Exhibit 99.1

FOR IMMEDIATE RELEASE

January 13, 2014

IBERIABANK Corporation Announces Agreement to Acquire Teche Holding Company

LAFAYETTE, LOUISIANA AND NEW IBERIA, LOUISIANA — IBERIABANK Corporation (NASDAQ: IBKC) (“IBKC”), holding company of the 126-year-old IBERIABANK (www.iberiabank.com) and Teche Holding Company (NYSE – MKT: TSH) (“Teche”), holding company of New Iberia, Louisiana-based Teche Federal Bank (www.teche.com) jointly announced today the signing of a definitive agreement for IBKC to acquire Teche via merger. The proposed merger of Teche with and into IBKC has been approved by the Board of Directors of each company and is expected to close in the second quarter of 2014. Completion of the transaction is subject to customary closing conditions, including the receipt of required regulatory approvals and the approval of Teche’s shareholders.

Patrick Little, Chairman, President, and Chief Executive Officer of Teche, commented, “Over the last 80 years, our financial institution successfully navigated many challenges and opportunities. We are very proud of our Acadiana heritage and the successful financial performance we have delivered for shareholders since we went public nearly 19 years ago. We believe this combination with IBKC provides tremendous value to our shareholders in both the near-term and long-term.”

Little continued, “We are pleased to team up with such a high-quality banking partner. Our clients will benefit from an expanded array of products and services, along with the added convenience of nearly 200 bank locations in six states.”

Daryl G. Byrd, President and Chief Executive Officer of IBKC, commented, “Teche and IBERIABANK share a common heritage. Our organizations were started only 30 miles apart as mutual thrift institutions. Each of us converted to stock form and subsequently to commercial bank charters, and

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we both grew to become leading financial institutions in the Acadiana region of Louisiana. Our respective holding companies were formed less than two weeks apart and our initial public offerings were also separated by less than two weeks. As the financial services industry changed, our respective companies evolved to become commercial banks, while maintaining a focus on high-quality lending, capital strength, and excellent client service. Our companies not only survived many interest rate upheavals and banking panics, but prospered throughout those cycles.”

Byrd continued, “This combination is consistent with our stated efforts to improve our operating efficiency, appropriately deploy our capital, and enhance shareholder returns. We believe this transaction is a ‘win-win’ scenario for our respective shareholders and the communities we serve.”

Under the terms of the merger agreement, shareholders of Teche will receive 1.162 shares of IBKC common stock for each share of Teche common stock outstanding, subject to certain market price adjustments provided for in the merger agreement. All unexercised Teche stock options, whether or not vested, will be cashed out and shares of restricted stock will become fully vested in connection with the transaction. If the transaction closes at June 30, 2014, Teche would have an aggregate of approximately 2,234,000 shares, assuming the full exercise of then vested options and full issuance of the restricted shares.

Based on IBKC’s closing stock price on January 10, 2014 of $62.10, the transaction would have an aggregate estimated pro forma value of $161 million, or $72.16 per Teche common share, equal to a 32% increase over the closing price for Teche common stock of $54.50 per share on January 10, 2014. Assuming full exercise of options and vesting of restricted stock, the aggregate transaction value equated to 1.71 times adjusted book value and 1.78 times adjusted tangible book value at September 30, 2013, assuming the exercise of options on a pro forma basis.

IBKC currently estimates annual pre-tax expense reductions associated with transaction will be in excess of 50% of Teche’s annual expenses in fiscal 2013. Assuming the transaction is completed in the second quarter of 2014, the expense savings are estimated to be fully achieved by the first quarter of 2015. The transaction is expected to be accretive to IBKC’s fully diluted earnings per share by approximately 6%, assuming synergies are fully phased in and excluding estimated acquisition and conversion related costs of approximately $22 million on a pre-tax basis.

