2021      2020 
Foreign currency translation: 
                                                                                  USD (910)   USD (1,487) 
Beginning balance..................................................... 
                                                                                  (323)     (374) 
Gains (losses) on foreign currency translation................................... 
Less: Tax provision /(benefit).............................................       24        10 
Net gains (losses) on foreign currency translation..............................  (347)     (384) 
(Gains) losses reclassified to earnings........................................   -         24 
Less: Tax provision /(benefit).............................................       -         - 
Net (gains) losses reclassified to earnings....................................   -         24 
Other comprehensive income (loss), net of tax.................................    (347)     (360) 
Ending balance.......................................................             USD (1,257) USD (1,847)

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Table of Contents                                                                Three Months Ended 
                                                                                 March 31 
 
Pension and other postretirement benefits                                        2021   2020 
Beginning balance.....................................................           USD (32) USD (3) 
Current year prior service credit (cost).......................................  -      - 
Less: Tax provision /(benefit)............................................       -      - 
Net current year prior service credit (cost)...................................  -      - 
Amortization of prior service (credit) cost..................................... (10)   (9) 
Less: Tax provision /(benefit).............................................      (2)    (2) 
Net amortization of prior service (credit) cost................................. (8)    (7) 
Other comprehensive income (loss), net of tax.................................   (8)     7. 
Ending balance.......................................................            USD (40) USD (10) 
Derivative financial instruments 
Beginning balance.....................................................           USD - USD (97) 
Gains (losses) deferred..................................................        79         1. 
Less: Tax provision /(benefit)............................................       16         3. 
Net gains (losses) deferred.............................................         63         5. 
(Gains) losses reclassified to earnings........................................  (118)     (70) 
Less: Tax provision /(benefit).............................................      (24)      (15) 
Net (gains) losses reclassified to earnings..................................... (94)      (55) 
Other comprehensive income (loss), net of tax.................................   (31)      (60) 
Ending balance.......................................................            USD (31)    USD (157) 
Available-for-sale securities 
Beginning balance.....................................................           USD 54      USD 20 
Gains (losses) deferred..................................................        (21)      (22) 
Less: Tax provision /(benefit)............................................       (5)        4. 
Net gains (losses) deferred.............................................         (16)      (18) 
(Gains) losses reclassified to earnings........................................  -         - 
Less: Tax provision /(benefit).............................................      -         - 
Net (gains) losses reclassified to earnings..................................... -         - 
Other comprehensive income (loss), net of tax.................................   (16)      (18) 
Ending balance.......................................................            USD 38      USD 2 
Total AOCI Ending Balance at March 31...............................             USD (1,290) USD (2,012)

14. Environmental and legal matters

The Company is regulated by federal, state and international environmental laws governing its use, transport and disposal of substances and control of emissions. In addition to governing our manufacturing and other operations, these laws often impact the development of our products, including, but not limited to, required compliance with air emissions standards applicable to internal combustion engines. We have made, and will continue to make, significant research and development and capital expenditures to comply with these emissions standards.

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We are engaged in remedial activities at a number of locations, often with other companies, pursuant to federal and state laws. When it is probable we will pay remedial costs at a site, and those costs can be reasonably estimated, we accrue the investigation, remediation, and operating and maintenance costs against our earnings. We accrue costs based on consideration of currently available data and information with respect to each individual site, including available technologies, current applicable laws and regulations, and prior remediation experience. Where no amount within a range of estimates is more likely, we accrue the minimum. Where multiple potentially responsible parties are involved, we consider our proportionate share of the probable costs. In formulating the estimate of probable costs, we do not consider amounts expected to be recovered from insurance companies or others. We reassess these accrued amounts on a quarterly basis. The amount recorded for environmental remediation is not material and is included in Accrued expenses. We

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