UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, DC 20549

SCHEDULE 14A

(Rule 14a-101)

INFORMATION REQUIRED IN PROXY STATEMENT

SCHEDULE 14A INFORMATION

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

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¨ Preliminary Proxy Statement

¨ Confidential, For Use of the Commission Only (as permitted by Rule 14a-6(e)(2))

¨ Definitive Proxy Statement

¨ Definitive Additional Materials

x Soliciting Materials Pursuant to § 240.14a-12

CARMIKE CINEMAS, INC.

(Name of Registrant as Specified in its Charter)

(Name of Person(s) Filing Proxy Statement, if Other Than the Registrant)

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Carmike Cinemas, Inc. is providing the following information regarding its previously announced definitive merger agreement with AMC Entertainment Holdings, Inc.:

• The Carmike Board of Directors unanimously determined that AMC’s offer is in the best interests of Carmike’s shareholders and unanimously approved the transaction

• The Board made this determination after thoughtful consideration of the options available to the Company, including the level of interest from other third parties and the value potential of Carmike’s standalone plan

• Carmike did not receive any offers that provided greater value than AMC’s $30 per share offer

• J.P. Morgan was Carmike’s financial advisor and provided the Board with a fairness opinion in connection with the AMC definitive merger agreement

• On a firm value to next twelve months (NTM) EBITDA basis, this deal values Carmike at 8.0x 2016E EBITDA based on FactSet consensus as of 3/7/2016

• This represents a multiple that is higher than Carmike’s average trading multiples for the past 1-, 3-, 5- and 10-year periods, of approximately 6.8x, 6.7x, 6.1x and 6.2x, respectively (Source: FactSet)

• Carmike’s firm value to NTM EBITDA multiples have traded above 8.0x approximately 4.6% of the time over the last 10 years (Source: FactSet)

• We would also note that Carmike has historically traded, on average, at a discount to Regal, Cinemark and AMC over the past several years:

• A discount of approximately 1.4x to Regal’s average NTM multiple over the last 10 years

• A discount of approximately 1.2x to Cinemark’s average NTM multiple over the last 7 years; and

• A discount of approximately 0.9x to AMC’s average NTM multiple over the last 2 years (Source: FactSet)

• The transaction value to last twelve months (LTM) EBITDA multiple implied by the transaction is higher than any comparable, large-scale theatre transaction multiple over the last 10 years, representing a multiple of 8.8x LTM EBITDA, based on $126 million of adjusted EBITDA for 2015

• The $126 million of adjusted EBITDA for 2015 includes stock-based compensation expense and expenses related to M&A, since a substantial driver of our growth plan is our ability to execute successfully on M&A

• The 8.8x LTM EBITDA multiple represents a higher multiple than the two most relevant transactions during this period — Wanda’s acquisition of AMC in 2012 and Cinemark’s acquisition of Century Theatres in 2006

• The $2.6 billion purchase price paid in Wanda’s acquisition of AMC implied a multiple of approximately 7.1x LTM EBITDA

• Based on a transaction value of approximately $2.6 billion and AMC’s LTM adjusted EBITDA of March 29, 2012 of $368 million (including stock-based compensation) (Source: AMC’s SEC filings)

• Cinemark’s $1.04 billion acquisition of Century Theatres implied a multiple of approximately 8.6x LTM EBITDA

• Based on a transaction value of approximately $1.04 billion and Century’s LTM adjusted EBITDA of $120.8 million (Source: Cinemark’s SEC filings)

• We do not consider the acquisition of Vue Entertainment to be a comparable transaction in light of, among other things, differences in market fundamentals between mature U.S. markets and Vue’s positioning at the time in European markets with greater opportunities for growth

• In considering alternatives to the transaction, the Carmike Board was focused on the standalone value of the Company and what the Company could potentially be able to achieve on its own, which requires the continued successful execution of the Company’s acquisition strategy and the uncertainties and risks associated with that strategy

• The $30 per share offer represents a higher price than the value of the Company considering recent trading levels, which indicates that Carmike was able to realize a portion of the value ascribed to the estimated synergies, less the cost required to achieve them

• The cost savings and other synergies that AMC estimates to be realized as part of the transaction would not be available to Carmike on a standalone basis

Important Additional Information Regarding the Merger Will Be Filed With The SEC

This communication may be deemed to be solicitation material in respect of the proposed merger. In connection with the proposed merger, Carmike Cinemas, Inc. (“Carmike”) will file with the Securities and Exchange Commission (the “SEC”) and furnish to its stockholders a proxy statement and other relevant documents. BEFORE MAKING ANY VOTING DECISION, CARMIKE’S STOCKHOLDERS ARE URGED TO READ THE PROXY STATEMENT IN ITS ENTIRETY WHEN IT BECOMES AVAILABLE AND ANY OTHER DOCUMENTS TO BE FILED WITH THE SEC IN CONNECTION WITH THE PROPOSED MERGER OR INCORPORATED BY REFERENCE IN THE PROXY STATEMENT BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED MERGER. Carmike’s stockholders will be able to obtain a free copy of the proxy statement, when available, and other relevant documents filed by Carmike with the SEC at the SEC’s website at www.sec.gov. In addition, Carmike’s stockholders may obtain a free copy of the proxy statement, when available, and other relevant documents from Carmike’s website at http://www.carmikeinvestors.com/.

