Interest Rate Risk
As of September 30, 2019, we had interest rate swap and collar agreements to hedge our exposure to interest rate movements and to manage our interest expense. As of September 30, 2019, 75% of our debt was fixed and 25% was variable, which includes the effects of the interest rate swaps and collars. The notional amount of outstanding debt associated with the interest rate derivative agreements as of September 30, 2019 was $1.7 billion. As of December 31, 2018, 72% of our debt was fixed and 28% was variable, which includes the effects of the interest rate swaps. The notional amount of our outstanding debt associated with the interest rate swap agreements was $1.0 billion as of December 31, 2018. The change in our fixed rate percentage from December 31, 2018 to September 30, 2019 was due to an additional interest rate swap executed and the repayment of certain variable rate debt. Based on our September 30, 2019 outstanding variable rate debt balance, a one percentage point increase in annual LIBOR interest rates would increase our annual interest expense by approximately $11.2 million excluding the effects of capitalization of interest.
Foreign Currency Exchange Rate Risk
As of September 30, 2019, we had foreign currency derivatives to hedge the exposure to volatility in foreign currency exchange rates related to our ship construction contracts denominated in euros. These derivatives hedge the foreign currency exchange rate risk on a portion of the payments on our ship construction contracts. The payments not hedged aggregate €2.0 billion, or $2.2 billion based on the euro/U.S. dollar exchange rate as of September 30, 2019. As of December 31, 2018, the payments not hedged aggregated €2.2 billion, or $2.5 billion, based on the euro/U.S. dollar exchange rate as of December 31, 2018. The change from December 31, 2018 to September 30, 2019 was due to additional foreign exchange derivatives executed. We estimate that a 10% change in the euro as of September 30, 2019 would result in a $0.2 billion change in the U.S. dollar value of the foreign currency denominated remaining payments.
Fuel Price Risk
Our exposure to market risk for changes in fuel prices relates to the forecasted purchases of fuel on our ships. Fuel expense, as a percentage of our total cruise operating expense, was 10.0% and 10.7% for the three months ended September 30, 2019 and 2018, respectively, and 10.7% and 11.3% for the nine months ended September 30, 2019 and 2018, respectively. We use fuel derivative agreements to mitigate the financial impact of fluctuations in fuel prices and as of September 30, 2019, we had hedged approximately 70%, 56%, 50% and 18% of our remaining 2019, 2020, 2021 and 2022 projected metric tons of fuel purchases, respectively. As of December 31, 2018, we had hedged approximately 57%, 53% and 33% of our 2019, 2020 and 2021 projected metric tons of fuel purchases, respectively. Additional hedges executed between December 31, 2018 and September 30, 2019 have lowered our fuel price risk.
We estimate that a 10% increase in our weighted-average fuel price would increase our anticipated 2019 fuel expense by $10.2 million. This increase would be partially offset by an increase in the fair value of our fuel swap agreements of $5.4 million. Fair value of our derivative contracts is derived using valuation models that utilize the income valuation approach. These valuation models take into account the contract terms such as maturity, as well as other inputs such as fuel types, fuel curves, creditworthiness of the counterparty and the Company, as well as other data points.
Item 4. Controls and Procedures
Evaluation of Disclosure Controls and Procedures
Our management has evaluated, with the participation of our Chief Executive Officer and Chief Financial Officer, the effectiveness of our disclosure controls and procedures, as such term is defined in Rule 13a-15(e) under the Securities Exchange Act of 1934, as amended, as of September 30, 2019. There are inherent limitations in the effectiveness of any system of disclosure controls and procedures, including the possibility of human error and the circumvention or overriding of the controls and procedures. Accordingly, even effective disclosure controls and procedures can only provide reasonable assurance of achieving their control objectives. Based upon management’s evaluation, our Chief Executive Officer and Chief Financial Officer concluded that our disclosure controls and procedures were effective as of September 30, 2019 to provide reasonable assurance that the information required to be disclosed by us in the reports we