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Stock compensation (Details) - USD ($) $ / shares in Units, $ in Millions | 3 Months Ended
--- | ---
Mar. 31, 2020 | Mar. 31, 2019
Stock compensation |  |
Stock compensation expense | $ 42.5 | $ 40.6
Stock Compensation Expense Capitalized | $ 0.2 | 0.1
Assumed annualized forfeiture rate (as a percent) | 5.00% |
Weighted-average fair value assumptions |  |
Valuation method | Black-Scholes valuation model |
Dividend yield (as a percent) | 0.00% |
Research and Development Expense |  |
Stock compensation |  |
Stock compensation expense | $ 28.7 | 27.4
Selling, General and Administrative Expenses |  |
Stock compensation |  |
Stock compensation expense | 13.6 | 13.0
Cost of product revenues |  |
Stock compensation |  |
Stock compensation expense | $ 0.2 | $ 0.2
Employee Stock |  |
Weighted-average fair value assumptions |  |
Average risk-free interest rates (as a percent) | 0.23% | 2.27%
Average expected life (in years) | 3 months | 3 months
Volatility (as a percent) | 52.00% | 34.00%
Weighted-average fair value (in dollars per share) | $ 16.00 | $ 13.31
Stock Options |  |
Weighted-average fair value assumptions |  |
Average risk-free interest rates (as a percent) | 1.56% | 2.51%
Average expected life (in years) | 4 years 7 months 24 days | 5 years 3 months 29 days
Volatility (as a percent) | 40.00% | 45.00%
Weighted-average fair value (in dollars per share) | $ 28.43 | $ 31.50
Unrecognized compensation |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 95.8 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards | 1 year 4 months 24 days |
Restricted Stock Units (RSUs) |  |
Unrecognized compensation |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 93.3 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards | 1 year 9 months 18 days |
Performance Stock Units (PSUs) |  |
Unrecognized compensation |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 29.5 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards | 1 year 9 months 18 days |

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- Definition The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(iii) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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