The transaction is expected to have little impact on IBKC’s capital ratios, but would dilute tangible book value per share by approximately 2.1% on a pro forma basis at September 30, 2013, excluding the estimated acquisition and conversion costs and 2.9% on a pro forma basis at December 31, 2014, including those costs. The tangible book value dilution, including one-time acquisition and conversion costs, is expected to be earned back within four years from the completion of the transaction. The estimated internal rate of return for the transaction is expected to be greater than 20%, and, therefore, in excess of IBKC’s cost of capital.

On a pro forma basis at June 30, 2013, the combined franchise would hold deposit market share positions in the following metropolitan statistical areas (“MSAs”)

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About Teche Holding Company

Teche is the bank holding company for Teche Federal Bank with 20 commercial bank branch offices servicing south Louisiana. Teche serves clients in Lafayette (four offices), New Iberia (three offices), Baton Rouge (three offices), Houma-Thibodaux (three offices), Franklin (two offices) and five other locations. At September 30, 2013, Teche had:

Teche had no brokered deposits and 256 full-time employees at September 30, 2013. For the fiscal year ended September 30, 2013, Teche reported net income of $8.7 million. For the quarter ended September 30, 2013, Teche reported net income of $2.1 million, a 4.08% net interest margin, 0.47% cost of interest bearing deposits, and 0.97% cost of interest bearing liabilities.

Teche’s common stock trades on the NYSE MKT LLC under the symbol “TSH.” Teche’s market capitalization was approximately $112 million, based on the NYSE MKT closing stock price on January 10, 2014.

About IBERIABANK Corporation

IBKC is a financial holding company with 264 combined offices, including 168 bank branch offices and four LPOs in Louisiana, Arkansas, Tennessee, Alabama, Texas, and Florida, 21 title insurance offices in Arkansas and Louisiana, and mortgage representatives in 62 locations in 12 states. IBERIABANK has eight locations with representatives of IBERIA Wealth Advisors in four states, and one IBERIA Capital Partners, L.L.C. office in New Orleans.

IBKC’s common stock trades on the NASDAQ Global Select Market under the symbol “IBKC.” IBKC’s market capitalization was approximately $1.8 billion, based on the NASDAQ Global Select Market closing stock price on January 10, 2014.

The following 13 investment firms currently provide equity research coverage on IBKC:

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Additional Information

Teche was advised by the investment banking firm Sheshunoff & Co. and the law firm of Spidi & Fisch, PC, Washington, DC. IBKC was advised by the investment banking firm Keefe, Bruyette & Woods, Inc. and the law firm of Jones Walker LLP.

IBKC has prepared a PowerPoint presentation that supplements information contained in this press release. The PowerPoint presentation may be accessed on IBKC’s web site, www.iberiabank.com, under “Investor Relations” and then “Presentations.” IBKC will host a conference call associated with this announcement on Monday, January 13, 2014, beginning at 10:00 a.m. Central Time by dialing 1-888-276-0009. The confirmation code for the call is 316095. A replay of the call will be available until midnight Central Time on January 20, 2014 by dialing 1-800-475-6701. The confirmation code for the replay is 316095.