Participants in the Solicitation

Carmike and its directors, executive officers and certain other members of management and employees of Carmike may be deemed to be “participants” in the solicitation of proxies from Carmike’s stockholders in connection with the proposed merger. Information regarding the interests of the persons who may, under the rules of the SEC, be considered participants in the solicitation of Carmike’s stockholders in connection with the proposed merger, which may be different than those of Carmike’s stockholders generally, will be set forth in the proxy statement and the other relevant documents to be filed with the SEC. Carmike stockholders can find information about Carmike and its directors and executive officers and their ownership of Carmike’s common stock in Carmike’s annual report on Form 10-K for the fiscal year ended December 31, 2015, which was filed with the SEC on February 29, 2016, and in its definitive proxy statement for its most recent annual meeting of stockholders, which was filed with the SEC on April 17, 2015, and in Forms 4 of directors and executive officers filed with the SEC. Additional information regarding the interests of such individuals in the proposed merger will be included in the proxy statement relating to the proposed merger when it is filed with the SEC. These documents may be obtained free of charge from the SEC’s website at www.sec.gov and Carmike’s website at www.carmikeinvestors.com.

Disclosure Regarding Forward-Looking Statements

This communication contains forward-looking statements within the meaning of the federal securities laws. Statements that are not historical facts, including statements about our beliefs, expectations and future performance, are forward-looking statements. Forward-looking statements include statements preceded by, followed by or that include the words, “believes,” “expects,” “anticipates,” “plans,” “estimates,” “seeks” or similar expressions. Forward-looking statements are only predictions and are not guarantees of performance. These statements are based on beliefs and assumptions of management, which in turn are based on currently available information. The forward-looking statements also involve risks and uncertainties, which could cause actual results to differ materially from those contained in any forward-looking statement. Many of these factors are beyond our ability to control or predict. Important factors that could cause actual results to differ materially from those contained in any forward-looking statement include, but are not limited to: the occurrence of any event, change or other circumstances that could give rise to the termination of the merger agreement with AMC; the inability to complete the proposed merger due to the failure to obtain Carmike stockholder or regulatory approval for the proposed merger or the failure to satisfy other conditions of the

proposed merger within the proposed timeframe or at all; disruption in key business activities or any impact on Carmike’s relationships with third parties as a result of the announcement of the proposed merger; the failure to obtain the necessary financing arrangements as set forth in the debt commitment letters delivered pursuant to the merger agreement with AMC, or the failure of the proposed merger to close for any other reason; risks related to disruption of management’s attention from Carmike’s ongoing business operations due to the proposed merger; the outcome of any legal proceedings, regulatory proceedings or enforcement matters that may be instituted against Carmike and others relating to the merger agreement with AMC; the risk that the pendency of the proposed merger disrupts current plans and operations and the potential difficulties in employee retention as a result of the pendency of the proposed merger; the amount of the costs, fees, expenses and charges related to the proposed merger; adverse regulatory decisions; unanticipated changes in the markets for Carmike’s business segments; general economic conditions in Carmike’s regional and national markets; Carmike’s ability to comply with covenants contained in the agreements governing Carmike’s indebtedness; Carmike’s ability to operate at expected levels of cash flow; financial market conditions including, but not limited to, changes in interest rates and the availability and cost of capital; Carmike’s ability to meet its contractual obligations, including all outstanding financing commitments; the availability of suitable motion pictures for exhibition in Carmike’s markets; competition in Carmike’s markets; competition with other forms of entertainment; the effect of Carmike’s leverage on its financial condition; prices and availability of operating supplies; the impact of continued cost control procedures on operating results; the impact of asset impairments; the impact of terrorist acts; changes in tax laws, regulations and rates; and financial, legal, tax, regulatory, legislative or accounting changes or actions that may affect the overall performance of Carmike’s business.

Consider these factors carefully in evaluating the forward-looking statements. Additional factors that may cause results to differ materially from those described in the forward-looking statements are set forth in Carmike’s Annual Report on Form 10-K for the fiscal year ended December 31, 2015, which was filed with the SEC on February 29, 2016, under the heading “Item 1A. Risk Factors,” and in its subsequently filed reports with the SEC, including Forms 10-Q and 8-K. Readers are cautioned not to place undue reliance on the forward-looking statements included in this communication, which speak only as of the date hereof. Carmike does not undertake to update any of these statements in light of new information or future events, except as required by applicable law.