Allowances for Doubtful Accounts
Changes in the allowances for doubtful accounts were as follows: | | | | | | | | | | | | | | | | | | | Year Ended December 31, | (in millions) | 2021 | | 2020 | | 2019 | Balance at beginning of year | $ | 11.4 | | | $ | 6.7 | | | $ | 6.5 | | Additions charged to expense | 0.9 | | | 8.0 | | | 1.6 | | Deductions - write offs | (1.9) | | | (3.0) | | | (2.6) | | Acquisitions | — | | | — | | | 1.3 | | Foreign exchange changes | (0.4) | | | (0.3) | | | (0.1) | | Balance at end of year | $ | 10.0 | | | $ | 11.4 | | | $ | 6.7 | |
Allowances for Sales Discounts and Other Credits
Changes in the allowances for sales discounts and returns were as follows: | | | | | | | | | | | | | | | | | | | Year Ended December 31, | (in millions) | 2021 | | 2020 | | 2019 | Balance at beginning of year | $ | 12.2 | | | $ | 7.7 | | | $ | 7.8 | | Additions charged to expense | 28.9 | | | 12.2 | | | 13.5 | | Deductions | (25.8) | | | (7.9) | | | (13.7) | | | | | | | | | | | | | | Foreign exchange changes | (0.1) | | | 0.2 | | | 0.1 | | Balance at end of year | $ | 15.2 | | | $ | 12.2 | | | $ | 7.7 | |
Allowances for Cash Discounts
Changes in the allowances for cash discounts were as follows: | | | | | | | | | | | | | | | | | | | Year Ended December 31, | (in millions) | 2021 | | 2020 | | 2019 | Balance at beginning of year | $ | 1.9 | | | $ | 2.0 | | | $ | 1.7 | | Additions charged to expense | 22.8 | | | 19.7 | | | 22.2 | | Deductions - discounts taken | (22.2) | | | (19.9) | | | (21.8) | | | | | | | | Foreign exchange changes | (0.1) | | | 0.1 | | | (0.1) | | Balance at end of year | $ | 2.4 | | | $ | 1.9 | | | $ | 2.0 | |
Warranty Reserves
Changes in the reserve for warranty claims were as follows: | | | | | | | | | | | | | | | | | | | Year Ended December 31, | (in millions) | 2021 | | 2020 | | 2019 | Balance at beginning of year | $ | 6.1 | | | $ | 5.4 | | | $ | 4.9 | | Provision for warranties issued | 2.9 | | | 3.5 | | | 3.9 | | Deductions - settlements made (in cash or in kind) | (2.9) | | | (3.1) | | | (3.4) | | | | | | | | Foreign exchange changes | (0.4) | | | 0.3 | | | — | | Balance at end of year | $ | 5.7 | | | $ | 6.1 | | | $ | 5.4 | |
Income Tax Valuation Allowance
Changes in the deferred tax valuation allowances were as follows: | | | | | | | | | | | | | | | | | | | Year Ended December 31, | (in millions) | 2021 | | 2020 | | 2019 | Balance at beginning of year | $ | 55.4 | | | $ | 51.6 | | | $ | 50.8 | | | | | | | | (Credits) debits to expense | (2.2) | | | 2.2 | | | 0.4 | | | | | | | | | | | | | | Foreign exchange changes | (0.8) | | | 1.6 | | | 0.4 | | Balance at end of year | $ | 52.4 | | | $ | 55.4 | | | $ | 51.6 | |
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