Caution About Forward-Looking Statements

This release contains “forward-looking statements” as defined in the Private Securities Litigation Reform Act of 1995. In general, forward-looking statements usually use words such as “may,” “believe,” “expect,” “anticipate,” “intend,” “will,” “should,” “plan,” “estimate,” “predict,” “continue” and “potential” or the negative of these terms or other comparable terminology, including statements related to the expected timing of the closing of the proposed merger, the expected returns and other benefits of the proposed merger to shareholders, expected improvement in operating efficiency resulting from the merger, estimated expense reductions resulting from the transaction and the timing of achievement of such reductions, the impact on and timing of the recovery of the impact on tangible book value, and the effect of the merger on IBKC’s capital ratios. Forward-looking statements represent management’s beliefs, based upon information available at the time the statements are made, with regard to the matters addressed; they are not guarantees of future performance. Forward-looking statements are subject to numerous assumptions, risks and uncertainties that change over time and could cause actual results or financial condition to differ materially from those expressed in or implied by such statements and there can be no assurances that: the proposed merger will close when expected, the expected returns and other benefits of the proposed merger to shareholders will be achieved, the expected operating efficiency will result, estimated expense reductions resulting from the transaction will occur as and when expected, the impact on tangible book value will be recovered or as expected or that the effect on IBKC’s capital ratios will be as expected. Factors that could cause or contribute to such differences include, but are not limited to, the possibility that expected benefits may not materialize in the time frame expected or at all, or may be more costly to achieve; that the merger transaction may not be timely completed, if at all; that prior to completion of the merger transaction or thereafter, IBKC’s and Teche’s respective businesses may not perform as expected due to transaction-related uncertainties or other factors; that the parties are unable to implement successful integration strategies; that the required regulatory, shareholder, or other closing conditions are not satisfied in a timely manner, or at all; reputational risks and the reaction of the parties’ customers to the merger transaction; diversion of management time to merger-related issues; and other factors and risk influences contained in the cautionary language included under the headings “Management’s Discussion and Analysis of Financial Condition and Results of Operations” and “Risk Factors” in IBKC’s Form 10-K for the fiscal year ended December 31, 2012, and Form 10-Qs for the quarters ended March 31, 2013, June 30, 2013 and September 30, 2013 and other documents subsequently filed by IBKC with the SEC and under “Management’s Discussion and Analysis of Financial Condition and Results of Operations” contained in Teche’s Form 10-K for the fiscal year ended September 30, 2013, and other documents subsequently filed by Teche with the SEC. Consequently, no

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forward-looking statement can be guaranteed. Neither IBKC nor Teche undertakes any obligation to update or revise any forward-looking statements, whether as a result of new information, future events or otherwise. For any forward-looking statements made in this press release or any related documents, IBKC and Teche claim protection of the safe harbor for forward-looking statements contained in the Private Securities Litigation Reform Act of 1995.

This communication is being made in respect of the proposed merger transaction involving IBKC and Teche. This communication does not constitute an offer to sell or the solicitation of an offer to buy any securities or a solicitation of any vote or approval. In connection with the proposed merger, IBKC will file with the SEC a registration statement on Form S-4 that will include a proxy statement/prospectus for the shareholders of Teche. IBKC also plans to file other documents with the SEC regarding the proposed merger transaction. Teche will mail the final proxy statement/prospectus to its shareholders. BEFORE MAKING ANY VOTING OR INVESTMENT DECISION, INVESTORS ARE URGED TO READ THE PROXY STATEMENT/PROSPECTUS REGARDING THE PROPOSED TRANSACTION AND ANY OTHER RELEVANT DOCUMENTS CAREFULLY IN THEIR ENTIRETY WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED TRANSACTION. The proxy statement/prospectus, as well as other filings containing information about IBKC and Teche, will be available without charge, at the SEC’s Internet site (http://www.sec.gov). Copies of the proxy statement/prospectus and the filings with the SEC that will be incorporated by reference in the proxy statement/prospectus can also be obtained, when available, without charge, from the IBKC’s website (http://www.iberiabank.com), under the heading “Investor Information” and on Teche’s website at http://www.teche.com.

IBKC and Teche, and certain of their respective directors, executive officers and other members of management and employees may be deemed to be participants in the solicitation of proxies from the shareholders of Teche in respect of the proposed merger transaction. Information regarding the directors and executive officers of IBKC is set forth in the definitive proxy statement for IBKC’s 2013 annual meeting of shareholders, as filed with the SEC on April 12, 2013 and in Forms 3, 4 and 5 filed with the SEC by its officers and directors. Information regarding the directors and executive officers of Teche is set forth in the definitive proxy statement for Teche’s 2014 annual meeting of shareholders, as filed with the SEC on December 30, 2013 and in Forms 3, 4 and 5 filed with the SEC by its officers and directors. Additional information regarding the interests of such participants will be included in the proxy statement/prospectus and other relevant documents regarding the proposed merger transaction filed with the SEC when they become available.

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