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Up to $75,000,000 of Common Shares We have entered into an Open Market Sales AgreementSM(the “Sales Agreement”) with Jefferies LLC (“Jefferies”),relating to the sale of our common shares, par value $0.01 per share (the “common shares”), offered by thisprospectus supplement and the accompanying prospectus. In accordance with the terms of the Sales Agreement, wemay offer and sell our common shares having an aggregate offering amount of up to $75,000,000 from time to timethrough or to Jefferies, acting as sales agent or principal. Our common shares are listed on The Nasdaq Global Select Market (“Nasdaq”) under the symbol “CCEC”. The lastreported sale price of our common shares on Nasdaq on January 24, 2025 was $18.23 per share. Sales of our common shares, if any, under this prospectus supplement and the accompanying prospectus may bemade by any method permitted that is deemed an “at the market offering” as defined in Rule 415(a)(4) under theSecurities Act of 1933, as amended (the “Securities Act”). Jefferies is not required to sell any specific number ordollar amount of our common shares, but will act as a sales agent using commercially reasonable efforts consistentwith its normal trading and sales practices to sell on our behalf all of the common shares requested to be sold by us,on mutually agreed terms between Jefferies and us. There is no arrangement for funds to be received in any escrow,trust, or similar arrangement. Jefferies will be entitled to compensation at a commission rate of up to 2.5% of the gross proceeds of commonshares sold under the Sales Agreement. In connection with the sale of our common shares on our behalf, Jefferieswill be deemed to be an “underwriter” within the meaning of the Securities Act, and the compensation of Jefferieswill be deemed to be underwriting commissions or discounts. We have also agreed to provide indemnification andcontribution to Jefferies with respect to certain liabilities, including liabilities under the Securities Act. See “Plan ofDistribution” beginning on page S-14 for additional information regarding the compensation to be paid to Jefferies. Investing in our common shares involves a high degree of risk. We urge you to carefullyread in their entirety the section entitled “Risk Factors” beginning on page S-10, thesection entitled “Item 3. Key Information–D. Risk Factors” in our Annual Report on Form20-F for the year ended December 31, 2023, and Exhibit 99.8 to our Report on Form 6-Kfurnished to the Securities and Exchange Commission (the “SEC”) on August 26, 2024,which are incorporated herein by reference, and all other information included or incorporated by reference in this prospectus supplement and the accompanyingprospectus, before making a decision to invest in our securities. Neither the Securities and Exchange Commission nor any state securities commission has approved ordisapproved of these securities or determined if this prospectus supplement or the accompanying prospectusis truthful or complete. Any representation to the contrary is a criminal offense. Jefferies The date of this prospectus supplement is January 27, 2025. Table of Contents TABLE OF CONTENTS PROSPECTUS SUPPLEMENT ABOUT THIS PROSPECTUS SUPPLEMENTS-3INCORPORATION OF DOCUMENTS BY REFERENCES-4CAUTIONARY STATEMENT REGARDING FORWARD-LOOKING STATEMENTSS-6SUMMARYS-8THE OFFERINGS-9RISK FACTORSS-10USE OF PROCEEDSS-12CAPITALIZATION AND INDEBTEDNESSS-13PLAN OF DISTRIBUTIONS-14EXPENSES RELATING TO THIS OFFERINGS-16VALIDITY OF SECURITIESS-17EXPERTSS-18 PROSPECTUS ABOUT THIS PROSPECTUSCAPITAL CLEAN ENERGY CARRIERS CORP. WHERE YOU CAN FIND MORE INFORMATION4INCORPORATION OF DOCUMENTS BY REFERENCE5CAUTIONARY NOTE REGARDING FORWARD-LOOKING STATEMENTS7RISK FACTORS9CAPITALIZATION10USE OF PROCEEDS13DESCRIPTION OF THE COMMON SHARES14DESCRIPTION OF PREFERRED SHARES15DESCRIPTION OF DEBT SECURITIES16DESCRIPTION OF RIGHTS28MATERIAL UNITED STATES FEDERAL INCOME TAX CONSIDERATIONS29PLAN OF DISTRIBUTION40SERVICE OF PROCESS AND ENFORCEMENT OF CIVIL LIABILITIES42VALIDITY OF SECURITIES43EXPERTS43EXPENSES44S-1 Table of Contents NEITHER WE NOR JEFFERIES HAVE AUTHORIZED ANY OTHER PERSON TO GIVE ANYINFORMATION NOT CONTAINED IN OR INCORPORATED BY REFERENCE INTO THIS PROSPECTUSSUPPLEMENT OR THE ACCOMPANYING PROSPECTUS OR IN ANY FREE WRITING PROSPECTUS WEHAVE AUTHORIZED FOR USE IN CONNECTION WITH THIS OFFERING. NEITHER WE NOR JEFFERIESTAKE ANY RESPONSIBILITY FOR, AND CAN PROVIDE NO ASSURANCE AS TO THE RELIABILITY OF,ANY OTHER INFORMATION THAT OTHERS MAY GIVE YOU. THIS PROSPECTUS SUPPLEMENT, THEACCOMPANYING PROSPECTUS AND ANY FREE WRITING PROSPECTUS WE HAVE AUTHORIZEDFOR USE IN CONNECTION WITH THIS OFFERING CONSTITUTE AN OFFER TO SELL COMMONSHARES ONLY UNDER CIRCUMSTANCES AND IN JURISDICTIONS WHERE IT IS LAWFUL TO DO SO.PERSONS OUTSIDE THE UNITED STATES WHO COME INTO POSSESSION OF THIS PROSPECTUSSUPPLEMENT AND THE ACCOMPANYING PROSPECTUS ARE ADVISED TO INFORM THEMSELVESABOUT, AND TO OBSERVE ANY RESTRICTIONS