Foreign Currency Exchange Rate Risk
As of June 30, 2020, 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 €2.5 billion, or $2.8 billion based on the euro/U.S. dollar exchange rate as of June 30, 2020. As of December 31, 2019, the payments not hedged aggregated €3.0 billion, or $3.4 billion, based on the euro/U.S. dollar exchange rate as of December 31, 2019. The change from December 31, 2019 to June 30, 2020 was due to the delivery of Seven Seas Splendor. We estimate that a 10% change in the euro as of June 30, 2020 would result in a $0.3 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 16.2% and 10.5% for the three months ended June 30, 2020 and 2019, respectively, and 13.4% and 11.1% for the six months ended June 30, 2020 and 2019, respectively. We use fuel derivative agreements to mitigate the financial impact of fluctuations in fuel prices and as of June 30, 2020, we had hedged approximately 80%, 52%, 36% and 13% of our remaining 2020, 2021, 2022 and 2023 projected metric tons of fuel purchases, respectively. As of December 31, 2019, we had hedged approximately 56%, 50% and 18% of our 2020, 2021 and 2022 projected metric tons of fuel purchases, respectively. Additional hedges were executed between December 31, 2019 and June 30, 2020 to lower our fuel price risk.
We estimate that a 10% increase in our weighted-average fuel price would increase our anticipated 2020 fuel expense by $9.2 million. This increase would be partially offset by an increase in the fair value of our fuel swap agreements of $7.7 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 June 30, 2020. 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 June 30, 2020 to provide reasonable assurance that the information required to be disclosed by us in the reports we file or submit under the Securities Exchange Act of 1934, as amended, is recorded, processed, summarized and reported within the time periods specified in the rules and forms of the SEC, and that it is accumulated and communicated to our management, including our Chief Executive Officer and Chief Financial Officer, as appropriate, to allow timely decisions regarding required disclosure.
Changes in Internal Control Over Financial Reporting
There have been no changes in our internal control over financial reporting during the quarter ended June 30, 2020 that have materially affected, or are reasonably likely to materially affect, our internal control over financial reporting.
Limitations on the Effectiveness of Controls
It should be noted that any system of controls, however well designed and operated, can provide only reasonable, and not absolute, assurance that the objectives of the system will be met. In addition, the design of any control system is